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English Language Arts Kindergarten Standards Grade Core Area # Timeline Standard CC.K.R.L.1 Key Ideas and Details: With prompting and support, ask and answer questions about key K R.L 1 details in a text. CC.K.R.L.2 Key Ideas and Details: With prompting and support, retell familiar stories, including key K R.L 2 details. CC.K.R.L.3 Key Ideas and Details: With prompting and support, identify characters, settings, and major K R.L 3 events in a story. K R.L 4 CC.K.R.L.4 Craft and Structure: Ask and answer questions about unknown words in a text. K R.L 5 CC.K.R.L.5 Craft and Structure: Recognize common types of texts (e.g., storybooks, poems). CC.K.R.L.6 Craft and Structure: With prompting and support, name the author and illustrator of a story K R.L 6 and define the role of each in telling the story. CC.K.R.L.7 Integration of Knowledge and Ideas: With prompting and support, describe the relationship K R.L 7 between illustrations and the story in which they appear (e.g., what moment in a story an illustration depicts). CC.K.R.L.9 Integration of Knowledge and Ideas: With prompting and support, compare and contrast the K R.L 9 adventures and experiences of characters in familiar stories. CC.K.R.L.10 Range of Reading and Level of Text Complexity: Actively engage in group reading activities K R.L 10 with purpose and understanding. CC.K.R.I.1 Key Ideas and Details: With prompting and support, ask and answer questions about key K R.I 1 details in a text. CC.K.R.I.2 Key Ideas and Details: With prompting and support, identify the main topic and retell key K R.I 2 details of a text. CC.K.R.I.3 Key Ideas and Details: With prompting and support, describe the connection between two K R.I 3 individuals, events, ideas, or pieces of information in a text. CC.K.R.I.4 Craft and Structure: With prompting and support, ask and answer questions about unknown K R.I 4 words in a text. K R.I 5 CC.K.R.I.5 Craft and Structure: Identify the front cover, back cover, and title page of a book. CC.K.R.I.6 Craft and Structure: Name the author and illustrator of a text and define the role of each in K R.I 6 presenting the ideas or information in a text. CC.K.R.I.7 Integration of Knowledge and Ideas: With prompting and support, describe the relationship K R.I 7 between illustrations and the text in which they appear (e.g., what person, place, thing, or idea in the text an illustration depicts). CC.K.R.I.8 Integration of Knowledge and Ideas: With prompting and support, identify the reasons an K R.I 8 author gives to support points in a text. CC.K.R.I.9 Integration of Knowledge and Ideas: With prompting and support, identify basic similarities in K R.I 9 and differences between two texts on the same topic (e.g., in illustrations, descriptions, or procedures). CC.K.R.I.10 Range of Reading and Level of Text Complexity: Actively engage in group reading activities K R.I 10 with purpose and understanding. K R.F 1 CC.K.R.F.1 Print Concepts: Demonstrate understanding of the organization and basic features of print. K R.F 1.a CC.K.R.F.1.a Print Concepts: Follow words from left to right, top to bottom, and page by page. CC.K.R.F.1.b Print Concepts: Recognize that spoken words are represented in written language by K R.F 1.b specific sequences of letters. K R.F 1.c CC.K.R.F.1.c Print Concepts: Understand that words are separated by spaces in print. K R.F 1.d CC.K.R.F.1.d Print Concepts: Recognize and name all upper- and lowercase letters of the alphabet. CC.K.R.F.2 Phonological Awareness: Demonstrate understanding of spoken words, syllables, and sounds K R.F 2 (phonemes). K R.F 2.a CC.K.R.F.2.a Phonological Awareness: Recognize and produce rhyming words. K R.F 2.b CC.K.R.F.2.b Phonological Awareness: Count, pronounce, blend, and segment syllables in spoken words. CC.K.R.F.2.c Phonological Awareness: Blend and segment onsets and rimes of single-syllable spoken K R.F 2.c words. CC.K.R.F.2.d Phonological Awareness: d. Isolate and pronounce the initial, medial vowel, and final K R.F 2.d sounds (phonemes) in three-phoneme (consonant-vowel-consonant, or CVC) words.*(This does not include CVCs ending with /l/, /r/,or /x/.) CC.K.R.F.2.e Phonological Awareness: Add or substitute individual sounds (phonemes) in simple, one- K R.F 2.e syllable words to make new words. CC.K.R.F.3 Phonics and Word Recognition: Know and apply grade-level phonics and word analysis skills K R.F 3 in decoding words. CC.K.R.F.3.a Phonics and Word Recognition: Demonstrate basic knowledge of letter-sound K R.F 3.a correspondences by producing the primary or most frequent sound for each consonant. CC.K.R.F.3.b Phonics and Word Recognition: Associate the long and short sounds with the common K R.F 3.b spellings (graphemes) for the five major vowels. CC.K.R.F.3.c Phonics and Word Recognition: Read common high-frequency words by sight. (e.g., the, of, K R.F 3.c to, you, she, my, is, are, do, does). CC.K.R.F.3.d Phonics and Word Recognition: Distinguish between similarly spelled words by identifying K R.F 3.d the sounds of the letters that differ. K R.F 4 CC.K.R.F.4 Fluency: Read emergent-reader texts with purpose and understanding. CC.K.W.1 Text Types and Purposes: Use a combination of drawing, dictating, and writing to compose K W 1 opinion pieces in which they tell a reader the topic or the name of the book they are writing about and state an opinion or preference about the topic or book (e.g., My favorite book is . . .). CC.K.W.2 Text Types and Purposes: Use a combination of drawing, dictating, and writing to compose K W 2 informative/explanatory texts in which they name what they are writing about and supply some information about the topic. CC.K.W.3 Text Types and Purposes: Use a combination of drawing, dictating, and writing to narrate a K W 3 single event or several loosely linked events, tell about the events in the order in which they occurred, and provide a reaction to what happened. CC.K.W.5 Production and Distribution of Writing: With guidance and support from adults, respond to K W 5 questions and suggestions from peers and add details to strengthen writing as needed. CC.K.W.6 Production and Distribution of Writing: With guidance and support from adults, explore a K W 6 variety of digital tools to produce and publish writing, including in collaboration with peers. CC.K.W.7 Research to Build and Present Knowledge: Participate in shared research and writing projects K W 7 (e.g., explore a number of books by a favorite author and express opinions about them). CC.K.W.8 Research to Build and Present Knowledge: With guidance and support from adults, recall K W 8 information from experiences or gather information from provided sources to answer a question. CC.K.SL.1 Comprehension and Collaboration: Participate in collaborative conversations with diverse K SL 1 partners about kindergarten topics and texts with peers and adults in small and larger groups. CC.K.SL.1.a Comprehension and Collaboration: Follow agreed-upon rules for discussions (e.g., listening K SL 1.a to others and taking turns speaking about the topics and texts under discussion). K SL 1.b CC.K.SL.1.b Comprehension and Collaboration: Continue a conversation through multiple exchanges. CC.K.SL.2 Comprehension and Collaboration: Confirm understanding of a text read aloud or information K SL 2 presented orally or through other media by asking and answering questions about key details and requesting clarification if something is not understood. CC.K.SL.3 Comprehension and Collaboration: Ask and answer questions in order to seek help, get K SL 3 information, or clarify something that is not understood. CC.K.SL.4 Presentation of Knowledge and Ideas: Describe familiar people, places, things, and events K SL 4 and, with prompting and support, provide additional detail. CC.K.SL.5 Presentation of Knowledge and Ideas: Add drawings or other visual displays to descriptions as K SL 5 desired to provide additional detail. CC.K.SL.6 Presentation of Knowledge and Ideas: Speak audibly and express thoughts, feelings, and ideas K SL 6 clearly. CC.K.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard K L 1 English grammar and usage when writing or speaking. K L 1.a CC.K.L.1.a Conventions of Standard English: Print many upper- and lowercase letters. K L 1.b CC.K.L.1.b Conventions of Standard English: Use frequently occurring nouns and verbs. CC.K.L.1.c Conventions of Standard English: Form regular plural nouns orally by adding /s/ or /es/ (e.g., K L 1.c dog, dogs; wish, wishes). CC.K.L.1.d Conventions of Standard English: Understand and use question words (interrogatives) (e.g., K L 1.d who, what, where, when, why, how). CC.K.L.1.e Conventions of Standard English: Use the most frequently occurring prepositions (e.g., to, K L 1.e from, in, out, on, off, for, of, by, with). CC.K.L.1.f Conventions of Standard English: Produce and expand complete sentences in shared language K L 1.f activities. CC.K.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard K L 2 English capitalization, punctuation, and spelling when writing. K L 2.a CC.K.L.2.a Conventions of Standard English: Capitalize the first word in a sentence and the pronoun I. K L 2.b CC.K.L.2.b Conventions of Standard English: Recognize and name end punctuation. CC.K.L.2.c Conventions of Standard English: Write a letter or letters for most consonant and short-vowel K L 2.c sounds (phonemes). CC.K.L.2.d Conventions of Standard English: Spell simple words phonetically, drawing on knowledge of K L 2.d sound-letter relationships. CC.K.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple- K L 4 meaning words and phrases based on kindergarten reading and content. CC.K.L.4.a Vocabulary Acquisition and Use: Identify new meanings for familiar words and apply them K L 4.a accurately (e.g., knowing duck is a bird and learning the verb to duck). CC.K.L.4.b Vocabulary Acquisition and Use: Use the most frequently occurring inflections and affixes K L 4.b (e.g., -ed, -s, re-, un-, pre-, -ful, -less) as a clue to the meaning of an unknown word. CC.K.L.5 Vocabulary Acquisition and Use: With guidance and support from adults, explore word K L 5 relationships and nuances in word meanings. CC.K.L.5.a Vocabulary Acquisition and Use: Sort common objects into categories (e.g., shapes, foods) to K L 5.a gain a sense of the concepts the categories represent. CC.K.L.5.b Vocabulary Acquisition and Use: Demonstrate understanding of frequently occurring verbs K L 5.b and adjectives by relating them to their opposites (antonyms). CC.K.L.5.c Vocabulary Acquisition and Use: Identify real-life connections between words and their use K L 5.c (e.g., note places at school that are colorful). CC.K.L.5.d Vocabulary Acquisition and Use: Distinguish shades of meaning among verbs describing the K L 5.d same general action (e.g., walk, march, strut, prance) by acting out the meanings. CC.K.L.6 Vocabulary Acquisition and Use: Use words and phrases acquired through conversations, K L 6 reading and being read to, and responding to texts. Mathematics Kindergarten Standards Grade Core Area # Timeline Standard K CC 1 CC.K.CC.1 Know number names and the count sequence. Count to 100 by ones and by tens. CC.K.CC.2 Know number names and the count sequence. Count forward beginning from a given K CC 2 number within the known sequence (instead of having to begin at 1). CC.K.CC.3 Know number names and the count sequence. Write numbers from 0 to 20. Represent a K CC 3 number of objects with a written numeral 0-20 (with 0 representing a count of no objects). CC.K.CC.4 Count to tell the number of objects. Understand the relationship between numbers and K CC 4 quantities; connect counting to cardinality. CC.K.CC.4a When counting objects, say the number names in the standard order, pairing each object K CC 4a with one and only one number name and each number name with one and only one object. CC.K.CC.4b Understand that the last number name said tells the number of objects counted. The K CC 4b number of objects is the same regardless of their arrangement or the order in which they were counted. K CC 4c CC.K.CC.4c Understand that each successive number name refers to a quantity that is one larger. CC.K.CC.5 Count to tell the number of objects. Count to answer “how many?” questions about as many K CC 5 as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. CC.K.CC.6 Compare numbers. Identify whether the number of objects in one group is greater than, less K CC 6 than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. (Include groups with up to ten objects.) K CC 7 CC.K.CC.7 Compare numbers. Compare two numbers between 1 and 10 presented as written numerals. CC.K.OA.1 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Represent addition and subtraction with objects, fingers, mental images, K OA 1 drawings (drawings need not show details, but should show the mathematics in the problem), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. CC.K.OA.2 Understand addition as putting together and adding to, and understand subtraction as K OA 2 taking apart and taking from. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. CC.K.OA.3 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Decompose numbers less than or equal to 10 into pairs in more than one K OA 3 way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). CC.K.OA.4 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. For any number from 1 to 9, find the number that makes 10 when added K OA 4 to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. CC.K.OA.5 Understand addition as putting together and adding to, and understand subtraction as K OA 5 taking apart and taking from. Fluently add and subtract within 5. CC.K.NBT.1 Work with numbers 11-19 to gain foundations for place value. Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and K NBT 1 record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. CC.K.MD.1 Describe and compare measurable attributes. Describe measurable attributes of objects, K MD 1 such as length or weight. Describe several measurable attributes of a single object. CC.K.MD.2 Describe and compare measurable attributes. Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and K MD 2 describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. CC.K.MD.3 Classify objects and count the number of objects in each category. Classify objects into K MD 3 given categories; count the numbers of objects in each category and sort the categories by count. (Limit category counts to be less than or equal to 10.) CC.K.G.1 Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Describe objects in the environment using names of shapes, and describe the K G 1 relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. CC.K.G.2 Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, K G 2 cylinders, and spheres). Correctly name shapes regardless of their orientations or overall size. CC.K.G.3 Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, K G 3 cylinders, and spheres). Identify shapes as two-dimensional (lying in a plane, “flat”) or three- dimensional (“solid”). CC.K.G.4 Analyze, compare, create, and compose shapes. Analyze and compare two- and three- dimensional shapes, in different sizes and orientations, using informal language to describe their K G 4 similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). CC.K.G.5 Analyze, compare, create, and compose shapes. Model shapes in the world by building shapes K G 5 from components (e.g., sticks and clay balls) and drawing shapes. CC.K.G.6 Analyze, compare, create, and compose shapes. Compose simple shapes to form larger K G 6 shapes. For example, "can you join these two triangles with full sides touching to make a rectangle?” English/Language Arts 1st Grade Standards Grade Core Area # Timeline Standard 1 R.L 1 CC.1.R.L.1 Key Ideas and Details: Ask and answer questions about key details in a text. CC.1.R.L.2 Key Ideas and Details: Retell stories, including key details, and demonstrate understanding of their 1 R.L 2 central message or lesson. 1 R.L 3 CC.1.R.L.3 Key Ideas and Details: Describe characters, settings, and major events in a story, using key details. CC.1.R.L.4 Craft and Structure: Identify words and phrases in stories or poems that suggest feelings or appeal 1 R.L 4 to the senses. CC.1.R.L.5 Craft and Structure: Explain major differences between books that tell stories and books that give 1 R.L 5 information, drawing on a wide reading of a range of text types. 1 R.L 6 CC.1.R.L.6 Craft and Structure: Identify who is telling the story at various points in a text. CC.1.R.L.7 Integration of Knowledge and Ideas: Use illustrations and details in a story to describe its 1 R.L 7 characters, setting, or events. CC.1.R.L.9 Integration of Knowledge and Ideas: Compare and contrast the adventures and experiences of 1 R.L 9 characters in stories. CC.1.R.L.10 Range of Reading and Level of Text Complexity: With prompting and support, read prose and 1 R.L 10 poetry of appropriate complexity for grade 1. 1 R.I 1 CC.1.R.I.1 Key Ideas and Details: Ask and answer questions about key details in a text. 1 R.I 2 CC.1.R.I.2 Key Ideas and Details: Identify the main topic and retell key details of a text. CC.1.R.I.3 Key Ideas and Details: Describe the connection between two individuals, events, ideas, or pieces of 1 R.I 3 information in a text. CC.1.R.I.4 Craft and Structure: Ask and answer questions to help determine or clarify the meaning of words 1 R.I 4 and phrases in a text. CC.1.R.I.5 Craft and Structure: Know and use various text features (e.g., headings, tables of contents, 1 R.I 5 glossaries, electronic menus, icons) to locate key facts or information in a text. CC.1.R.I.6 Craft and Structure: Distinguish between information provided by pictures or other illustrations and 1 R.I 6 information provided by the words in a text. CC.1.R.I.7 Integration of Knowledge and Ideas: Use the illustrations and details in a text to describe its key 1 R.I 7 ideas. 1 R.I 8 CC.1.R.I.8 Integration of Knowledge and Ideas: Identify the reasons an author gives to support points in a text. CC.1.R.I.9 Integration of Knowledge and Ideas: Identify basic similarities in and differences between two texts 1 R.I 9 on the same topic (e.g., in illustrations, descriptions, or procedures). CC.1.R.I.10 Range of Reading and Level of Text Complexity: With prompting and support, read informational 1 R.I 10 texts appropriately complex for grade 1. 1 R.F 1 CC.1.R.F.1 Print Concepts: Demonstrate understanding of the organization and basic features of print. CC.1.R.F.1.a Print Concepts: Recognize the distinguishing features of a sentence (e.g., first word, 1 R.F 1.a capitalization, ending punctuation). CC.1.R.F.2 Phonological Awareness: Demonstrate understanding of spoken words, syllables, and sounds 1 R.F 2 (phonemes). CC.1.R.F.2.a Phonological Awareness: Distinguish long from short vowel sounds in spoken single-syllable 1 R.F 2.a words . CC.1.R.F.2.b Phonological Awareness: Orally produce single-syllable words by blending sounds (phonemes), 1 R.F 2.b including consonant blends. CC.1.R.F.2.c Phonological Awareness: Isolate and pronounce initial, medial vowel, and final sounds 1 R.F 2.c (phonemes) in spoken single-syllable words. CC.1.R.F.2.d Phonological Awareness: Segment spoken single-syllable words into their complete sequence of 1 R.F 2.d individual sounds (phonemes). CC.1.R.F.3 Phonics and Word Recognition: Know and apply grade-level phonics and word analysis skills in 1 R.F 3 decoding words. CC.1.R.F.3.a Phonics and Word Recognition: Know the spelling-sound correspondences for common 1 R.F 3.a consonant digraphs (two letters that represent one sound). 1 R.F 3.b CC.1.R.F.3.b Phonics and Word Recognition: Decode regularly spelled one-syllable words. CC.1.R.F.3.c Phonics and Word Recognition: Know final -e and common vowel team conventions for 1 R.F 3.c representing long vowel sounds. CC.1.R.F.3.d Phonics and Word Recognition: Use knowledge that every syllable must have a vowel sound to 1 R.F 3.d determine the number of syllables in a printed word. CC.1.R.F.3.e Phonics and Word Recognition: Decode two-syllable words following basic patterns by breaking 1 R.F 3.e the words into syllables. 1 R.F 3.f CC.1.R.F.3.f Phonics and Word Recognition: Read words with inflectional endings. 1 R.F 3.g CC.1.R.F.3.g Phonics and Word Recognition: Recognize and read grade-appropriate irregularly spelled words. 1 R.F 4 CC.1.R.F.4 Read with sufficient accuracy and fluency to support comprehension. 1 R.F 4.a CC.1.R.F.4.a Read on-level text with purpose and understanding. 1 R.F 4.b CC.1.R.F.4.b Read on-level text orally with accuracy, appropriate rate, and expression. CC.1.R.F.4.c Use context to confirm or self-correct word recognition and understanding, rereading as 1 R.F 4.c necessary. CC.1.W.1 Text Types and Purposes: Write opinion pieces in which they introduce the topic or name the book 1 W 1 they are writing about, state an opinion, supply a reason for the opinion, and provide some sense of closure. CC.1.W.2 Text Types and Purposes: Write informative/explanatory texts in which they name a topic, supply 1 W 2 some facts about the topic, and provide some sense of closure. CC.1.W.3 Text Types and Purposes: Write narratives in which they recount two or more appropriately 1 W 3 sequenced events, include some details regarding what happened, use temporal words to signal event order, and provide some sense of closure. CC.1.W.5 Production and Distribution of Writing: With guidance and support from adults, focus on a topic, 1 W 5 respond to questions and suggestions from peers, and add details to strengthen writing as needed. CC.1.W.6 Production and Distribution of Writing: With guidance and support from adults, use a variety of 1 W 6 digital tools to produce and publish writing, including in collaboration with peers. CC.1.W.7 Research to Build and Present Knowledge: Participate in shared research and writing projects (e.g., 1 W 7 explore a number of “how-to” books on a given topic and use them to write a sequence of instructions). CC.1.W.8 Research to Build and Present Knowledge: With guidance and support from adults, recall 1 W 8 information from experiences or gather information from provided sources to answer a question. CC.1.SL.1 Comprehension and Collaboration: Participate in collaborative conversations with diverse partners 1 SL 1 about grade 1 topics and texts with peers and adults in small and larger groups. CC.1.SL.1.a Comprehension and Collaboration: Follow agreed-upon rules for discussions (e.g., listening to 1 SL 1.a others with care, speaking one at a time about the topics and texts under discussion). CC.1.SL.1.b Comprehension and Collaboration: Build on others’ talk in conversations by responding to the 1 SL 1.b comments of others through multiple exchanges. CC.1.SL.1.c Comprehension and Collaboration: Ask questions to clear up any confusion about the topics and 1 SL 1.c texts under discussion. CC.1.SL.2 Comprehension and Collaboration: Ask and answer questions about key details in a text read aloud 1 SL 2 or information presented orally or through other media. CC.1.SL.3 Comprehension and Collaboration: Ask and answer questions about what a speaker says in order to 1 SL 3 gather additional information or clarify something that is not understood. CC.1.SL.4 Presentation of Knowledge and Ideas: Describe people, places, things, and events with relevant 1 SL 4 details, expressing ideas and feelings clearly. CC.1.SL.5 Presentation of Knowledge and Ideas: Add drawings or other visual displays to descriptions when 1 SL 5 appropriate to clarify ideas, thoughts, and feelings. CC.1.SL.6 Presentation of Knowledge and Ideas: Produce complete sentences when appropriate to task and 1 SL 6 situation. (See grade 1 Language standards 1 and 3 on page 26 for specific expectations.) CC.1.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English 1 L 1 grammar and usage when writing or speaking. 1 L 1.a CC.1.L.1.a Conventions of Standard English: Print all upper- and lowercase letters. 1 L 1.b CC.1.L.1.b Conventions of Standard English: Use common, proper, and possessive nouns. CC.1.L.1.c Conventions of Standard English: Use singular and plural nouns with matching verbs in basic 1 L 1.c sentences (e.g., He hops; We hop). CC.1.L.1.d Conventions of Standard English: Use personal, possessive, and indefinite pronouns (e.g., I, me, my; 1 L 1.d they, them, their, anyone, everything). CC.1.L.1.e Conventions of Standard English: Use verbs to convey a sense of past, present, and future (e.g., 1 L 1.e Yesterday I walked home; Today I walk home; Tomorrow I will walk home). 1 L 1.f CC.1.L.1.f Conventions of Standard English: Use frequently occurring adjectives. CC.1.L.1.g Conventions of Standard English: Use frequently occurring conjunctions (e.g., and, but, or, so, 1 L 1.g because). 1 L 1.h CC.1.L.1.h Conventions of Standard English: Use determiners (e.g., articles, demonstratives). CC.1.L.1.i Conventions of Standard English: Use frequently occurring prepositions (e.g., during, beyond, 1 L 1.i toward). CC.1.L.1.j Conventions of Standard English: Produce and expand complete simple and compound declarative, 1 L 1.j interrogative, imperative, and exclamatory sentences in response to prompts. CC.1.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English 1 L 2 capitalization, punctuation, and spelling when writing. 1 L 2.a CC.1.L.2.a Conventions of Standard English: Capitalize dates and names of people. 1 L 2.b CC.1.L.2.b Conventions of Standard English: Use end punctuation for sentences. 1 L 2.c CC.1.L.2.c Conventions of Standard English: Use commas in dates and to separate single words in a series. CC.1.L.2.d Conventions of Standard English: Use conventional spelling for words with common spelling 1 L 2.d patterns and for frequently occurring irregular words. CC.1.L.2.e Conventions of Standard English: Spell untaught words phonetically, drawing on phonemic 1 L 2.e awareness and spelling conventions. CC.1.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple-meaning 1 L 4 words and phrases based on grade 1 reading and content, choosing flexibly from an array of strategies. CC.1.L.4.a Vocabulary Acquisition and Use: Use sentence-level context as a clue to the meaning of a word or 1 L 4.a phrase. CC.1.L.4.b Vocabulary Acquisition and Use: Use frequently occurring affixes as a clue to the meaning of a 1 L 4.b word. CC.1.L.4.c Vocabulary Acquisition and Use: Identify frequently occurring root words (e.g., look) and their 1 L 4.c inflectional forms (e.g., looks, looked, looking). CC.1.L.5 Vocabulary Acquisition and Use: With guidance and support from adults, demonstrate understanding 1 L 5 of word relationships and nuances in word meanings. CC.1.L.5.a Vocabulary Acquisition and Use: Sort words into categories (e.g., colors, clothing) to gain a sense of 1 L 5.a the concepts the categories represent. CC.1.L.5.b Vocabulary Acquisition and Use: Define words by category and by one or more key attributes (e.g., 1 L 5.b a duck is a bird that swims; a tiger is a large cat with stripes). CC.1.L.5.c Vocabulary Acquisition and Use: Identify real-life connections between words and their use (e.g., 1 L 5.c note places at home that are cozy). CC.1.L.5.d Vocabulary Acquisition and Use: Distinguish shades of meaning among verbs differing in manner 1 L 5.d (e.g., look, peek, glance, stare, glare, scowl) and adjectives differing in intensity (e.g., large, gigantic) by defining or choosing them or by acting out the meanings. CC.1.L.6 Vocabulary Acquisition and Use: Use words and phrases acquired through conversations, reading and 1 L 6 being read to, and responding to texts, including using frequently occurring conjunctions to signal simple relationships (e.g., I named my hamster Nibblet because she nibbles too much because she likes that). Mathematics 1st Grade Grade Core Area # Timeline Standard CC.1.OA.1 Represent and solve problems involving addition and subtraction. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking 1 OA 1 apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. CC.1.OA.2 Represent and solve problems involving addition and subtraction. Solve word problems that call for 1 OA 2 addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. CC.1.OA.3 Understand and apply properties of operations and the relationship between addition and subtraction. Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is 1 OA 3 known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) (Students need not use formal terms for these properties.) CC.1.OA.4 Understand and apply properties of operations and the relationship between addition and 1 OA 4 subtraction. Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. CC.1.OA.5 Add and subtract within 20. Relate counting to addition and subtraction (e.g., by counting on 2 to 1 OA 5 add 2). CC.1.OA.6 Add and subtract within 20. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); 1 OA 6 decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). CC.1.OA.7 Work with addition and subtraction equations. Understand the meaning of the equal sign, and 1 OA 7 determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. CC.1.OA.8 Work with addition and subtraction equations. Determine the unknown whole number in an 1 OA 8 addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ＿ – 3, 6 + 6 = ＿. CC.1.NBT.1 Extend the counting sequence. Count to 120, starting at any number less than 120. In this range, 1 NBT 1 read and write numerals and represent a number of objects with a written numeral. CC.1.NBT.2 Understand place value. Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: -- a. 10 can be thought of as a bundle of ten ones — called a “ten.” 1 NBT 2 -- b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. -- c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). CC.1.NBT.3 Understand place value. Compare two two-digit numbers based on meanings of the tens and ones 1 NBT 3 digits, recording the results of comparisons with the symbols >, =, and <. CC.1.NBT.4 Use place value understanding and properties of operations to add and subtract. Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or 1 NBT 4 the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. CC.1.NBT.5 Use place value understanding and properties of operations to add and subtract. Given a two-digit 1 NBT 5 number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. CC.1.NBT.6 Use place value understanding and properties of operations to add and subtract. Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using 1 NBT 6 concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. CC.1.MD.1 Measure lengths indirectly and by iterating length units. Order three objects by length; compare 1 MD 1 the lengths of two objects indirectly by using a third object. CC.1.MD.2 Measure lengths indirectly and by iterating length units. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand 1 MD 2 that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. 1 MD 3 CC.1.MD.3 Tell and write time. Tell and write time in hours and half-hours using analog and digital clocks. CC.1.MD.4 Represent and interpret data. Organize, represent, and interpret data with up to three categories; 1 MD 4 ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. CC.1.G.1 Reason with shapes and their attributes. Distinguish between defining attributes (e.g., triangles are 1 G 1 closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); for a wide variety of shapes; build and draw shapes to possess defining attributes. CC.1.G.2 Reason with shapes and their attributes. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular 1 G 2 prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names such as “right rectangular prism.”) CC.1.G.3 Reason with shapes and their attributes. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth 1 G 3 of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. English/Language Arts 2nd Grade Standards Grade Core Area # Timeline Standard CC.2.R.L.1 Key Ideas and Details: Ask and answer such questions as who, what, where, when, why, and 2 R.L 1 how to demonstrate understanding of key details in a text. CC.2.R.L.2 Key Ideas and Details: Recount stories, including fables and folktales from diverse cultures, and 2 R.L 2 determine their central message, lesson, or moral. CC.2.R.L.3 Key Ideas and Details: Describe how characters in a story respond to major events and 2 R.L 3 challenges. CC.2.R.L.4 Craft and Structure: Describe how words and phrases (e.g., regular beats, alliteration, rhymes, 2 R.L 4 repeated lines) supply rhythm and meaning in a story, poem, or song. CC.2.R.L.5 Craft and Structure: Describe the overall structure of a story, including describing how the 2 R.L 5 beginning introduces the story and the ending concludes the action. CC.2.R.L.6 Craft and Structure: Acknowledge differences in the points of view of characters, including by 2 R.L 6 speaking in a different voice for each character when reading dialogue aloud. CC.2.R.L.7 Integration of Knowledge and Ideas: Use information gained from the illustrations and words in 2 R.L 7 a print or digital text to demonstrate understanding of its characters, setting, or plot. CC.2.R.L.9 Integration of Knowledge and Ideas: Compare and contrast two or more versions of the same 2 R.L 9 story (e.g., Cinderella stories) by different authors or from different cultures. CC.2.R.L.10 Range of Reading and Level of Text Complexity: By the end of the year, read and comprehend 2 R.L 10 literature, including prose and poetry, in the grades 2–3 text complexity band proficiently, with scaffolding as needed at the high end of the range. CC.2.R.I.1 Key Ideas and Details: Ask and answer such questions as who, what, where, when, why, and how 2 R.I 1 to demonstrate understanding of key details in a text. CC.2.R.I.2 Key Ideas and Details: Identify the main topic of a multiparagraph text as well as the focus of 2 R.I 2 specific paragraphs within the text. CC.2.R.I.3 Key Ideas and Details: Describe the connection between a series of historical events, scientific 2 R.I 3 ideas or concepts, or steps in technical procedures in a text. CC.2.R.I.4 Craft and Structure: Determine the meaning of words and phrases in a text relevant to a grade 2 2 R.I 4 topic or subject area. CC.2.R.I.5 Craft and Structure: Know and use various text features (e.g., captions, bold print, subheadings, 2 R.I 5 glossaries, indexes, electronic menus, icons) to locate key facts or information in a text efficiently. CC.2.R.I.6 Craft and Structure: Identify the main purpose of a text, including what the author wants to 2 R.I 6 answer, explain, or describe. CC.2.R.I.7 Integration of Knowledge and Ideas: Explain how specific images (e.g., a diagram showing how a 2 R.I 7 machine works) contribute to and clarify a text. CC.2.R.I.8 Integration of Knowledge and Ideas: Describe how reasons support specific points the author 2 R.I 8 makes in a text. CC.2.R.I.9 Integration of Knowledge and Ideas: Compare and contrast the most important points presented 2 R.I 9 by two texts on the same topic. CC.2.R.I.10 Range of Reading and Level of Text Complexity: By the end of year, read and comprehend 2 R.I 10 informational texts, including history/social studies, science, and technical texts, in the grades 2–3 text complexity band proficiently, with scaffolding as needed at the high end of the range. CC.2.R.F.3 Phonics and Word Recognition: Know and apply grade-level phonics and word analysis skills in 2 R.F 3 decoding words. CC.2.R.F.3.a Phonics and Word Recognition: Distinguish long and short vowels when reading regularly 2 R.F 3.a spelled one-syllable words. CC.2.R.F.3.b Phonics and Word Recognition: Know spelling-sound correspondences for additional common 2 R.F 3.b vowel teams. 2 R.F 3.c CC.2.R.F.3.c Phonics and Word Recognition: Decode regularly spelled two-syllable words with long vowels. 2 R.F 3.d CC.2.R.F.3.d Phonics and Word Recognition: Decode words with common prefixes and suffixes. CC.2.R.F.3.e Phonics and Word Recognition: Identify words with inconsistent but common spelling-sound 2 R.F 3.e correspondences. CC.2.R.F.3.f Phonics and Word Recognition: Recognize and read grade-appropriate irregularly spelled 2 R.F 3.f words. 2 R.F 4 CC.2.R.F.4 Fluency: Read with sufficient accuracy and fluency to support comprehension. 2 R.F 4.a CC.2.R.F.4.a Read on-level text with purpose and understanding. 2 R.F 4.b CC.2.R.F.4.b Read on-level text orally with accuracy, appropriate rate, and expression. CC.2.R.F.4.c Use context to confirm or self-correct word recognition and understanding, rereading as 2 R.F 4.c necessary. CC.2.W.1 Text Types and Purposes: Write opinion pieces in which they introduce the topic or book they are 2 W 1 writing about, state an opinion, supply reasons that support the opinion, use linking words (e.g., because, and, also) to connect opinion and reasons, and provide a concluding statement or section. CC.2.W.2 Text Types and Purposes: Write informative/explanatory texts in which they introduce a topic, 2 W 2 use facts and definitions to develop points, and provide a concluding statement or section. CC.2.W.3 Text Types and Purposes: Write narratives in which they recount a well-elaborated event or short 2 W 3 sequence of events, include details to describe actions, thoughts, and feelings, use temporal words to signal event order, and provide a sense of closure. CC.2.W.5 Production and Distribution of Writing: With guidance and support from adults and peers, focus 2 W 5 on a topic and strengthen writing as needed by revising and editing. CC.2.W.6 Production and Distribution of Writing: With guidance and support from adults, use a variety of 2 W 6 digital tools to produce and publish writing, including in collaboration with peers. CC.2.W.7 Research to Build and Present Knowledge: Participate in shared research and writing projects 2 W 7 (e.g., read a number of books on a single topic to produce a report; record science observations). CC.2.W.8 Research to Build and Present Knowledge: Recall information from experiences or gather 2 W 8 information from provided sources to answer a question. CC.2.SL.1 Comprehension and Collaboration: Participate in collaborative conversations with diverse 2 SL 1 partners about grade 2 topics and texts with peers and adults in small and larger groups. CC.2.SL.1.a Comprehension and Collaboration: Follow agreed-upon rules for discussions (e.g., gaining the 2 SL 1.a floor in respectful ways, listening to others with care, speaking one at a time about the topics and texts under discussion). CC.2.SL.1.b Comprehension and Collaboration: Build on others’ talk in conversations by linking their 2 SL 1.b comments to the remarks of others. CC.2.SL.1.c Comprehension and Collaboration: Ask for clarification and further explanation as needed 2 SL 1.c about the topics and texts under discussion. CC.2.SL.2 Comprehension and Collaboration: Recount or describe key ideas or details from a text read 2 SL 2 aloud or information presented orally or through other media. CC.2.SL.3 Comprehension and Collaboration: Ask and answer questions about what a speaker says in order 2 SL 3 to clarify comprehension, gather additional information, or deepen understanding of a topic or issue. CC.2.SL.4 Presentation of Knowledge and Ideas: Tell a story or recount an experience with appropriate 2 SL 4 facts and relevant, descriptive details, speaking audibly in coherent sentences. CC.2.SL.5 Presentation of Knowledge and Ideas: Create audio recordings of stories or poems; add drawings 2 SL 5 or other visual displays to stories or recounts of experiences when appropriate to clarify ideas, thoughts, and feelings. CC.2.SL.6 Presentation of Knowledge and Ideas: Produce complete sentences when appropriate to task 2 SL 6 and situation in order to provide requested detail or clarification. (See grade 2 Language standards 1and 3 on page 26 for specific expectations.) CC.2.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English 2 L 1 grammar and usage when writing or speaking. 2 L 1.a CC.2.L.1.a Conventions of Standard English: Use collective nouns (e.g., group). CC.2.L.1.b Conventions of Standard English: Form and use frequently occurring irregular plural nouns (e.g., 2 L 1.b feet, children, teeth, mice, fish). 2 L 1.c CC.2.L.1.c Conventions of Standard English: Use reflexive pronouns (e.g., myself, ourselves). CC.2.L.1.d Conventions of Standard English: Form and use the past tense of frequently occurring irregular 2 L 1.d verbs (e.g., sat, hid, told). CC.2.L.1.e Conventions of Standard English: Use adjectives and adverbs, and choose between them 2 L 1.e depending on what is to be modified. CC.2.L.1.f Conventions of Standard English: Produce, expand, and rearrange complete simple and 2 L 1.f compound sentences (e.g., The boy watched the movie; The little boy watched the movie; The action movie was watched by the little boy). CC.2.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English 2 L 2 capitalization, punctuation, and spelling when writing. 2 L 2.a CC.2.L.2.a Conventions of Standard English: Capitalize holidays, product names, and geographic names. 2 L 2.b CC.2.L.2.b Conventions of Standard English: Use commas in greetings and closings of letters. CC.2.L.2.c Conventions of Standard English: Use an apostrophe to form contractions and frequently 2 L 2.c occurring possessives. CC.2.L.2.d Conventions of Standard English: Generalize learned spelling patterns when writing words (e.g., 2 L 2.d cage → badge; boy → boil). CC.2.L.2.e Conventions of Standard English: Consult reference materials, including beginning dictionaries, 2 L 2.e as needed to check and correct spellings CC.2.L.3 Knowledge of Language: Use knowledge of language and its conventions when writing, speaking, 2 L 3 reading, or listening. 2 L 3.a CC.2.L.3.a Knowledge of Language: Compare formal and informal uses of English. CC.2.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple- 2 L 4 meaning words and phrases based on grade 2 reading and content, choosing flexibly from an array of strategies. CC.2.L.4.a Vocabulary Acquisition and Use: Use sentence-level context as a clue to the meaning of a word 2 L 4.a or phrase. CC.2.L.4.b Vocabulary Acquisition and Use: Determine the meaning of the new word formed when a 2 L 4.b known prefix is added to a known word (e.g., happy/unhappy, tell/retell). CC.2.L.4.c Vocabulary Acquisition and Use: Use a known root word as a clue to the meaning of an unknown 2 L 4.c word with the same root (e.g., addition, additional). CC.2.L.4.d Vocabulary Acquisition and Use: Use knowledge of the meaning of individual words to predict 2 L 4.d the meaning of compound words (e.g., birdhouse, lighthouse, housefly; bookshelf, notebook, bookmark). CC.2.L.4.e Vocabulary Acquisition and Use: Use glossaries and beginning dictionaries, both print and digital, 2 L 4.e to determine or clarify the meaning of words and phrases. CC.2.L.5 Vocabulary Acquisition and Use: Demonstrate understanding of word relationships and nuances in 2 L 5 word meanings. CC.2.L.5.a Vocabulary Acquisition and Use: Identify real-life connections between words and their use (e.g., 2 L 5.a describe foods that are spicy or juicy). CC.2.L.5.b Vocabulary Acquisition and Use: Distinguish shades of meaning among closely related verbs 2 L 5.b (e.g., toss, throw, hurl) and closely related adjectives (e.g., thin, slender, skinny, scrawny). CC.2.L.6 Vocabulary Acquisition and Use: Use words and phrases acquired through conversations, reading 2 L 6 and being read to, and responding to texts, including using adjectives and adverbs to describe (e.g., When other kids are happy that makes me happy). Mathematics 2nd Grade Standards Grade Core Area # Timeline Standard CC.2.OA.1 Represent and solve problems involving addition and subtraction. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, 2 OA 1 putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. CC.2.OA.2 Add and subtract within 20. Fluently add and subtract within 20 using mental strategies. By end 2 OA 2 of Grade 2, know from memory all sums of two one-digit numbers. CC.2.OA.3 Work with equal groups of objects to gain foundations for multiplication. Determine whether a 2 OA 3 group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. CC.2.OA.4 Work with equal groups of objects to gain foundations for multiplication. Use addition to find 2 OA 4 the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. CC.2.NBT.1 Understand place value. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 2 NBT 1 -- a. 100 can be thought of as a bundle of ten tens — called a “hundred.” -- b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). 2 NBT 2 CC.2.NBT.2 Understand place value. Count within 1000; skip-count by 5s, 10s, and 100s. CC.2.NBT.3 Understand place value. Read and write numbers to 1000 using base-ten numerals, number 2 NBT 3 names, and expanded form. CC.2.NBT.4 Understand place value. Compare two three-digit numbers based on meanings of the 2 NBT 4 hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. CC.2.NBT.5 Use place value understanding and properties of operations to add and subtract. Fluently add 2 NBT 5 and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. CC.2.NBT.6 Use place value understanding and properties of operations to add and subtract. Add up to 2 NBT 6 four two-digit numbers using strategies based on place value and properties of operations. CC.2.NBT.7 Use place value understanding and properties of operations to add and subtract. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written 2 NBT 7 method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. CC.2.NBT.8 Use place value understanding and properties of operations to add and subtract. Mentally add 2 NBT 8 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. CC.2.NBT.9 Use place value understanding and properties of operations to add and subtract. Explain why 2 NBT 9 addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.) CC.2.MD.1 Measure and estimate lengths in standard units. Measure the length of an object by selecting 2 MD 1 and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. CC.2.MD.2 Measure and estimate lengths in standard units. Measure the length of an object twice, using 2 MD 2 length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. CC.2.MD.3 Measure and estimate lengths in standard units. Estimate lengths using units of inches, feet, 2 MD 3 centimeters, and meters. CC.2.MD.4 Measure and estimate lengths in standard units. Measure to determine how much longer one 2 MD 4 object is than another, expressing the length difference in terms of a standard length unit. CC.2.MD.5 Relate addition and subtraction to length. Use addition and subtraction within 100 to solve 2 MD 5 word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. CC.2.MD.6 Relate addition and subtraction to length. Represent whole numbers as lengths from 0 on a 2 MD 6 number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, … , and represent whole-number sums and differences within 100 on a number line diagram. CC.2.MD.7 Work with time and money. Tell and write time from analog and digital clocks to the nearest 2 MD 7 five minutes, using a.m. and p.m. CC.2.MD.8 Work with time and money. Solve word problems involving dollar bills, quarters, dimes, nickels, 2 MD 8 and pennies, using $ (dollars) and ¢ (cents) symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? CC.2.MD.9 Represent and interpret data. Generate measurement data by measuring lengths of several 2 MD 9 objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. CC.2.MD.10 Represent and interpret data. Draw a picture graph and a bar graph (with single-unit scale) to 2 MD 10 represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. CC.2.G.1 Reason with shapes and their attributes. Recognize and draw shapes having specified attributes, 2 G 1 such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. (Sizes are compared directly or visually, not compared by measuring.) CC.2.G.2 Reason with shapes and their attributes. Partition a rectangle into rows and columns of same-size 2 G 2 squares and count to find the total number of them. CC.2.G.3 Reason with shapes and their attributes. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the 2 G 3 whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. English/Language Arts 3rd Grade Standards Grade Core Area # Timeline Standard CC.3.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English 3 L 1 grammar and usage when writing or speaking. CC.3.L.1.a Conventions of Standard English: Explain the function of nouns, pronouns, verbs, adjectives, and 3 L 1.a adverbs in general and their functions in particular sentences. 3 L 1.b CC.3.L.1.b Conventions of Standard English: Form and use regular and irregular plural nouns. CC.3.R.L.1 Key Ideas and Details: Ask and answer questions to demonstrate understanding of a text, referring 3 R.L 1 explicitly to the text as the basis for the answers. CC.3.R.L.2 Key Ideas and Details: Recount stories, including fables, folktales, and myths from diverse cultures; 3 R.L 2 determine the central message, lesson, or moral and explain how it is conveyed through key details in the text. CC.3.R.L.3 Key Ideas and Details: Describe characters in a story (e.g., their traits, motivations, or feelings) and 3 R.L 3 explain how their actions contribute to the sequence of events. CC.3.R.L.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, 3 R.L 4 distinguishing literal from nonliteral language. CC.3.R.L.5 Craft and Structure: Refer to parts of stories, dramas, and poems when writing or speaking about a 3 R.L 5 text, using terms such as chapter, scene, and stanza; describe how each successive part builds on earlier sections. CC.3.R.L.6 Craft and Structure: Distinguish their own point of view from that of the narrator or those of the 3 R.L 6 characters. CC.3.R.L.7 Integration of Knowledge and Ideas: Explain how specific aspects of a text’s illustrations contribute to 3 R.L 7 what is conveyed by the words in a story (e.g., create mood, emphasize aspects of a character or setting). CC.3.R.L.9 Integration of Knowledge and Ideas: Compare and contrast the themes, settings, and plots of stories 3 R.L 9 written by the same author about the same or similar characters (e.g., in books from a series). CC.3.R.L.10 Range of Reading and Complexity of Text: 10. By the end of the year, read and comprehend literature, 3 R.L 10 including stories, dramas, and poetry, at the high end of the grades 2–3 text complexity band independently and proficiently. CC.3.R.I.1 Key Ideas and Details: Ask and answer questions to demonstrate understanding of a text, referring 3 R.I 1 explicitly to the text as the basis for the answers. CC.3.R.I.2 Key Ideas and Details: Determine the main idea of a text; recount the key details and explain how they 3 R.I 2 support the main idea. CC.3.R.I.3 Key Ideas and Details: Describe the relationship between a series of historical events, scientific ideas or 3 R.I 3 concepts, or steps in technical procedures in a text, using language that pertains to time, sequence, and cause/effect. CC.3.R.I.4 Craft and Structure: Determine the meaning of general academic and domain-specific words and 3 R.I 4 phrases in a text relevant to a grade 3 topic or subject area. CC.3.R.I.5 Craft and Structure: Use text features and search tools (e.g., key words, sidebars, hyperlinks) to locate 3 R.I 5 information relevant to a given topic efficiently. 3 R.I 6 CC.3.R.I.6 Craft and Structure: Distinguish their own point of view from that of the author of a text. CC.3.R.I.7 Integration of Knowledge and Ideas: Use information gained from illustrations (e.g., maps, 3 R.I 7 photographs) and the words in a text to demonstrate understanding of the text (e.g., where, when, why, and how key events occur). CC.3.R.I.8 Integration of Knowledge and Ideas: Describe the logical connection between particular sentences and 3 R.I 8 paragraphs in a text (e.g., comparison, cause/effect, first/second/third in a sequence). CC.3.R.I.9 Integration of Knowledge and Ideas: Compare and contrast the most important points and key details 3 R.I 9 presented in two texts on the same topic. CC.3.R.I.10 Range of Reading and Level of Text Complexity: By the end of the year, read and comprehend 3 R.I 10 informational texts, including history/social studies, science, and technical texts, at the high end of the grades 2–3 text complexity band independently and proficiently. CC.3.R.F.3 Phonics and Word Recognition: Know and apply grade-level phonics and word analysis skills in 3 R.F 3 decoding words. CC.3.R.F.3.a Phonics and Word Recognition: Identify and know the meaning of the most common prefixes and 3 R.F 3.a derivational suffixes. 3 R.F 3.b CC.3.R.F.3.b Phonics and Word Recognition: Decode words with common Latin suffixes. 3 R.F 3.c CC.3.R.F.3.c Phonics and Word Recognition: Decode multisyllable words. 3 R.F 3.d CC.3.R.F.3.d Phonics and Word Recognition: Read grade-appropriate irregularly spelled words. 3 R.F 4 CC.3.R.F.4 Fluency: Read with sufficient accuracy and fluency to support comprehension. 3 R.F 4.a CC.3.R.F.4.a Fluency: Read on-level text with purpose and understanding. 3 R.F 4.b CC.3.R.F.4.b Fluency: Read grade-level prose and poetry orally with accuracy, appropriate rate, and expression. CC.3.R.F.4.c Fluency: Use context to confirm or self-correct word recognition and understanding, rereading as 3 R.F 4.c necessary. CC.3.W.1 Text Types and Purposes: Write opinion pieces on familiar topics or texts, supporting a point of view 3 W 1 with reasons. CC.3.W.1.a Text Types and Purposes: Introduce the topic or text they are writing about, state an opinion, and 3 W 1.a create an organizational structure that lists reasons. 3 W 1.b CC.3.W.1.b Text Types and Purposes: Provide reasons that support the opinion. CC.3.W.1.c Text Types and Purposes: Use linking words and phrases (e.g., because, therefore, since, for example) 3 W 1.c to connect opinion and reasons. 3 W 1.d CC.3.W.1.d Text Types and Purposes: Provide a concluding statement or section. CC.3.W.2 Text Types and Purposes: Write informative/explanatory texts to examine a topic and convey ideas and 3 W 2 information clearly. CC.3.W.2.a Text Types and Purposes: Introduce a topic and group related information together; include 3 W 2.a illustrations when useful to aiding comprehension. 3 W 2.b CC.3.W.2.b Text Types and Purposes: Develop the topic with facts, definitions, and details. CC.3.W.2.c Text Types and Purposes: Use linking words and phrases (e.g., also, another, and, more, but) to 3 W 2.c connect ideas within categories of information. 3 W 2.d CC.3.W.2.d Text Types and Purposes: Provide a concluding statement or section. CC.3.W.3 Text Types and Purposes: Write narratives to develop real or imagined experiences or events using 3 W 3 effective technique, descriptive details, and clear event sequences. CC.3.W.3.a Text Types and Purposes: Establish a situation and introduce a narrator and/or characters; organize an 3 W 3.a event sequence that unfolds naturally. CC.3.W.3.b Text Types and Purposes: Use dialogue and descriptions of actions, thoughts, and feelings to develop 3 W 3.b experiences and events or show the response of characters to situations. 3 W 3.c CC.3.W.3.c Text Types and Purposes: Use temporal words and phrases to signal event order. 3 W 3.d CC.3.W.3.d Text Types and Purposes: Provide a sense of closure. CC.3.W.4 Production and Distribution of Writing: With guidance and support from adults, produce writing in 3 W 4 which the development and organization are appropriate to task and purpose. (Grade-specific expectations for writing types are defined in standards 1–3 above.) CC.3.W.5 Production and Distribution of Writing: With guidance and support from peers and adults, develop and 3 W 5 strengthen writing as needed by planning, revising, and editing. (Editing for conventions should demonstrate command of Language standards 1–3 up to and including grade 3 on page 29.) CC.3.W.6 Production and Distribution of Writing: With guidance and support from adults, use technology to 3 W 6 produce and publish writing (using keyboarding skills) as well as to interact and collaborate with others. CC.3.W.7 Research to Build and Present Knowledge: Conduct short research projects that build knowledge about 3 W 7 a topic. CC.3.W.8 Research to Build and Present Knowledge: Recall information from experiences or gather information 3 W 8 from print and digital sources; take brief notes on sources and sort evidence into provided categories. CC.3.W.10 Range of Writing: Write routinely over extended time frames (time for research, reflection, and 3 W 10 revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. CC.3.SL.1 Comprehension and Collaboration: Engage effectively in a range of collaborative discussions (one-on- 3 SL 1 one, in groups, and teacher-led) with diverse partners on grade 3 topics and texts, building on others’ ideas and expressing their own clearly. CC.3.SL.1.a Comprehension and Collaboration: Come to discussions prepared, having read or studied required 3 SL 1.a material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. CC.3.SL.1.b Comprehension and Collaboration: Follow agreed-upon rules for discussions (e.g., gaining the floor in 3 SL 1.b respectful ways, listening to others with care, speaking one at a time about the topics and texts under discussion). CC.3.SL.1.c Comprehension and Collaboration: Ask questions to check understanding of information presented, 3 SL 1.c stay on topic, and link their comments to the remarks of others. CC.3.SL.1.d Comprehension and Collaboration: Explain their own ideas and understanding in light of the 3 SL 1.d discussion. CC.3.SL.2 Comprehension and Collaboration: Determine the main ideas and supporting details of a text read 3 SL 2 aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. CC.3.SL.3 Comprehension and Collaboration: Ask and answer questions about information from a speaker, 3 SL 3 offering appropriate elaboration and detail. CC.3.SL.4 Presentation of Knowledge and Ideas: Report on a topic or text, tell a story, or recount an experience 3 SL 4 with appropriate facts and relevant, descriptive details, speaking clearly at an understandable pace. CC.3.SL.5 Presentation of Knowledge and Ideas: Create engaging audio recordings of stories or poems that 3 SL 5 demonstrate fluid reading at an understandable pace; add visual displays when appropriate to emphasize or enhance certain facts or details. CC.3.SL.6 Presentation of Knowledge and Ideas: Speak in complete sentences when appropriate to task and 3 SL 6 situation in order to provide requested detail or clarification. (See grade 3 Language standards 1 and 3 on page 26 for specific expectations.) CC.3.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English 3 SL 6 grammar and usage when writing or speaking. CC.3.L.1.a Conventions of Standard English: Explain the function of nouns, pronouns, verbs, adjectives, and 3 L 1.a adverbs in general and their functions in particular sentences. 3 L 1.b CC.3.L.1.b Conventions of Standard English: Form and use regular and irregular plural nouns 3 L 1.c CC.3.L.1.c Conventions of Standard Engligh: Use abstract nouns (e.g., childhood). 3 L 1.d CC.3.L.1.d Conventions of Standard English: Form and use regular and irregular verbs. 3 L 1.e CC.3.L.1.e Conventions of Standard English: Form and use the simple (e.g., I walked; I walk; I will walk) verb tenses. 3 L 1.f CC.3.L.1.f Conventions of Standard English: Ensure subject-verb and pronoun-antecedent agreement.* CC.3.L.1.g Conventions of Standard English: Form and use comparative and superlative adjectives and adverbs, 3 L 1.g and choose between them depending on what is to be modified. 3 L 1.h CC.3.L.1.h Conventions of Standard English: Use coordinating and subordinating conjunctions. 3 L 1.i CC.3.L.1.i Conventions of Standard English: Produce simple, compound, and complex sentences. CC.3.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English 3 L 2 capitalization, punctuation, and spelling when writing. 3 L 2.a CC.3.L.2.a Conventions of Standard English: Capitalize appropriate words in titles. 3 L 2.b CC.3.L.2.b Conventions of Standard English: Use commas in addresses. 3 L 2.c CC.3.L.2.c Conventions of Standard English: Use commas and quotation marks in dialogue. 3 L 2.d CC.3.L.2.d Conventions of Standard English: Form and use possessives. CC.3.L.2.e Conventions of Standard English: Use conventional spelling for high-frequency and other studied words 3 L 2.e and for adding suffixes to base words (e.g., sitting, smiled, cries, happiness). CC.3.L.2.f Conventions of Standard English: Use spelling patterns and generalizations (e.g., word families, position- 3 L 2.f based spellings, syllable patterns, ending rules, meaningful word parts) in writing words. CC.3.L.2.g Conventions of Standard English: Consult reference materials, including beginning dictionaries, as 3 L 2.g needed to check and correct spellings. CC.3.L.3 Knowledge of Language: Use knowledge of language and its conventions when writing, speaking, reading, 3 L 3 or listening. 3 L 3.a CC.3.L.3.a Knowledge of Language: Choose words and phrases for effect.* CC.3.L.3.b Knowledge of Language: Recognize and observe differences between the conventions of spoken and 3 L 3.b written standard English. CC.3.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple-meaning 3 L 4 word and phrases based on grade 3 reading and content, choosing flexibly from a range of strategies. CC.3.L.4.a Vocabulary Acquisition and Use: Use sentence-level context as a clue to the meaning of a word or 3 L 4.a phrase. CC.3.L.4.b Vocabulary Acquisition and Use: Determine the meaning of the new word formed when a known affix 3 L 4.b is added to a known word (e.g., agreeable/disagreeable, comfortable/uncomfortable, care/careless, heat/preheat). CC.3.L.4.c Vocabulary Acquisition and Use: Use a known root word as a clue to the meaning of an unknown word 3 L 4.c with the same root (e.g., company, companion). CC.3.L.4.d Vocabulary Acquisition and Use: Use glossaries or beginning dictionaries, both print and digital, to 3 L 4.d determine or clarify the precise meaning of key words and phrases. CC.3.L.5 Vocabulary Acquisition and Use: Demonstrate understanding of word relationships and nuances in word 3 L 5 meanings. CC.3.L.5.a Vocabulary Acquisition and Use: Distinguish the literal and nonliteral meanings of words and phrases in 3 L 5.a context (e.g., take steps). CC.3.L.5.b Vocabulary Acquisition and Use: Identify real-life connections between words and their use (e.g., 3 L 5.b describe people who are friendly or helpful). CC.3.L.5.c Vocabulary Acquisition and Use: Distinguish shades of meaning among related words that describe 3 L 5.c states of mind or degrees of certainty (e.g., knew, believed, suspected, heard, wondered). CC.3.L.6 Vocabulary Acquisition and Use: Acquire and use accurately grade-appropriate conversational, general 3 L 6 academic, and domain-specific words and phrases, including those that signal spatial and temporal relationships (e.g., After dinner that night we went looking for them). Mathematics 3rd Grade Standards Grade Core Area # Timeline Standard CC.3.OA.1 Represent and solve problems involving multiplication and division. Interpret products of whole 3 OA 1 numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. CC.3.OA.2 Represent and solve problems involving multiplication and division. Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are 3 OA 2 partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. CC.3.OA.3 Represent and solve problems involving multiplication and division. Use multiplication and division 3 OA 3 within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. CC.3.OA.4 Represent and solve problems involving multiplication and division. Determine the unknown whole 3 OA 4 number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = __÷ 3, 6 × 6 = ?. CC.3.OA.5 Understand properties of multiplication and the relationship between multiplication and division. Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15 then 15 × 2 3 OA 5 = 30, or by 5 × 2 = 10 then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) (Students need not use formal terms for these properties.) CC.3.OA.6 Understand properties of multiplication and the relationship between multiplication and division. 3 OA 6 Understand division as an unknown-factor problem. For example, divide 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. CC.3.OA.7 Multiply and divide within 100. Fluently multiply and divide within 100, using strategies such as the 3 OA 7 relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of one-digit numbers. CC.3.OA.8 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and 3 OA 8 estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) CC.3.OA.9 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them 3 OA 9 using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. CC.3.NBT.1 Use place value understanding and properties of operations to perform multi-digit arithmetic. Use 3 NBT 1 place value understanding to round whole numbers to the nearest 10 or 100. CC.3.NBT.2 Use place value understanding and properties of operations to perform multi-digit arithmetic. 3 NBT 2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. (A range of algorithms may be used.) CC.3.NBT.3 Use place value understanding and properties of operations to perform multi-digit arithmetic. 3 NBT 3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. (A range of algorithms may be used.) CC.3.NF.1 Develop understanding of fractions as numbers. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a 3 NF 1 parts of size 1/b. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) CC.3.NF.2 Develop understanding of fractions as numbers. Understand a fraction as a number on the number 3 NF 2 line; represent fractions on a number line diagram. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) CC.3.NF.2a Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part 3 NF 2a based at 0 locates the number 1/b on the number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) CC.3.NF.2b Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize 3 NF 2b that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) CC.3.NF.3 Develop understanding of fractions as numbers. Explain equivalence of fractions in special cases, and 3 NF 3 compare fractions by reasoning about their size. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) CC.3.NF.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a 3 NF 3a number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) CC.3.NF.3b Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3), Explain why the 3 NF 3b fractions are equivalent, e.g., by using a visual fraction model. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) CC.3.NF.3c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a 3 NF 3c number line diagram. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) CC.3.NF.3d Compare two fractions with the same numerator or the same denominator, by reasoning about their size, Recognize that valid comparisons rely on the two fractions referring to the same whole. Record the 3 NF 3d results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) CC.3.MD.1 Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Tell and write time to the nearest minute and measure time intervals in minutes. Solve 3 MD 1 word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. CC.3.MD.2 Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^3 and finding the geometric volume of 3 MD 2 a container.) Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems (problems involving notions of “times as much.”) CC.3.MD.3 Represent and interpret data. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems 3 MD 3 using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. CC.3.MD.4 Represent and interpret data. Generate measurement data by measuring lengths using rulers 3 MD 4 marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters. CC.3.MD.5 Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Recognize area as an attribute of plane figures and understand concepts of area measurement. -- a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can 3 MD 5 be used to measure area. -- b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. CC.3.MD.6 Geometric measurement: understand concepts of area and relate area to multiplication and to 3 MD 6 addition. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). CC.3.MD.7 Geometric measurement: understand concepts of area and relate area to multiplication and to 3 MD 7 addition. Relate area to the operations of multiplication and addition. CC.3.MD.7a Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is 3 MD 7a the same as would be found by multiplying the side lengths. CC.3.MD.7b Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of 3 MD 7b solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. CC.3.MD.7c Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a 3 MD 7c and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. CC.3.MD.7d Recognize area as additive. Find areas of rectilinear figures by decomposing them into non- 3 MD 7d overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. CC.3.MD.8 Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. Solve real world and mathematical problems involving perimeters of 3 MD 8 polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different area or with the same area and different perimeter. CC.3.G.1 Reason with shapes and their attributes. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared 3 G 1 attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. CC.3.G.2 Reason with shapes and their attributes. Partition shapes into parts with equal areas. Express the area 3 G 2 of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part is 1/4 of the area of the shape. English/Language Arts 4th Grade Standards Grade Core Area # Timeline Standard CC.4.R.L.1 Key Ideas and Details: Refer to details and examples in a text when explaining what the text says 4 R.L 1 explicitly and when drawing inferences from the text. CC.4.R.L.2 Key Ideas and Details: Determine a theme of a story, drama, or poem from details in the text; 4 R.L 2 summarize the text. CC.4.R.L.3 Key Ideas and Details: Describe in depth a character, setting, or event in a story or drama, drawing 4 R.L 3 on specific details in the text (e.g., a character’s thoughts, words, or actions). 4 R.L 4 CC.4.R.L.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, including those that allude to significant characters found in mythology (e.g., Herculean). CC.4.R.L.5 Craft and Structure: Explain major differences between poems, drama, and prose, and refer to the 4 R.L 5 structural elements of poems (e.g., verse, rhythm, meter) and drama (e.g., casts of characters, setting descriptions, dialogue, stage directions) when writing or speaking about a text. CC.4.R.L.6 Craft and Structure: Compare and contrast the point of view from which different stories are 4 R.L 6 narrated, including the difference between first- and third-person narrations. CC.4.R.L.7 Integration of Knowledge and Ideas: Make connections between the text of a story or drama and 4 R.L 7 a visual or oral presentation of the text, identifying where each version reflects specific descriptions and directions in the text. CC.4.R.L.9 Integration of Knowledge and Ideas: Compare and contrast the treatment of similar themes and 4 R.L 9 topics (e.g., opposition of good and evil) and patterns of events (e.g., the quest) in stories, myths, and traditional literature from different cultures. CC.4.R.L.10 Range of Reading and Complexity of Text: By the end of the year, read and comprehend 4 R.L 10 literature, including stories, dramas, and poetry, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range. CC.4.R.I.1 Key Ideas and Details: Refer to details and examples in a text when explaining what the text says 4 R.I 1 explicitly and when drawing inferences from the text. CC.4.R.I.2 Key Ideas and Details: Determine the main idea of a text and explain how it is supported by key 4 R.I 2 details; summarize the text. 4 R.I 3 CC.4.R.I.3 Key Ideas and Details: Explain events, procedures, ideas, or concepts in a historical, scientific, or technical text, including what happened and why, based on specific information in the text. CC.4.R.I.4 Craft and Structure: Determine the meaning of general academic and domain-specific words or 4 R.I 4 phrases in a text relevant to a grade 4 topic or subject area. 4 R.I 5 CC.4.R.I.5 Craft and Structure: Describe the overall structure (e.g., chronology, comparison, cause/effect, problem/solution) of events, ideas, concepts, or information in a text or part of a text. CC.4.R.I.6 Craft and Structure: Compare and contrast a firsthand and secondhand account of the same event 4 R.I 6 or topic; describe the differences in focus and the information provided. CC.4.R.I.7 Integration of Knowledge and Ideas: Interpret information presented visually, orally, or 4 R.I 7 quantitatively (e.g., in charts, graphs, diagrams, time lines, animations, or interactive elements on Web pages) and explain how the information contributes to an understanding of the text in which it appears. CC.4.R.I.8 Integration of Knowledge and Ideas: Explain how an author uses reasons and evidence to support 4 R.I 8 particular points in a text. CC.4.R.I.9 Integration of Knowledge and Ideas: Integrate information from two texts on the same topic in 4 R.I 9 order to write or speak about the subject knowledgeably. CC.4.R.I.10 Range of Reading and Complexity of Text: By the end of year, read and comprehend 4 R.I 10 informational texts, including history/social studies, science, and technical texts, in the grades 4–5 text complexity band proficiently, with scaffolding as necessary at the high end of the range. CC.4.R.F.3 Phonics and Word Recognition: Know and apply grade-level phonics and word analysis skills in 4 R.F 3 decoding words. CC.4.R.F.3.a Phonics and Word Recognition: Use combined knowledge of all letter-sound correspondences, 4 R.F 3.a syllabication patterns, and morphology (e.g., roots and affixes) to read accurately unfamiliar multisyllabic words in context and out of context. 4 R.F 4 CC.4.R.F.4 Fluency: Read with sufficient accuracy and fluency to support comprehension. 4 R.F 4.a CC.4.R.F.4.a Fluency: Read on-level text with purpose and understanding. 4 R.F 4.b CC.4.R.F.4.b Fluency: Read on-level prose and poetry orally with accuracy, appropriate rate, and expression. CC.4.R.F.4.c Fluency: Use context to confirm or self-correct word recognition and understanding, rereading 4 R.F 4.c as necessary. CC.4.W.1 Text Types and Purposes: Write opinion pieces on topics or texts, supporting a point of view with 4 W 1 reasons and information. 4 W 1.a CC.4.W.1.a Text Types and Purposes: Introduce a topic or text clearly, state an opinion, and create an organizational structure in which related ideas are grouped to support the writer’s purpose. 4 W 1.b CC.4.W.1.b Text Types and Purposes: Provide reasons that are supported by facts and details. CC.4.W.1.c Text Types and Purposes: Link opinion and reasons using words and phrases (e.g., for instance, in 4 W 1.c order to, in addition). CC.4.W.1.d Text Types and Purposes: Provide a concluding statement or section related to the opinion 4 W 1.d presented. CC.4.W.2 Text Types and Purposes: Write informative/explanatory texts to examine a topic and convey ideas 4 W 2 and information clearly. CC.4.W.2.a Text Types and Purposes: Introduce a topic clearly and group related information in paragraphs 4 W 2.a and sections; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. CC.4.W.2.b Text Types and Purposes: Develop the topic with facts, definitions, concrete details, quotations, 4 W 2.b or other information and examples related to the topic. CC.4.W.2.c Text Types and Purposes: Link ideas within categories of information using words and phrases 4 W 2.c (e.g., another, for example, also, because). CC.4.W.2.d Text Types and Purposes: Use precise language and domain-specific vocabulary to inform about 4 W 2.d or explain the topic. CC.4.W.2.e Text Types and Purposes: Provide a concluding statement or section related to the information 4 W 2.e or explanation presented. CC.4.W.3 Text Types and Purposes: Write narratives to develop real or imagined experiences or events using 4 W 3 effective technique, descriptive details, and clear event sequences. CC.4.W.3.a Text Types and Purposes: Orient the reader by establishing a situation and introducing a narrator 4 W 3.a and/or characters; organize an event sequence that unfolds naturally. CC.4.W.3.b Text Types and Purposes: Use dialogue and description to develop experiences and events or 4 W 3.b show the responses of characters to situations. CC.4.W.3.c Text Types and Purposes: Use a variety of transitional words and phrases to manage the 4 W 3.c sequence of events. CC.4.W.3.d Text Types and Purposes: Use concrete words and phrases and sensory details to convey 4 W 3.d experiences and events precisely. CC.4.W.3.e Text Types and Purposes: Provide a conclusion that follows from the narrated experiences or 4 W 3.e events. CC.4.W.4 Production and Distribution of Writing: Produce clear and coherent writing in which the 4 W 4 development and organization are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) CC.4.W.5 Production and Distribution of Writing: With guidance and support from peers and adults, develop 4 W 5 and strengthen writing as needed by planning, revising, and editing.(Editing for conventions should demonstrate command of Language standards 1–3up to and including grade 4 on page 29.) CC.4.W.6 Production and Distribution of Writing: With some guidance and support from adults, use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with 4 W 6 others; demonstrate sufficient command of keyboarding skills to type a minimum of one page in a single sitting. CC.4.W.7 Research to Build and Present Knowledge: Conduct short research projects that build knowledge 4 W 7 through investigation of different aspects of a topic. CC.4.W.8 Research to Build and Present Knowledge: Recall relevant information from experiences or gather 4 W 8 relevant information from print and digital sources; take notes and categorize information, and provide a list of sources. CC.4.W.9 Research to Build and Present Knowledge: Draw evidence from literary or informational texts to 4 W 9 support analysis, reflection, and research. CC.4.W.9.a Research to Build and Present Knowledge: Apply grade 4 Reading standards to literature (e.g., 4 W 9.a “Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text [e.g., a character’s thoughts, words, or actions].”). 4 W 9.b CC.4.W.9.b Research to Build and Present Knowledge: Apply grade 4 Reading standards to informational texts (e.g., “Explain how an author uses reasons and evidence to support particular points in a text”). CC.4.W.10 Range of Writing: Write routinely over extended time frames (time for research, reflection, and 4 W 10 revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. CC.4.SL.1 Comprehension and Collaboration: Engage effectively in a range of collaborative discussions (one- 4 SL 1 on-one, in groups, and teacher-led)with diverse partners on grade 4 topics and texts, building on others’ ideas and expressing their own clearly. CC.4.SL.1.a Comprehension and Collaboration: Come to discussions prepared, having read or studied 4 SL 1.a required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. CC.4.SL.1.b Comprehension and Collaboration: Follow agreed-upon rules for discussions and carry out 4 SL 1.b assigned roles. 4 SL 1.c CC.4.SL.1.c Comprehension and Collaboration: Pose and respond to specific questions to clarify or follow up on information, and make comments that contribute to the discussion and link to the remarks of others. CC.4.SL.1.d Comprehension and Collaboration: Review the key ideas expressed and explain their own ideas 4 SL 1.d and understanding in light of the discussion. 4 SL 2 CC.4.SL.2 Comprehension and Collaboration: Paraphrase portions of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. CC.4.SL.3 Comprehension and Collaboration: Identify the reasons and evidence a speaker provides to 4 SL 3 support particular points. CC.4.SL.4 Presentation of Knowledge and Ideas: Report on a topic or text, tell a story, or recount an 4 SL 4 experience in an organized manner, using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace. CC.4.SL.5 Presentation of Knowledge and Ideas: Add audio recordings and visual displays to presentations 4 SL 5 when appropriate to enhance the development of main ideas or themes. CC.4.SL.6 Presentation of Knowledge and Ideas: Differentiate between contexts that call for formal English (e.g., presenting ideas) and situations where informal discourse is appropriate (e.g., small-group discussion); 4 SL 6 use formal English when appropriate to task and situation. (See grade 4 Language standards 1 and 3 on page 28 for specific expectations.) CC.4.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English 4 L 1 grammar and usage when writing or speaking. CC.4.L.1.a Conventions of Standard English: Use relative pronouns (who, whose, whom, which, that) and 4 L 1.a relative adverbs (where, when, why). CC.4.L.1.b Conventions of Standard English: Form and use the progressive (e.g., I was walking; I am walking; I 4 L 1.b will be walking) verb tenses. CC.4.L.1.c Conventions of Standard English: Use modal auxiliaries (e.g., can, may, must) to convey various 4 L 1.c conditions. CC.4.L.1.d Conventions of Standard English: Order adjectives within sentences according to conventional 4 L 1.d patterns (e.g., a small red bag rather than a red small bag). 4 L 1.e CC.4.L.1.e Conventions of Standard English: Form and use prepositional phrases. CC.4.L.1.f Conventions of Standard English: Produce complete sentences, recognizing and correcting 4 L 1.f inappropriate fragments and run-ons.* CC.4.L.1.g Conventions of Standard English: Correctly use frequently confused words (e.g., to, too, two; 4 L 1.g there, their).* CC.4.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English 4 L 2 capitalization, punctuation, and spelling when writing. 4 L 2.a CC.4.L.2.a Conventions of Standard English: Use correct capitalization. CC.4.L.2.b Conventions of Standard English: Use commas and quotation marks to mark direct speech and 4 L 2.b quotations from a text. CC.4.L.2.c Conventions of Standard English: Use a comma before a coordinating conjunction in a compound 4 L 2.c sentence. CC.4.L.2.d Conventions of Standard English: Spell grade-appropriate words correctly, consulting references 4 L 2.d as needed. CC.4.L.3 Knowledge of Language: Use knowledge of language and its conventions when writing, speaking, 4 L 3 reading, or listening. 4 L 3.a CC.4.L.3.a Knowledge of Language: Choose words and phrases to convey ideas precisely.* 4 L 3.b CC.4.L.3.b Knowledge of Language: Choose punctuation for effect.* 4 L 3.c CC.4.L.3.c Knowledge of Language: Differentiate between contexts that call for formal English (e.g., presenting ideas) and situations where informal discourse is appropriate (e.g., small-group discussion). CC.4.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple- 4 L 4 meaning words and phrases based on grade 4 reading and content, choosing flexibly from a range of strategies. CC.4.L.4.a Vocabulary Acquisition and Use: Use context (e.g., definitions, examples, or restatements in text) 4 L 4.a as a clue to the meaning of a word or phrase. CC.4.L.4.b Vocabulary Acquisition and Use: Use common, grade-appropriate Greek and Latin affixes and 4 L 4.b roots as clues to the meaning of a word (e.g., telegraph, photograph, autograph). CC.4.L.4.c Vocabulary Acquisition and Use: Consult reference materials (e.g., dictionaries, glossaries, 4 L 4.c thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases. CC.4.L.5 Vocabulary Acquisition and Use: Demonstrate understanding of figurative language, word 4 L 5 relationships, and nuances in word meanings. CC.4.L.5.a Vocabulary Acquisition and Use: Explain the meaning of simple similes and metaphors (e.g., as 4 L 5.a pretty as a picture) in context. CC.4.L.5.b Vocabulary Acquisition and Use: Recognize and explain the meaning of common idioms, adages, 4 L 5.b and proverbs. 4 L 5.c CC.4.L.5.c Vocabulary Acquisition and Use: Demonstrate understanding of words by relating them to their opposites (antonyms) and to words with similar but not identical meanings (synonyms). CC.4.L.6 Vocabulary Acquisition and Use: Acquire and use accurately grade-appropriate general academic 4 L 6 and domain-specific words and phrases, including those that signal precise actions, emotions, or states of being (e.g., quizzed, whined, stammered) and that are basic to a particular topic (e.g., wildlife, conservation, and endangered when discussing animal preservation). Mathematics 4th Grade Standards Grade Core Area # Timeline Standard CC.4.OA.1 Use the four operations with whole numbers to solve problems. Interpret a multiplication equation 4 OA 1 as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. CC.4.OA.2 Use the four operations with whole numbers to solve problems. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the 4 OA 2 unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. CC.4.OA.3 Use the four operations with whole numbers to solve problems. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems 4 OA 3 in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. CC.4.OA.4 Gain familiarity with factors and multiples. Find all factor pairs for a whole number in the range 1- 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole 4 OA 4 number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. CC.4.OA.5 Generate and analyze patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule 4 OA 5 “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. CC.4.NBT.1 Generalize place value understanding for multi-digit whole numbers. Recognize that in a multi-digit 4 NBT 1 whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.) CC.4.NBT.2 Generalize place value understanding for multi-digit whole numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit 4 NBT 2 numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.) CC.4.NBT.3 Generalize place value understanding for multi-digit whole numbers. Use place value 4 NBT 3 understanding to round multi-digit whole numbers to any place. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.) CC.4.NBT.4 Use place value understanding and properties of operations to perform multi-digit arithmetic. 4 NBT 4 Fluently add and subtract multi-digit whole numbers using the standard algorithm. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.) CC.4.NBT.5 Use place value understanding and properties of operations to perform multi-digit arithmetic. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit 4 NBT 5 numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.) CC.4.NBT.6 Use place value understanding and properties of operations to perform multi-digit arithmetic. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication 4 NBT 6 and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.) CC.4.NF.1 Extend understanding of fraction equivalence and ordering. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the 4 NF 1 parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.) CC.4.NF.2 Extend understanding of fraction equivalence and ordering. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by 4 NF 2 comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.) CC.4.NF.3 Build fractions from unit fractions by applying and extending previous understandings of operations 4 NF 3 on whole numbers. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.) CC.4.NF.3a Understand addition and subtraction of fractions as joining and 4 NF 3a separating parts referring to the same whole. CC.4.NF.3b Decompose a fraction into a sum of fractions with the same denominator in more than one way, 4 NF 3b recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. CC.4.NF.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number 4 NF 3c with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. 4 NF 3d CC.4.NF.3d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. CC.4.NF.4 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a 4 NF 4 whole number. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.) 4 NF 4a CC.4.NF.4a Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4). CC.4.NF.4b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction 4 NF 4b by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) CC.4.NF.4c Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual 4 NF 4c fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? CC.4.NF.5 Understand decimal notation for fractions, and compare decimal fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100 and add 3/10 + 4/100 = 4 NF 5 34/100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.) CC.4.NF.6 Understand decimal notation for fractions, and compare decimal fractions. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 4 NF 6 meters; locate 0.62 on a number line diagram. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.) CC.4.NF.7 Understand decimal notation for fractions, and compare decimal fractions. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons comparisons are valid only when two 4 NF 7 decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.) CC.4.MD.1 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; 4 MD 1 lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example: Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …. CC.4.MD.2 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Use the four operations to solve word problems involving distances, intervals of time, liquid 4 MD 2 volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. CC.4.MD.3 Solve problems involving measurement and conversion of measurements from a larger unit to a 4 MD 3 smaller unit. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. CC.4.MD.4 Represent and interpret data. Make a line plot to display a data set of measurements in fractions of 4 MD 4 a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. CC.4.MD.5 Geometric measurement: understand concepts of angle and measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of 4 MD 5 angle measurement: -- a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. -- b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. CC.4.MD.6 Geometric measurement: understand concepts of angle and measure angles. Measure angles in 4 MD 6 whole-number degrees using a protractor. Sketch angles of specified measure. CC.4.MD.7 Geometric measurement: understand concepts of angle and measure angles. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the 4 MD 7 whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. CC.4.G.1 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Draw 4 G 1 points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. CC.4.G.2 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Classify 4 G 2 two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. CC.4.G.3 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 4 G 3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. English/Language Arts 5th Grade Standards Grade Core Area # Timeline Standard CC.5.R.L.1 Key Ideas and Details: Quote accurately from a text when explaining what the text says explicitly 5 R.L 1 and when drawing inferences from the text. CC.5.R.L.2 Key Ideas and Details: Determine a theme of a story, drama, or poem from details in the text, 5 R.L 2 including how characters in a story or drama respond to challenges or how the speaker in a poem reflects upon a topic; summarize the text. CC.5.R.L.3 Key Ideas and Details: Compare and contrast two or more characters, settings, or events in a 5 R.L 3 story or drama, drawing on specific details in the text (e.g., how characters interact). CC.5.R.L.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, 5 R.L 4 including figurative language such as metaphors and similes. CC.5.R.L.5 Craft and Structure: Explain how a series of chapters, scenes, or stanzas fits together to provide 5 R.L 5 the overall structure of a particular story, drama, or poem. CC.5.R.L.6 Craft and Structure: Describe how a narrator’s or speaker’s point of view influences how events 5 R.L 6 are described. CC.5.R.L.7 Integration of Knowledge and Ideas: Analyze how visual and multimedia elements contribute to 5 R.L 7 the meaning, tone, or beauty of a text (e.g., graphic novel; multimedia presentation of fiction, folktale, myth, poem). CC.5.R.L.9 Integration of Knowledge and Ideas: Compare and contrast stories in the same genre (e.g., 5 R.L 9 mysteries and adventure stories) on their approaches to similar themes and topics. CC.5.R.L.10 Range of Reading and Complexity of Text: By the end of the year, read and comprehend 5 R.L 10 literature, including stories, dramas, and poetry, at the high end of the grades 4–5 text complexity band independently and proficiently. CC.5.R.I.1 Key Ideas and Details: Quote accurately from a text when explaining what the text says explicitly 5 R.I 1 and when drawing inferences from the text. CC.5.R.I.2 Key Ideas and Details: Determine two or more main ideas of a text and explain how they are 5 R.I 2 supported by key details; summarize the text. CC.5.R.I.3 Key Ideas and Details: Explain the relationships or interactions between two or more individuals, 5 R.I 3 events, ideas, or concepts in a historical, scientific, or technical text based on specific information in the text. CC.5.R.I.4 Craft and Structure: Determine the meaning of general academic and domain-specific words and 5 R.I 4 phrases in a text relevant to a grade 5 topic or subject area. CC.5.R.I.5 Craft and Structure: Compare and contrast the overall structure (e.g., chronology, comparison, 5 R.I 5 cause/effect, problem/solution) of events, ideas, concepts, or information in two or more texts. CC.5.R.I.6 Craft and Structure: Analyze multiple accounts of the same event or topic, noting important 5 R.I 6 similarities and differences in the point of view they represent. CC.5.R.I.7 Integration of Knowledge and Ideas: Draw on information from multiple print or digital sources, 5 R.I 7 demonstrating the ability to locate an answer to a question quickly or to solve a problem efficiently. CC.5.R.I.8 Integration of Knowledge and Ideas: Explain how an author uses reasons and evidence to 5 R.I 8 support particular points in a text, identifying which reasons and evidence support which point(s). CC.5.R.I.9 Integration of Knowledge and Ideas: Integrate information from several texts on the same topic 5 R.I 9 in order to write or speak about the subject knowledgeably. CC.5.R.I.10 Range of Reading and Complexity of Text: By the end of the year, read and comprehend 5 R.I 10 informational texts, including history/social studies, science, and technical texts, at the high end of the grades 4–5 text complexity band independently and proficiently. CC.5.R.F.3 Phonics and Word Recognition: Know and apply grade-level phonics and word analysis skills in 5 R.F 3 decoding words. CC.5.R.F.3.a Phonics and Word Recognition: Use combined knowledge of all letter-sound correspondences, 5 R.F 3.a syllabication patterns, and morphology (e.g., roots and affixes) to read accurately unfamiliar multisyllabic words in context and out of context. 5 R.F 4 CC.5.R.F.4 Fluency: Read with sufficient accuracy and fluency to support comprehension. 5 R.F 4.a CC.5.R.F.4.a Fluency: Read grade-level text with purpose and understanding. CC.5.R.F.4.b Fluency: Read grade-level prose and poetry orally with accuracy, appropriate rate, and 5 R.F 4.b expression. CC.5.R.F.4.c Fluency: Use context to confirm or self-correct word recognition and understanding, rereading 5 R.F 4.c as necessary. CC.5.W.1 Text Types and Purposes: Write opinion pieces on topics or texts, supporting a point of view with 5 W 1 reasons and information. CC.5.W.1.a Text Types and Purposes: Introduce a topic or text clearly, state an opinion, and create an 5 W 1.a organizational structure in which ideas are logically grouped to support the writer’s purpose. CC.5.W.1.b Text Types and Purposes: Provide logically ordered reasons that are supported by facts and 5 W 1.b details. CC.5.W.1.c Text Types and Purposes: Link opinion and reasons using words, phrases, and clauses (e.g., 5 W 1.c consequently, specifically). CC.5.W.1.d Text Types and Purposes: Provide a concluding statement or section related to the opinion 5 W 1.d presented. CC.5.W.2 Text Types and Purposes: Write informative/explanatory texts to examine a topic and convey 5 W 2 ideas and information clearly. CC.5.W.2.a Text Types and Purposes: Introduce a topic clearly, provide a general observation and focus, 5 W 2.a and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. CC.5.W.2.b Text Types and Purposes: Develop the topic with facts, definitions, concrete details, quotations, 5 W 2.b or other information and examples related to the topic. CC.5.W.2.c Text Types and Purposes: Link ideas within and across categories of information using words, 5 W 2.c phrases, and clauses (e.g., in contrast, especially). CC.5.W.2.d Text Types and Purposes: Use precise language and domain-specific vocabulary to inform about 5 W 2.d or explain the topic. CC.5.W.2.e Text Types and Purposes: Provide a concluding statement or section related to the information 5 W 2.e or explanation presented. CC.5.W.3 Text Types and Purposes: Write narratives to develop real or imagined experiences or events 5 W 3 using effective technique, descriptive details, and clear event sequences. CC.5.W.3.a Text Types and Purposes: Orient the reader by establishing a situation and introducing a 5 W 3.a narrator and/or characters; organize an event sequence that unfolds naturally. CC.5.W.3.b Text Types and Purposes: Use narrative techniques, such as dialogue, description, and pacing, 5 W 3.b to develop experiences and events or show the responses of characters to situations. CC.5.W.3.c Text Types and Purposes: Use a variety of transitional words, phrases, and clauses to manage 5 W 3.c the sequence of events. CC.5.W.3.d Text Types and Purposes: Use concrete words and phrases and sensory details to convey 5 W 3.d experiences and events precisely. CC.5.W.3.e Text Types and Purposes: Provide a conclusion that follows from the narrated experiences or 5 W 3.e events. CC.5.W.4 Production and Distribution of Writing: Produce clear and coherent writing in which the 5 W 4 development and organization are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) CC.5.W.5 Production and Distribution of Writing: With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new 5 W 5 approach.(Editing for conventions should demonstrate command of Language standards 1–3up to and including grade 5 on page 29.) CC.5.W.6 Production and Distribution of Writing: With some guidance and support from adults, use technology, including the Internet, to produce and publish writing as well as to interact and collaborate 5 W 6 with others; demonstrate sufficient command of keyboarding skills to type a minimum of two pages in a single sitting. CC.5.W.7 Research to Build and Present Knowledge: Conduct short research projects that use several 5 W 7 sources to build knowledge through investigation of different aspects of a topic. CC.5.W.8 Research to Build and Present Knowledge: Recall relevant information from experiences or 5 W 8 gather relevant information from print and digital sources; summarize or paraphrase information in notes and finished work, and provide a list of sources. CC.5.W.9 Research to Build and Present Knowledge: Draw evidence from literary or informational texts to 5 W 9 support analysis, reflection, and research. CC.5.W.9.a Research to Build and Present Knowledge: Apply grade 5 Reading standards to literature (e.g., 5 W 9.a “Compare and contrast two or more characters, settings, or events in a story or a drama, drawing on specific details in the text [e.g., how characters interact]”). CC.5.W.9.b Research to Build and Present Knowledge: Apply grade 5 Reading standards to informational 5 W 9.b texts (e.g., “Explain how an author uses reasons and evidence to support particular points in a text, identifying which reasons and evidence support which point[s]”). CC.5.W.10 Range of Writing: Write routinely over extended time frames (time for research, reflection, and 5 W 10 revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. CC.5.SL.1 Comprehension and Collaboration: Engage effectively in a range of collaborative discussions (one- 5 SL 1 on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. CC.5.SL.1.a Comprehension and Collaboration: Come to discussions prepared, having read or studied 5 SL 1.a required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. CC.5.SL.1.b Comprehension and Collaboration: Follow agreed-upon rules for discussions and carry out 5 SL 1.b assigned roles. CC.5.SL.1.c Comprehension and Collaboration: Pose and respond to specific questions by making 5 SL 1.c comments that contribute to the discussion and elaborate on the remarks of others. CC.5.SL.1.d Comprehension and Collaboration: Review the key ideas expressed and draw conclusions in 5 SL 1.d light of information and knowledge gained from the discussions. CC.5.SL.2 Comprehension and Collaboration: Summarize written a text read aloud or information 5 SL 2 presented in diverse media and formats, including visually, quantitatively, and orally. CC.5.SL.3 Comprehension and Collaboration: Summarize the points a speaker makes and explain how each 5 SL 3 claim is supported by reasons and evidence. CC.5.SL.4 Presentation of Knowledge and Ideas: Report on a topic or text or present an opinion, 5 SL 4 sequencing ideas logically and using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace. CC.5.SL.5 Presentation of Knowledge and Ideas: Include multimedia components (e.g., graphics, sound) 5 SL 5 and visual displays in presentations when appropriate to enhance the development of main ideas or themes. CC.5.SL.6 Presentation of Knowledge and Ideas: Adapt speech to a variety of contexts and tasks, using 5 SL 6 formal English when appropriate to task and situation. (See grade 5 Language standards 1 and 3 on page 28 for specific expectations.) CC.5.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English 5 L 1 grammar and usage when writing or speaking. CC.5.L.1.a Conventions of Standard English: Explain the function of conjunctions, prepositions, and 5 L 1.a interjections in general and their function in particular sentences. CC.5.L.1.b Conventions of Standard English: Form and use the perfect (e.g., I had walked; I have walked; I 5 L 1.b will have walked) verb tenses. CC.5.L.1.c Conventions of Standard English: Use verb tense to convey various times, sequences, states, and 5 L 1.c conditions. 5 L 1.d CC.5.L.1.d Conventions of Standard English: Recognize and correct inappropriate shifts in verb tense.* 5 L 1.e CC.5.L.1.e Conventions of Standard English: Use correlative conjunctions (e.g., either/or, neither/nor). CC.5.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English 5 L 2 capitalization, punctuation, and spelling when writing. 5 L 2.a CC.5.L.2.a Conventions of Standard English: Use punctuation to separate items in a series.* CC.5.L.2.b Conventions of Standard English: Use a comma to separate an introductory element from the 5 L 2.b rest of the sentence. CC.5.L.2.c Conventions of Standard English: Use a comma to set off the words yes and no (e.g., Yes, thank 5 L 2.c you), to set off a tag question from the rest of the sentence (e.g., It’s true, isn’t it?), and to indicate direct address (e.g., Is that you, Steve?). CC.5.L.2.d Conventions of Standard English: Use underlining, quotation marks, or italics to indicate titles of 5 L 2.d works. CC.5.L.2.e Conventions of Standard English: Spell grade-appropriate words correctly, consulting references 5 L 2.e as needed. CC.5.L.3 Knowledge of Language: Use knowledge of language and its conventions when writing, speaking, 5 L 3 reading, or listening. CC.5.L.3.a Knowledge of Language: Expand, combine, and reduce sentences for meaning, reader/listener 5 L 3.a interest, and style. CC.5.L.3.b Knowledge of Language: Compare and contrast the varieties of English (e.g., dialects, registers) 5 L 3.b used in stories, dramas, or poems. CC.5.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple- 5 L 4 meaning words and phrases based on grade 5 reading and content, choosing flexibly from a range of strategies. CC.5.L.4.a Vocabulary Acquisition and Use: Use context (e.g., cause/effect relationships and comparisons in 5 L 4.a text) as a clue to the meaning of a word or phrase. CC.5.L.4.b Vocabulary Acquisition and Use: Use common, grade-appropriate Greek and Latin affixes and 5 L 4.b roots as clues to the meaning of a word (e.g., photograph, photosynthesis). CC.5.L.4.c Vocabulary Acquisition and Use: Consult reference materials (e.g., dictionaries, glossaries, 5 L 4.c thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases. CC.5.L.5 Vocabulary Acquisition and Use: Demonstrate understanding of figurative language, word 5 L 5 relationships, and nuances in word meanings. CC.5.L.5.a Vocabulary Acquisition and Use: Interpret figurative language, including similes and metaphors, 5 L 5.a in context. CC.5.L.5.b Vocabulary Acquisition and Use: Recognize and explain the meaning of common idioms, adages, 5 L 5.b and proverbs. CC.5.L.5.c Vocabulary Acquisition and Use: Use the relationship between particular words (e.g., synonyms, 5 L 5.c antonyms, homographs) to better understand each of the words. CC.5.L.6 Vocabulary Acquisition and Use: Acquire and use accurately grade-appropriate general academic 5 L 6 and domain-specific words and phrases, including those that signal contrast, addition, and other logical relationships (e.g., however, although, nevertheless, similarly, moreover, in addition). Mathematics 5th Grade Standards Grade Core Area # Timeline Standard CC.5.OA.1 Write and interpret numerical expressions. Use parentheses, brackets, or braces in numerical 5 OA 1 expressions, and evaluate expressions with these symbols. CC.5.OA.2 Write and interpret numerical expressions. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the 5 OA 2 calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. CC.5.OA.3 Analyze patterns and relationships. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For 5 OA 3 example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. CC.5.NBT.1 Understand the place value system. Recognize that in a multi-digit number, a digit in one 5 NBT 1 place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. CC.5.NBT.2 Understand the place value system. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point 5 NBT 2 when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10. 5 NBT 3 CC.5.NBT.3 Understand the place value system. Read, write, and compare decimals to thousandths. CC.5.NBT.3a Read and write decimals to thousandths using base-ten numerals, number names, and 5 NBT 3a expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). CC.5.NBT.3b Compare two decimals to thousandths based on meanings of the digits in each place, using 5 NBT 3b >, =, and < symbols to record the results of comparisons. CC.5.NBT.4 Understand the place value system. Use place value understanding to round decimals to any 5 NBT 4 place. CC.5.NBT.5 Perform operations with multi-digit whole numbers and with decimals to hundredths. 5 NBT 5 Fluently multiply multi-digit whole numbers using the standard algorithm. CC.5.NBT.6 Perform operations with multi-digit whole numbers and with decimals to hundredths. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using 5 NBT 6 strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. CC.5.NBT.7 Perform operations with multi-digit whole numbers and with decimals to hundredths. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies 5 NBT 7 based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. CC.5.NF.1 Use equivalent fractions as a strategy to add and subtract fractions. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent 5 NF 1 fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) CC.5.NF.2 Use equivalent fractions as a strategy to add and subtract fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike 5 NF 2 denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 by observing that 3/7 < 1/2. CC.5.NF.3 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, 5 NF 3 interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3 and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? CC.5.NF.4 Apply and extend previous understandings of multiplication and division to multiply and divide 5 NF 4 fractions. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. CC.5.NF.4a Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 5 NF 4a 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) CC.5.NF.4b Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by 5 NF 4b multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. CC.5.NF.5 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Interpret multiplication as scaling (resizing) by: -- a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. 5 NF 5 -- b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a) / (n×b) to the effect of multiplying a/b by 1. CC.5.NF.6 Apply and extend previous understandings of multiplication and division to multiply and divide 5 NF 6 fractions. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. CC.5.NF.7 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Apply and extend previous understandings of division to divide unit fractions by whole 5 NF 7 numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.) CC.5.NF.7a Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4 and use a visual fraction model to show the quotient. 5 NF 7a Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. CC.5.NF.7b Interpret division of a whole number by a unit fraction, and compute such quotients. For 5 NF 7b example, create a story context for 4 ÷ (1/5) and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. CC.5.NF.7c Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to 5 NF 7c represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? CC.5.MD.1 Convert like measurement units within a given measurement system. Convert among 5 MD 1 different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step real world problems. CC.5.MD.2 Represent and interpret data. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving 5 MD 2 information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. CC.5.MD.3 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. 5 MD 3 -- a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. -- b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. CC.5.MD.4 Geometric measurement: understand concepts of volume and relate volume to multiplication 5 MD 4 and to addition. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. CC.5.MD.5 Geometric measurement: understand concepts of volume and relate volume to multiplication 5 MD 5 and to addition. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. CC.5.MD.5a Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge 5 MD 5a lengths, equivalently by multiplying the height by the area of the base. Represent three-fold whole- number products as volumes, e.g., to represent the associative property of multiplication. CC.5.MD.5b Apply the formulas V =(l)(w)(h) and V = (b)(h) for rectangular prisms to find volumes of right 5 MD 5b rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. CC.5.MD.5c Recognize volume as additive. Find volumes of solid figures composed of two non- 5 MD 5c overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. CC.5.G.1 Graph points on the coordinate plane to solve real-world and mathematical problems. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by 5 G 1 using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). CC.5.G.2 Graph points on the coordinate plane to solve real-world and mathematical problems. 5 G 2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. CC.5.G.3 Classify two-dimensional figures into categories based on their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that 5 G 3 category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. CC.5.G.4 Classify two-dimensional figures into categories based on their properties. Classify two- 5 G 4 dimensional figures in a hierarchy based on properties. English/Language Arts 6th Grade Standards Grade Core Area # Timeline Standard CC.6.R.L.1 Key Ideas and Details: Cite textual evidence to support analysis of what the text says explicitly as 6 R.L 1 well as inferences drawn from the text. CC.6.R.L.2 Key Ideas and Details: Determine a theme or central idea of a text and how it is conveyed through 6 R.L 2 particular details; provide a summary of the text distinct from personal opinions or judgments. CC.6.R.L.3 Key Ideas and Details: Describe how a particular story’s or drama’s plot unfolds in a series of 6 R.L 3 episodes as well as how the characters respond or change as the plot moves toward a resolution. CC.6.R.L.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, 6 R.L 4 including figurative and connotative meanings; analyze the impact of a specific word choice on meaning and tone. CC.6.R.L.5 Craft and Structure: Analyze how a particular sentence, chapter, scene, or stanza fits into the 6 R.L 5 overall structure of a text and contributes to the development of the theme, setting, or plot. CC.6.R.L.6 Craft and Structure: Explain how an author develops the point of view of the narrator or speaker in 6 R.L 6 a text. CC.6.R.L.7 Integration of Knowledge and Ideas: Compare and contrast the experience of reading a story, 6 R.L 7 drama, or poem to listening to or viewing an audio, video, or live version of the text, including contrasting what they “see” and “hear” when reading the text to what they perceive when they listen or watch. CC.6.R.L.9 Integration of Knowledge and Ideas: Compare and contrast texts in different forms or genres (e.g., 6 R.L 9 stories and poems; historical novels and fantasy stories) in terms of their approaches to similar themes and topics. CC.6.R.L.10 Range of Reading and Level of Text Complexity: By the end of the year, read and comprehend 6 R.L 10 literature, including stories, dramas, and poems, in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range. CC.6.R.I.1 Key Ideas and Details: Cite textual evidence to support analysis of what the text says explicitly as 6 R.I 1 well as inferences drawn from the text. CC.6.R.I.2 Key Ideas and Details: Determine a central idea of a text and how it is conveyed through particular 6 R.I 2 details; provide a summary of the text distinct from personal opinions or judgments. CC.6.R.I.3 Key Ideas and Details: Analyze in detail how a key individual, event, or idea is introduced, 6 R.I 3 illustrated, and elaborated in a text (e.g., through examples or anecdotes). CC.6.R.I.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, 6 R.I 4 including figurative, connotative, and technical meanings. CC.6.R.I.5 Craft and Structure: Analyze how a particular sentence, paragraph, chapter, or section fits into the 6 R.I 5 overall structure of a text and contributes to the development of the ideas. CC.6.R.I.6 Craft and Structure: Determine an author’s point of view or purpose in a text and explain how it is 6 R.I 6 conveyed in the text. CC.6.R.I.7 Integration of Knowledge and Ideas: Integrate information presented in different media or formats 6 R.I 7 (e.g., visually, quantitatively) as well as in words to develop a coherent understanding of a topic or issue. CC.6.R.I.8 Integration of Knowledge and Ideas: Trace and evaluate the argument and specific claims in a text, 6 R.I 8 distinguishing claims that are supported by reasons and evidence from claims that are not. CC.6.R.I.9 Integration of Knowledge and Ideas: Compare and contrast one author’s presentation of events 6 R.I 9 with that of another (e.g., a memoir written by and a biography on the same person). CC.6.R.I.10 Range of Reading and Level of Text Complexity: By the end of the year, read and comprehend 6 R.I 10 literary nonfiction in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range. CC.6.W.1 Text Types and Purposes: Write arguments to support claims with clear reasons and relevant 6 W 1 evidence. 6 W 1.a CC.6.W.1.a Text Types and Purposes: Introduce claim(s) and organize the reasons and evidence clearly. CC.6.W.1.b Text Types and Purposes: Support claim(s) with clear reasons and relevant evidence, using 6 W 1.b credible sources and demonstrating an understanding of the topic or text. CC.6.W.1.c Text Types and Purposes: Use words, phrases, and clauses to clarify the relationships among 6 W 1.c claim(s) and reasons. 6 W 1.d CC.6.W.1.d Text Types and Purposes: Establish and maintain a formal style. CC.6.W.1.e Text Types and Purposes: Provide a concluding statement or section that follows from the 6 W 1.e argument presented. CC.6.W.2 Text Types and Purposes: Write informative/explanatory texts to examine a topic and convey ideas, 6 W 2 concepts, and information through the selection, organization, and analysis of relevant content. CC.6.W.2.a Text Types and Purposes: Introduce a topic; organize ideas, concepts, and information, using 6 W 2.a strategies such as definition, classification, comparison/contrast, and cause/effect; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension. CC.6.W.2.b Text Types and Purposes: Develop the topic with relevant facts, definitions, concrete details, 6 W 2.b quotations, or other information and examples. CC.6.W.2.c Text Types and Purposes: Use appropriate transitions to clarify the relationships among ideas and 6 W 2.c concepts. CC.6.W.2.d Text Types and Purposes: Use precise language and domain-specific vocabulary to inform about 6 W 2.d or explain the topic. 6 W 2.e CC.6.W.2.e Text Types and Purposes: Establish and maintain a formal style. CC.6.W.2.f Text Types and Purposes: Provide a concluding statement or section that follows from the 6 W 2.f information or explanation presented. CC.6.W.3 Text Types and Purposes: Write narratives to develop real or imagined experiences or events using 6 W 3 effective technique, relevant descriptive details, and well-structured event sequences. CC.6.W.3.a Text Types and Purposes: Engage and orient the reader by establishing a context and introducing 6 W 3.a a narrator and/or characters; organize an event sequence that unfolds naturally and logically. CC.6.W.3.b Text Types and Purposes: Use narrative techniques, such as dialogue, pacing, and description, to 6 W 3.b develop experiences, events, and/or characters. CC.6.W.3.c Text Types and Purposes: Use a variety of transition words, phrases, and clauses to convey 6 W 3.c sequence and signal shifts from one time frame or setting to another. CC.6.W.3.d Text Types and Purposes: Use precise words and phrases, relevant descriptive details, and 6 W 3.d sensory language to convey experiences and events. CC.6.W.3.e Text Types and Purposes: Provide a conclusion that follows from the narrated experiences or 6 W 3.e events. CC.6.W.4 Production and Distribution of Writing: Produce clear and coherent writing in which the 6 W 4 development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) CC.6.W.5 Production and Distribution of Writing: With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new 6 W 5 approach.(Editing for conventions should demonstrate command of Language standards 1–3up to and including grade 6 on page53.) CC.6.W.6 Production and Distribution of Writing: Use technology, including the Internet, to produce and 6 W 6 publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of three pages in a single sitting. CC.6.W.7 Research to Build and Present Knowledge: Conduct short research projects to answer a question, 6 W 7 drawing on several sources and refocusing the inquiry when appropriate. CC.6.W.8 Research to Build and Present Knowledge: Gather relevant information from multiple print and 6 W 8 digital sources; assess the credibility of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and providing basic bibliographic information for sources. CC.6.W.9 Research to Build and Present Knowledge: Draw evidence from literary or informational texts to 6 W 9 support analysis, reflection, and research. CC.6.W.9.a Research to Build and Present Knowledge: Apply grade 6 Reading standards to literature (e.g., 6 W 9.a “Compare and contrast texts in different forms or genres [e.g., stories and poems; historical novels and fantasy stories]in terms of their approaches to similar themes and topics”). CC.6.W.9.b Research to Build and Present Knowledge: Apply grade 6 Reading standards to literary nonfiction 6 W 9.b (e.g., “Trace and evaluate the argument and specific claims in a text, distinguishing claims that are supported by reasons and evidence from claims that are not”). CC.6.W.10 Range of Writing: Write routinely over extended time frames (time for research, reflection, and 6 W 10 revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. CC.6.SL.1 Comprehension and Collaboration: Engage effectively in a range of collaborative discussions (one- 6 SL 1 on-one, in groups, and teacher-led) with diverse partners on grade 6 topics, texts, and issues, building on others’ ideas and expressing their own clearly. CC.6.SL.1.a Comprehension and Collaboration: Come to discussions prepared, having read or studied required 6 SL 1.a material; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion. CC.6.SL.1.b Comprehension and Collaboration: Follow rules for collegial discussions, set specific goals and 6 SL 1.b deadlines, and define individual roles as needed. CC.6.SL.1.c Comprehension and Collaboration: Pose and respond to specific questions with elaboration and 6 SL 1.c detail by making comments that contribute to the topic, text, or issue under discussion. CC.6.SL.1.d Comprehension and Collaboration: Review the key ideas expressed and demonstrate 6 SL 1.d understanding of multiple perspectives through reflection and paraphrasing. CC.6.SL.2 Comprehension and Collaboration: Interpret information presented in diverse media and formats 6 SL 2 (e.g., visually, quantitatively, orally) and explain how it contributes to a topic, text, or issue under study. CC.6.SL.3 Comprehension and Collaboration: Delineate a speaker’s argument and specific claims, 6 SL 3 distinguishing claims that are supported by reasons and evidence from claims that are not. CC.6.SL.4 Presentation of Knowledge and Ideas: Present claims and findings, sequencing ideas logically and 6 SL 4 using pertinent descriptions, facts, and details to accentuate main ideas or themes; use appropriate eye contact, adequate volume, and clear pronunciation. CC.6.SL.5 Presentation of Knowledge and Ideas: Include multimedia components (e.g., graphics, images, 6 SL 5 music, sound) and visual displays in presentations to clarify information. CC.6.SL.6 Presentation of Knowledge and Ideas: Adapt speech to a variety of contexts and tasks, 6 SL 6 demonstrating command of formal English when indicated or appropriate. (See grade 6 Language standards 1 and 3 on page 53 for specific expectations.) CC.6.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English 6 L 1 grammar and usage when writing or speaking. CC.6.L.1.a Conventions of Standard English: Ensure that pronouns are in the proper case (subjective, 6 L 1.a objective, possessive). 6 L 1.b CC.6.L.1.b Conventions of Standard English: Use intensive pronouns (e.g., myself, ourselves). CC.6.L.1.c Conventions of Standard English: Recognize and correct inappropriate shifts in pronoun number 6 L 1.c and person.* CC.6.L.1.d Conventions of Standard English: Recognize and correct vague pronouns (i.e., ones with unclear or 6 L 1.d ambiguous antecedents).* CC.6.L.1.e Conventions of Standard English: Recognize variations from standard English in their own and 6 L 1.e others' writing and speaking, and identify and use strategies to improve expression in conventional language.* CC.6.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English 6 L 2 capitalization, punctuation, and spelling when writing. CC.6.L.2.a Conventions of Standard English: Use punctuation (commas, parentheses, dashes) to set off 6 L 2.a nonrestrictive/parenthetical elements.* 6 L 2.b CC.6.L.2.b Conventions of Standard English: Spell correctly. CC.6.L.3 Knowledge of Language: Use knowledge of language and its conventions when writing, speaking, 6 L 3 reading, or listening. 6 L 3.a CC.6.L.3.a Knowledge of Language: Vary sentence patterns for meaning, reader/listener interest, and style.* 6 L 3.b CC.6.L.3.b Knowledge of Language: Maintain consistency in style and tone.* CC.6.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple-meaning 6 L 4 words and phrases based on grade 6 reading and content, choosing flexibly from a range of strategies. CC.6.L.4.a Vocabulary Acquisition and Use: Use context (e.g., the overall meaning of a sentence or paragraph; 6 L 4.a a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. CC.6.L.4.b Vocabulary Acquisition and Use: Use common, grade-appropriate Greek or Latin affixes and roots 6 L 4.b as clues to the meaning of a word (e.g., audience, auditory, audible). CC.6.L.4.c Vocabulary Acquisition and Use: Consult reference materials (e.g., dictionaries, glossaries, 6 L 4.c thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech. CC.6.L.4.d Vocabulary Acquisition and Use: Verify the preliminary determination of the meaning of a word or 6 L 4.d phrase (e.g., by checking the inferred meaning in context or in a dictionary). CC.6.L.5 Vocabulary Acquisition and Use: Demonstrate understanding of figurative language, word 6 L 5 relationships, and nuances in word meanings. 6 L 5.a CC.6.L.5.a Vocabulary Acquisition and Use: Interpret figures of speech (e.g., personification) in context. CC.6.L.5.b Vocabulary Acquisition and Use: Use the relationship between particular words (e.g., cause/effect, 6 L 5.b part/whole, item/category) to better understand each of the words. CC.6.L.5.c Vocabulary Acquisition and Use: Distinguish among the connotations (associations) of words with 6 L 5.c similar denotations (definitions) (e.g., stingy, scrimping, economical, unwasteful, thrifty). CC.6.L.6 Vocabulary Acquisition and Use: Acquire and use accurately grade-appropriate general academic and 6 L 6 domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression. Mathematics 6th Grade Standards Grade Core Area # Timeline Standard CC.6.RP.1 Understand ratio concepts and use ratio reasoning to solve problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio 6 RP 1 of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” CC.6.RP.2 Understand ratio concepts and use ratio reasoning to solve problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0 (b not equal to zero), and use rate language in the context 6 RP 2 of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." (Expectations for unit rates in this grade are limited to non-complex fractions.) CC.6.RP.3 Understand ratio concepts and use ratio reasoning to solve problems. Use ratio and rate reasoning 6 RP 3 to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. CC.6.RP.3a Make tables of equivalent ratios relating quantities with whole-number measurements, find 6 RP 3a missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. CC.6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed. For example, If 6 RP 3b it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? CC.6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the 6 RP 3c quantity); solve problems involving finding the whole given a part and the percent. CC.6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately 6 RP 3d when multiplying or dividing quantities. CC.6.NS.1 Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the 6 NS 1 relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? CC.6.NS.2 Compute fluently with multi-digit numbers and find common factors and multiples. Fluently divide 6 NS 2 multi-digit numbers using the standard algorithm. CC.6.NS.3 Compute fluently with multi-digit numbers and find common factors and multiples. Fluently add, 6 NS 3 subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. CC.6.NS.4 Compute fluently with multi-digit numbers and find common factors and multiples. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of 6 NS 4 two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). CC.6.NS.5 Apply and extend previous understandings of numbers to the system of rational numbers. Understand that positive and negative numbers are used together to describe quantities having opposite 6 NS 5 directions or values (e.g., temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. CC.6.NS.6 Apply and extend previous understandings of numbers to the system of rational numbers. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate 6 NS 6 axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. CC.6.NS.6a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number 6 NS 6a line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. CC.6.NS.6b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the 6 NS 6b coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. CC.6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line 6 NS 6c diagram; find and position pairs of integers and other rational numbers on a coordinate plane. CC.6.NS.7 Apply and extend previous understandings of numbers to the system of rational numbers. 6 NS 7 Understand ordering and absolute value of rational numbers. CC.6.NS.7a Interpret statements of inequality as statements about the relative position of two numbers on a 6 NS 7a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. CC.6.NS.7b Write, interpret, and explain statements of order for rational numbers in real-world contexts. For 6 NS 7b example, write –3°C > –7°C to express the fact that –3°C is warmer than –7°C. CC.6.NS.7c Understand the absolute value of a rational number as its distance from 0 on the number line; 6 NS 7c interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. CC.6.NS.7d Distinguish comparisons of absolute value from statements about order. For example, recognize 6 NS 7d that an account balance less than –30 dollars represents a debt greater than 30 dollars. CC.6.NS.8 Apply and extend previous understandings of numbers to the system of rational numbers. Solve real- world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include 6 NS 8 use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. CC.6.EE.1 Apply and extend previous understandings of arithmetic to algebraic expressions. Write and 6 EE 1 evaluate numerical expressions involving whole-number exponents. CC.6.EE.2 Apply and extend previous understandings of arithmetic to algebraic expressions. Write, read, and 6 EE 2 evaluate expressions in which letters stand for numbers. CC.6.EE.2a Write expressions that record operations with numbers and with letters standing for numbers. For 6 EE 2a example, express the calculation “Subtract y from 5” as 5 – y. CC.6.EE.2b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, 6 EE 2b coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. CC.6.EE.2c Evaluate expressions at specific values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, including those involving whole-number 6 EE 2c exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s^3 and A = 6 s^2 to find the volume and surface area of a cube with sides of length s = 1/2. CC.6.EE.3 Apply and extend previous understandings of arithmetic to algebraic expressions. Apply the 6 EE 3 properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y CC.6.EE.4 Apply and extend previous understandings of arithmetic to algebraic expressions. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value 6 EE 4 is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. CC.6.EE.5 Reason about and solve one-variable equations and inequalities. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation 6 EE 5 or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. CC.6.EE.6 Reason about and solve one-variable equations and inequalities. Use variables to represent numbers 6 EE 6 and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. CC.6.EE.7 Reason about and solve one-variable equations and inequalities. Solve real-world and mathematical 6 EE 7 problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. CC.6.EE.8 Reason about and solve one-variable equations and inequalities. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that 6 EE 8 inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. CC.6.EE.9 Represent and analyze quantitative relationships between dependent and independent variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other 6 EE 9 quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. CC.6.G.1 Solve real-world and mathematical problems involving area, surface area, and volume. Find area of 6 G 1 right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. and mathematical problems involving area, surface area, and volume. Find the CC.6.G.2 Solve real-world volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by 6 G 2 multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. CC.6.G.3 Solve real-world and mathematical problems involving area, surface area, and volume. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a 6 G 3 side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. CC.6.G.4 Solve real-world and mathematical problems involving area, surface area, and volume. Represent 6 G 4 three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. CC.6.SP.1 Develop understanding of statistical variability. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, 6 SP 1 “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. CC.6.SP.2 Develop understanding of statistical variability. Understand that a set of data collected to answer a 6 SP 2 statistical question has a distribution which can be described by its center, spread, and overall shape. CC.6.SP.3 Develop understanding of statistical variability. Recognize that a measure of center for a numerical 6 SP 3 data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. CC.6.SP.4 Summarize and describe distributions. Display numerical data in plots on a number line, including 6 SP 4 dot plots, histograms, and box plots. CC.6.SP.5 Summarize and describe distributions. Summarize numerical data sets in relation to their context, 6 SP 5 such as by: -- a. Reporting the number of observations. English/Language Arts 7th Grade Standards Grade Core Area # Timeline Standard CC.7.R.L.1 Key Ideas and Details: Cite several pieces of textual evidence to support analysis of what the text 7 R.L 1 says explicitly as well as inferences drawn from the text. CC.7.R.L.2 Key Ideas and Details: Determine a theme or central idea of a text and analyze its development 7 R.L 2 over the course of the text; provide an objective summary of the text. CC.7.R.L.3 Key Ideas and Details: Analyze how particular elements of a story or drama interact (e.g., how 7 R.L 3 setting shapes the characters or plot). CC.7.R.L.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, 7 R.L 4 including figurative and connotative meanings; analyze the impact of rhymes and other repetitions of sounds (e.g., alliteration) on a specific verse or stanza of a poem or section of a story or drama. CC.7.R.L.5 Craft and Structure: Analyze how a drama’s or poem’s form or structure (e.g., soliloquy, sonnet) 7 R.L 5 contributes to its meaning. CC.7.R.L.6 Craft and Structure: Analyze how an author develops and contrasts the points of view of different 7 R.L 6 characters or narrators in a text. CC.7.R.L.7 Integration of Knowledge and Ideas: Compare and contrast a written story, drama, or poem to its 7 R.L 7 audio, filmed, staged, or multimedia version, analyzing the effects of techniques unique to each medium (e.g., lighting, sound, color, or camera focus and angles in a film). CC.7.R.L.9 Integration of Knowledge and Ideas: Compare and contrast a fictional portrayal of a time, place, or 7 R.L 9 character and a historical account of the same period as a means of understanding how authors of fiction use or alter history. CC.7.R.L.10 Range of Reading and Level of Text Complexity: By the end of the year, read and comprehend 7 R.L 10 literature, including stories, dramas, and poems, in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range. CC.7.R.I.1 Key Ideas and Details: Cite several pieces of textual evidence to support analysis of what the text 7 R.I 1 says explicitly as well as inferences drawn from the text. CC.7.R.I.2 Key Ideas and Details: Determine two or more central ideas in a text and analyze their 7 R.I 2 development over the course of the text; provide an objective summary of the text. CC.7.R.I.3 Key Ideas and Details: Analyze the interactions between individuals, events, and ideas in a text 7 R.I 3 (e.g., how ideas influence individuals or events, or how individuals influence ideas or events). CC.7.R.I.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, 7 R.I 4 including figurative, connotative, and technical meanings; analyze the impact of a specific word choice on meaning and tone. CC.7.R.I.5 Craft and Structure: Analyze the structure an author uses to organize a text, including how the 7 R.I 5 major sections contribute to the whole and to the development of the ideas. CC.7.R.I.6 Craft and Structure: Determine an author’s point of view or purpose in a text and analyze how the 7 R.I 6 author distinguishes his or her position from that of others. CC.7.R.I.7 Integration of Knowledge and Ideas: Compare and contrast a text to an audio, video, or multimedia 7 R.I 7 version of the text, analyzing each medium’s portrayal of the subject (e.g., how the delivery of a speech affects the impact of the words). CC.7.R.I.8 Integration of Knowledge and Ideas: Trace and evaluate the argument and specific claims in a text, 7 R.I 8 assessing whether the reasoning is sound and the evidence is relevant and sufficient to support the claims. CC.7.R.I.9 Integration of Knowledge and Ideas: Analyze how two or more authors writing about the same 7 R.I 9 topic shape their presentations of key information by emphasizing different evidence or advancing different interpretations of facts. CC.7.R.I.10 Range of Reading and Level of Text Complexity: By the end of the year, read and comprehend 7 R.I 10 literary nonfiction in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range. CC.7.W.1 Text Types and Purposes: Write arguments to support claims with clear reasons and relevant 7 W 1 evidence. CC.7.W.1.a Text Types and Purposes: Introduce claim(s), acknowledge alternate or opposing claims, and 7 W 1.a organize the reasons and evidence logically. CC.7.W.1.b Text Types and Purposes: Support claim(s) with logical reasoning and relevant evidence, using 7 W 1.b accurate, credible sources and demonstrating an understanding of the topic or text. CC.7.W.1.c Text Types and Purposes: Use words, phrases, and clauses to create cohesion and clarify the 7 W 1.c relationships among claim(s), reasons, and evidence. 7 W 1.d CC.7.W.1.d Text Types and Purposes: Establish and maintain a formal style. CC.7.W.1.e Text Types and Purposes: Provide a concluding statement or section that follows from and 7 W 1.e supports the argument presented. CC.7.W.2 Text Types and Purposes: Write informative/explanatory texts to examine a topic and convey ideas, 7 W 2 concepts, and information through the selection, organization, and analysis of relevant content. CC.7.W.2.a Text Types and Purposes: Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information, using strategies such as definition, classification, comparison/contrast, and 7 W 2.a cause/effect; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension. CC.7.W.2.b Text Types and Purposes: Develop the topic with relevant facts, definitions, concrete details, 7 W 2.b quotations, or other information and examples. CC.7.W.2.c Text Types and Purposes: Use appropriate transitions to create cohesion and clarify the 7 W 2.c relationships among ideas and concepts. CC.7.W.2.d Text Types and Purposes: Use precise language and domain-specific vocabulary to inform about 7 W 2.d or explain the topic. 7 W 2.e CC.7.W.2.e Text Types and Purposes: Establish and maintain a formal style. CC.7.W.2.f Text Types and Purposes: Provide a concluding statement or section that follows from and 7 W 2.f supports the information or explanation presented. CC.7.W.3 Text Types and Purposes: Write narratives to develop real or imagined experiences or events using 7 W 3 effective technique, relevant descriptive details, and well-structured event sequences. CC.7.W.3.a Text Types and Purposes: Engage and orient the reader by establishing a context and point of 7 W 3.a view and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically. CC.7.W.3.b Text Types and Purposes: Use narrative techniques, such as dialogue, pacing, and description, to 7 W 3.b develop experiences, events, and/or characters. CC.7.W.3.c Text Types and Purposes: Use a variety of transition words, phrases, and clauses to convey 7 W 3.c sequence and signal shifts from one time frame or setting to another. CC.7.W.3.d Text Types and Purposes: Use precise words and phrases, relevant descriptive details, and 7 W 3.d sensory language to capture the action and convey experiences and events. CC.7.W.3.e Text Types and Purposes: Provide a conclusion that follows from and reflects on the narrated 7 W 3.e experiences or events. CC.7.W.4 Production and Distribution of Writing: Produce clear and coherent writing in which the 7 W 4 development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) CC.7.W.5 Production and Distribution of Writing: With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, 7 W 5 focusing on how well purpose and audience have been addressed. (Editing for conventions should demonstrate command of Language standards 1–3 up to and including grade 7 on page 53.) CC.7.W.6 Production and Distribution of Writing: Use technology, including the Internet, to produce and 7 W 6 publish writing and link to and cite sources as well as to interact and collaborate with others, including linking to and citing sources. CC.7.W.7 Research to Build and Present Knowledge: Conduct short research projects to answer a question, 7 W 7 drawing on several sources and generating additional related, focused questions for further research and investigation. CC.7.W.8 Research to Build and Present Knowledge: Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote 7 W 8 or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation. CC.7.W.9 Research to Build and Present Knowledge: Draw evidence from literary or informational texts to 7 W 9 support analysis, reflection, and research. CC.7.W.9.a Research to Build and Present Knowledge: Apply grade 7 Reading standards to literature (e.g., 7 W 9.a “Compare and contrast a fictional portrayal of a time, place, or character and a historical account of the same period as a means of understanding how authors of fiction use or alter history”). CC.7.W.9.b Research to Build and Present Knowledge: Apply grade 7 Reading standards to literary nonfiction 7 W 9.b (e.g. “Trace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient to support the claims”). CC.7.W.10 Range of Writing: Write routinely over extended time frames (time for research, reflection, and 7 W 10 revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. CC.7.SL.1 Comprehension and Collaboration: Engage effectively in a range of collaborative discussions (one- 7 SL 1 on-one, in groups, and teacher-led) with diverse partners on grade 7 topics, texts, and issues, building on others’ ideas and expressing their own clearly. CC.7.SL.1.a Comprehension and Collaboration: Come to discussions prepared, having read or researched 7 SL 1.a material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion. CC.7.SL.1.b Comprehension and Collaboration: Follow rules for collegial discussions, track progress toward 7 SL 1.b specific goals and deadlines, and define individual roles as needed. CC.7.SL.1.c Comprehension and Collaboration: Pose questions that elicit elaboration and respond to others’ 7 SL 1.c questions and comments with relevant observations and ideas that bring the discussion back on topic as needed. CC.7.SL.1.d Comprehension and Collaboration: Acknowledge new information expressed by others and, when 7 SL 1.d warranted, modify their own views. CC.7.SL.2 Comprehension and Collaboration: Analyze the main ideas and supporting details presented in 7 SL 2 diverse media and formats (e.g., visually, quantitatively, orally) and explain how the ideas clarify a topic, text, or issue under study. CC.7.SL.3 Comprehension and Collaboration: Delineate a speaker’s argument and specific claims, evaluating 7 SL 3 the soundness of the reasoning and the relevance and sufficiency of the evidence. CC.7.SL.4 Presentation of Knowledge and Ideas: Present claims and findings, emphasizing salient points in a 7 SL 4 focused, coherent manner with pertinent descriptions, facts, details, and examples; use appropriate eye contact, adequate volume, and clear pronunciation. CC.7.SL.5 Presentation of Knowledge and Ideas: Include multimedia components and visual displays in 7 SL 5 presentations to clarify claims and findings and emphasize salient points CC.7.SL.6 Presentation of Knowledge and Ideas: Adapt speech to a variety of contexts and tasks, 7 SL 6 demonstrating command of formal English when indicated or appropriate. CC.7.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English 7 L 1 grammar and usage when writing or speaking. CC.7.L.1.a Conventions of Standard English: Explain the function of phrases and clauses in general and their 7 L 1.a function in specific sentences. CC.7.L.1.b Conventions of Standard English: Choose among simple, compound, complex, and compound- 7 L 1.b complex sentences to signal differing relationships among ideas. CC.7.L.1.c Conventions of Standard English: Place phrases and clauses within a sentence, recognizing and 7 L 1.c correcting misplaced and dangling modifiers.* CC.7.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English 7 L 2 capitalization, punctuation, and spelling when writing. CC.7.L.2.a Conventions of Standard English: Use a comma to separate coordinate adjectives (e.g., It was a 7 L 2.a fascinating, enjoyable movie but not He wore an old[,] green shirt). 7 L 2.b CC.7.L.2.b Conventions of Standard English: Spell correctly. CC.7.L.3 Knowledge of Language: Use knowledge of language and its conventions when writing, speaking, 7 L 3 reading, or listening. CC.7.L.3.a Knowledge of Language: Choose language that expresses ideas precisely and concisely, recognizing 7 L 3.a and eliminating wordiness and redundancy.* CC.7.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple-meaning 7 L 4 words and phrases based on grade 7 reading and content, choosing flexibly from a range of strategies. CC.7.L.4.a Vocabulary Acquisition and Use: Use context (e.g., the overall meaning of a sentence or paragraph; 7 L 4.a a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. CC.7.L.4.b Vocabulary Acquisition and Use: Use common, grade-appropriate Greek or Latin affixes and roots 7 L 4.b as clues to the meaning of a word (e.g., belligerent, bellicose, rebel). CC.7.L.4.c Vocabulary Acquisition and Use: Consult general and specialized reference materials (e.g., 7 L 4.c dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech. CC.7.L.4.d Vocabulary Acquisition and Use: Verify the preliminary determination of the meaning of a word or 7 L 4.d phrase (e.g., by checking the inferred meaning in context or in a dictionary). CC.7.L.5 Vocabulary Acquisition and Use: Demonstrate understanding of figurative language, word 7 L 5 relationships, and nuances in word meanings. CC.7.L.5.a Vocabulary Acquisition and Use: Interpret figures of speech (e.g., literary, biblical, and mythological 7 L 5.a allusions) in context. CC.7.L.5.b Vocabulary Acquisition and Use: Use the relationship between particular words (e.g., 7 L 5.b synonym/antonym, analogy) to better understand each of the words. CC.7.L.5.c Vocabulary Acquisition and Use: Distinguish among the connotations (associations) of words with 7 L 5.c similar denotations (definitions) (e.g., refined, respectful, polite, diplomatic, condescending). CC.7.L.6 Vocabulary Acquisition and Use: Acquire and use accurately grade-appropriate general academic and 7 L 6 domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression. Mathematics 7th Grade Standards Grade Core Area # Timeline Standard CC.7.RP.1 Analyze proportional relationships and use them to solve real-world and mathematical problems. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities 7 RP 1 measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour. CC.7.RP.2 Analyze proportional relationships and use them to solve real-world and mathematical problems. 7 RP 2 Recognize and represent proportional relationships between quantities. CC.7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent 7 RP 2a ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. CC.7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and 7 RP 2b verbal descriptions of proportional relationships. CC.7.RP.2c Represent proportional relationships by equations. For example, if total cost t is proportional to 7 RP 2c the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. CC.7.RP.2d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the 7 RP 2d situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. CC.7.RP.3 Analyze proportional relationships and use them to solve real-world and mathematical problems. 7 RP 3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. CC.7.NS.1 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of addition and subtraction to add 7 NS 1 and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. CC.7.NS.1a Describe situations in which opposite quantities combine to make 0. For example, a hydrogen 7 NS 1a atom has 0 charge because its two constituents are oppositely charged. CC.7.NS.1b Understand p + q as the number located a distance |q| from p, in the positive or negative 7 NS 1b direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. CC.7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show 7 NS 1c that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. 7 NS 1d CC.7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers. CC.7.NS.2 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, 7 NS 2 and divide rational numbers. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. CC.7.NS.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to 7 NS 2a products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. CC.7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient 7 NS 2b of integers (with non-zero divisor) is a rational number. If p and q are integers then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts. 7 NS 2c CC.7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers. CC.7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a 7 NS 2d rational number terminates in 0s or eventually repeats. CC.7.NS.3 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Solve real-world and mathematical problems involving the four operations with 7 NS 3 rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) CC.7.EE.1 Use properties of operations to generate equivalent expressions. Apply properties of operations as 7 EE 1 1 strategies to add, subtract, factor, and expand linear expressions with rational coefficients. CC.7.EE.2 Use properties of operations to generate equivalent expressions. Understand that rewriting an 7 EE 2 2 expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.” CC.7.EE.3 Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and 7 EE 3 3 assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. CC.7.EE.4 Solve real-life and mathematical problems using numerical and algebraic expressions and 7 EE 4 4 equations. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. CC.7.EE.4a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an 7 EE 4a 4a arithmetic solution, identifying the sequence of the operations used in each approach. For example, The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? CC.7.EE.4b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the 7 EE 4b 4b problem. For example, As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. CC.7.G.1 Draw, construct, and describe geometrical figures and describe the relationships between them. 7 G 1 1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. CC.7.G.2 Draw, construct, and describe geometrical figures and describe the relationships between them. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. 7 G 2 2 Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. CC.7.G.3 Draw, construct, and describe geometrical figures and describe the relationships between them. 7 G 3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. CC.7.G.4 Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 7 G 4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. CC.7.G.5 Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 7 G 5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. CC.7.G.6 Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 7 G 6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three- dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. CC.7.SP.1 Use random sampling to draw inferences about a population. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about 7 SP 1 a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. CC.7.SP.2 Use random sampling to draw inferences about a population. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, 7 SP 2 estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. CC.7.SP.3 Draw informal comparative inferences about two populations. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players 7 SP 3 on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. CC.7.SP.4 Draw informal comparative inferences about two populations. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences 7 SP 4 about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. CC.7.SP.5 Investigate chance processes and develop, use, and evaluate probability models. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event 7 SP 5 occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. CC.7.SP.6 Investigate chance processes and develop, use, and evaluate probability models. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long- 7 SP 6 run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. CC.7.SP.7 Investigate chance processes and develop, use, and evaluate probability models. Develop a 7 SP 7 probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. CC.7.SP.7a Develop a uniform probability model by assigning equal probability to all outcomes, and use the 7 SP 7a model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. CC.7.SP.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will 7 SP 7b land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? CC.7.SP.8 Investigate chance processes and develop, use, and evaluate probability models. Find probabilities 7 SP 8 of compound events using organized lists, tables, tree diagrams, and simulation. CC.7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of 7 SP 8a outcomes in the sample space for which the compound event occurs. CC.7.SP.8b Represent sample spaces for compound events using methods such as organized lists, tables and 7 SP 8b tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. CC.7.SP.8c Design and use a simulation to generate frequencies for compound events. For example, use 7 SP 8c random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? English/Language Arts 8th Grade Standards Grade Core Area # Timeline Standard CC.8.R.L.1 Key Ideas and Details: Cite the textual evidence that most strongly supports an analysis of what 8 R.L 1 the text says explicitly as well as inferences drawn from the text. CC.8.R.L.2 Key Ideas and Details: Determine a theme or central idea of a text and analyze its development 8 R.L 2 over the course of the text, including its relationship to the characters, setting, and plot; provide an objective summary of the text. CC.8.R.L.3 Key Ideas and Details: Analyze how particular lines of dialogue or incidents in a story or drama 8 R.L 3 propel the action, reveal aspects of a character, or provoke a decision. CC.8.R.L.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, 8 R.L 4 including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts. CC.8.R.L.5 Craft and Structure: Compare and contrast the structure of two or more texts and analyze how 8 R.L 5 the differing structure of each text contributes to its meaning and style. CC.8.R.L.6 Craft and Structure: Analyze how differences in the points of view of the characters and the 8 R.L 6 audience or reader (e.g., created through the use of dramatic irony) create such effects as suspense or humor. CC.8.R.L.7 Integration of Knowledge and Ideas: Analyze the extent to which a filmed or live production of a 8 R.L 7 story or drama stays faithful to or departs from the text or script, evaluating the choices made by the director or actors. CC.8.R.L.9 Integration of Knowledge and Ideas: Analyze how a modern work of fiction draws on themes, 8 R.L 9 patterns of events, or character types from myths, traditional stories, or religious works such as the Bible, including describing how the material is rendered new. CC.8.R.L.10 Range of Reading and Level of Text Complexity: By the end of the year, read and comprehend 8 R.L 10 literature, including stories, dramas, and poems, at the high end of grades 6–8 text complexity band independently and proficiently. CC.8.R.I.1 Key Ideas and Details: Cite the textual evidence that most strongly supports an analysis of what 8 R.I 1 the text says explicitly as well as inferences drawn from the text. CC.8.R.I.2 Key Ideas and Details: Determine a central idea of a text and analyze its development over the 8 R.I 2 course of the text, including its relationship to supporting ideas; provide an objective summary of the text. CC.8.R.I.3 Key Ideas and Details: Analyze how a text makes connections among and distinctions between 8 R.I 3 individuals, ideas, or events (e.g., through comparisons, analogies, or categories). CC.8.R.I.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, 8 R.I 4 including figurative, connotative, and technical meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts. CC.8.R.I.5 Craft and Structure: Analyze in detail the structure of a specific paragraph in a text, including the 8 R.I 5 role of particular sentences in developing and refining a key concept. CC.8.R.I.6 Craft and Structure: Determine an author’s point of view or purpose in a text and analyze how the 8 R.I 6 author acknowledges and responds to conflicting evidence or viewpoints. CC.8.R.I.7 Integration of Knowledge and Ideas: Evaluate the advantages and disadvantages of using different 8 R.I 7 mediums (e.g., print or digital text, video, multimedia) to present a particular topic or idea. CC.8.R.I.8 Integration of Knowledge and Ideas: Delineate and evaluate the argument and specific claims in a 8 R.I 8 text, assessing whether the reasoning is sound and the evidence is relevant and sufficient; recognize when irrelevant evidence is introduced. CC.8.R.I.9 Integration of Knowledge and Ideas: Analyze a case in which two or more texts provide conflicting 8 R.I 9 information on the same topic and identify where the texts disagree on matters of fact or interpretation. CC.8.R.I.10 Range of Reading and Level of Text Complexity: By the end of the year, read and comprehend 8 R.I 10 literary nonfiction at the high end of the grades 6–8 text complexity band independently and proficiently. CC.8.W.1 Text Types and Purposes: Write arguments to support claims with clear reasons and relevant 8 W 1 evidence. CC.8.W.1.a Text Types and Purposes: Introduce claim(s), acknowledge and distinguish the claim(s) from 8 W 1.a alternate or opposing claims, and organize the reasons and evidence logically. CC.8.W.1.b Text Types and Purposes: Support claim(s) with logical reasoning and relevant evidence, using 8 W 1.b accurate, credible sources and demonstrating an understanding of the topic or text. CC.8.W.1.c Text Types and Purposes: Use words, phrases, and clauses to create cohesion and clarify the 8 W 1.c relationships among claim(s), counterclaims, reasons, and evidence. 8 W 1.d CC.8.W.1.d Text Types and Purposes: Establish and maintain a formal style. CC.8.W.1.e Text Types and Purposes: Provide a concluding statement or section that follows from and 8 W 1.e supports the argument presented. CC.8.W.2 Text Types and Purposes: Write informative/explanatory texts to examine a topic and convey 8 W 2 ideas, concepts, and information through the selection, organization, and analysis of relevant content. CC.8.W.2.a Text Types and Purposes: Introduce a topic clearly, previewing what is to follow; organize ideas, 8 W 2.a concepts, and information into broader categories; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension. CC.8.W.2.b Text Types and Purposes: Develop the topic with relevant, well-chosen facts, definitions, 8 W 2.b concrete details, quotations, or other information and examples. CC.8.W.2.c Text Types and Purposes: Use appropriate and varied transitions to create cohesion and clarify 8 W 2.c the relationships among ideas and concepts. CC.8.W.2.d Text Types and Purposes: Use precise language and domain-specific vocabulary to inform about 8 W 2.d or explain the topic. 8 W 2.e CC.8.W.2.e Text Types and Purposes: Establish and maintain a formal style. CC.8.W.2.f Text Types and Purposes: Provide a concluding statement or section that follows from and 8 W 2.f supports the information or explanation presented. CC.8.W.3 Text Types and Purposes: Write narratives to develop real or imagined experiences or events 8 W 3 using effective technique, relevant descriptive details, and well-structured event sequences. CC.8.W.3.a Text Types and Purposes: Engage and orient the reader by establishing a context and point of 8 W 3.a view and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically. CC.8.W.3.b Text Types and Purposes: Use narrative techniques, such as dialogue, pacing, description, and 8 W 3.b reflection, to develop experiences, events, and/or characters. CC.8.W.3.c Text Types and Purposes: Use a variety of transition words, phrases, and clauses to convey 8 W 3.c sequence, signal shifts from one time frame or setting to another, and show the relationships among experiences and events. CC.8.W.3.d Text Types and Purposes: Use precise words and phrases, relevant descriptive details, and 8 W 3.d sensory language to capture the action and convey experiences and events. CC.8.W.3.e Text Types and Purposes: Provide a conclusion that follows from and reflects on the narrated 8 W 3.e experiences or events. CC.8.W.4 Production and Distribution of Writing: Produce clear and coherent writing in which the 8 W 4 development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) CC.8.W.5 Production and Distribution of Writing: With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new 8 W 5 approach, focusing on how well purpose and audience have been addressed. (Editing for conventions should demonstrate command of Language standards 1–3 up to and including grade 8 on page 53.) CC.8.W.6 Production and Distribution of Writing: Use technology, including the Internet, to produce and 8 W 6 publish writing and present the relationships between information and ideas efficiently as well as to interact and collaborate with others. CC.8.W.7 Research to Build and Present Knowledge: Conduct short research projects to answer a question 8 W 7 (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration. CC.8.W.8 Research to Build and Present Knowledge: Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote 8 W 8 or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation. CC.8.W.9 Research to Build and Present Knowledge: Draw evidence from literary or informational texts to 8 W 9 support analysis, reflection, and research. CC.8.W.9.a Research to Build and Present Knowledge: Apply grade 8 Reading standards to literature (e.g., “Analyze how a modern work of fiction draws on themes, patterns of events, or character types from 8 W 9.a myths, traditional stories, or religious works such as the Bible, including describing how the material is rendered new”). CC.8.W.9.b Research to Build and Present Knowledge: Apply grade 8 Reading standards to literary nonfiction (e.g., “Delineate and evaluate the argument and specific claims in a text, assessing whether the 8 W 9.b reasoning is sound and the evidence is relevant and sufficient; recognize when irrelevant evidence is introduced”). CC.8.W.10 Range of Writing: Write routinely over extended time frames (time for research, reflection, and 8 W 10 revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. CC.8.SL.1 Comprehension and Collaboration: Engage effectively in a range of collaborative discussions (one- 8 SL 1 on-one, in groups, and teacher-led) with diverse partners on grade 8 topics, texts, and issues, building on others’ ideas and expressing their own clearly. CC.8.SL.1.a Comprehension and Collaboration: Come to discussions prepared, having read or researched 8 SL 1.a material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion. CC.8.SL.1.b Comprehension and Collaboration: Follow rules for collegial discussions and decision-making, 8 SL 1.b track progress toward specific goals and deadlines, and define individual roles as needed. CC.8.SL.1.c Comprehension and Collaboration: Pose questions that connect the ideas of several speakers 8 SL 1.c and respond to others’ questions and comments with relevant evidence, observations, and ideas. CC.8.SL.1.d Comprehension and Collaboration: Acknowledge new information expressed by others, and, 8 SL 1.d when warranted, qualify or justify their own views in light of the evidence presented. CC.8.SL.2 Comprehension and Collaboration: Analyze the purpose of information presented in diverse 8 SL 2 media and formats (e.g., visually, quantitatively, orally) and evaluate the motives (e.g., social, commercial, political) behind its presentation. CC.8.SL.3 Comprehension and Collaboration: Delineate a speaker’s argument and specific claims, evaluating 8 SL 3 the soundness of the reasoning and relevance and sufficiency of the evidence and identifying when irrelevant evidence is introduced. CC.8.SL.4 Presentation of Knowledge and Ideas: Present claims and findings, emphasizing salient points in a 8 SL 4 focused, coherent manner with relevant evidence, sound valid reasoning, and well-chosen details; use appropriate eye contact, adequate volume, and clear pronunciation. CC.8.SL.5 Presentation of Knowledge and Ideas: Integrate multimedia and visual displays into presentations 8 SL 5 to clarify information, strengthen claims and evidence, and add interest. CC.8.SL.6 Presentation of Knowledge and Ideas: Adapt speech to a variety of contexts and tasks, 8 SL 6 demonstrating command of formal English when indicated or appropriate. (See grade 8 Language standards 1 and 3 on page 53 for specific expectations.) CC.8.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English 8 L 1 grammar and usage when writing or speaking. CC.8.L.1.a Conventions of Standard English: Explain the function of verbals (gerunds, participles, infinitives) 8 L 1.a in general and their function in particular sentences. 8 L 1.b CC.8.L.1.b Conventions of Standard English: Form and use verbs in the active and passive voice. CC.8.L.1.c Conventions of Standard English: Form and use verbs in the indicative, imperative, interrogative, 8 L 1.c conditional, and subjunctive mood. CC.8.L.1.d Conventions of Standard English: Recognize and correct inappropriate shifts in verb voice and 8 L 1.d mood.* CC.8.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English 8 L 2 capitalization, punctuation, and spelling when writing. CC.8.L.2.a Conventions of Standard English: Use punctuation (comma, ellipsis, dash) to indicate a pause or 8 L 2.a break. 8 L 2.b CC.8.L.2.b Conventions of Standard English: Use an ellipsis to indicate an omission. 8 L 2.c CC.8.L.2.c Conventions of Standard English: Spell correctly. CC.8.L.3 Knowledge of Language: Use knowledge of language and its conventions when writing, speaking, 8 L 3 reading, or listening. CC.8.L.3.a Knowledge of Language: Use verbs in the active and passive voice and in the conditional and 8 L 3.a subjunctive mood to achieve particular effects (e.g., emphasizing the actor or the action; expressing uncertainty or describing a state contrary to fact). CC.8.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple- 8 L 4 meaning words or phrases based on grade 8 reading and content, choosing flexibly from a range of strategies. CC.8.L.4.a Vocabulary Acquisition and Use: Use context (e.g., the overall meaning of a sentence or 8 L 4.a paragraph; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. CC.8.L.4.b Vocabulary Acquisition and Use: Use common, grade-appropriate Greek or Latin affixes and roots 8 L 4.b as clues to the meaning of a word (e.g., precede, recede, secede). CC.8.L.4.c Vocabulary Acquisition and Use: Consult general and specialized reference materials (e.g., 8 L 4.c dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech. CC.8.L.4.d Vocabulary Acquisition and Use: Verify the preliminary determination of the meaning of a word 8 L 4.d or phrase (e.g., by checking the inferred meaning in context or in a dictionary). CC.8.L.5 Vocabulary Acquisition and Use: Demonstrate understanding of figurative language, word 8 L 5 relationships, and nuances in word meanings. 8 L 5.a CC.8.L.5.a Vocabulary Acquisition and Use: Interpret figures of speech (e.g. verbal irony, puns) in context. CC.8.L.5.b Vocabulary Acquisition and Use: Use the relationship between particular words to better 8 L 5.b understand each of the words. CC.8.L.5.c Vocabulary Acquisition and Use: Distinguish among the connotations (associations) of words with 8 L 5.c similar denotations (definitions) (e.g., bullheaded, willful, firm, persistent, resolute). CC.8.L.6 Vocabulary Acquisition and Use: Acquire and use accurately grade-appropriate general academic 8 L 6 and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression. Mathematics 8th Grade Standards Grade Core Area # Timeline Standard CC.8.NS.1.Understand informally that evey number has a decimal expansion; the rational numbers are those 8 NS 1 with decimal expansions that terminate in 0's or eventually repeat. Know that other numbers are call irrational. CC.8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For 8 NS 2 example,by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. CC.8.EE.1 Work with radicals and integer exponents. Know and apply the properties of integer exponents to 8 EE 1 generate equivalent numerical expressions. For example, 3^2 × 3^(–5) = 3^(–3) = 1/(3^3) = 1/27. CC.8.EE.2 Work with radicals and integer exponents. Use square root and cube root symbols to represent 8 EE 2 solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. CC.8.EE.3 Work with radicals and integer exponents. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times 8 EE 3 as much one is than the other. For example, estimate the population of the United States as 3 × 10^8 and the population of the world as 7 × 10^9, and determine that the world population is more than 20 times larger. CC.8.EE.4 Work with radicals and integer exponents. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and 8 EE 4 choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. CC.8.EE.5 Understand the connections between proportional relationships, lines, and linear equations. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different 8 EE 5 proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. CC.8.EE.6 Understand the connections between proportional relationships, lines, and linear equations. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line 8 EE 6 in the coordinate plane; derive the equation y =mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. CC.8.EE.7 Analyze and solve linear equations and pairs of simultaneous linear equations. Solve linear 8 EE 7 equations in one variable. CC.8.EE.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation 8 EE 7a into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). CC.8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions 8 EE 7b require expanding expressions using the distributive property and collecting like terms. CC.8.EE.8 Analyze and solve linear equations and pairs of simultaneous linear equations. Analyze and solve 8 EE 8 pairs of simultaneous linear equations. CC.8.EE.8a Understand that solutions to a system of two linear equations in two variables correspond to 8 EE 8a points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. CC.8.EE.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by 8 EE 8b graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. CC.8.EE.8c Solve real-world and mathematical problems leading to two linear equations in two variables. For 8 EE 8c example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. CC.8.F.1 Define, evaluate, and compare functions. Understand that a function is a rule that assigns to each 8 F 1 input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.) CC.8.F.2 Define, evaluate, and compare functions. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a 8 F 2 linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. CC.8.F.3 Define, evaluate, and compare functions. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the 8 F 3 function A = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. CC.8.F.4 Use functions to model relationships between quantities. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a 8 F 4 description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. CC.8.F.5 Use functions to model relationships between quantities. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, 8 F 5 linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. CC.8.G.1 Understand congruence and similarity using physical models, transparencies, or geometry software. Verify experimentally the properties of rotations, reflections, and translations: 8 G 1 -- a. Lines are taken to lines, and line segments to line segments of the same length. -- b. Angles are taken to angles of the same measure. -- c. Parallel lines are taken to parallel lines. CC.8.G.2 Understand congruence and similarity using physical models, transparencies, or geometry software. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first 8 G 2 by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. CC.8.G.3 Understand congruence and similarity using physical models, transparencies, or geometry software. 8 G 3 Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. CC.8.G.4 Understand congruence and similarity using physical models, transparencies, or geometry software. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by 8 G 4 a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. CC.8.G.5 Understand congruence and similarity using physical models, transparencies, or geometry software. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the 8 G 5 angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the three angles appear to form a line, and give an argument in terms of transversals why this is so. CC.8.G.6 Understand and apply the Pythagorean Theorem. Explain a proof of the Pythagorean Theorem and 8 G 6 its converse. CC.8.G.7 Understand and apply the Pythagorean Theorem. Apply the Pythagorean Theorem to determine 8 G 7 unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. CC.8.G.8 Understand and apply the Pythagorean Theorem. Apply the Pythagorean Theorem to find the 8 G 8 distance between two points in a coordinate system. CC.8.G.9 Solve real-world and mathematical problems involving volume of cylinders, cones and spheres. 8 G 9 Know the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. CC.8.SP.1 Investigate patterns of association in bivariate data. Construct and interpret scatter plots for 8 SP 1 bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. CC.8.SP.2 Investigate patterns of association in bivariate data. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, 8 SP 2 informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. CC.8.SP.3 Investigate patterns of association in bivariate data. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in 8 SP 3 a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. CC.8.SP.4 Investigate patterns of association in bivariate data. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from 8 SP 4 the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? English/Language Arts 9 - 10th Grade Standards Grade Core Area # Timeline Standard CC.9-10.R.L.1 Key Ideas and Details: Cite strong and thorough textual evidence to support analysis of what the text 9-10 R.L 1 says explicitly as well as inferences drawn from the text. CC.9-10.R.L.2 Key Ideas and Details: Determine a theme or central idea of a text and analyze in detail its development 9-10 R.L 2 over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text. CC.9-10.R.L.3 Key Ideas and Details: Analyze how complex characters (e.g., those with multiple or conflicting 9-10 R.L 3 motivations) develop over the course of a text, interact with other characters, and advance the plot or develop the theme. CC.9-10.R.L.4 Craft and Structure: Determine the meaning of words and phrases as they are used in the text, 9-10 R.L 4 including figurative and connotative meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language evokes a sense of time and place; how it sets a formal or informal tone). CC.9-10.R.L.5 Craft and Structure: Analyze how an author’s choices concerning how to structure a text, order events 9-10 R.L 5 within it (e.g., parallel plots), and manipulate time (e.g., pacing, flashbacks) create such effects as mystery, tension, or surprise. CC.9-10.R.L.6 Craft and Structure: Analyze a particular point of view or cultural experience reflected in a work of 9-10 R.L 6 literature from outside the United States, drawing on a wide reading of world literature. CC.9-10.R.L.7 Integration of Knowledge and Ideas: Analyze the representation of a subject or a key scene in two 9-10 R.L 7 different artistic mediums, including what is emphasized or absent in each treatment (e.g., Auden’s “Musée des Beaux Arts” and Breughel’s Landscape with the Fall of Icarus). CC.9-10.R.L.9 Integration of Knowledge and Ideas: Analyze how an author draws on and transforms source material 9-10 R.L 9 in a specific work (e.g., how Shakespeare treats a theme or topic from Ovid or the Bible or how a later author draws on a play by Shakespeare). CC.9-10.R.L.10 Range of Reading and Level of Text Complexity: By the end of grade 9, read and comprehend literature, including stories, dramas, and poems, in the grades 9–10 text complexity band proficiently, with 9-10 R.L 10 scaffolding as needed at the high end of the range. By the end of grade 10, read and comprehend literature, including stories, dramas, and poems, at the high end of the grades 9–10 text complexity band independently and proficiently. CC.9-10.R.I.1 Key Ideas and Details: Cite strong and thorough textual evidence to support analysis of what the text 9-10 R.I 1 says explicitly as well as inferences drawn from the text. CC.9-10.R.I.2 Key Ideas and Details: Determine a central idea of a text and analyze its development over the course of 9-10 R.I 2 the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text. CC.9-10.R.I.3 Key Ideas and Details: Analyze how the author unfolds an analysis or series of ideas or events, including 9-10 R.I 3 the order in which the points are made, how they are introduced and developed, and the connections that are drawn between them. CC.9-10.R.I.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, including 9-10 R.I 4 figurative, connotative, and technical meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language of a court opinion differs from that of a newspaper). CC.9-10.R.I.5 Craft and Structure: Analyze in detail how an author’s ideas or claims are developed and refined by 9-10 R.I 5 particular sentences, paragraphs, or larger portions of a text (e.g., a section or chapter). CC.9-10.R.I.6 Craft and Structure: Determine an author’s point of view or purpose in a text and analyze how an 9-10 R.I 6 author uses rhetoric to advance that point of view or purpose. CC.9-10.R.I.7 Integration of Knowledge and Ideas: Analyze various accounts of a subject told in different mediums 9-10 R.I 7 (e.g., a person’s life story in both print and multimedia), determining which details are emphasized in each account. CC.9-10.R.I.8 Integration of Knowledge and Ideas: Delineate and evaluate the argument and specific claims in a text, 9-10 R.I 8 assessing whether the reasoning is valid and the evidence is relevant and sufficient; identify false statements and fallacious reasoning. CC.9-10.R.I.9 Integration of Knowledge and Ideas: Analyze seminal U.S. documents of historical and literary 9-10 R.I 9 significance (e.g., Washington’s Farewell Address, the Gettysburg Address, Roosevelt’s Four Freedoms speech, King’s "Letter From Birmingham Jail"), including how they address related themes and concepts. CC.9-10.R.I.10 Range of Reading and Level of Text Complexity: By the end of grade 9, read and comprehend literary nonfiction in the grades 9–10 text complexity band proficiently, with scaffolding as needed at the high end of the 9-10 R.I 10 range. By the end of grade 10, read and comprehend literary nonfiction at the high end of the grades 9–10 text complexity band independently and proficiently. CC.9-10.W.1 Text Types and Purposes: Write arguments to support claims in an analysis of substantive topics or 9-10 W 1 texts, using valid reasoning and relevant and sufficient evidence. CC.9-10.W.1.a Text Types and Purposes: Introduce precise claim(s), distinguish the claim(s) from alternate or 9-10 W 1.a opposing claims, and create an organization that establishes clear relationships among claim(s), counterclaims, reasons, and evidence. CC.9-10.W.1.b Text Types and Purposes: Develop claim(s) and counterclaims fairly, supplying evidence for each while 9-10 W 1.b pointing out the strengths and limitations of both in a manner that anticipates the audience’s knowledge level and concerns. CC.9-10.W.1.c Text Types and Purposes: Use words, phrases, and clauses to link the major sections of the text, create 9-10 W 1.c cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims. CC.9-10.W.1.d Text Types and Purposes: Establish and maintain a formal style and objective tone while attending to 9-10 W 1.d the norms and conventions of the discipline in which they are writing. CC.9-10.W.1.e Text Types and Purposes: Provide a concluding statement or section that follows from and supports 9-10 W 1.e the argument presented. CC.9-10.W.2 Text Types and Purposes: Write informative/explanatory texts to examine and convey complex ideas, 9-10 W 2 concepts, and information clearly and accurately through the effective selection, organization, and analysis of content. CC.9-10.W.2.a Text Types and Purposes: Introduce a topic; organize complex ideas, concepts, and information to 9-10 W 2.a make important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension. CC.9-10.W.2.b Text Types and Purposes: Develop the topic with well-chosen, relevant, and sufficient facts, extended 9-10 W 2.b definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic. CC.9-10.W.2.c Text Types and Purposes: Use appropriate and varied transitions to link the major sections of the text, 9-10 W 2.c create cohesion, and clarify the relationships among complex ideas and concepts. CC.9-10.W.2.d Text Types and Purposes: Use precise language and domain-specific vocabulary to manage the 9-10 W 2.d complexity of the topic. CC.9-10.W.2.e Text Types and Purposes: Establish and maintain a formal style and objective tone while attending to 9-10 W 2.e the norms and conventions of the discipline in which they are writing. CC.9-10.W.2.f Text Types and Purposes: Provide a concluding statement or section that follows from and supports 9-10 W 2.f the information or explanation presented (e.g., articulating implications or the significance of the topic). CC.9-10.W.3 Text Types and Purposes: Write narratives to develop real or imagined experiences or events using 9-10 W 3 effective technique, well-chosen details, and well-structured event sequences. CC.9-10.W.3.a Text Types and Purposes: Engage and orient the reader by setting out a problem, situation, or 9-10 W 3.a observation, establishing one or multiple point(s) of view, and introducing a narrator and/or characters; create a smooth progression of experiences or events. CC.9-10.W.3.b Text Types and Purposes: Use narrative techniques, such as dialogue, pacing, description, reflection, 9-10 W 3.b and multiple plot lines, to develop experiences, events, and/or characters. CC.9-10.W.3.c Text Types and Purposes: Use a variety of techniques to sequence events so that they build on one 9-10 W 3.c another to create a coherent whole. CC.9-10.W.3.d Text Types and Purposes: Use precise words and phrases, telling details, and sensory language to 9-10 W 3.d convey a vivid picture of the experiences, events, setting, and/or characters. CC.9-10.W.3.e Text Types and Purposes: Provide a conclusion that follows from and reflects on what is experienced, 9-10 W 3.e observed, or resolved over the course of the narrative. CC.9-10.W.4 Production and Distribution of Writing: Produce clear and coherent writing in which the development, 9-10 W 4 organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) CC.9-10.W.5 Production and Distribution of Writing: Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose 9-10 W 5 and audience. (Editing for conventions should demonstrate command of Language standards 1–3 on up to and including grades 9-10 page 55.) CC.9-10.W.6 Production and Distribution of Writing: Use technology, including the Internet, to produce, publish, and 9-10 W 6 update individual or shared writing products, taking advantage of technology’s capacity to link to other information and to display information flexibly and dynamically. CC.9-10.W.7 Research to Build and Present Knowledge: Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when 9-10 W 7 appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation. CC.9-10.W.8 Research to Build and Present Knowledge: Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the usefulness of each source in answering the 9-10 W 8 research question; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and following a standard format for citation. CC.9-10.W.9 Research to Build and Present Knowledge: Draw evidence from literary or informational texts to support 9-10 W 9 analysis, reflection, and research. CC.9-10.W.9.a Research to Build and Present Knowledge: Apply grades 9–10 Reading standards to literature(e.g., 9-10 W 9.a “Analyze how an author draws on and transforms source material in a specific work [e.g., how Shakespeare treats a theme or topic from Ovid or the Bible or how a later author draws on a play by Shakespeare]”). CC.9-10.W.9.b Research to Build and Present Knowledge: Apply grades 9–10 Reading standards to literary nonfiction 9-10 W 9.b (e.g., “Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is valid and the evidence is relevant and sufficient; identify false statements and fallacious reasoning”). CC.9-10.W.10 Range of Writing: Write routinely over extended time frames (time for research, reflection, and 9-10 W 10 revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences. CC.9-10.SL.1 Comprehension and Collaboration: Initiate and participate effectively in a range of collaborative 9-10 SL 1 discussions (one-on-one, in groups, and teacher-led) with diverse partners on grades 9–10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively. CC.9-10.SL.1.a Comprehension and Collaboration: Come to discussions prepared, having read and researched 9-10 SL 1.a material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas. CC.9-10.SL.1.b Comprehension and Collaboration: Work with peers to set rules for collegial discussions and decision- 9-10 SL 1.b making (e.g., informal consensus, taking votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed. CC.9-10.SL.1.c Comprehension and Collaboration: Propel conversations by posing and responding to questions that 9-10 SL 1.c relate the current discussion to broader themes or larger ideas; actively incorporate others into the discussion; and clarify, verify, or challenge ideas and conclusions. CC.9-10.SL.1.d Comprehension and Collaboration: Respond thoughtfully to diverse perspectives, summarize points of 9-10 SL 1.d agreement and disagreement, and, when warranted, qualify or justify their own views and understanding and make new connections in light of the evidence and reasoning presented. CC.9-10.SL.2 Comprehension and Collaboration: Integrate multiple sources of information presented in diverse media 9-10 SL 2 or formats (e.g., visually, quantitatively, orally) evaluating the credibility and accuracy of each source. CC.9-10.SL.3 Comprehension and Collaboration: Evaluate a speaker’s point of view, reasoning, and use of evidence 9-10 SL 3 and rhetoric, identifying any fallacious reasoning or exaggerated or distorted evidence. CC.9-10.SL.4 Presentation of Knowledge and Ideas: Present information, findings, and supporting evidence clearly, 9-10 SL 4 concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task. CC.9-10.SL.5 Presentation of Knowledge and Ideas: Make strategic use of digital media (e.g., textual, graphical, audio, 9-10 SL 5 visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest. CC.9-10.SL.6 Presentation of Knowledge and Ideas: Adapt speech to a variety of contexts and tasks, demonstrating 9-10 SL 6 command of formal English when indicated or appropriate. (See grades 9-10 Language standards 1 and 3 on pages 54 for specific expectations.) CC.9-10.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English 9-10 L 1 grammar and usage when writing or speaking. 9-10 L 1.a CC.9-10.L.1.a Conventions of Standard English: Use parallel structure.* CC.9-10.L.1.b Conventions of Standard English: Use various types of phrases (noun, verb, adjectival, adverbial, 9-10 L 1.b participial, prepositional, absolute) and clauses (independent, dependent; noun, relative, adverbial) to convey specific meanings and add variety and interest to writing or presentations. CC.9-10.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English 9-10 L 2 capitalization, punctuation, and spelling when writing. CC.9-10.L.2.a Conventions of Standard English: Use a semicolon (and perhaps a conjunctive adverb) to link two or 9-10 L 2.a more closely related independent clauses. 9-10 L 2.b CC.9-10.L.2.b Conventions of Standard English: Use a colon to introduce a list or quotation. 9-10 L 2.c CC.9-10.L.2.c Conventions of Standard English: Spell correctly. CC.9-10.L.3 Knowledge of Language: Apply knowledge of language to understand how language functions in different 9-10 L 3 contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening. CC.9-10.L.3.a Knowledge of Language: Write and edit work so that it conforms to the guidelines in a style manual 9-10 L 3.a (e.g., MLA Handbook, Turabian’s Manual for Writers) appropriate for the discipline and writing type. CC.9-10.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple-meaning 9-10 L 4 words and phrases based on grades 9–10 reading and content, choosing flexibly from a range of strategies. CC.9-10.L.4.a Vocabulary Acquisition and Use: Use context (e.g., the overall meaning of a sentence, paragraph, or 9-10 L 4.a text; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. CC.9-10.L.4.b Vocabulary Acquisition and Use: Identify and correctly use patterns of word changes that indicate 9-10 L 4.b different meanings or parts of speech (e.g., analyze, analysis, analytical; advocate, advocacy). CC.9-10.L.4.c Vocabulary Acquisition and Use: Consult general and specialized reference materials (e.g., dictionaries, 9-10 L 4.c glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, or its etymology. CC.9-10.L.4.d Vocabulary Acquisition and Use: Verify the preliminary determination of the meaning of a word or 9-10 L 4.d phrase (e.g., by checking the inferred meaning in context or in a dictionary). CC.9-10.L.5 Vocabulary Acquisition and Use: Demonstrate understanding of figurative language, word relationships, 9-10 L 5 and nuances in word meanings. CC.9-10.L.5.a Vocabulary Acquisition and Use: Interpret figures of speech (e.g., satire, sarcasm) in context and analyze 9-10 L 5.a their role in the text. 9-10 L 5.b CC.9-10.L.5.b Vocabulary Acquisition and Use: Analyze nuances in the meaning of words with similar denotations. CC.9-10.L.6 Vocabulary Acquisition and Use: Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading, writing, speaking, and listening at the college and career readiness level; 9-10 L 6 demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression CC.9-10.R.H.1 Key Ideas and Details: Cite specific textual evidence to support analysis of primary and secondary 9-10 R.H 1 sources, attending to such features as the date and origin of the information. CC.9-10.R.H.2 Key Ideas and Details: Determine the central ideas or information of a primary or secondary source; 9-10 R.H 2 provide an accurate summary of how key events or ideas develop over the course of the text. CC.9-10.R.H.3 Key Ideas and Details: Analyze in detail a series of events described in a text; determine whether 9-10 R.H 3 earlier events caused later ones or simply preceded them. CC.9-10.R.H.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, including 9-10 R.H 4 vocabulary describing political, social, or economic aspects of history/social science. CC.9-10.R.H.5 Craft and Structure: Analyze how a text uses structure to emphasize key points or advance an 9-10 R.H 5 explanation or analysis CC.9-10.R.H.6 Craft and Structure: Compare the point of view of two or more authors for how they treat the same or 9-10 R.H 6 similar topics, including which details they include and emphasize in their respective accounts. CC.9-10.R.H.7 Integration of Knowledge and Ideas: Integrate quantitative or technical analysis (e.g., charts, research 9-10 R.H 7 data) with qualitative analysis in print or digital text. CC.9-10.R.H.8 Integration of Knowledge and Ideas: Assess the extent to which the reasoning and evidence in a text 9-10 R.H 8 support the author’s claims. CC.9-10.R.H.9 Integration of Knowledge and Ideas: Compare and contrast treatments of the same topic in several 9-10 R.H 9 primary and secondary sources. CC.9-10.R.H.10 Range of Reading and Level of Text Complexity: By the end of grade 10, read and comprehend 9-10 R.H 10 history/social studies texts in the grades 9–10 text complexity band independently and proficiently. CC.9-10.R.ST.1 Key Ideas and Details: Cite specific textual evidence to support analysis of science and technical texts, 9-10 R.ST 1 attending to the precise details of explanations or descriptions. CC.9-10.R.ST.2 Key Ideas and Details: Determine the central ideas or conclusions of a text; trace the text’s 9-10 R.ST 2 explanation or depiction of a complex process, phenomenon, or concept; provide an accurate summary of the text. CC.9-10.R.ST.3 Key Ideas and Details: Follow precisely a complex multistep procedure when carrying out 9-10 R.ST 3 experiments, taking measurements, or performing technical tasks attending to special cases or exceptions defined in the text. CC.9-10.R.ST.4 Craft and Structure: Determine the meaning of symbols, key terms, and other domain-specific words 9-10 R.ST 4 and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics. CC.9-10.R.ST.5 Craft and Structure: Analyze the structure of the relationships among concepts in a text, including 9-10 R.ST 5 relationships among key terms (e.g., force, friction, reaction force, energy). CC.9-10.R.ST.6 Craft and Structure: Analyze the author’s purpose in providing an explanation, describing a procedure, 9-10 R.ST 6 or discussing an experiment in a text, defining the question the author seeks to address. CC.9-10.R.ST.7 Integration of Knowledge and Ideas: Translate quantitative or technical information expressed in 9-10 R.ST 7 words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words. CC.9-10.R.ST.8 Integration of Knowledge and Ideas: Assess the extent to which the reasoning and evidence in a text 9-10 R.ST 8 support the author’s claim or a recommendation for solving a scientific or technical problem. CC.9-10.R.ST.9 Integration of Knowledge and Ideas: Compare and contrast findings presented in a text to those from 9-10 R.ST 9 other sources (including their own experiments), noting when the findings support or contradict previous explanations or accounts. CC.9-10.R.ST.10 Range of Reading and Level of Text Complexity: By the end of grade 10, read and comprehend 9-10 R.ST 10 science/technical texts in the grades 9–10 text complexity band independently and proficiently 9-10 W.HST 1 CC.9-10.W.HST.1 Text Types and Purposes: Write arguments focused on discipline-specific content. CC.9-10.W.HST.1.a Text Types and Purposes: Introduce precise claim(s), distinguish the claim(s) from alternate or 9-10 W.HST 1.a opposing claims, and create an organization that establishes clear relationships among the claim(s), counterclaims, reasons, and evidence. CC.9-10.W.HST.1.b Text Types and Purposes: Develop claim(s) and counterclaims fairly, supplying data and evidence 9-10 W.HST 1.b for each while pointing out the strengths and limitations of both claim(s) and counterclaims in a discipline- appropriate form and in a manner that anticipates the audience’s knowledge level and concerns. CC.9-10.W.HST.1.c Text Types and Purposes: Use words, phrases, and clauses to link the major sections of the text, 9-10 W.HST 1.c create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims. CC.9-10.W.HST.1.d Text Types and Purposes: Establish and maintain a formal style and objective tone while attending 9-10 W.HST 1.d to the norms and conventions of the discipline in which they are writing. CC.9-10.W.HST.1.e Text Types and Purposes: Provide a concluding statement or section that follows from or supports 9-10 W.HST 1.e the argument presented. CC.9-10.W.HST.2 Text Types and Purposes: Write informative/explanatory texts, including the narration of historical 9-10 W.HST 2 events, scientific procedures/ experiments, or technical processes. CC.9-10.W.HST.2.a Text Types and Purposes: Introduce a topic and organize ideas, concepts, and information to 9-10 W.HST 2.a make important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension. CC.9-10.W.HST.2.b Text Types and Purposes: Develop the topic with well-chosen, relevant, and sufficient facts, 9-10 W.HST 2.b extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic. CC.9-10.W.HST.2.c Text Types and Purposes: Use varied transitions and sentence structures to link the major sections 9-10 W.HST 2.c of the text, create cohesion, and clarify the relationships among ideas and concepts. CC.9-10.W.HST.2.d Text Types and Purposes: Use precise language and domain-specific vocabulary to manage the 9-10 W.HST 2.d complexity of the topic and convey a style appropriate to the discipline and context as well as to the expertise of likely readers. CC.9-10.W.HST.2.e Text Types and Purposes: Establish and maintain a formal style and objective tone while attending 9-10 W.HST 2.e to the norms and conventions of the discipline in which they are writing. CC.9-10.W.HST.2.f Text Types and Purposes: Provide a concluding statement or section that follows from and 9-10 W.HST 2.f supports the information or explanation presented (e.g., articulating implications or the significance of the topic). CC.9-10.W.HST.4 Production and Distribution of Writing: Produce clear and coherent writing in which the 9-10 W.HST 4 development, organization, and style are appropriate to task, purpose, and audience. CC.9-10.W.HST.5 Production and Distribution of Writing: Develop and strengthen writing as needed by planning, 9-10 W.HST 5 revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience. CC.9-10.W.HST.6 Production and Distribution of Writing: Use technology, including the Internet, to produce, publish, 9-10 W.HST 6 and update individual or shared writing products, taking advantage of technology’s capacity to link to other information and to display information flexibly and dynamically. CC.9-10.W.HST.7 Research to Build and Present Knowledge: Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the 9-10 W.HST 7 inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation. CC.9-10.W.HST.8 Research to Build and Present Knowledge: Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the usefulness of each source in answering the 9-10 W.HST 8 research question; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and following a standard format for citation. CC.9-10.W.HST.9 Research to Build and Present Knowledge: Draw evidence from informational texts to support 9-10 W.HST 9 analysis, reflection, and research. CC.9-10.W.HST.10 Range of Writing: Write routinely over extended time frames (time for reflection and revision) and 9-10 W.HST 10 shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. Mathematics 9 - 12th Grade Standards Grade Core Area # Timeline Standard CC.9-12.N.RN.1 Extend the properties of exponents to rational exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, 9-12 N RN.1 allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want [5^(1/3)]^3 = 5^[(1/3) x 3] to hold, so [5^(1/3)]^3 must equal 5. CC.9-12.N.RN.2 Extend the properties of exponents to rational exponents. Rewrite expressions involving radicals 9-12 N RN.2 and rational exponents using the properties of exponents. CC.9-12.N.RN.3 Use properties of rational and irrational numbers. Explain why the sum or product of rational 9-12 N RN.3 numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. CC.9-12.N.Q.1 Reason quantitatively and use units to solve problems. Use units as a way to understand problems 9-12 N Q.1 and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.* CC.9-12.N.Q.2 Reason quantitatively and use units to solve problems. Define appropriate quantities for the 9-12 N Q.2 purpose of descriptive modeling.* CC.9-12.N.Q.3 Reason quantitatively and use units to solve problems. Choose a level of accuracy appropriate to 9-12 N Q.3 limitations on measurement when reporting quantities.* CC.9-12.N.CN.1 Perform arithmetic operations with complex numbers. Know there is a complex number i such that 9-12 N CN.1 i^2 = −1, and every complex number has the form a + bi with a and b real. CC.9-12.N.CN.2 Perform arithmetic operations with complex numbers. Use the relation i2 = –1 and the 9-12 N CN.2 commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. CC.9-12.N.CN.3 (+) Perform arithmetic operations with complex numbers. Find the conjugate of a complex number; 9-12 N CN.3 use conjugates to find moduli and quotients of complex numbers. CC.9-12.N.CN.4 (+) Represent complex numbers and their operations on the complex plane. Represent complex 9-12 N CN.4 numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. CC.9-12.N.CN.5 (+) Represent complex numbers and their operations on the complex plane. Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use 9-12 N CN.5 properties of this representation for computation. For example, (-1 + √3i)^3 = 8 because (-1 + √3i) has modulus 2 and argument 120°. CC.9-12.N.CN.6 (+) Represent complex numbers and their operations on the complex plane. Calculate the distance 9-12 N CN.6 between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. CC.9-12.N.CN.7 Use complex numbers in polynomial identities and equations. Solve quadratic equations with real 9-12 N CN.7 coefficients that have complex solutions. CC.9-12.N.CN.8 (+) Use complex numbers in polynomial identities and equations. Extend polynomial identities to 9-12 N CN.8 the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i). CC.9-12.N.CN.9 (+) Use complex numbers in polynomial identities and equations. Know the Fundamental Theorem 9-12 N CN.9 of Algebra; show that it is true for quadratic polynomials. CC.9-12.N.VM.1 (+) Represent and model with vector quantities. Recognize vector quantities as having both 9-12 N VM.1 magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v(bold), |v|, ||v||, v(not bold)). CC.9-12.N.VM.2 (+) Represent and model with vector quantities. Find the components of a vector by subtracting 9-12 N VM.2 the coordinates of an initial point from the coordinates of a terminal point. CC.9-12.N.VM.3 (+) Represent and model with vector quantities. Solve problems involving velocity and other 9-12 N VM.3 quantities that can be represented by vectors. CC.9-12.N.VM.4 (+) Perform operations on vectors. Add and subtract vectors. 9-12 N VM.4 CC.9-12.N.VM.4a (+) Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the 9-12 N VM.4a magnitude of a sum of two vectors is typically not the sum of the magnitudes. CC.9-12.N.VM.4b (+) Given two vectors in magnitude and direction form, determine the magnitude and direction 9-12 N VM.4b of their sum. CC.9-12.N.VM.4c (+) Understand vector subtraction v – w as v + (–w), where (–w) is the additive inverse of w, with 9-12 N VM.4c the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise. 9-12 N VM.5 CC.9-12.N.VM.5 (+) Perform operations on vectors. Multiply a vector by a scalar. CC.9-12.N.VM.5a (+) Represent scalar multiplication graphically by scaling vectors and possibly reversing their 9-12 N VM.5a direction; perform scalar multiplication component-wise, e.g., as c(v(sub x), v(sub y)) = (cv(sub x), cv(sub y)). CC.9-12.N.VM.5b (+) Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of 9-12 N VM.5b cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0). CC.9-12.N.VM.6 (+) Perform operations on matrices and use matrices in applications. Use matrices to represent 9-12 N VM.6 and manipulate data, e.g., to represent payoffs or incidence relationships in a network. CC.9-12.N.VM.7 (+) Perform operations on matrices and use matrices in applications. Multiply matrices by scalars 9-12 N VM.7 to produce new matrices, e.g., as when all of the payoffs in a game are doubled. CC.9-12.N.VM.8 (+) Perform operations on matrices and use matrices in applications. Add, subtract, and multiply 9-12 N VM.8 matrices of appropriate dimensions. CC.9-12.N.VM.9 (+) Perform operations on matrices and use matrices in applications. Understand that, unlike 9-12 N VM.9 multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. CC.9-12.N.VM.10 (+) Perform operations on matrices and use matrices in applications. Understand that the zero 9-12 N VM.10 and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. CC.9-12.N.VM.11 (+) Perform operations on matrices and use matrices in applications. Multiply a vector (regarded 9-12 N VM.11 as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. CC.9-12.N.VM.12 (+) Perform operations on matrices and use matrices in applications. Work with 2 X 2 matrices as 9-12 N VM.12 transformations of the plane, and interpret the absolute value of the determinant in terms of area. CC.9-12.A.SSE.1 Interpret the structure of expressions. Interpret expressions that represent a quantity in terms of 9-12 A SSE.1 its context.* 9-12 A SSE.1a CC.9-12.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients.* CC.9-12.A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity. For 9-12 A SSE.1b example, interpret P(1+r)^n as the product of P and a factor not depending on P.* CC.9-12.A.SSE.2 Interpret the structure of expressions. Use the structure of an expression to identify ways to 9-12 A SSE.2 rewrite it. For example, see x^4 – y^4 as (x^2)^2 – (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 – y^2)(x^2 + y^2). CC.9-12.A.SSE.3 Write expressions in equivalent forms to solve problems. Choose and produce an equivalent form 9-12 A SSE.3 of an expression to reveal and explain properties of the quantity represented by the expression.* 9-12 A SSE.3a CC.9-12.A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines.* CC.9-12.A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the 9-12 A SSE.3b function it defines.* CC.9-12.A.SSE.3c Use the properties of exponents to transform expressions for exponential functions. For example 9-12 A SSE.3c the expression 1.15^t can be rewritten as [1.15^(1/12)]^(12t) ≈ 1.012^(12t) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.* CC.9-12.A.SSE.4 Write expressions in equivalent forms to solve problems. Derive the formula for the sum of a finite 9-12 A SSE.4 geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.* CC.9-12.A.APR.1 Perform arithmetic operations on polynomials. Understand that polynomials form a system 9-12 A APR.1 analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. CC.9-12.A.APR.2 Understand the relationship between zeros and factors of polynomial. Know and apply the 9-12 A APR.2 Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). CC.9-12.A.APR.3 Understand the relationship between zeros and factors of polynomials. Identify zeros of 9-12 A APR.3 polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. CC.9-12.A.APR.4 Use polynomial identities to solve problems. Prove polynomial identities and use them to describe 9-12 A APR.4 numerical relationships. For example, the polynomial identity (x^2 + y^2)^2 = (x^2 – y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples. CC.9-12.A.APR.5 (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a 9-12 A APR.5 positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.1 CC.9-12.A.APR.6 Rewrite rational expressions. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than 9-12 A APR.6 the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. CC.9-12.A.APR.7 (+) Rewrite rational expressions. Understand that rational expressions form a system analogous to 9-12 A APR.7 the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. CC.9-12.A.CED.1 Create equations that describe numbers or relationship. Create equations and inequalities in one 9-12 A CED.1 variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.* CC.9-12.A.CED.2 Create equations that describe numbers or relationship. Create equations in two or more 9-12 A CED.2 variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.* CC.9-12.A.CED.3 Create equations that describe numbers or relationship. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable 9-12 A CED.3 options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.* CC.9-12.A.CED.4 Create equations that describe numbers or relationship. Rearrange formulas to highlight a 9-12 A CED.4 quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.* CC.9-12.A.REI.1 Understand solving equations as a process of reasoning and explain the reasoning. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting 9-12 A REI.1 from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. CC.9-12.A.REI.2 Understand solving equations as a process of reasoning and explain the reasoning. Solve simple 9-12 A REI.2 rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. CC.9-12.A.REI.3 Solve equations and inequalities in one variable. Solve linear equations and inequalities in one 9-12 A REI.3 variable, including equations with coefficients represented by letters. 9-12 A REI.4 CC.9-12.A.REI.4 Solve equations and inequalities in one variable. Solve quadratic equations in one variable. CC.9-12.A.REI.4a Use the method of completing the square to transform any quadratic equation in x into an 9-12 A REI.4a equation of the form (x – p)^2 = q that has the same solutions. Derive the quadratic formula from this form. CC.9-12.A.REI.4b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the 9-12 A REI.4b square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. CC.9-12.A.REI.5 Solve systems of equations. Prove that, given a system of two equations in two variables, replacing 9-12 A REI.5 one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. CC.9-12.A.REI.6 Solve systems of equations. Solve systems of linear equations exactly and approximately (e.g., with 9-12 A REI.6 graphs), focusing on pairs of linear equations in two variables. CC.9-12.A.REI.7 Solve systems of equations. Solve a simple system consisting of a linear equation and a quadratic 9-12 A REI.7 equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x^2 + y^2 = 3. CC.9-12.A.REI.8 (+) Solve systems of equations. Represent a system of linear equations as a single matrix equation 9-12 A REI.8 in a vector variable. CC.9-12.A.REI.9 (+) Solve systems of equations. Find the inverse of a matrix if it exists and use it to solve systems of 9-12 A REI.9 linear equations (using technology for matrices of dimension 3 × 3 or greater). CC.9-12.A.REI.10 Represent and solve equations and inequalities graphically. Understand that the graph of an 9-12 A REI.10 equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). CC.9-12.A.REI.11 Represent and solve equations and inequalities graphically. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); 9-12 A REI.11 find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* CC.9-12.A.REI.12 Represent and solve equations and inequalities graphically. Graph the solutions to a linear 9-12 A REI.12 inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. CC.9-12.F.IF.1 Understand the concept of a function and use function notation. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one 9-12 F IF.1 element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). CC.9-12.F.IF.2 Understand the concept of a function and use function notation. Use function notation, evaluate 9-12 F IF.2 functions for inputs in their domains, and interpret statements that use function notation in terms of a context. CC.9-12.F.IF.3 Understand the concept of a function and use function notation. Recognize that sequences are 9-12 F IF.3 functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1 (n is greater than or equal to 1). CC.9-12.F.IF.4 Interpret functions that arise in applications in terms of the context. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and 9-12 F IF.4 sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* CC.9-12.F.IF.5 Interpret functions that arise in applications in terms of the context. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) 9-12 F IF.5 gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.* CC.9-12.F.IF.6 Interpret functions that arise in applications in terms of the context. Calculate and interpret the 9-12 F IF.6 average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* CC.9-12.F.IF.7 Analyze functions using different representations. Graph functions expressed symbolically and show 9-12 F IF.7 key features of the graph, by hand in simple cases and using technology for more complicated cases.* 9-12 F IF.7a CC.9-12.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.* CC.9-12.F.IF.7b Graph square root, cube root, and piecewise-defined functions, including step functions and 9-12 F IF.7b absolute value functions.* CC.9-12.F.IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and 9-12 F IF.7c showing end behavior.* CC.9-12.F.IF.7d (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are 9-12 F IF.7d available, and showing end behavior.* CC.9-12.F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and 9-12 F IF.7e trigonometric functions, showing period, midline, and amplitude.* CC.9-12.F.IF.8 Analyze functions using different representations. Write a function defined by an expression in 9-12 F IF.8 different but equivalent forms to reveal and explain different properties of the function. CC.9-12.F.IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, 9-12 F IF.8a extreme values, and symmetry of the graph, and interpret these in terms of a context. CC.9-12.F.IF.8b Use the properties of exponents to interpret expressions for exponential functions. For example, 9-12 F IF.8b identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^(12t), y = (1.2)^(t/10), and classify them as representing exponential growth and decay. CC.9-12.F.IF.9 Analyze functions using different representations. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For 9-12 F IF.9 example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. CC.9-12.F.BF.1 Build a function that models a relationship between two quantities. Write a function that describes 9-12 F BF.1 a relationship between two quantities.* 9-12 F BF.1a CC.9-12.F.BF.1a Determine an explicit expression, a recursive process, or steps for calculation from a context. CC.9-12.F.BF.1b Combine standard function types using arithmetic operations. For example, build a function that 9-12 F BF.1b models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. CC.9-12.F.BF.1c (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of 9-12 F BF.1c height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. CC.9-12.F.BF.2 Build a function that models a relationship between two quantities. Write arithmetic and geometric 9-12 F BF.2 sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* CC.9-12.F.BF.3 Build new functions from existing functions. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. 9-12 F BF.3 Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 9-12 F BF.4 CC.9-12.F.BF.4 Build new functions from existing functions. Find inverse functions. CC.9-12.F.BF.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an 9-12 F BF.4a expression for the inverse. For example, f(x) =2(x^3) or f(x) = (x+1)/(x-1) for x ≠ 1 (x not equal to 1). 9-12 F BF.4b CC.9-12.F.BF.4b (+) Verify by composition that one function is the inverse of another. CC.9-12.F.BF.4c (+) Read values of an inverse function from a graph or a table, given that the function has an 9-12 F BF.4c inverse. 9-12 F BF.4d CC.9-12.F.BF.4d (+) Produce an invertible function from a non-invertible function by restricting the domain. CC.9-12.F.BF.5 (+) Build new functions from existing functions. Understand the inverse relationship between 9-12 F BF.5 exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. CC.9-12.F.LE.1 Construct and compare linear, quadratic, and exponential models and solve problems. Distinguish 9-12 F LE.1 between situations that can be modeled with linear functions and with exponential functions.* CC.9-12.F.LE.1a Prove that linear functions grow by equal differences over equal intervals and that exponential 9-12 F LE.1a functions grow by equal factors over equal intervals.* CC.9-12.F.LE.1b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to 9-12 F LE.1b another.* CC.9-12.F.LE.1c Recognize situations in which a quantity grows or decays by a constant percent rate per unit 9-12 F LE.1c interval relative to another.* CC.9-12.F.LE.2 Construct and compare linear, quadratic, and exponential models and solve problems. Construct 9-12 F LE.2 linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).* CC.9-12.F.LE.3 Construct and compare linear, quadratic, and exponential models and solve problems. Observe 9-12 F LE.3 using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.* CC.9-12.F.LE.4 Construct and compare linear, quadratic, and exponential models and solve problems. For 9-12 F LE.4 exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.* CC.9-12.F.LE.5 Interpret expressions for functions in terms of the situation they 9-12 F LE.5 model. Interpret the parameters in a linear or exponential function in terms of a context.* CC.9-12.F.TF.1 Extend the domain of trigonometric functions using the unit circle. Understand radian measure of an 9-12 F TF.1 angle as the length of the arc on the unit circle subtended by the angle. CC.9-12.F.TF.2 Extend the domain of trigonometric functions using the unit circle. Explain how the unit circle in the 9-12 F TF.2 coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. CC.9-12.F.TF.3 (+) Extend the domain of trigonometric functions using the unit circle. Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express 9-12 F TF.3 the values of sine, cosine, and tangent for π - x, π + x, and 2π - x in terms of their values for x, where x is any real number. CC.9-12.F.TF.4 (+) Extend the domain of trigonometric functions using the unit circle. Use the unit circle to explain 9-12 F TF.4 symmetry (odd and even) and periodicity of trigonometric functions. CC.9-12.F.TF.5 Model periodic phenomena with trigonometric functions. Choose trigonometric functions to model 9-12 F TF.5 periodic phenomena with specified amplitude, frequency, and midline.* CC.9-12.F.TF.6 (+) Model periodic phenomena with trigonometric functions. Understand that restricting a 9-12 F TF.6 trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. CC.9-12.F.TF.7 (+) Model periodic phenomena with trigonometric functions. Use inverse functions to solve 9-12 F TF.7 trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.* CC.9-12.F.TF.8 Prove and apply trigonometric identities. Prove the Pythagorean identity (sin A)^2 + (cos A)^2 = 1 9-12 F TF.8 and use it to find sin A, cos A, or tan A, given sin A, cos A, or tan A, and the quadrant of the angle. CC.9-12.F.TF.9 (+) Prove and apply trigonometric identities. Prove the addition and subtraction formulas for sine, 9-12 F TF.9 cosine, and tangent and use them to solve problems. CC.9-12.G.CO.1 Experiment with transformations in the plane. Know precise definitions of angle, circle, 9-12 G CO.1 perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. CC.9-12.G.CO.2 Experiment with transformations in the plane. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as 9-12 G CO.2 inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). CC.9-12.G.CO.3 Experiment with transformations in the plane. Given a rectangle, parallelogram, trapezoid, or 9-12 G CO.3 regular polygon, describe the rotations and reflections that carry it onto itself. CC.9-12.G.CO.4 Experiment with transformations in the plane. Develop definitions of rotations, reflections, and 9-12 G CO.4 translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. CC.9-12.G.CO.5 Experiment with transformations in the plane. Given a geometric figure and a rotation, reflection, 9-12 G CO.5 or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. CC.9-12.G.CO.6 Understand congruence in terms of rigid motions. Use geometric descriptions of rigid motions to 9-12 G CO.6 transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. CC.9-12.G.CO.7 Understand congruence in terms of rigid motions. Use the definition of congruence in terms of 9-12 G CO.7 rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. CC.9-12.G.CO.8 Understand congruence in terms of rigid motions. Explain how the criteria for triangle congruence 9-12 G CO.8 (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. CC.9-12.G.CO.9 Prove geometric theorems. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and 9-12 G CO.9 corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. CC.9-12.G.CO.10 Prove geometric theorems. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment 9-12 G CO.10 joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. CC.9-12.G.CO.11 Prove geometric theorems. Prove theorems about parallelograms. Theorems include: opposite 9-12 G CO.11 sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. CC.9-12.G.CO.12 Make geometric constructions. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). 9-12 G CO.12 Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. CC.9-12.G.CO.13 Make geometric constructions. Construct an equilateral triangle, a square, and a regular hexagon 9-12 G CO.13 inscribed in a circle. CC.9-12.G.SRT.1 Understand similarity in terms of similarity transformations. Verify experimentally the properties of dilations given by a center and a scale factor: 9-12 G SRT.1 -- a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. -- b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. CC.9-12.G.SRT.2 Understand similarity in terms of similarity transformations. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity 9-12 G SRT.2 transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. CC.9-12.G.SRT.3 Understand similarity in terms of similarity transformations. Use the properties of similarity 9-12 G SRT.3 transformations to establish the AA criterion for two triangles to be similar. CC.9-12.G.SRT.4 Prove theorems involving similarity. Prove theorems about triangles. Theorems include: a line 9-12 G SRT.4 parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. CC.9-12.G.SRT.5 Prove theorems involving similarity. Use congruence and similarity criteria for triangles to solve 9-12 G SRT.5 problems and to prove relationships in geometric figures. CC.9-12.G.SRT.6 Define trigonometric ratios and solve problems involving right triangles. Understand that by 9-12 G SRT.6 similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. CC.9-12.G.SRT.7 Define trigonometric ratios and solve problems involving right triangles. Explain and use the 9-12 G SRT.7 relationship between the sine and cosine of complementary angles. CC.9-12.G.SRT.8 Define trigonometric ratios and solve problems involving right triangles. Use trigonometric ratios 9-12 G SRT.8 and the Pythagorean Theorem to solve right triangles in applied problems. CC.9-12.G.SRT.9 (+) Apply trigonometry to general triangles. Derive the formula A = (1/2)ab sin(C) for the area of a 9-12 G SRT.9 triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. SRT.1 CC.9-12.G.SRT.10 (+) Apply trigonometry to general triangles. Prove the Laws of Sines and Cosines and use them to 9-12 G 0 solve problems. CC.9-12.G.SRT.11 (+) Apply trigonometry to general triangles. Understand and apply the Law of Sines and the Law SRT.1 9-12 G of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant 1 forces). 9-12 G C.1 CC.9-12.G.C.1 Understand and apply theorems about circles. Prove that all circles are similar. CC.9-12.G.C.2 Understand and apply theorems about circles. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed 9-12 G C.2 angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. CC.9-12.G.C.3 Understand and apply theorems about circles. Construct the inscribed and circumscribed circles of a 9-12 G C.3 triangle, and prove properties of angles for a quadrilateral inscribed in a circle. CC.9-12.G.C.4 (+) Understand and apply theorems about circles. Construct a tangent line from a point outside a 9-12 G C.4 given circle to the circle. CC.9-12.G.C.5 Find arc lengths and areas of sectors of circles. Derive using similarity the fact that the length of the 9-12 G C.5 arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. CC.9-12.G.GPE.1 Translate between the geometric description and the equation for a conic section. Derive the 9-12 G GPE.1 equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. CC.9-12.G.GPE.2 Translate between the geometric description and the equation for a conic section. Derive the 9-12 G GPE.2 equation of a parabola given a focus and directrix. CC.9-12.G.GPE.3 (+) Translate between the geometric description and the equation for a conic section. Derive the 9-12 G GPE.3 equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. CC.9-12.G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or 9-12 G GPE.4 disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). CC.9-12.G.GPE.5 Use coordinates to prove simple geometric theorems algebraically. Prove the slope criteria for 9-12 G GPE.5 parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). CC.9-12.G.GPE.6 Use coordinates to prove simple geometric theorems algebraically. Find the point on a directed 9-12 G GPE.6 line segment between two given points that partitions the segment in a given ratio. CC.9-12.G.GPE.7 Use coordinates to prove simple geometric theorems algebraically. Use coordinates to compute 9-12 G GPE.7 perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.* CC.9-12.G.GMD.1 Explain volume formulas and use them to solve problems. Give an informal argument for the GMD. 9-12 G formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection 1 arguments, Cavalieri’s principle, and informal limit arguments. GMD. CC.9-12.G.GMD.2 (+) Explain volume formulas and use them to solve problems. Give an informal argument using 9-12 G 2 Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures. GMD. CC.9-12.G.GMD.3 Explain volume formulas and use them to solve problems. Use volume formulas for cylinders, 9-12 G 3 pyramids, cones, and spheres to solve problems.* CC.9-12.G.GMD.4 Visualize relationships between two-dimensional and three-dimensional objects. Identify the GMD. 9-12 G shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects 4 generated by rotations of two-dimensional objects. CC.9-12.G.MG.1 Apply geometric concepts in modeling situations. Use geometric shapes, their measures, and their 9-12 G MG.1 properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* CC.9-12.G.MG.2 Apply geometric concepts in modeling situations. Apply concepts of density based on area and 9-12 G MG.2 volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).* CC.9-12.G.MG.3 Apply geometric concepts in modeling situations. Apply geometric methods to solve design 9-12 G MG.3 problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).* CC.9-12.S.ID.1 Summarize, represent, and interpret data on a single count or measurement variable. Represent 9-12 S ID.1 data with plots on the real number line (dot plots, histograms, and box plots).* CC.9-12.S.ID.2 Summarize, represent, and interpret data on a single count or measurement variable. Use statistics 9-12 S ID.2 appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.* CC.9-12.S.ID.3 Summarize, represent, and interpret data on a single count or measurement variable. Interpret 9-12 S ID.3 differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).* CC.9-12.S.ID.4 Summarize, represent, and interpret data on a single count or measurement variable. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. 9-12 S ID.4 Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.* CC.9-12.S.ID.5 Summarize, represent, and interpret data on two categorical and quantitative variables. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the 9-12 S ID.5 data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.* Standards Code: OA=Operations and Algebraic Thinking, NBT=Number and Operations in Base 10, MD=Measurements and Data, G=Geometry, NF=Number and Operations-Fractions, RP=Rations and Proportional Relationships, NS= Number System, EE=Expressions and Equations, SP=Statistics and Probability, CC.9-12.S.ID.6 Summarize, represent, and interpret data on two categorical and quantitative variables. Represent 9-12 S ID.6 data on two quantitative variables on a scatter plot, and describe how the variables are related.* CC.9-12.S.ID.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. 9-12 S ID.6a Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.* 9-12 S ID.6b CC.9-12.S.ID.6b Informally assess the fit of a function by plotting and analyzing residuals.* 9-12 S ID.6c CC.9-12.S.ID.6c Fit a linear function for a scatter plot that suggests a linear association.* CC.9-12.S.ID.7 Interpret linear models. Interpret the slope (rate of change) and the intercept (constant term) of a 9-12 S ID.7 linear model in the context of the data.* CC.9-12.S.ID.8 Interpret linear models. Compute (using technology) and interpret the correlation coefficient of a 9-12 S ID.8 linear fit.* 9-12 S ID.9 CC.9-12.S.ID.9 Interpret linear models. Distinguish between correlation and causation.* CC.9-12.S.IC.1 Understand and evaluate random processes underlying statistical experiments. Understand statistics 9-12 S IC.1 as a process for making inferences about population parameters based on a random sample from that population.* CC.9-12.S.IC.2 Understand and evaluate random processes underlying statistical experiments. Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model 9-12 S IC.2 says a spinning coin falls heads up with probability 0. 5. Would a result of 5 tails in a row cause you to question the model?* CC.9-12.S.IC.3 Make inferences and justify conclusions from sample surveys, experiments, and observational 9-12 S IC.3 studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.* CC.9-12.S.IC.4 Make inferences and justify conclusions from sample surveys, experiments, and observational 9-12 S IC.4 studies. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.* CC.9-12.S.IC.5 Make inferences and justify conclusions from sample surveys, experiments, and observational 9-12 S IC.5 studies. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.* CC.9-12.S.IC.6 Make inferences and justify conclusions from sample surveys, experiments, and observational 9-12 S IC.6 studies. Evaluate reports based on data.* CC.9-12.S.CP.2 Understand independence and conditional probability and use them to interpret data. Understand 9-12 S CP.2 that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.* CC.9-12.S.CP.3 Understand independence and conditional probability and use them to interpret data. Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that 9-12 S CP.3 the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.* CC.9-12.S.CP.4 Understand independence and conditional probability and use them to interpret data. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate 9-12 S CP.4 conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.* CC.9-12.S.CP.5 Understand independence and conditional probability and use them to interpret data. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday 9-12 S CP.5 situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.* CC.9-12.S.CP.6 Use the rules of probability to compute probabilities of compound events in a uniform probability 9-12 S CP.6 model. Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.* CC.9-12.S.CP.7 Use the rules of probability to compute probabilities of compound events in a uniform probability 9-12 S CP.7 model. Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.* CC.9-12.S.CP.8 (+) Use the rules of probability to compute probabilities of compound events in a uniform 9-12 S CP.8 probability model. Apply the general Multiplication Rule in a uniform probability model, P(A and B) = [P(A)]x[P(B|A)] =[P(B)]x[P(A|B)], and interpret the answer in terms of the model.* CC.9-12.S.CP.9 (+) Use the rules of probability to compute probabilities of compound events in a uniform 9-12 S CP.9 probability model. Use permutations and combinations to compute probabilities of compound events and solve problems.* CC.9-12.S.MD.1 (+) Calculate expected values and use them to solve problems. Define a random variable for a 9-12 S MD.1 quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.* CC.9-12.S.MD.2 (+) Calculate expected values and use them to solve problems. Calculate the expected value of a 9-12 S MD.2 random variable; interpret it as the mean of the probability distribution.* CC.9-12.S.MD.3 (+) Calculate expected values and use them to solve problems. Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the 9-12 S MD.3 expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.* CC.9-12.S.MD.4 (+) Calculate expected values and use them to solve problems. Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected 9-12 S MD.4 value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?* CC.9-12.S.MD.5 (+) Use probability to evaluate outcomes of decisions. Weigh the possible outcomes of a decision 9-12 S MD.5 by assigning probabilities to payoff values and finding expected values.* CC.9-12.S.MD.5a (+) Find the expected payoff for a game of chance. For example, find the expected winnings from 9-12 S MD.5a a state lottery ticket or a game at a fast-food restaurant.* CC.9-12.S.MD.5b (+) Evaluate and compare strategies on the basis of expected values. For example, compare a MD.5 9-12 S high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of b having a minor or a major accident.* CC.9-12.S.MD.6 (+) Use probability to evaluate outcomes of decisions. Use probabilities to make fair decisions (e.g., 9-12 S MD.6 drawing by lots, using a random number generator).* CC.9-12.S.MD.7 (+) Use probability to evaluate outcomes of decisions. Analyze decisions and strategies using 9-12 S MD.7 probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).* English/Language Arts 11 -12th Grade Standards Grade Core Area # Timeline Standard CC.11-12.R.L.1 Key Ideas and Details: Cite strong and thorough textual evidence to support analysis of what the 11-12 R.L 1 text says explicitly as well as inferences drawn from the text, including determining where the text leaves matters uncertain. CC.11-12.R.L.2 Key Ideas and Details: Determine two or more themes or central ideas of a text and analyze their 11-12 R.L 2 development over the course of the text, including how they interact and build on one another to produce a complex account; provide an objective summary of the text. CC.11-12.R.L.3 Key Ideas and Details: Analyze the impact of the author’s choices regarding how to develop and 11-12 R.L 3 relate elements of a story or drama (e.g., where a story is set, how the action is ordered, how the characters are introduced and developed). CC.11-12.R.L.4 Craft and Structure: Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, 11-12 R.L 4 including words with multiple meanings or language that is particularly fresh, engaging, or beautiful. (Include Shakespeare as well as other authors.) CC.11-12.R.L.5 Craft and Structure: Analyze how an author’s choices concerning how to structure specific parts of 11-12 R.L 5 a text (e.g., the choice of where to begin or end a story, the choice to provide a comedic or tragic resolution) contribute to its overall structure and meaning as well as its aesthetic impact. CC.11-12.R.L.6 Craft and Structure: Analyze a case in which grasping point of view requires distinguishing what is 11-12 R.L 6 directly stated in a text from what is really meant (e.g., satire, sarcasm, irony, or understatement). CC.11-12.R.L.7 Integration of Knowledge and Ideas: Analyze multiple interpretations of a story, drama, or poem 11-12 R.L 7 (e.g., recorded or live production of a play or recorded novel or poetry), evaluating how each version interprets the source text. (Include at least one play by Shakespeare and one play by an American dramatist.) CC.11-12.R.L.9 Integration of Knowledge and Ideas: Demonstrate knowledge of eighteenth-, nineteenth- and 11-12 R.L 9 early-twentieth-century foundational works of American literature, including how two or more texts from the same period treat similar themes or topics. CC.11-12.R.L.10 Range of Reading and Level of Text Complexity: By the end of grade 11, read and comprehend literature, including stories, dramas, and poems, in the grades 11–CCR text complexity band proficiently, with 11-12 R.L 10 scaffolding as needed at the high end of the range. By the end of grade 12, read and comprehend literature, including stories, dramas, and poems, at the high end of the grades 11–CCR text complexity band independently and proficiently. CC.11-12.R.I.1 Key Ideas and Details: Cite strong and thorough textual evidence to support analysis of what the 11-12 R.I 1 text says explicitly as well as inferences drawn from the text, including determining where the text leaves matters uncertain. CC.11-12.R.I.2 Key Ideas and Details: Determine two or more central ideas of a text and analyze their 11-12 R.I 2 development over the course of the text, including how they interact and build on one another to provide a complex analysis; provide an objective summary of the text. CC.11-12.R.I.3 Key Ideas and Details: Analyze a complex set of ideas or sequence of events and explain how 11-12 R.I 3 specific individuals, ideas, or events interact and develop over the course of the text. CC.11-12.R.I.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, 11-12 R.I 4 including figurative, connotative, and technical meanings; analyze how an author uses and refines the meaning of a key term or terms over the course of a text (e.g., how Madison defines faction in Federalist No. 10). CC.11-12.R.I.5 Craft and Structure: Analyze and evaluate the effectiveness of the structure an author uses in his 11-12 R.I 5 or her exposition or argument, including whether the structure makes points clear, convincing, and engaging. CC.11-12.R.I.6 Craft and Structure: Determine an author’s point of view or purpose in a text in which the rhetoric 11-12 R.I 6 is particularly effective, analyzing how style and content contribute to the power, persuasiveness, or beauty of the text. CC.11-12.R.I.7 Integration of Knowledge and Ideas: Integrate and evaluate multiple sources of information 11-12 R.I 7 presented in different media or formats (e.g., visually, quantitatively) as well as in words in order to address a question or solve a problem. CC.11-12.R.I.8 Integration of Knowledge and Ideas: Delineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional principles and use of legal reasoning (e.g., in U.S. Supreme Court 11-12 R.I 8 majority opinions and dissents) and the premises, purposes, and arguments in works of public advocacy (e.g., The Federalist, presidential addresses). CC.11-12.R.I.9 Integration of Knowledge and Ideas: Analyze seventeenth-, eighteenth-, and nineteenth-century foundational U.S. documents of historical and literary significance (including The Declaration of Independence, 11-12 R.I 9 the Preamble to the Constitution, the Bill of Rights, and Lincoln’s Second Inaugural Address) for their themes, purposes, and rhetorical features. CC.11-12.R.I.10 Range of Reading and Level of Text Complexity: By the end of grade 11, read and comprehend literary nonfiction in the grades 11–CCR text complexity band proficiently, with scaffolding as needed at the high 11-12 R.I 10 end of the range. By the end of grade 12, read and comprehend literary nonfiction at the high end of the grades 11–CCR text complexity band independently and proficiently. CC.11-12.W.1 Text Types and Purposes: Write arguments to support claims in an analysis of substantive topics or 11-12 W 1 texts, using valid reasoning and relevant and sufficient evidence. CC.11-12.W.1.a Text Types and Purposes: Introduce precise, knowledgeable claim(s), establish the significance of 11-12 W 1.a the claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that logically sequences claim(s), counterclaims, reasons, and evidence. CC.11-12.W.1.b Text Types and Purposes: Develop claim(s) and counterclaims fairly and thoroughly, supplying 11-12 W 1.b the most relevant evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audience’s knowledge level, concerns, values, and possible biases. CC.11-12.W.1.c Text Types and Purposes: Use words, phrases, and clauses as well as varied syntax to link the 11-12 W 1.c major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims. CC.11-12.W.1.d Text Types and Purposes: Establish and maintain a formal style and objective tone while 11-12 W 1.d attending to the norms and conventions of the discipline in which they are writing. CC.11-12.W.1.e Text Types and Purposes: Provide a concluding statement or section that follows from and 11-12 W 1.e supports the argument presented. CC.11-12.W.2 Text Types and Purposes: Write informative/explanatory texts to examine and convey complex 11-12 W 2 ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content. CC.11-12.W.2.a Text Types and Purposes: Introduce a topic; organize complex ideas, concepts, and information 11-12 W 2.a so that each new element builds on that which precedes it to create a unified whole; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension. CC.11-12.W.2.b Text Types and Purposes: Develop the topic thoroughly by selecting the most significant and 11-12 W 2.b relevant facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic. CC.11-12.W.2.c Text Types and Purposes: Use appropriate and varied transitions and syntax to link the major 11-12 W 2.c sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts. CC.11-12.W.2.d Text Types and Purposes: Use precise language, domain-specific vocabulary, and techniques such 11-12 W 2.d as metaphor, simile, and analogy to manage the complexity of the topic. CC.11-12.W.2.e Text Types and Purposes: Establish and maintain a formal style and objective tone while 11-12 W 2.e attending to the norms and conventions of the discipline in which they are writing. CC.11-12.W.2.f Text Types and Purposes: Provide a concluding statement or section that follows from and 11-12 W 2.f supports the information or explanation presented (e.g., articulating implications or the significance of the topic). CC.11-12.W.3 Text Types and Purposes: Write narratives to develop real or imagined experiences or events using 11-12 W 3 effective technique, well-chosen details, and well-structured event sequences. CC.11-12.W.3.a Text Types and Purposes: Engage and orient the reader by setting out a problem, situation, or 11-12 W 3.a observation and its significance, establishing one or multiple point(s) of view, and introducing a narrator and/or characters; create a smooth progression of experiences or events. CC.11-12.W.3.b Text Types and Purposes: Use narrative techniques, such as dialogue, pacing, description, 11-12 W 3.b reflection, and multiple plot lines, to develop experiences, events, and/or characters. CC.11-12.W.3.c Text Types and Purposes: Use a variety of techniques to sequence events so that they build on 11-12 W 3.c one another to create a coherent whole and build toward a particular tone and outcome (e.g., a sense of mystery, suspense, growth, or resolution). CC.11-12.W.3.d Text Types and Purposes: Use precise words and phrases, telling details, and sensory language to 11-12 W 3.d convey a vivid picture of the experiences, events, setting, and/or characters. CC.11-12.W.3.e Text Types and Purposes: Provide a conclusion that follows from and reflects on what is 11-12 W 3.e experienced, observed, or resolved over the course of the narrative. CC.11-12.W.4 Production and Distribution of Writing: Produce clear and coherent writing in which the 11-12 W 4 development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) CC.11-12.W.5 Production and Distribution of Writing: Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a 11-12 W 5 specific purpose and audience. (Editing for conventions should demonstrate command of Language standards 1–3 up to and including grades 11-12 on page 55.) CC.11-12.W.6 Production and Distribution of Writing: Use technology, including the Internet, to produce, publish, 11-12 W 6 and update individual or shared writing products in response to ongoing feedback, including new arguments or information. CC.11-12.W.7 Research to Build and Present Knowledge: Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the 11-12 W 7 inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation. CC.11-12.W.8 Research to Build and Present Knowledge: Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the strengths and limitations of each source 11-12 W 8 in terms of the task, purpose, and audience; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and overreliance on any one source and following a standard format for citation. CC.11-12.W.9 Research to Build and Present Knowledge: Draw evidence form literary or informational texts to 11-12 W 9 support analysis, reflection, and research. CC.11-12.W.9.a Research to Build and Present Knowledge: Apply grades 11–12 Reading standards to literature 11-12 W 9.a (e.g., “Demonstrate knowledge of eighteenth-, nineteenth- and early-twentieth-century foundational works of American literature, including how two or more texts from the same period treat similar themes or topics”). CC.11-12.W.9.b Research to Build and Present Knowledge: Apply grades 11–12 Reading standards to literary nonfiction (e.g., “Delineate and evaluate the reasoning in seminal U.S. texts, including the application of 11-12 W 9.b constitutional principles and use of legal reasoning [e.g., in U.S. Supreme Court Case majority opinions and dissents) and the premises, purposes, and arguments in works of public advocacy (e.g., The Federalist, presidential addresses]”). CC.11-12.W.10 Range of Writing: Write routinely over extended time frames (time for research, reflection, and 11-12 W 10 revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences. CC.11-12.SL.1 Comprehension and Collaboration: Initiate and participate effectively in a range of collaborative 11-12 SL 1 discussions (one-on-one, in groups, and teacher-led) with diverse partners on grades 11–12 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively. CC.11-12.SL.1.a Comprehension and Collaboration: Come to discussions prepared, having read and researched 11-12 SL 1.a material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas. CC.11-12.SL.1.b Comprehension and Collaboration: Work with peers to promote civil, democratic discussions and 11-12 SL 1.b decision-making, set clear goals and deadlines, and establish individual roles as needed. CC.11-12.SL.1.c Comprehension and Collaboration: Propel conversations by posing and responding to questions 11-12 SL 1.c that probe reasoning and evidence; ensure a hearing for a full range of positions on a topic or issue; clarify, verify, or challenge ideas and conclusions; and promote divergent and creative perspectives. CC.11-12.SL.1.d Comprehension and Collaboration: Respond thoughtfully to diverse perspectives; synthesize 11-12 SL 1.d comments, claims, and evidence made on all sides of an issue; resolve contradictions when possible; and determine what additional information or research is required to deepen the investigation or complete the task. CC.11-12.SL.2 Comprehension and Collaboration: Integrate multiple sources of information presented in diverse 11-12 SL 2 formats and media (e.g., visually, quantitatively, orally) in order to make informed decisions and solve problems, evaluating the credibility and accuracy of each source and noting any discrepancies among the data. CC.11-12.SL.3 Comprehension and Collaboration: Evaluate a speaker’s point of view, reasoning, and use of 11-12 SL 3 evidence and rhetoric, assessing the stance, premises, links among ideas, word choice, points of emphasis, and tone used. CC.11-12.SL.4 Presentation of Knowledge and Ideas: Present information, findings, and supporting evidence, conveying a clear and distinct perspective, such that listeners can follow the line of reasoning, alternative or 11-12 SL 4 opposing perspectives are addressed, and the organization, development, substance, and style are appropriate to purpose, audience, and a range or formal and informal tasks. CC.11-12.SL.5 Presentation of Knowledge and Ideas: Make strategic use of digital media (e.g., textual, graphical, 11-12 SL 5 audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest. CC.11-12.SL.6 Presentation of Knowledge and Ideas: Adapt speech to a variety of contexts and tasks, 11-12 SL 6 demonstrating a command of formal English when indicated or appropriate. (See grades 11-12 Language standards 1 and 3 on page 54 for specific expectations.) CC.11-12.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English 11-12 L 1 grammar and usage when writing or speaking. CC.11-12.L.1.a Conventions of Standard English: Apply the understanding that usage is a matter of convention, 11-12 L 1.a can change over time, and is sometimes contested. CC.11-12.L.1.b Conventions of Standard English: Resolve issues of complex or contested usage, consulting 11-12 L 1.b references (e.g., Merriam-Webster’s Dictionary of English Usage, Garner’s Modern American English) as needed. CC.11-12.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English 11-12 L 2 capitalization, punctuation, and spelling when writing. 11-12 L 2.a CC.11-12.L.2.a Conventions of Standard English: Observe hyphenation conventions. 11-12 L 2.b CC.11-12.L.2.b Conventions of Standard English: Spell correctly. CC.11-12.L.3 Knowledge of Language: Apply knowledge of language to understand how language functions in 11-12 L 3 different contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening. CC.11-12.L.3.a Knowledge of Language: Vary syntax for effect, consulting references (e.g., Tufte’s Artful 11-12 L 3.a Sentences) for guidance as needed; apply an understanding of syntax to the study of complex texts when reading. CC.11-12.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple- 11-12 L 4 meaning words and phrases based on grades 11–12 reading and content, choosing flexibly from a range of strategies. CC.11-12.L.4.a Vocabulary Acquisition and Use: Use context (e.g., the overall meaning of a sentence, paragraph, 11-12 L 4.a or text; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. CC.11-12.L.4.b Vocabulary Acquisition and Use: Identify and correctly use patterns of word changes that indicate 11-12 L 4.b different meanings or parts of speech (e.g., conceive, conception, conceivable). CC.11-12.L.4.c Vocabulary Acquisition and Use: Consult general and specialized reference materials (e.g., 11-12 L 4.c dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, its etymology, or its standard usage. CC.11-12.L.4.d Vocabulary Acquisition and Use: Verify the preliminary determination of the meaning of a word or 11-12 L 4.d phrase (e.g., by checking the inferred meaning in context or in a dictionary). CC.11-12.L.5 Vocabulary Acquisition and Use: Demonstrate understanding of figurative language, word 11-12 L 5 relationships, and nuances in word meanings. CC.11-12.L.5.a Vocabulary Acquisition and Use: Interpret figures of speech (e.g., hyperbole, paradox) in context 11-12 L 5.a and analyze their role in the text. CC.11-12.L.5.b Vocabulary Acquisition and Use: Analyze nuances in the meaning of words with similar 11-12 L 5.b denotations. CC.11-12.L.6 Vocabulary Acquisition and Use: Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading, writing, speaking, and listening at the college and career readiness 11-12 L 6 level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression. CC.11-12.R.H.1 Key Ideas and Details: Cite specific textual evidence to support analysis of primary and secondary 11-12 R.H 1 sources, connecting insights gained from specific details to an understanding of the text as a whole. CC.11-12.R.H.2 Key Ideas and Details: Determine the central ideas or information of a primary or secondary 11-12 R.H 2 source; provide an accurate summary that makes clear the relationships among the key details and ideas. CC.11-12.R.H.3 Key Ideas and Details: Evaluate various explanations for actions or events and determine which 11-12 R.H 3 explanation best accords with textual evidence, acknowledging where the text leaves matters uncertain. CC.11-12.R.H.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, 11-12 R.H 4 including analyzing how an author uses and refines the meaning of a key term over the course of a text (e.g., how Madison defines faction in Federalist No. 10). CC.11-12.R.H.5 Craft and Structure: Analyze in detail how a complex primary source is structured, including how 11-12 R.H 5 key sentences, paragraphs, and larger portions of the text contribute to the whole. CC.11-12.R.H.6 Craft and Structure: Evaluate authors’ differing points of view on the same historical event or 11-12 R.H 6 issue by assessing the authors’ claims, reasoning, and evidence. CC.11-12.R.H.7 Integration of Knowledge and Ideas: Integrate and evaluate multiple sources of information 11-12 R.H 7 presented in diverse formats and media (e.g., visually, quantitatively, as well as in words) in order to address a question or solve a problem. CC.11-12.R.H.8 Integration of Knowledge and Ideas: Evaluate an author’s premises, claims, and evidence by 11-12 R.H 8 corroborating or challenging them with other information. CC.11-12.R.H.9 Integration of Knowledge and Ideas: Integrate information from diverse sources, both primary 11-12 R.H 9 and secondary, into a coherent understanding of an idea or event, noting discrepancies among sources. CC.11-12.R.H.10 Range of Reading and Level of Text Complexity: By the end of grade 12, read and comprehend 11-12 R.H 10 history/social studies texts in the grades 11–12 text complexity band independently and proficiently. CC.11-12.R.ST.1 Key Ideas and Details: Cite specific textual evidence to support analysis of science and technical 11-12 R.ST 1 texts, attending to important distinctions the author makes and to any gaps or inconsistencies in the account. CC.11-12.R.ST.2 Key Ideas and Details: Determine the central ideas or conclusions of a text; summarize complex 11-12 R.ST 2 concepts, processes, or information presented in a text by paraphrasing them in simpler but still accurate terms. CC.11-12.R.ST.3 Key Ideas and Details: Follow precisely a complex multistep procedure when carrying out 11-12 R.ST 3 experiments, taking measurements, or performing technical tasks; analyze the specific results based on explanations in the text. CC.11-12.R.ST.4 Craft and Structure: Determine the meaning of symbols, key terms, and other domain-specific 11-12 R.ST 4 words and phrases as they are used in a specific scientific or technical context relevant to grades 11–12 texts and topics. CC.11-12.R.ST.5 Craft and Structure: Analyze how the text structures information or ideas into categories or 11-12 R.ST 5 hierarchies, demonstrating understanding of the information or ideas. CC.11-12.R.ST.6 Craft and Structure: Analyze the author’s purpose in providing an explanation, describing a 11-12 R.ST 6 procedure, or discussing an experiment in a text, identifying important issues that remain unresolved. CC.11-12.R.ST.7 Integration of Knowledge and Ideas: Integrate and evaluate multiple sources of information 11-12 R.ST 7 presented in diverse formats and media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem. CC.11-12.R.ST.8 Integration of Knowledge and Ideas: Evaluate the hypotheses, data, analysis, and conclusions in a 11-12 R.ST 8 science or technical text, verifying the data when possible and corroborating or challenging conclusions with other sources of information. CC.11-12.R.ST.9 Integration of Knowledge and Ideas: Synthesize information from a range of sources (e.g., texts, 11-12 R.ST 9 experiments, simulations) into a coherent understanding of a process, phenomenon, or concept, resolving conflicting information when possible. CC.11-12.R.ST.10 Range of Reading and Level of Text Complexity: By the end of grade 12, read and comprehend 11-12 R.ST 10 science/technical texts in the grades 11–12 text complexity band independently and proficiently. 11-12 W.HST 1 CC.11-12.W.HST.1 Text Types and Purposes: Write arguments focused on discipline-specific content. CC.11-12.W.HST.1.a Text Types and Purposes: Introduce precise, knowledgeable claim(s), establish the 11-12 W.HST 1.a significance of the claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that logically sequences the claim(s), counterclaims, reasons, and evidence. CC.11-12.W.HST.1.b Text Types and Purposes: Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant data and evidence for each while pointing out the strengths and limitations of both 11-12 W.HST 1.b claim(s) and counterclaims in a discipline-appropriate form that anticipates the audience’s knowledge level, concerns, values, and possible biases. CC.11-12.W.HST.1.c Text Types and Purposes: Use words, phrases, and clauses as well as varied syntax to link the 11-12 W.HST 1.c major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims. CC.11-12.W.HST.1.d Text Types and Purposes: Establish and maintain a formal style and objective tone while 11-12 W.HST 1.d attending to the norms and conventions of the discipline in which they are writing. CC.11-12.W.HST.1.e Text Types and Purposes: Provide a concluding statement or section that follows from or 11-12 W.HST 1.e supports the argument presented. CC.11-12.W.HST.2 Text Types and Purposes: Write informative/explanatory texts, including the narration of 11-12 W.HST 2 historical events, scientific procedures/ experiments, or technical processes. CC.11-12.W.HST.2.a Text Types and Purposes: Introduce a topic and organize complex ideas, concepts, and 11-12 W.HST 2.a information so that each new element builds on that which precedes it to create a unified whole; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension. CC.11-12.W.HST.2.b Text Types and Purposes: Develop the topic thoroughly by selecting the most significant and 11-12 W.HST 2.b relevant facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic. CC.11-12.W.HST.2.c Text Types and Purposes: Use varied transitions and sentence structures to link the major 11-12 W.HST 2.c sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts. CC.11-12.W.HST.2.d Text Types and Purposes: Use precise language, domain-specific vocabulary and techniques 11-12 W.HST 2.d such as metaphor, simile, and analogy to manage the complexity of the topic; convey a knowledgeable stance in a style that responds to the discipline and context as well as to the expertise of likely readers. CC.11-12.W.HST.2.e Text Types and Purposes: Provide a concluding statement or section that follows from and 11-12 W.HST 2.e supports the information or explanation provided (e.g., articulating implications or the significance of the topic). CC.11-12.W.HST.4 Production and Distribution of Writing: Produce clear and coherent writing in which the 11-12 W.HST 4 development, organization, and style are appropriate to task, purpose, and audience. CC.11-12.W.HST.5 Production and Distribution of Writing: Develop and strengthen writing as needed by planning, 11-12 W.HST 5 revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience. CC.11-12.W.HST.6 Production and Distribution of Writing: Use technology, including the Internet, to produce, 11-12 W.HST 6 publish, and update individual or shared writing products in response to ongoing feedback, including new arguments or information. CC.11-12.W.HST.7 Research to Build and Present Knowledge: Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the 11-12 W.HST 7 inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation. CC.11-12.W.HST.8 Research to Build and Present Knowledge: Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the strengths and limitations 11-12 W.HST 8 of each source in terms of the specific task, purpose, and audience; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and overreliance on any one source and following a standard format for citation. CC.11-12.W.HST.9 Research to Build and Present Knowledge: Draw evidence from informational texts to support 11-12 W.HST 9 analysis, reflection, and research. CC.11-12.W.HST.10 Range of Writing: Write routinely over extended time frames (time for reflection and 11-12 W.HST 10 revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. Mathematics 9 - 12th Grade Standards Grade Core Area # Timeline Standard CC.9-12.N.RN.1 Extend the properties of exponents to rational exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, 9-12 N RN.1 allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want [5^(1/3)]^3 = 5^[(1/3) x 3] to hold, so [5^(1/3)]^3 must equal 5. CC.9-12.N.RN.2 Extend the properties of exponents to rational exponents. Rewrite expressions involving 9-12 N RN.2 radicals and rational exponents using the properties of exponents. CC.9-12.N.RN.3 Use properties of rational and irrational numbers. Explain why the sum or product of rational 9-12 N RN.3 numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. CC.9-12.N.Q.1 Reason quantitatively and use units to solve problems. Use units as a way to understand 9-12 N Q.1 problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.* CC.9-12.N.Q.2 Reason quantitatively and use units to solve problems. Define appropriate quantities for the 9-12 N Q.2 purpose of descriptive modeling.* CC.9-12.N.Q.3 Reason quantitatively and use units to solve problems. Choose a level of accuracy appropriate 9-12 N Q.3 to limitations on measurement when reporting quantities.* CC.9-12.N.CN.1 Perform arithmetic operations with complex numbers. Know there is a complex number i 9-12 N CN.1 such that i^2 = −1, and every complex number has the form a + bi with a and b real. CC.9-12.N.CN.2 Perform arithmetic operations with complex numbers. Use the relation i2 = –1 and the 9-12 N CN.2 commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. CC.9-12.N.CN.3 (+) Perform arithmetic operations with complex numbers. Find the conjugate of a complex 9-12 N CN.3 number; use conjugates to find moduli and quotients of complex numbers. CC.9-12.N.CN.4 (+) Represent complex numbers and their operations on the complex plane. Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary 9-12 N CN.4 numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. CC.9-12.N.CN.5 (+) Represent complex numbers and their operations on the complex plane. Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex 9-12 N CN.5 plane; use properties of this representation for computation. For example, (-1 + √3i)^3 = 8 because (-1 + √3i) has modulus 2 and argument 120°. CC.9-12.N.CN.6 (+) Represent complex numbers and their operations on the complex plane. Calculate the 9-12 N CN.6 distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. CC.9-12.N.CN.7 Use complex numbers in polynomial identities and equations. Solve quadratic equations with 9-12 N CN.7 real coefficients that have complex solutions. CC.9-12.N.CN.8 (+) Use complex numbers in polynomial identities and equations. Extend polynomial 9-12 N CN.8 identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i). CC.9-12.N.CN.9 (+) Use complex numbers in polynomial identities and equations. Know the Fundamental 9-12 N CN.9 Theorem of Algebra; show that it is true for quadratic polynomials. CC.9-12.N.VM.1 (+) Represent and model with vector quantities. Recognize vector quantities as having both 9-12 N VM.1 magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v(bold), |v|, ||v||, v(not bold)). CC.9-12.N.VM.2 (+) Represent and model with vector quantities. Find the components of a vector by 9-12 N VM.2 subtracting the coordinates of an initial point from the coordinates of a terminal point. CC.9-12.N.VM.3 (+) Represent and model with vector quantities. Solve problems involving velocity and other 9-12 N VM.3 quantities that can be represented by vectors. CC.9-12.N.VM.4 (+) Perform operations on vectors. Add and subtract vectors. 9-12 N VM.4 CC.9-12.N.VM.4a (+) Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand 9-12 N VM.4a that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. CC.9-12.N.VM.4b (+) Given two vectors in magnitude and direction form, determine the magnitude and 9-12 N VM.4b direction of their sum. CC.9-12.N.VM.4c (+) Understand vector subtraction v – w as v + (–w), where (–w) is the additive inverse of w, 9-12 N VM.4c with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise. 9-12 N VM.5 CC.9-12.N.VM.5 (+) Perform operations on vectors. Multiply a vector by a scalar. CC.9-12.N.VM.5a (+) Represent scalar multiplication graphically by scaling vectors and possibly reversing 9-12 N VM.5a their direction; perform scalar multiplication component-wise, e.g., as c(v(sub x), v(sub y)) = (cv(sub x), cv(sub y)). CC.9-12.N.VM.5b (+) Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the 9-12 N VM.5b direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0). CC.9-12.N.VM.6 (+) Perform operations on matrices and use matrices in applications. Use matrices to 9-12 N VM.6 represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. CC.9-12.N.VM.7 (+) Perform operations on matrices and use matrices in applications. Multiply matrices by 9-12 N VM.7 scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. CC.9-12.N.VM.8 (+) Perform operations on matrices and use matrices in applications. Add, subtract, and 9-12 N VM.8 multiply matrices of appropriate dimensions. CC.9-12.N.VM.9 (+) Perform operations on matrices and use matrices in applications. Understand that, 9-12 N VM.9 unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. CC.9-12.N.VM.10 (+) Perform operations on matrices and use matrices in applications. Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in 9-12 N VM.10 the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. CC.9-12.N.VM.11 (+) Perform operations on matrices and use matrices in applications. Multiply a vector 9-12 N VM.11 (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. CC.9-12.N.VM.12 (+) Perform operations on matrices and use matrices in applications. Work with 2 X 2 9-12 N VM.12 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. CC.9-12.A.SSE.1 Interpret the structure of expressions. Interpret expressions that represent a quantity in 9-12 A SSE.1 terms of its context.* 9-12 A SSE.1a CC.9-12.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients.* CC.9-12.A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity. 9-12 A SSE.1b For example, interpret P(1+r)^n as the product of P and a factor not depending on P.* CC.9-12.A.SSE.2 Interpret the structure of expressions. Use the structure of an expression to identify ways to 9-12 A SSE.2 rewrite it. For example, see x^4 – y^4 as (x^2)^2 – (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 – y^2)(x^2 + y^2). CC.9-12.A.SSE.3 Write expressions in equivalent forms to solve problems. Choose and produce an equivalent 9-12 A SSE.3 form of an expression to reveal and explain properties of the quantity represented by the expression.* 9-12 A SSE.3a CC.9-12.A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines.* CC.9-12.A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value 9-12 A SSE.3b of the function it defines.* CC.9-12.A.SSE.3c Use the properties of exponents to transform expressions for exponential functions. For 9-12 A SSE.3c example the expression 1.15^t can be rewritten as [1.15^(1/12)]^(12t) ≈ 1.012^(12t) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.* CC.9-12.A.SSE.4 Write expressions in equivalent forms to solve problems. Derive the formula for the sum of 9-12 A SSE.4 a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.* CC.9-12.A.APR.1 Perform arithmetic operations on polynomials. Understand that polynomials form a system 9-12 A APR.1 analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. CC.9-12.A.APR.2 Understand the relationship between zeros and factors of polynomial. Know and apply the 9-12 A APR.2 Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). CC.9-12.A.APR.3 Understand the relationship between zeros and factors of polynomials. Identify zeros of 9-12 A APR.3 polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. CC.9-12.A.APR.4 Use polynomial identities to solve problems. Prove polynomial identities and use them to 9-12 A APR.4 describe numerical relationships. For example, the polynomial identity (x^2 + y^2)^2 = (x^2 – y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples. CC.9-12.A.APR.5 (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y 9-12 A APR.5 for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.1 CC.9-12.A.APR.6 Rewrite rational expressions. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) 9-12 A APR.6 less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. CC.9-12.A.APR.7 (+) Rewrite rational expressions. Understand that rational expressions form a system 9-12 A APR.7 analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. CC.9-12.A.CED.1 Create equations that describe numbers or relationship. Create equations and inequalities 9-12 A CED.1 in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.* CC.9-12.A.CED.2 Create equations that describe numbers or relationship. Create equations in two or more 9-12 A CED.2 variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.* CC.9-12.A.CED.3 Create equations that describe numbers or relationship. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non- 9-12 A CED.3 viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.* CC.9-12.A.CED.4 Create equations that describe numbers or relationship. Rearrange formulas to highlight a 9-12 A CED.4 quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.* CC.9-12.A.REI.1 Understand solving equations as a process of reasoning and explain the reasoning. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous 9-12 A REI.1 step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. CC.9-12.A.REI.2 Understand solving equations as a process of reasoning and explain the reasoning. Solve 9-12 A REI.2 simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. CC.9-12.A.REI.3 Solve equations and inequalities in one variable. Solve linear equations and inequalities in 9-12 A REI.3 one variable, including equations with coefficients represented by letters. 9-12 A REI.4 CC.9-12.A.REI.4 Solve equations and inequalities in one variable. Solve quadratic equations in one variable. CC.9-12.A.REI.4a Use the method of completing the square to transform any quadratic equation in x into an 9-12 A REI.4a equation of the form (x – p)^2 = q that has the same solutions. Derive the quadratic formula from this form. CC.9-12.A.REI.4b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing 9-12 A REI.4b the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. CC.9-12.A.REI.5 Solve systems of equations. Prove that, given a system of two equations in two variables, 9-12 A REI.5 replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. CC.9-12.A.REI.6 Solve systems of equations. Solve systems of linear equations exactly and approximately 9-12 A REI.6 (e.g., with graphs), focusing on pairs of linear equations in two variables. CC.9-12.A.REI.7 Solve systems of equations. Solve a simple system consisting of a linear equation and a 9-12 A REI.7 quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x^2 + y^2 = 3. CC.9-12.A.REI.8 (+) Solve systems of equations. Represent a system of linear equations as a single matrix 9-12 A REI.8 equation in a vector variable. CC.9-12.A.REI.9 (+) Solve systems of equations. Find the inverse of a matrix if it exists and use it to solve 9-12 A REI.9 systems of linear equations (using technology for matrices of dimension 3 × 3 or greater). CC.9-12.A.REI.10 Represent and solve equations and inequalities graphically. Understand that the graph of an 9-12 A REI.10 equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). CC.9-12.A.REI.11 Represent and solve equations and inequalities graphically. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the 9-12 A REI.11 equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* CC.9-12.A.REI.12 Represent and solve equations and inequalities graphically. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and 9-12 A REI.12 graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. CC.9-12.F.IF.1 Understand the concept of a function and use function notation. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain 9-12 F IF.1 exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). CC.9-12.F.IF.2 Understand the concept of a function and use function notation. Use function notation, 9-12 F IF.2 evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. CC.9-12.F.IF.3 Understand the concept of a function and use function notation. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the 9-12 F IF.3 Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1 (n is greater than or equal to 1). CC.9-12.F.IF.4 Interpret functions that arise in applications in terms of the context. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the 9-12 F IF.4 quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* CC.9-12.F.IF.5 Interpret functions that arise in applications in terms of the context. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the 9-12 F IF.5 function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.* CC.9-12.F.IF.6 Interpret functions that arise in applications in terms of the context. Calculate and interpret 9-12 F IF.6 the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* CC.9-12.F.IF.7 Analyze functions using different representations. Graph functions expressed symbolically and 9-12 F IF.7 show key features of the graph, by hand in simple cases and using technology for more complicated cases.* 9-12 F IF.7a CC.9-12.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.* CC.9-12.F.IF.7b Graph square root, cube root, and piecewise-defined functions, including step functions and 9-12 F IF.7b absolute value functions.* CC.9-12.F.IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and 9-12 F IF.7c showing end behavior.* CC.9-12.F.IF.7d (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations 9-12 F IF.7d are available, and showing end behavior.* CC.9-12.F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and 9-12 F IF.7e trigonometric functions, showing period, midline, and amplitude.* CC.9-12.F.IF.8 Analyze functions using different representations. Write a function defined by an expression in 9-12 F IF.8 different but equivalent forms to reveal and explain different properties of the function. CC.9-12.F.IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, 9-12 F IF.8a extreme values, and symmetry of the graph, and interpret these in terms of a context. CC.9-12.F.IF.8b Use the properties of exponents to interpret expressions for exponential functions. For 9-12 F IF.8b example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^(12t), y = (1.2)^(t/10), and classify them as representing exponential growth and decay. CC.9-12.F.IF.9 Analyze functions using different representations. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For 9-12 F IF.9 example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. CC.9-12.F.BF.1 Build a function that models a relationship between two quantities. Write a function that 9-12 F BF.1 describes a relationship between two quantities.* 9-12 F BF.1a CC.9-12.F.BF.1a Determine an explicit expression, a recursive process, or steps for calculation from a context. CC.9-12.F.BF.1b Combine standard function types using arithmetic operations. For example, build a function 9-12 F BF.1b that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. CC.9-12.F.BF.1c (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a 9-12 F BF.1c function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. CC.9-12.F.BF.2 Build a function that models a relationship between two quantities. Write arithmetic and 9-12 F BF.2 geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* CC.9-12.F.BF.3 Build new functions from existing functions. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k 9-12 F BF.3 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 9-12 F BF.4 CC.9-12.F.BF.4 Build new functions from existing functions. Find inverse functions. CC.9-12.F.BF.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an 9-12 F BF.4a expression for the inverse. For example, f(x) =2(x^3) or f(x) = (x+1)/(x-1) for x ≠ 1 (x not equal to 1). 9-12 F BF.4b CC.9-12.F.BF.4b (+) Verify by composition that one function is the inverse of another. CC.9-12.F.BF.4c (+) Read values of an inverse function from a graph or a table, given that the function has an 9-12 F BF.4c inverse. 9-12 F BF.4d CC.9-12.F.BF.4d (+) Produce an invertible function from a non-invertible function by restricting the domain. CC.9-12.F.BF.5 (+) Build new functions from existing functions. Understand the inverse relationship between 9-12 F BF.5 exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. CC.9-12.F.LE.1 Construct and compare linear, quadratic, and exponential models and solve problems. 9-12 F LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.* CC.9-12.F.LE.1a Prove that linear functions grow by equal differences over equal intervals and that 9-12 F LE.1a exponential functions grow by equal factors over equal intervals.* CC.9-12.F.LE.1b. Recognize situations in which one quantity changes at a constant rate per unit interval 9-12 F LE.1b relative to another.* CC.9-12.F.LE.1c Recognize situations in which a quantity grows or decays by a constant percent rate per unit 9-12 F LE.1c interval relative to another.* CC.9-12.F.LE.2 Construct and compare linear, quadratic, and exponential models and solve problems. 9-12 F LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).* CC.9-12.F.LE.3 Construct and compare linear, quadratic, and exponential models and solve problems. 9-12 F LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.* CC.9-12.F.LE.4 Construct and compare linear, quadratic, and exponential models and solve problems. For 9-12 F LE.4 exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.* CC.9-12.F.LE.5 Interpret expressions for functions in terms of the situation they 9-12 F LE.5 model. Interpret the parameters in a linear or exponential function in terms of a context.* CC.9-12.F.TF.1 Extend the domain of trigonometric functions using the unit circle. Understand radian 9-12 F TF.1 measure of an angle as the length of the arc on the unit circle subtended by the angle. CC.9-12.F.TF.2 Extend the domain of trigonometric functions using the unit circle. Explain how the unit circle 9-12 F TF.2 in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. CC.9-12.F.TF.3 (+) Extend the domain of trigonometric functions using the unit circle. Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to 9-12 F TF.3 express the values of sine, cosine, and tangent for π - x, π + x, and 2π - x in terms of their values for x, where x is any real number. CC.9-12.F.TF.4 (+) Extend the domain of trigonometric functions using the unit circle. Use the unit circle to 9-12 F TF.4 explain symmetry (odd and even) and periodicity of trigonometric functions. CC.9-12.F.TF.5 Model periodic phenomena with trigonometric functions. Choose trigonometric functions to 9-12 F TF.5 model periodic phenomena with specified amplitude, frequency, and midline.* CC.9-12.F.TF.6 (+) Model periodic phenomena with trigonometric functions. Understand that restricting a 9-12 F TF.6 trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. CC.9-12.F.TF.7 (+) Model periodic phenomena with trigonometric functions. Use inverse functions to solve 9-12 F TF.7 trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.* CC.9-12.F.TF.8 Prove and apply trigonometric identities. Prove the Pythagorean identity (sin A)^2 + (cos A)^2 9-12 F TF.8 = 1 and use it to find sin A, cos A, or tan A, given sin A, cos A, or tan A, and the quadrant of the angle. CC.9-12.F.TF.9 (+) Prove and apply trigonometric identities. Prove the addition and subtraction formulas for 9-12 F TF.9 sine, cosine, and tangent and use them to solve problems. CC.9-12.G.CO.1 Experiment with transformations in the plane. Know precise definitions of angle, circle, 9-12 G CO.1 perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. CC.9-12.G.CO.2 Experiment with transformations in the plane. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the 9-12 G CO.2 plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). CC.9-12.G.CO.3 Experiment with transformations in the plane. Given a rectangle, parallelogram, trapezoid, or 9-12 G CO.3 regular polygon, describe the rotations and reflections that carry it onto itself. CC.9-12.G.CO.4 Experiment with transformations in the plane. Develop definitions of rotations, reflections, 9-12 G CO.4 and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. CC.9-12.G.CO.5 Experiment with transformations in the plane. Given a geometric figure and a rotation, 9-12 G CO.5 reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. CC.9-12.G.CO.6 Understand congruence in terms of rigid motions. Use geometric descriptions of rigid 9-12 G CO.6 motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. CC.9-12.G.CO.7 Understand congruence in terms of rigid motions. Use the definition of congruence in terms 9-12 G CO.7 of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. CC.9-12.G.CO.8 Understand congruence in terms of rigid motions. Explain how the criteria for triangle 9-12 G CO.8 congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. CC.9-12.G.CO.9 Prove geometric theorems. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are 9-12 G CO.9 congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. CC.9-12.G.CO.10 Prove geometric theorems. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the 9-12 G CO.10 segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. CC.9-12.G.CO.11 Prove geometric theorems. Prove theorems about parallelograms. Theorems include: 9-12 G CO.11 opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. CC.9-12.G.CO.12 Make geometric constructions. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric 9-12 G CO.12 software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. CC.9-12.G.CO.13 Make geometric constructions. Construct an equilateral triangle, a square, and a regular 9-12 G CO.13 hexagon inscribed in a circle. CC.9-12.G.SRT.1 Understand similarity in terms of similarity transformations. Verify experimentally the properties of dilations given by a center and a scale factor: 9-12 G SRT.1 -- a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. -- b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. CC.9-12.G.SRT.2 Understand similarity in terms of similarity transformations. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using 9-12 G SRT.2 similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. CC.9-12.G.SRT.3 Understand similarity in terms of similarity transformations. Use the properties of similarity 9-12 G SRT.3 transformations to establish the AA criterion for two triangles to be similar. CC.9-12.G.SRT.4 Prove theorems involving similarity. Prove theorems about triangles. Theorems include: a 9-12 G SRT.4 line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. CC.9-12.G.SRT.5 Prove theorems involving similarity. Use congruence and similarity criteria for triangles to 9-12 G SRT.5 solve problems and to prove relationships in geometric figures. CC.9-12.G.SRT.6 Define trigonometric ratios and solve problems involving right triangles. Understand that by 9-12 G SRT.6 similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. CC.9-12.G.SRT.7 Define trigonometric ratios and solve problems involving right triangles. Explain and use the 9-12 G SRT.7 relationship between the sine and cosine of complementary angles. CC.9-12.G.SRT.8 Define trigonometric ratios and solve problems involving right triangles. Use trigonometric 9-12 G SRT.8 ratios and the Pythagorean Theorem to solve right triangles in applied problems. CC.9-12.G.SRT.9 (+) Apply trigonometry to general triangles. Derive the formula A = (1/2)ab sin(C) for the 9-12 G SRT.9 area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. CC.9-12.G.SRT.10 (+) Apply trigonometry to general triangles. Prove the Laws of Sines and Cosines and use 9-12 G SRT.10 them to solve problems. CC.9-12.G.SRT.11 (+) Apply trigonometry to general triangles. Understand and apply the Law of Sines and 9-12 G SRT.11 the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). 9-12 G C.1 CC.9-12.G.C.1 Understand and apply theorems about circles. Prove that all circles are similar. CC.9-12.G.C.2 Understand and apply theorems about circles. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed 9-12 G C.2 angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. CC.9-12.G.C.3 Understand and apply theorems about circles. Construct the inscribed and circumscribed 9-12 G C.3 circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. CC.9-12.G.C.4 (+) Understand and apply theorems about circles. Construct a tangent line from a point 9-12 G C.4 outside a given circle to the circle. CC.9-12.G.C.5 Find arc lengths and areas of sectors of circles. Derive using similarity the fact that the length 9-12 G C.5 of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. CC.9-12.G.GPE.1 Translate between the geometric description and the equation for a conic section. Derive 9-12 G GPE.1 the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. CC.9-12.G.GPE.2 Translate between the geometric description and the equation for a conic section. Derive 9-12 G GPE.2 the equation of a parabola given a focus and directrix. CC.9-12.G.GPE.3 (+) Translate between the geometric description and the equation for a conic section. 9-12 G GPE.3 Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. CC.9-12.G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or 9-12 G GPE.4 disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). CC.9-12.G.GPE.5 Use coordinates to prove simple geometric theorems algebraically. Prove the slope criteria 9-12 G GPE.5 for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). CC.9-12.G.GPE.6 Use coordinates to prove simple geometric theorems algebraically. Find the point on a 9-12 G GPE.6 directed line segment between two given points that partitions the segment in a given ratio. CC.9-12.G.GPE.7 Use coordinates to prove simple geometric theorems algebraically. Use coordinates to 9-12 G GPE.7 compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.* CC.9-12.G.GMD.1 Explain volume formulas and use them to solve problems. Give an informal argument for 9-12 G GMD.1 the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. CC.9-12.G.GMD.2 (+) Explain volume formulas and use them to solve problems. Give an informal argument 9-12 G GMD.2 using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures. CC.9-12.G.GMD.3 Explain volume formulas and use them to solve problems. Use volume formulas for 9-12 G GMD.3 cylinders, pyramids, cones, and spheres to solve problems.* CC.9-12.G.GMD.4 Visualize relationships between two-dimensional and three-dimensional objects. Identify 9-12 G GMD.4 the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. CC.9-12.G.MG.1 Apply geometric concepts in modeling situations. Use geometric shapes, their measures, 9-12 G MG.1 and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* CC.9-12.G.MG.2 Apply geometric concepts in modeling situations. Apply concepts of density based on area 9-12 G MG.2 and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).* CC.9-12.G.MG.3 Apply geometric concepts in modeling situations. Apply geometric methods to solve design 9-12 G MG.3 problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).* CC.9-12.S.ID.1 Summarize, represent, and interpret data on a single count or measurement variable. 9-12 S ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).* CC.9-12.S.ID.2 Summarize, represent, and interpret data on a single count or measurement variable. Use 9-12 S ID.2 statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.* CC.9-12.S.ID.3 Summarize, represent, and interpret data on a single count or measurement variable. 9-12 S ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).* CC.9-12.S.ID.4 Summarize, represent, and interpret data on a single count or measurement variable. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population 9-12 S ID.4 percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.* CC.9-12.S.ID.5 Summarize, represent, and interpret data on two categorical and quantitative variables. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in 9-12 S ID.5 the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.* Standards Code: OA=Operations and Algebraic Thinking, NBT=Number and Operations in Base 10, MD=Measurements and Data, G=Geometry, NF=Number and Operations-Fractions, RP=Rations and Proportional Relationships, NS= Number System, EE=Expressions and Equations, SP=Statistics and Probability, CC.9-12.S.ID.6 Summarize, represent, and interpret data on two categorical and quantitative variables. 9-12 S ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.* CC.9-12.S.ID.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the 9-12 S ID.6a data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.* 9-12 S ID.6b CC.9-12.S.ID.6b Informally assess the fit of a function by plotting and analyzing residuals.* 9-12 S ID.6c CC.9-12.S.ID.6c Fit a linear function for a scatter plot that suggests a linear association.* CC.9-12.S.ID.7 Interpret linear models. Interpret the slope (rate of change) and the intercept (constant term) 9-12 S ID.7 of a linear model in the context of the data.* CC.9-12.S.ID.8 Interpret linear models. Compute (using technology) and interpret the correlation coefficient 9-12 S ID.8 of a linear fit.* 9-12 S ID.9 CC.9-12.S.ID.9 Interpret linear models. Distinguish between correlation and causation.* CC.9-12.S.IC.1 Understand and evaluate random processes underlying statistical experiments. Understand 9-12 S IC.1 statistics as a process for making inferences about population parameters based on a random sample from that population.* CC.9-12.S.IC.2 Understand and evaluate random processes underlying statistical experiments. Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For 9-12 S IC.2 example, a model says a spinning coin falls heads up with probability 0. 5. Would a result of 5 tails in a row cause you to question the model?* CC.9-12.S.IC.3 Make inferences and justify conclusions from sample surveys, experiments, and observational 9-12 S IC.3 studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.* CC.9-12.S.IC.4 Make inferences and justify conclusions from sample surveys, experiments, and observational 9-12 S IC.4 studies. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.* CC.9-12.S.IC.5 Make inferences and justify conclusions from sample surveys, experiments, and observational 9-12 S IC.5 studies. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.* CC.9-12.S.IC.6 Make inferences and justify conclusions from sample surveys, experiments, and observational 9-12 S IC.6 studies. Evaluate reports based on data.* CC.9-12.S.CP.2 Understand independence and conditional probability and use them to interpret data. 9-12 S CP.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.* CC.9-12.S.CP.3 Understand independence and conditional probability and use them to interpret data. Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and 9-12 S CP.3 B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.* CC.9-12.S.CP.4 Understand independence and conditional probability and use them to interpret data. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to 9-12 S CP.4 approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.* CC.9-12.S.CP.5 Understand independence and conditional probability and use them to interpret data. Recognize and explain the concepts of conditional probability and independence in everyday language and 9-12 S CP.5 everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.* CC.9-12.S.CP.6 Use the rules of probability to compute probabilities of compound events in a uniform 9-12 S CP.6 probability model. Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.* CC.9-12.S.CP.7 Use the rules of probability to compute probabilities of compound events in a uniform 9-12 S CP.7 probability model. Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.* CC.9-12.S.CP.8 (+) Use the rules of probability to compute probabilities of compound events in a uniform 9-12 S CP.8 probability model. Apply the general Multiplication Rule in a uniform probability model, P(A and B) = [P(A)]x[P(B|A)] =[P(B)]x[P(A|B)], and interpret the answer in terms of the model.* CC.9-12.S.CP.9 (+) Use the rules of probability to compute probabilities of compound events in a uniform 9-12 S CP.9 probability model. Use permutations and combinations to compute probabilities of compound events and solve problems.* CC.9-12.S.MD.1 (+) Calculate expected values and use them to solve problems. Define a random variable for 9-12 S MD.1 a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.* CC.9-12.S.MD.2 (+) Calculate expected values and use them to solve problems. Calculate the expected value 9-12 S MD.2 of a random variable; interpret it as the mean of the probability distribution.* CC.9-12.S.MD.3 (+) Calculate expected values and use them to solve problems. Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be 9-12 S MD.3 calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.* CC.9-12.S.MD.4 (+) Calculate expected values and use them to solve problems. Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; 9-12 S MD.4 find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?* CC.9-12.S.MD.5 (+) Use probability to evaluate outcomes of decisions. Weigh the possible outcomes of a 9-12 S MD.5 decision by assigning probabilities to payoff values and finding expected values.* CC.9-12.S.MD.5a (+) Find the expected payoff for a game of chance. For example, find the expected winnings 9-12 S MD.5a from a state lottery ticket or a game at a fast-food restaurant.* CC.9-12.S.MD.5b (+) Evaluate and compare strategies on the basis of expected values. For example, 9-12 S MD.5b compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.* CC.9-12.S.MD.6 (+) Use probability to evaluate outcomes of decisions. Use probabilities to make fair 9-12 S MD.6 decisions (e.g., drawing by lots, using a random number generator).* CC.9-12.S.MD.7 (+) Use probability to evaluate outcomes of decisions. Analyze decisions and strategies using 9-12 S MD.7 probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).* English Language Arts Kindergarten Standards Grade Core Area # Timeline K R.L 1 K R.L 2 K R.L 3 K R.L 4 K R.L 5 K R.L 6 K R.L 7 K R.L 9 K R.L 10 K R.I 1 K R.I 2 K R.I 3 K R.I 4 K R.I 5 K R.I 6 K R.I 7 K R.I 8 K R.I 9 K R.I 10 K R.F 1 K R.F 1.a K R.F 1.b K R.F 1.c K R.F 1.d K R.F 2 K R.F 2.a K R.F 2.b K R.F 2.c K R.F 2.d K R.F 2.e K R.F 3 K R.F 3.a K R.F 3.b K R.F 3.c K R.F 3.d K R.F 4 K W 1 K W 2 K W 3 K W 5 K W 6 K W 7 K W 8 K SL 1 K SL 1.a K SL 1.b K SL 2 K SL 3 K SL 4 K SL 5 K SL 6 K L 1 K L 1.a K L 1.b K L 1.c K L 1.d K L 1.e K L 1.f K L 2 K L 2.a K L 2.b K L 2.c K L 2.d K L 4 K L 4.a K L 4.b K L 5 K L 5.a K L 5.b K L 5.c K L 5.d K L 6 Mathematics Kindergarten Standards Grade Core Area # Timeline K CC 1 K CC 2 K CC 3 K CC 4 K CC 4a K CC 4b K CC 4c K CC 5 K CC 6 K CC 7 K OA 1 K OA 2 K OA 3 K OA 4 K OA 5 K NBT 1 K MD 1 K MD 2 K MD 3 K G 1 K G 2 K G 3 K G 4 K G 5 K G 6 English/Language Arts 1st Grade Standards Grade Core Area # Timeline 1 R.L 1 1 R.L 2 1 R.L 3 1 R.L 4 1 R.L 5 1 R.L 6 1 R.L 7 1 R.L 9 1 R.L 10 1 R.I 1 1 R.I 2 1 R.I 3 1 R.I 4 1 R.I 5 1 R.I 6 1 R.I 7 1 R.I 8 1 R.I 9 1 R.I 10 1 R.F 1 1 R.F 1.a 1 R.F 2 1 R.F 2.a 1 R.F 2.b 1 R.F 2.c 1 R.F 2.d 1 R.F 3 1 R.F 3.a 1 R.F 3.b 1 R.F 3.c 1 R.F 3.d 1 R.F 3.e 1 R.F 3.f 1 R.F 3.g 1 R.F 4 1 R.F 4.a 1 R.F 4.b 1 R.F 4.c 1 W 1 1 W 2 1 W 3 1 W 5 1 W 6 1 W 7 1 W 8 1 SL 1 1 SL 1.a 1 SL 1.b 1 SL 1.c 1 SL 2 1 SL 3 1 SL 4 1 SL 5 1 SL 6 1 L 1 1 L 1.a 1 L 1.b 1 L 1.c 1 L 1.d 1 L 1.e 1 L 1.f 1 L 1.g 1 L 1.h 1 L 1.i 1 L 1.j 1 L 2 1 L 2.a 1 L 2.b 1 L 2.c 1 L 2.d 1 L 2.e 1 L 4 1 L 4.a 1 L 4.b 1 L 4.c 1 L 5 1 L 5.a 1 L 5.b 1 L 5.c 1 L 5.d 1 L 6 Mathematics 1st Grade Grade Core Area # Timeline 1 OA 1 1 OA 2 1 OA 3 1 OA 4 1 OA 5 1 OA 6 1 OA 7 1 OA 8 1 NBT 1 1 NBT 2 1 NBT 3 1 NBT 4 1 NBT 5 1 NBT 6 1 MD 1 1 MD 2 1 MD 3 1 MD 4 1 G 1 1 G 2 1 G 3 English/Language Arts 2nd Grade Standards Grade Core Area # Timeline 2 R.L 1 2 R.L 2 2 R.L 3 2 R.L 4 2 R.L 5 2 R.L 6 2 R.L 7 2 R.L 9 2 R.L 10 2 R.I 1 2 R.I 2 2 R.I 3 2 R.I 4 2 R.I 5 2 R.I 6 2 R.I 7 2 R.I 8 2 R.I 9 2 R.I 10 2 R.F 3 2 R.F 3.a 2 R.F 3.b 2 R.F 3.c 2 R.F 3.d 2 R.F 3.e 2 R.F 3.f 2 R.F 4 2 R.F 4.a 2 R.F 4.b 2 R.F 4.c 2 W 1 2 W 2 2 W 3 2 W 5 2 W 6 2 W 7 2 W 8 2 SL 1 2 SL 1.a 2 SL 1.b 2 SL 1.c 2 SL 2 2 SL 3 2 SL 4 2 SL 5 2 SL 6 2 L 1 2 L 1.a 2 L 1.b 2 L 1.c 2 L 1.d 2 L 1.e 2 L 1.f 2 L 2 2 L 2.a 2 L 2.b 2 L 2.c 2 L 2.d 2 L 2.e 2 L 3 2 L 3.a 2 L 4 2 L 4.a 2 L 4.b 2 L 4.c 2 L 4.d 2 L 4.e 2 L 5 2 L 5.a 2 L 5.b 2 L 6 Mathematics 2nd Grade Standards Grade Core Area # Timeline 2 OA 1 2 OA 2 2 OA 3 2 OA 4 2 NBT 1 2 NBT 2 2 NBT 3 2 NBT 4 2 NBT 5 2 NBT 6 2 NBT 7 2 NBT 8 2 NBT 9 2 MD 1 2 MD 2 2 MD 3 2 MD 4 2 MD 5 2 MD 6 2 MD 7 2 MD 8 2 MD 9 2 MD 10 2 G 1 2 G 2 2 G 3 English/Language Arts 3rd Grade Standards Grade Core Area # Timeline 3 L 1 3 L 1.a 3 L 1.b 3 R.L 1 3 R.L 2 3 R.L 3 3 R.L 4 3 R.L 5 3 R.L 6 3 R.L 7 3 R.L 9 3 R.L 10 3 R.I 1 3 R.I 2 3 R.I 3 3 R.I 4 3 R.I 5 3 R.I 6 3 R.I 7 3 R.I 8 3 R.I 9 3 R.I 10 3 R.F 3 3 R.F 3.a 3 R.F 3.b 3 R.F 3.c 3 R.F 3.d 3 R.F 4 3 R.F 4.a 3 R.F 4.b 3 R.F 4.c 3 W 1 3 W 1.a 3 W 1.b 3 W 1.c 3 W 1.d 3 W 2 3 W 2.a 3 W 2.b 3 W 2.c 3 W 2.d 3 W 3 3 W 3.a 3 W 3.b 3 W 3.c 3 W 3.d 3 W 4 3 W 5 3 W 6 3 W 7 3 W 8 3 W 10 3 SL 1 3 SL 1.a 3 SL 1.b 3 SL 1.c 3 SL 1.d 3 SL 2 3 SL 3 3 SL 4 3 SL 5 3 SL 6 3 SL 6 3 L 1.a 3 L 1.b 3 L 1.c 3 L 1.d 3 L 1.e 3 L 1.f 3 L 1.g 3 L 1.h 3 L 1.i 3 L 2 3 L 2.a 3 L 2.b 3 L 2.c 3 L 2.d 3 L 2.e 3 L 2.f 3 L 2.g 3 L 3 3 L 3.a 3 L 3.b 3 L 4 3 L 4.a 3 L 4.b 3 L 4.c 3 L 4.d 3 L 5 3 L 5.a 3 L 5.b 3 L 5.c 3 L 6 Mathematics 3rd Grade Standards Grade Core Area # Timeline 3 OA 1 3 OA 2 3 OA 3 3 OA 4 3 OA 5 3 OA 6 3 OA 7 3 OA 8 3 OA 9 3 NBT 1 3 NBT 2 3 NBT 3 3 NF 1 3 NF 2 3 NF 2a 3 NF 2b 3 NF 3 3 NF 3a 3 NF 3b 3 NF 3c 3 NF 3d 3 MD 1 3 MD 2 3 MD 3 3 MD 4 3 MD 5 3 MD 6 3 MD 7 3 MD 7a 3 MD 7b 3 MD 7c 3 MD 7d 3 MD 8 3 G 1 3 G 2 English/Language Arts 4th Grade Standards Grade Core Area # Timeline 4 R.L 1 4 R.L 2 4 R.L 3 4 R.L 4 4 R.L 5 4 R.L 6 4 R.L 7 4 R.L 9 4 R.L 10 4 R.I 1 4 R.I 2 4 R.I 3 4 R.I 4 4 R.I 5 4 R.I 6 4 R.I 7 4 R.I 8 4 R.I 9 4 R.I 10 4 R.F 3 4 R.F 3.a 4 R.F 4 4 R.F 4.a 4 R.F 4.b 4 R.F 4.c 4 W 1 4 W 1.a 4 W 1.b 4 W 1.c 4 W 1.d 4 W 2 4 W 2.a 4 W 2.b 4 W 2.c 4 W 2.d 4 W 2.e 4 W 3 4 W 3.a 4 W 3.b 4 W 3.c 4 W 3.d 4 W 3.e 4 W 4 4 W 5 4 W 6 4 W 7 4 W 8 4 W 9 4 W 9.a 4 W 9.b 4 W 10 4 SL 1 4 SL 1.a 4 SL 1.b 4 SL 1.c 4 SL 1.d 4 SL 2 4 SL 3 4 SL 4 4 SL 5 4 SL 6 4 L 1 4 L 1.a 4 L 1.b 4 L 1.c 4 L 1.d 4 L 1.e 4 L 1.f 4 L 1.g 4 L 2 4 L 2.a 4 L 2.b 4 L 2.c 4 L 2.d 4 L 3 4 L 3.a 4 L 3.b 4 L 3.c 4 L 4 4 L 4.a 4 L 4.b 4 L 4.c 4 L 5 4 L 5.a 4 L 5.b 4 L 5.c 4 L 6 Mathematics 4th Grade Standards Grade Core Area # Timeline 4 OA 1 4 OA 2 4 OA 3 4 OA 4 4 OA 5 4 NBT 1 4 NBT 2 4 NBT 3 4 NBT 4 4 NBT 5 4 NBT 6 4 NF 1 4 NF 2 4 NF 3 4 NF 3a 4 NF 3b 4 NF 3c 4 NF 3d 4 NF 4 4 NF 4a 4 NF 4b 4 NF 4c 4 NF 5 4 NF 6 4 NF 7 4 MD 1 4 MD 2 4 MD 3 4 MD 4 4 MD 5 4 MD 6 4 MD 7 4 G 1 4 G 2 4 G 3 English/Language Arts 5th Grade Standards Grade Core Area # Timeline 5 R.L 1 5 R.L 2 5 R.L 3 5 R.L 4 5 R.L 5 5 R.L 6 5 R.L 7 5 R.L 9 5 R.L 10 5 R.I 1 5 R.I 2 5 R.I 3 5 R.I 4 5 R.I 5 5 R.I 6 5 R.I 7 5 R.I 8 5 R.I 9 5 R.I 10 5 R.F 3 5 R.F 3.a 5 R.F 4 5 R.F 4.a 5 R.F 4.b 5 R.F 4.c 5 W 1 5 W 1.a 5 W 1.b 5 W 1.c 5 W 1.d 5 W 2 5 W 2.a 5 W 2.b 5 W 2.c 5 W 2.d 5 W 2.e 5 W 3 5 W 3.a 5 W 3.b 5 W 3.c 5 W 3.d 5 W 3.e 5 W 4 5 W 5 5 W 6 5 W 7 5 W 8 5 W 9 5 W 9.a 5 W 9.b 5 W 10 5 SL 1 5 SL 1.a 5 SL 1.b 5 SL 1.c 5 SL 1.d 5 SL 2 5 SL 3 5 SL 4 5 SL 5 5 SL 6 5 L 1 5 L 1.a 5 L 1.b 5 L 1.c 5 L 1.d 5 L 1.e 5 L 2 5 L 2.a 5 L 2.b 5 L 2.c 5 L 2.d 5 L 2.e 5 L 3 5 L 3.a 5 L 3.b 5 L 4 5 L 4.a 5 L 4.b 5 L 4.c 5 L 5 5 L 5.a 5 L 5.b 5 L 5.c 5 L 6 Mathematics 5th Grade Standards Grade Core Area # Timeline 5 OA 1 5 OA 2 5 OA 3 5 NBT 1 5 NBT 2 5 NBT 3 5 NBT 3a 5 NBT 3b 5 NBT 4 5 NBT 5 5 NBT 6 5 NBT 7 5 NF 1 5 NF 2 5 NF 3 5 NF 4 5 NF 4a 5 NF 4b 5 NF 5 5 NF 6 5 NF 7 5 NF 7a 5 NF 7b 5 NF 7c 5 MD 1 5 MD 2 5 MD 3 5 MD 4 5 MD 5 5 MD 5a 5 MD 5b 5 MD 5c 5 G 1 5 G 2 5 G 3 5 G 4 English/Language Arts 6th Grade Standards Grade Core Area # Timeline 6 R.L 1 6 R.L 2 6 R.L 3 6 R.L 4 6 R.L 5 6 R.L 6 6 R.L 7 6 R.L 9 6 R.L 10 6 R.I 1 6 R.I 2 6 R.I 3 6 R.I 4 6 R.I 5 6 R.I 6 6 R.I 7 6 R.I 8 6 R.I 9 6 R.I 10 6 W 1 6 W 1.a 6 W 1.b 6 W 1.c 6 W 1.d 6 W 1.e 6 W 2 6 W 2.a 6 W 2.b 6 W 2.c 6 W 2.d 6 W 2.e 6 W 2.f 6 W 3 6 W 3.a 6 W 3.b 6 W 3.c 6 W 3.d 6 W 3.e 6 W 4 6 W 5 6 W 6 6 W 7 6 W 8 6 W 9 6 W 9.a 6 W 9.b 6 W 10 6 SL 1 6 SL 1.a 6 SL 1.b 6 SL 1.c 6 SL 1.d 6 SL 2 6 SL 3 6 SL 4 6 SL 5 6 SL 6 6 L 1 6 L 1.a 6 L 1.b 6 L 1.c 6 L 1.d 6 L 1.e 6 L 2 6 L 2.a 6 L 2.b 6 L 3 6 L 3.a 6 L 3.b 6 L 4 6 L 4.a 6 L 4.b 6 L 4.c 6 L 4.d 6 L 5 6 L 5.a 6 L 5.b 6 L 5.c 6 L 6 Mathematics 6th Grade Standards Grade Core Area # Timeline 6 RP 1 6 RP 2 6 RP 3 6 RP 3a 6 RP 3b 6 RP 3c 6 RP 3d 6 NS 1 6 NS 2 6 NS 3 6 NS 4 6 NS 5 6 NS 6 6 NS 6a 6 NS 6b 6 NS 6c 6 NS 7 6 NS 7a 6 NS 7b 6 NS 7c 6 NS 7d 6 NS 8 6 EE 1 6 EE 2 6 EE 2a 6 EE 2b 6 EE 2c 6 EE 3 6 EE 4 6 EE 5 6 EE 6 6 EE 7 6 EE 8 6 EE 9 6 G 1 6 G 2 6 G 3 6 G 4 6 SP 1 6 SP 2 6 SP 3 6 SP 4 6 SP 5 English/Language Arts 7th Grade Standards Grade Core Area # Timeline 7 R.L 1 7 R.L 2 7 R.L 3 7 R.L 4 7 R.L 5 7 R.L 6 7 R.L 7 7 R.L 9 7 R.L 10 7 R.I 1 7 R.I 2 7 R.I 3 7 R.I 4 7 R.I 5 7 R.I 6 7 R.I 7 7 R.I 8 7 R.I 9 7 R.I 10 7 W 1 7 W 1.a 7 W 1.b 7 W 1.c 7 W 1.d 7 W 1.e 7 W 2 7 W 2.a 7 W 2.b 7 W 2.c 7 W 2.d 7 W 2.e 7 W 2.f 7 W 3 7 W 3.a 7 W 3.b 7 W 3.c 7 W 3.d 7 W 3.e 7 W 4 7 W 5 7 W 6 7 W 7 7 W 8 7 W 9 7 W 9.a 7 W 9.b 7 W 10 7 SL 1 7 SL 1.a 7 SL 1.b 7 SL 1.c 7 SL 1.d 7 SL 2 7 SL 3 7 SL 4 7 SL 5 7 SL 6 7 L 1 7 L 1.a 7 L 1.b 7 L 1.c 7 L 2 7 L 2.a 7 L 2.b 7 L 3 7 L 3.a 7 L 4 7 L 4.a 7 L 4.b 7 L 4.c 7 L 4.d 7 L 5 7 L 5.a 7 L 5.b 7 L 5.c 7 L 6 Mathematics 7th Grade Standards Grade Core Area # Timeline 7 RP 1 7 RP 2 7 RP 2a 7 RP 2b 7 RP 2c 7 RP 2d 7 RP 3 7 NS 1 7 NS 1a 7 NS 1b 7 NS 1c 7 NS 1d 7 NS 2 7 NS 2a 7 NS 2b 7 NS 2c 7 NS 2d 7 NS 3 7 EE 1 7 EE 2 7 EE 3 7 EE 4 7 EE 4a 7 EE 4b 7 G 1 7 G 2 7 G 3 7 G 4 7 G 5 7 G 6 7 SP 1 7 SP 2 7 SP 3 7 SP 4 7 SP 5 7 SP 6 7 SP 7 7 SP 7a 7 SP 7b 7 SP 8 7 SP 8a 7 SP 8b 7 SP 8c English/Language Arts 8th Grade Standards Grade Core Area # Timeline 8 R.L 1 8 R.L 2 8 R.L 3 8 R.L 4 8 R.L 5 8 R.L 6 8 R.L 7 8 R.L 9 8 R.L 10 8 R.I 1 8 R.I 2 8 R.I 3 8 R.I 4 8 R.I 5 8 R.I 6 8 R.I 7 8 R.I 8 8 R.I 9 8 R.I 10 8 W 1 8 W 1.a 8 W 1.b 8 W 1.c 8 W 1.d 8 W 1.e 8 W 2 8 W 2.a 8 W 2.b 8 W 2.c 8 W 2.d 8 W 2.e 8 W 2.f 8 W 3 8 W 3.a 8 W 3.b 8 W 3.c 8 W 3.d 8 W 3.e 8 W 4 8 W 5 8 W 6 8 W 7 8 W 8 8 W 9 8 W 9.a 8 W 9.b 8 W 10 8 SL 1 8 SL 1.a 8 SL 1.b 8 SL 1.c 8 SL 1.d 8 SL 2 8 SL 3 8 SL 4 8 SL 5 8 SL 6 8 L 1 8 L 1.a 8 L 1.b 8 L 1.c 8 L 1.d 8 L 2 8 L 2.a 8 L 2.b 8 L 2.c 8 L 3 8 L 3.a 8 L 4 8 L 4.a 8 L 4.b 8 L 4.c 8 L 4.d 8 L 5 8 L 5.a 8 L 5.b 8 L 5.c 8 L 6 Mathematics 8th Grade Standards Grade Core Area # Timeline 8 NS 1 8 NS 2 8 EE 1 8 EE 2 8 EE 3 8 EE 4 8 EE 5 8 EE 6 8 EE 7 8 EE 7a 8 EE 7b 8 EE 8 8 EE 8a 8 EE 8b 8 EE 8c 8 F 1 8 F 2 8 F 3 8 F 4 8 F 5 8 G 1 8 G 2 8 G 3 8 G 4 8 G 5 8 G 6 8 G 7 8 G 8 8 G 9 8 SP 1 8 SP 2 8 SP 3 8 SP 4 English/Language Arts 9 - 10th Grade Standards Grade Core Area # Timeline 9-10 R.L 1 9-10 R.L 2 9-10 R.L 3 9-10 R.L 4 9-10 R.L 5 9-10 R.L 6 9-10 R.L 7 9-10 R.L 9 9-10 R.L 10 9-10 R.I 1 9-10 R.I 2 9-10 R.I 3 9-10 R.I 4 9-10 R.I 5 9-10 R.I 6 9-10 R.I 7 9-10 R.I 8 9-10 R.I 9 9-10 R.I 10 9-10 W 1 9-10 W 1.a 9-10 W 1.b 9-10 W 1.c 9-10 W 1.d 9-10 W 1.e 9-10 W 2 9-10 W 2.a 9-10 W 2.b 9-10 W 2.c 9-10 W 2.d 9-10 W 2.e 9-10 W 2.f 9-10 W 3 9-10 W 3.a 9-10 W 3.b 9-10 W 3.c 9-10 W 3.d 9-10 W 3.e 9-10 W 4 9-10 W 5 9-10 W 6 9-10 W 7 9-10 W 8 9-10 W 9 9-10 W 9.a 9-10 W 9.b 9-10 W 10 9-10 SL 1 9-10 SL 1.a 9-10 SL 1.b 9-10 SL 1.c 9-10 SL 1.d 9-10 SL 2 9-10 SL 3 9-10 SL 4 9-10 SL 5 9-10 SL 6 9-10 L 1 9-10 L 1.a 9-10 L 1.b 9-10 L 2 9-10 L 2.a 9-10 L 2.b 9-10 L 2.c 9-10 L 3 9-10 L 3.a 9-10 L 4 9-10 L 4.a 9-10 L 4.b 9-10 L 4.c 9-10 L 4.d 9-10 L 5 9-10 L 5.a 9-10 L 5.b 9-10 L 6 9-10 R.H 1 9-10 R.H 2 9-10 R.H 3 9-10 R.H 4 9-10 R.H 5 9-10 R.H 6 9-10 R.H 7 9-10 R.H 8 9-10 R.H 9 9-10 R.H 10 9-10 R.ST 1 9-10 R.ST 2 9-10 R.ST 3 9-10 R.ST 4 9-10 R.ST 5 9-10 R.ST 6 9-10 R.ST 7 9-10 R.ST 8 9-10 R.ST 9 9-10 R.ST 10 9-10 W.HST 1 9-10 W.HST 1.a 9-10 W.HST 1.b 9-10 W.HST 1.c 9-10 W.HST 1.d 9-10 W.HST 1.e 9-10 W.HST 2 9-10 W.HST 2.a 9-10 W.HST 2.b 9-10 W.HST 2.c 9-10 W.HST 2.d 9-10 W.HST 2.e 9-10 W.HST 2.f 9-10 W.HST 4 9-10 W.HST 5 9-10 W.HST 6 9-10 W.HST 7 9-10 W.HST 8 9-10 W.HST 9 9-10 W.HST 10 Mathematics 9 - 12th Grade Standards Grade Core Area # Timeline 9-12 N RN.1 9-12 N RN.2 9-12 N RN.3 9-12 N Q.1 9-12 N Q.2 9-12 N Q.3 9-12 N CN.1 9-12 N CN.2 9-12 N CN.3 9-12 N CN.4 9-12 N CN.5 9-12 N CN.6 9-12 N CN.7 9-12 N CN.8 9-12 N CN.9 9-12 N VM.1 9-12 N VM.2 9-12 N VM.3 9-12 N VM.4 9-12 N VM.4a 9-12 N VM.4b 9-12 N VM.4c 9-12 N VM.5 9-12 N VM.5a 9-12 N VM.5b 9-12 N VM.6 9-12 N VM.7 9-12 N VM.8 9-12 N VM.9 9-12 N VM.10 9-12 N VM.11 9-12 N VM.12 9-12 A SSE.1 9-12 A SSE.1a 9-12 A SSE.1b 9-12 A SSE.2 9-12 A SSE.3 9-12 A SSE.3a 9-12 A SSE.3b 9-12 A SSE.3c 9-12 A SSE.4 9-12 A APR.1 9-12 A APR.2 9-12 A APR.3 9-12 A APR.4 9-12 A APR.5 9-12 A APR.6 9-12 A APR.7 9-12 A CED.1 9-12 A CED.2 9-12 A CED.3 9-12 A CED.4 9-12 A REI.1 9-12 A REI.2 9-12 A REI.3 9-12 A REI.4 9-12 A REI.4a 9-12 A REI.4b 9-12 A REI.5 9-12 A REI.6 9-12 A REI.7 9-12 A REI.8 9-12 A REI.9 9-12 A REI.10 9-12 A REI.11 9-12 A REI.12 9-12 F IF.1 9-12 F IF.2 9-12 F IF.3 9-12 F IF.4 9-12 F IF.5 9-12 F IF.6 9-12 F IF.7 9-12 F IF.7a 9-12 F IF.7b 9-12 F IF.7c 9-12 F IF.7d 9-12 F IF.7e 9-12 F IF.8 9-12 F IF.8a 9-12 F IF.8b 9-12 F IF.9 9-12 F BF.1 9-12 F BF.1a 9-12 F BF.1b 9-12 F BF.1c 9-12 F BF.2 9-12 F BF.3 9-12 F BF.4 9-12 F BF.4a 9-12 F BF.4b 9-12 F BF.4c 9-12 F BF.4d 9-12 F BF.5 9-12 F LE.1 9-12 F LE.1a 9-12 F LE.1b 9-12 F LE.1c 9-12 F LE.2 9-12 F LE.3 9-12 F LE.4 9-12 F LE.5 9-12 F TF.1 9-12 F TF.2 9-12 F TF.3 9-12 F TF.4 9-12 F TF.5 9-12 F TF.6 9-12 F TF.7 9-12 F TF.8 9-12 F TF.9 9-12 G CO.1 9-12 G CO.2 9-12 G CO.3 9-12 G CO.4 9-12 G CO.5 9-12 G CO.6 9-12 G CO.7 9-12 G CO.8 9-12 G CO.9 9-12 G CO.10 9-12 G CO.11 9-12 G CO.12 9-12 G CO.13 9-12 G SRT.1 9-12 G SRT.2 9-12 G SRT.3 9-12 G SRT.4 9-12 G SRT.5 9-12 G SRT.6 9-12 G SRT.7 9-12 G SRT.8 9-12 G SRT.9 9-12 G SRT.10 9-12 G SRT.11 9-12 G C.1 9-12 G C.2 9-12 G C.3 9-12 G C.4 9-12 G C.5 9-12 G GPE.1 9-12 G GPE.2 9-12 G GPE.3 9-12 G GPE.4 9-12 G GPE.5 9-12 G GPE.6 9-12 G GPE.7 9-12 G GMD.1 9-12 G GMD.2 9-12 G GMD.3 9-12 G GMD.4 9-12 G MG.1 9-12 G MG.2 9-12 G MG.3 9-12 S ID.1 9-12 S ID.2 9-12 S ID.3 9-12 S ID.4 9-12 S ID.5 Standards Code: OA=Operations and Algebraic Thinking, NBT=Number and Operations in Base 10, MD=Measurements a 9-12 S ID.6 9-12 S ID.6a 9-12 S ID.6b 9-12 S ID.6c 9-12 S ID.7 9-12 S ID.8 9-12 S ID.9 9-12 S IC.1 9-12 S IC.2 9-12 S IC.3 9-12 S IC.4 9-12 S IC.5 9-12 S IC.6 9-12 S CP.2 9-12 S CP.3 9-12 S CP.4 9-12 S CP.5 9-12 S CP.6 9-12 S CP.7 9-12 S CP.8 9-12 S CP.9 9-12 S MD.1 9-12 S MD.2 9-12 S MD.3 9-12 S MD.4 9-12 S MD.5 9-12 S MD.5a 9-12 S MD.5b 9-12 S MD.6 9-12 S MD.7 English/Language Arts 11 -12th Grade Standards Grade Core Area # Timeline 11-12 R.L 1 11-12 R.L 2 11-12 R.L 3 11-12 R.L 4 11-12 R.L 5 11-12 R.L 6 11-12 R.L 7 11-12 R.L 9 11-12 R.L 10 11-12 R.I 1 11-12 R.I 2 11-12 R.I 3 11-12 R.I 4 11-12 R.I 5 11-12 R.I 6 11-12 R.I 7 11-12 R.I 8 11-12 R.I 9 11-12 R.I 10 11-12 W 1 11-12 W 1.a 11-12 W 1.b 11-12 W 1.c 11-12 W 1.d 11-12 W 1.e 11-12 W 2 11-12 W 2.a 11-12 W 2.b 11-12 W 2.c 11-12 W 2.d 11-12 W 2.e 11-12 W 2.f 11-12 W 3 11-12 W 3.a 11-12 W 3.b 11-12 W 3.c 11-12 W 3.d 11-12 W 3.e 11-12 W 4 11-12 W 5 11-12 W 6 11-12 W 7 11-12 W 8 11-12 W 9 11-12 W 9.a 11-12 W 9.b 11-12 W 10 11-12 SL 1 11-12 SL 1.a 11-12 SL 1.b 11-12 SL 1.c 11-12 SL 1.d 11-12 SL 2 11-12 SL 3 11-12 SL 4 11-12 SL 5 11-12 SL 6 11-12 L 1 11-12 L 1.a 11-12 L 1.b 11-12 L 2 11-12 L 2.a 11-12 L 2.b 11-12 L 3 11-12 L 3.a 11-12 L 4 11-12 L 4.a 11-12 L 4.b 11-12 L 4.c 11-12 L 4.d 11-12 L 5 11-12 L 5.a 11-12 L 5.b 11-12 L 6 11-12 R.H 1 11-12 R.H 2 11-12 R.H 3 11-12 R.H 4 11-12 R.H 5 11-12 R.H 6 11-12 R.H 7 11-12 R.H 8 11-12 R.H 9 11-12 R.H 10 11-12 R.ST 1 11-12 R.ST 2 11-12 R.ST 3 11-12 R.ST 4 11-12 R.ST 5 11-12 R.ST 6 11-12 R.ST 7 11-12 R.ST 8 11-12 R.ST 9 11-12 R.ST 10 11-12 W.HST 1 11-12 W.HST 1.a 11-12 W.HST 1.b 11-12 W.HST 1.c 11-12 W.HST 1.d 11-12 W.HST 1.e 11-12 W.HST 2 11-12 W.HST 2.a 11-12 W.HST 2.b 11-12 W.HST 2.c 11-12 W.HST 2.d 11-12 W.HST 2.e 11-12 W.HST 4 11-12 W.HST 5 11-12 W.HST 6 11-12 W.HST 7 11-12 W.HST 8 11-12 W.HST 9 11-12 W.HST 10 Mathematics 9 - 12th Grade Standards Grade Core Area # Timeline 9-12 N RN.1 9-12 N RN.2 9-12 N RN.3 9-12 N Q.1 9-12 N Q.2 9-12 N Q.3 9-12 N CN.1 9-12 N CN.2 9-12 N CN.3 9-12 N CN.4 9-12 N CN.5 9-12 N CN.6 9-12 N CN.7 9-12 N CN.8 9-12 N CN.9 9-12 N VM.1 9-12 N VM.2 9-12 N VM.3 9-12 N VM.4 9-12 N VM.4a 9-12 N VM.4b 9-12 N VM.4c 9-12 N VM.5 9-12 N VM.5a 9-12 N VM.5b 9-12 N VM.6 9-12 N VM.7 9-12 N VM.8 9-12 N VM.9 9-12 N VM.10 9-12 N VM.11 9-12 N VM.12 9-12 A SSE.1 9-12 A SSE.1a 9-12 A SSE.1b 9-12 A SSE.2 9-12 A SSE.3 9-12 A SSE.3a 9-12 A SSE.3b 9-12 A SSE.3c 9-12 A SSE.4 9-12 A APR.1 9-12 A APR.2 9-12 A APR.3 9-12 A APR.4 9-12 A APR.5 9-12 A APR.6 9-12 A APR.7 9-12 A CED.1 9-12 A CED.2 9-12 A CED.3 9-12 A CED.4 9-12 A REI.1 9-12 A REI.2 9-12 A REI.3 9-12 A REI.4 9-12 A REI.4a 9-12 A REI.4b 9-12 A REI.5 9-12 A REI.6 9-12 A REI.7 9-12 A REI.8 9-12 A REI.9 9-12 A REI.10 9-12 A REI.11 9-12 A REI.12 9-12 F IF.1 9-12 F IF.2 9-12 F IF.3 9-12 F IF.4 9-12 F IF.5 9-12 F IF.6 9-12 F IF.7 9-12 F IF.7a 9-12 F IF.7b 9-12 F IF.7c 9-12 F IF.7d 9-12 F IF.7e 9-12 F IF.8 9-12 F IF.8a 9-12 F IF.8b 9-12 F IF.9 9-12 F BF.1 9-12 F BF.1a 9-12 F BF.1b 9-12 F BF.1c 9-12 F BF.2 9-12 F BF.3 9-12 F BF.4 9-12 F BF.4a 9-12 F BF.4b 9-12 F BF.4c 9-12 F BF.4d 9-12 F BF.5 9-12 F LE.1 9-12 F LE.1a 9-12 F LE.1b 9-12 F LE.1c 9-12 F LE.2 9-12 F LE.3 9-12 F LE.4 9-12 F LE.5 9-12 F TF.1 9-12 F TF.2 9-12 F TF.3 9-12 F TF.4 9-12 F TF.5 9-12 F TF.6 9-12 F TF.7 9-12 F TF.8 9-12 F TF.9 9-12 G CO.1 9-12 G CO.2 9-12 G CO.3 9-12 G CO.4 9-12 G CO.5 9-12 G CO.6 9-12 G CO.7 9-12 G CO.8 9-12 G CO.9 9-12 G CO.10 9-12 G CO.11 9-12 G CO.12 9-12 G CO.13 9-12 G SRT.1 9-12 G SRT.2 9-12 G SRT.3 9-12 G SRT.4 9-12 G SRT.5 9-12 G SRT.6 9-12 G SRT.7 9-12 G SRT.8 9-12 G SRT.9 9-12 G SRT.10 9-12 G SRT.11 9-12 G C.1 9-12 G C.2 9-12 G C.3 9-12 G C.4 9-12 G C.5 9-12 G GPE.1 9-12 G GPE.2 9-12 G GPE.3 9-12 G GPE.4 9-12 G GPE.5 9-12 G GPE.6 9-12 G GPE.7 9-12 G GMD.1 9-12 G GMD.2 9-12 G GMD.3 9-12 G GMD.4 9-12 G MG.1 9-12 G MG.2 9-12 G MG.3 9-12 S ID.1 9-12 S ID.2 9-12 S ID.3 9-12 S ID.4 9-12 S ID.5 Standards Code: OA=Operations and Algebraic Thinking, NBT=Number and Operations in Base 10, MD=Measurements a 9-12 S ID.6 9-12 S ID.6a 9-12 S ID.6b 9-12 S ID.6c 9-12 S ID.7 9-12 S ID.8 9-12 S ID.9 9-12 S IC.1 9-12 S IC.2 9-12 S IC.3 9-12 S IC.4 9-12 S IC.5 9-12 S IC.6 9-12 S CP.2 9-12 S CP.3 9-12 S CP.4 9-12 S CP.5 9-12 S CP.6 9-12 S CP.7 9-12 S CP.8 9-12 S CP.9 9-12 S MD.1 9-12 S MD.2 9-12 S MD.3 9-12 S MD.4 9-12 S MD.5 9-12 S MD.5a 9-12 S MD.5b 9-12 S MD.6 9-12 S MD.7 English Language Arts Kindergarten Standards Standard CC.K.R.L.1 Key Ideas and Details: With prompting and support, ask and answer questions about key details in a text. CC.K.R.L.2 Key Ideas and Details: With prompting and support, retell familiar stories, including key details. CC.K.R.L.3 Key Ideas and Details: With prompting and support, identify characters, settings, and major events in a story. CC.K.R.L.4 Craft and Structure: Ask and answer questions about unknown words in a text. CC.K.R.L.5 Craft and Structure: Recognize common types of texts (e.g., storybooks, poems). CC.K.R.L.6 Craft and Structure: With prompting and support, name the author and illustrator of a story and define the role of each in telling the story. CC.K.R.L.7 Integration of Knowledge and Ideas: With prompting and support, describe the relationship between illustrations and the story in which they appear (e.g., what moment in a story an illustration depicts). CC.K.R.L.9 Integration of Knowledge and Ideas: With prompting and support, compare and contrast the adventures and experiences of characters in familiar stories. CC.K.R.L.10 Range of Reading and Level of Text Complexity: Actively engage in group reading activities with purpose and understanding. CC.K.R.I.1 Key Ideas and Details: With prompting and support, ask and answer questions about key details in a text. CC.K.R.I.2 Key Ideas and Details: With prompting and support, identify the main topic and retell key details of a text. CC.K.R.I.3 Key Ideas and Details: With prompting and support, describe the connection between two individuals, events, ideas, or pieces of information in a text. CC.K.R.I.4 Craft and Structure: With prompting and support, ask and answer questions about unknown words in a text. CC.K.R.I.5 Craft and Structure: Identify the front cover, back cover, and title page of a book. CC.K.R.I.6 Craft and Structure: Name the author and illustrator of a text and define the role of each in presenting the ideas or information in a text. CC.K.R.I.7 Integration of Knowledge and Ideas: With prompting and support, describe the relationship between illustrations and the text in which they appear (e.g., what person, place, thing, or idea in the text an illustration depicts). CC.K.R.I.8 Integration of Knowledge and Ideas: With prompting and support, identify the reasons an author gives to support points in a text. CC.K.R.I.9 Integration of Knowledge and Ideas: With prompting and support, identify basic similarities in and differences between two texts on the same topic (e.g., in illustrations, descriptions, or procedures). CC.K.R.I.10 Range of Reading and Level of Text Complexity: Actively engage in group reading activities with purpose and understanding. CC.K.R.F.1 Print Concepts: Demonstrate understanding of the organization and basic features of print. CC.K.R.F.1.a Print Concepts: Follow words from left to right, top to bottom, and page by page. CC.K.R.F.1.b Print Concepts: Recognize that spoken words are represented in written language by specific sequences of letters. CC.K.R.F.1.c Print Concepts: Understand that words are separated by spaces in print. CC.K.R.F.1.d Print Concepts: Recognize and name all upper- and lowercase letters of the alphabet. CC.K.R.F.2 Phonological Awareness: Demonstrate understanding of spoken words, syllables, and sounds (phonemes). CC.K.R.F.2.a Phonological Awareness: Recognize and produce rhyming words. CC.K.R.F.2.b Phonological Awareness: Count, pronounce, blend, and segment syllables in spoken words. CC.K.R.F.2.c Phonological Awareness: Blend and segment onsets and rimes of single-syllable spoken words. CC.K.R.F.2.d Phonological Awareness: d. Isolate and pronounce the initial, medial vowel, and final sounds (phonemes) in three-phoneme (consonant-vowel-consonant, or CVC) words.*(This does not include CVCs ending with /l/, /r/,or /x/.) CC.K.R.F.2.e Phonological Awareness: Add or substitute individual sounds (phonemes) in simple, one- syllable words to make new words. CC.K.R.F.3 Phonics and Word Recognition: Know and apply grade-level phonics and word analysis skills in decoding words. CC.K.R.F.3.a Phonics and Word Recognition: Demonstrate basic knowledge of letter-sound correspondences by producing the primary or most frequent sound for each consonant. CC.K.R.F.3.b Phonics and Word Recognition: Associate the long and short sounds with the common spellings (graphemes) for the five major vowels. CC.K.R.F.3.c Phonics and Word Recognition: Read common high-frequency words by sight. (e.g., the, of, to, you, she, my, is, are, do, does). CC.K.R.F.3.d Phonics and Word Recognition: Distinguish between similarly spelled words by identifying the sounds of the letters that differ. CC.K.R.F.4 Fluency: Read emergent-reader texts with purpose and understanding. CC.K.W.1 Text Types and Purposes: Use a combination of drawing, dictating, and writing to compose opinion pieces in which they tell a reader the topic or the name of the book they are writing about and state an opinion or preference about the topic or book (e.g., My favorite book is . . .). CC.K.W.2 Text Types and Purposes: Use a combination of drawing, dictating, and writing to compose informative/explanatory texts in which they name what they are writing about and supply some information about the topic. CC.K.W.3 Text Types and Purposes: Use a combination of drawing, dictating, and writing to narrate a single event or several loosely linked events, tell about the events in the order in which they occurred, and provide a reaction to what happened. CC.K.W.5 Production and Distribution of Writing: With guidance and support from adults, respond to questions and suggestions from peers and add details to strengthen writing as needed. CC.K.W.6 Production and Distribution of Writing: With guidance and support from adults, explore a variety of digital tools to produce and publish writing, including in collaboration with peers. CC.K.W.7 Research to Build and Present Knowledge: Participate in shared research and writing projects (e.g., explore a number of books by a favorite author and express opinions about them). CC.K.W.8 Research to Build and Present Knowledge: With guidance and support from adults, recall information from experiences or gather information from provided sources to answer a question. CC.K.SL.1 Comprehension and Collaboration: Participate in collaborative conversations with diverse partners about kindergarten topics and texts with peers and adults in small and larger groups. CC.K.SL.1.a Comprehension and Collaboration: Follow agreed-upon rules for discussions (e.g., listening to others and taking turns speaking about the topics and texts under discussion). CC.K.SL.1.b Comprehension and Collaboration: Continue a conversation through multiple exchanges. CC.K.SL.2 Comprehension and Collaboration: Confirm understanding of a text read aloud or information presented orally or through other media by asking and answering questions about key details and requesting clarification if something is not understood. CC.K.SL.3 Comprehension and Collaboration: Ask and answer questions in order to seek help, get information, or clarify something that is not understood. CC.K.SL.4 Presentation of Knowledge and Ideas: Describe familiar people, places, things, and events and, with prompting and support, provide additional detail. CC.K.SL.5 Presentation of Knowledge and Ideas: Add drawings or other visual displays to descriptions as desired to provide additional detail. CC.K.SL.6 Presentation of Knowledge and Ideas: Speak audibly and express thoughts, feelings, and ideas clearly. CC.K.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. CC.K.L.1.a Conventions of Standard English: Print many upper- and lowercase letters. CC.K.L.1.b Conventions of Standard English: Use frequently occurring nouns and verbs. CC.K.L.1.c Conventions of Standard English: Form regular plural nouns orally by adding /s/ or /es/ (e.g., dog, dogs; wish, wishes). CC.K.L.1.d Conventions of Standard English: Understand and use question words (interrogatives) (e.g., who, what, where, when, why, how). CC.K.L.1.e Conventions of Standard English: Use the most frequently occurring prepositions (e.g., to, from, in, out, on, off, for, of, by, with). CC.K.L.1.f Conventions of Standard English: Produce and expand complete sentences in shared language activities. CC.K.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. CC.K.L.2.a Conventions of Standard English: Capitalize the first word in a sentence and the pronoun I. CC.K.L.2.b Conventions of Standard English: Recognize and name end punctuation. CC.K.L.2.c Conventions of Standard English: Write a letter or letters for most consonant and short-vowel sounds (phonemes). CC.K.L.2.d Conventions of Standard English: Spell simple words phonetically, drawing on knowledge of sound-letter relationships. CC.K.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple- meaning words and phrases based on kindergarten reading and content. CC.K.L.4.a Vocabulary Acquisition and Use: Identify new meanings for familiar words and apply them accurately (e.g., knowing duck is a bird and learning the verb to duck). CC.K.L.4.b Vocabulary Acquisition and Use: Use the most frequently occurring inflections and affixes (e.g., -ed, -s, re-, un-, pre-, -ful, -less) as a clue to the meaning of an unknown word. CC.K.L.5 Vocabulary Acquisition and Use: With guidance and support from adults, explore word relationships and nuances in word meanings. CC.K.L.5.a Vocabulary Acquisition and Use: Sort common objects into categories (e.g., shapes, foods) to gain a sense of the concepts the categories represent. CC.K.L.5.b Vocabulary Acquisition and Use: Demonstrate understanding of frequently occurring verbs and adjectives by relating them to their opposites (antonyms). CC.K.L.5.c Vocabulary Acquisition and Use: Identify real-life connections between words and their use (e.g., note places at school that are colorful). CC.K.L.5.d Vocabulary Acquisition and Use: Distinguish shades of meaning among verbs describing the same general action (e.g., walk, march, strut, prance) by acting out the meanings. CC.K.L.6 Vocabulary Acquisition and Use: Use words and phrases acquired through conversations, reading and being read to, and responding to texts. Mathematics Kindergarten Standards Standard CC.K.CC.1 Know number names and the count sequence. Count to 100 by ones and by tens. CC.K.CC.2 Know number names and the count sequence. Count forward beginning from a given number within the known sequence (instead of having to begin at 1). CC.K.CC.3 Know number names and the count sequence. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). CC.K.CC.4 Count to tell the number of objects. Understand the relationship between numbers and quantities; connect counting to cardinality. CC.K.CC.4a When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. CC.K.CC.4b Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. CC.K.CC.4c Understand that each successive number name refers to a quantity that is one larger. CC.K.CC.5 Count to tell the number of objects. Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. CC.K.CC.6 Compare numbers. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. (Include groups with up to ten objects.) CC.K.CC.7 Compare numbers. Compare two numbers between 1 and 10 presented as written numerals. CC.K.OA.1 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Represent addition and subtraction with objects, fingers, mental images, drawings (drawings need not show details, but should show the mathematics in the problem), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. CC.K.OA.2 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. CC.K.OA.3 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). CC.K.OA.4 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. CC.K.OA.5 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Fluently add and subtract within 5. CC.K.NBT.1 Work with numbers 11-19 to gain foundations for place value. Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. CC.K.MD.1 Describe and compare measurable attributes. Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. CC.K.MD.2 Describe and compare measurable attributes. Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. CC.K.MD.3 Classify objects and count the number of objects in each category. Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. (Limit category counts to be less than or equal to 10.) CC.K.G.1 Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. CC.K.G.2 Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Correctly name shapes regardless of their orientations or overall size. CC.K.G.3 Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Identify shapes as two-dimensional (lying in a plane, “flat”) or three- dimensional (“solid”). CC.K.G.4 Analyze, compare, create, and compose shapes. Analyze and compare two- and three- dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). CC.K.G.5 Analyze, compare, create, and compose shapes. Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. CC.K.G.6 Analyze, compare, create, and compose shapes. Compose simple shapes to form larger shapes. For example, "can you join these two triangles with full sides touching to make a rectangle?” English/Language Arts 1st Grade Standards Standard CC.1.R.L.1 Key Ideas and Details: Ask and answer questions about key details in a text. CC.1.R.L.2 Key Ideas and Details: Retell stories, including key details, and demonstrate understanding of their central message or lesson. CC.1.R.L.3 Key Ideas and Details: Describe characters, settings, and major events in a story, using key details. CC.1.R.L.4 Craft and Structure: Identify words and phrases in stories or poems that suggest feelings or appeal to the senses. CC.1.R.L.5 Craft and Structure: Explain major differences between books that tell stories and books that give information, drawing on a wide reading of a range of text types. CC.1.R.L.6 Craft and Structure: Identify who is telling the story at various points in a text. CC.1.R.L.7 Integration of Knowledge and Ideas: Use illustrations and details in a story to describe its characters, setting, or events. CC.1.R.L.9 Integration of Knowledge and Ideas: Compare and contrast the adventures and experiences of characters in stories. CC.1.R.L.10 Range of Reading and Level of Text Complexity: With prompting and support, read prose and poetry of appropriate complexity for grade 1. CC.1.R.I.1 Key Ideas and Details: Ask and answer questions about key details in a text. CC.1.R.I.2 Key Ideas and Details: Identify the main topic and retell key details of a text. CC.1.R.I.3 Key Ideas and Details: Describe the connection between two individuals, events, ideas, or pieces of information in a text. CC.1.R.I.4 Craft and Structure: Ask and answer questions to help determine or clarify the meaning of words and phrases in a text. CC.1.R.I.5 Craft and Structure: Know and use various text features (e.g., headings, tables of contents, glossaries, electronic menus, icons) to locate key facts or information in a text. CC.1.R.I.6 Craft and Structure: Distinguish between information provided by pictures or other illustrations and information provided by the words in a text. CC.1.R.I.7 Integration of Knowledge and Ideas: Use the illustrations and details in a text to describe its key ideas. CC.1.R.I.8 Integration of Knowledge and Ideas: Identify the reasons an author gives to support points in a text. CC.1.R.I.9 Integration of Knowledge and Ideas: Identify basic similarities in and differences between two texts on the same topic (e.g., in illustrations, descriptions, or procedures). CC.1.R.I.10 Range of Reading and Level of Text Complexity: With prompting and support, read informational texts appropriately complex for grade 1. CC.1.R.F.1 Print Concepts: Demonstrate understanding of the organization and basic features of print. CC.1.R.F.1.a Print Concepts: Recognize the distinguishing features of a sentence (e.g., first word, capitalization, ending punctuation). CC.1.R.F.2 Phonological Awareness: Demonstrate understanding of spoken words, syllables, and sounds (phonemes). CC.1.R.F.2.a Phonological Awareness: Distinguish long from short vowel sounds in spoken single-syllable words . CC.1.R.F.2.b Phonological Awareness: Orally produce single-syllable words by blending sounds (phonemes), including consonant blends. CC.1.R.F.2.c Phonological Awareness: Isolate and pronounce initial, medial vowel, and final sounds (phonemes) in spoken single-syllable words. CC.1.R.F.2.d Phonological Awareness: Segment spoken single-syllable words into their complete sequence of individual sounds (phonemes). CC.1.R.F.3 Phonics and Word Recognition: Know and apply grade-level phonics and word analysis skills in decoding words. CC.1.R.F.3.a Phonics and Word Recognition: Know the spelling-sound correspondences for common consonant digraphs (two letters that represent one sound). CC.1.R.F.3.b Phonics and Word Recognition: Decode regularly spelled one-syllable words. CC.1.R.F.3.c Phonics and Word Recognition: Know final -e and common vowel team conventions for representing long vowel sounds. CC.1.R.F.3.d Phonics and Word Recognition: Use knowledge that every syllable must have a vowel sound to determine the number of syllables in a printed word. CC.1.R.F.3.e Phonics and Word Recognition: Decode two-syllable words following basic patterns by breaking the words into syllables. CC.1.R.F.3.f Phonics and Word Recognition: Read words with inflectional endings. CC.1.R.F.3.g Phonics and Word Recognition: Recognize and read grade-appropriate irregularly spelled words. CC.1.R.F.4 Read with sufficient accuracy and fluency to support comprehension. CC.1.R.F.4.a Read on-level text with purpose and understanding. CC.1.R.F.4.b Read on-level text orally with accuracy, appropriate rate, and expression. CC.1.R.F.4.c Use context to confirm or self-correct word recognition and understanding, rereading as necessary. CC.1.W.1 Text Types and Purposes: Write opinion pieces in which they introduce the topic or name the book they are writing about, state an opinion, supply a reason for the opinion, and provide some sense of closure. CC.1.W.2 Text Types and Purposes: Write informative/explanatory texts in which they name a topic, supply some facts about the topic, and provide some sense of closure. CC.1.W.3 Text Types and Purposes: Write narratives in which they recount two or more appropriately sequenced events, include some details regarding what happened, use temporal words to signal event order, and provide some sense of closure. CC.1.W.5 Production and Distribution of Writing: With guidance and support from adults, focus on a topic, respond to questions and suggestions from peers, and add details to strengthen writing as needed. CC.1.W.6 Production and Distribution of Writing: With guidance and support from adults, use a variety of digital tools to produce and publish writing, including in collaboration with peers. CC.1.W.7 Research to Build and Present Knowledge: Participate in shared research and writing projects (e.g., explore a number of “how-to” books on a given topic and use them to write a sequence of instructions). CC.1.W.8 Research to Build and Present Knowledge: With guidance and support from adults, recall information from experiences or gather information from provided sources to answer a question. CC.1.SL.1 Comprehension and Collaboration: Participate in collaborative conversations with diverse partners about grade 1 topics and texts with peers and adults in small and larger groups. CC.1.SL.1.a Comprehension and Collaboration: Follow agreed-upon rules for discussions (e.g., listening to others with care, speaking one at a time about the topics and texts under discussion). CC.1.SL.1.b Comprehension and Collaboration: Build on others’ talk in conversations by responding to the comments of others through multiple exchanges. CC.1.SL.1.c Comprehension and Collaboration: Ask questions to clear up any confusion about the topics and texts under discussion. CC.1.SL.2 Comprehension and Collaboration: Ask and answer questions about key details in a text read aloud or information presented orally or through other media. CC.1.SL.3 Comprehension and Collaboration: Ask and answer questions about what a speaker says in order to gather additional information or clarify something that is not understood. CC.1.SL.4 Presentation of Knowledge and Ideas: Describe people, places, things, and events with relevant details, expressing ideas and feelings clearly. CC.1.SL.5 Presentation of Knowledge and Ideas: Add drawings or other visual displays to descriptions when appropriate to clarify ideas, thoughts, and feelings. CC.1.SL.6 Presentation of Knowledge and Ideas: Produce complete sentences when appropriate to task and situation. (See grade 1 Language standards 1 and 3 on page 26 for specific expectations.) CC.1.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. CC.1.L.1.a Conventions of Standard English: Print all upper- and lowercase letters. CC.1.L.1.b Conventions of Standard English: Use common, proper, and possessive nouns. CC.1.L.1.c Conventions of Standard English: Use singular and plural nouns with matching verbs in basic sentences (e.g., He hops; We hop). CC.1.L.1.d Conventions of Standard English: Use personal, possessive, and indefinite pronouns (e.g., I, me, my; they, them, their, anyone, everything). CC.1.L.1.e Conventions of Standard English: Use verbs to convey a sense of past, present, and future (e.g., Yesterday I walked home; Today I walk home; Tomorrow I will walk home). CC.1.L.1.f Conventions of Standard English: Use frequently occurring adjectives. CC.1.L.1.g Conventions of Standard English: Use frequently occurring conjunctions (e.g., and, but, or, so, because). CC.1.L.1.h Conventions of Standard English: Use determiners (e.g., articles, demonstratives). CC.1.L.1.i Conventions of Standard English: Use frequently occurring prepositions (e.g., during, beyond, toward). CC.1.L.1.j Conventions of Standard English: Produce and expand complete simple and compound declarative, interrogative, imperative, and exclamatory sentences in response to prompts. CC.1.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. CC.1.L.2.a Conventions of Standard English: Capitalize dates and names of people. CC.1.L.2.b Conventions of Standard English: Use end punctuation for sentences. CC.1.L.2.c Conventions of Standard English: Use commas in dates and to separate single words in a series. CC.1.L.2.d Conventions of Standard English: Use conventional spelling for words with common spelling patterns and for frequently occurring irregular words. CC.1.L.2.e Conventions of Standard English: Spell untaught words phonetically, drawing on phonemic awareness and spelling conventions. CC.1.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple- meaning words and phrases based on grade 1 reading and content, choosing flexibly from an array of strategies. CC.1.L.4.a Vocabulary Acquisition and Use: Use sentence-level context as a clue to the meaning of a word or phrase. CC.1.L.4.b Vocabulary Acquisition and Use: Use frequently occurring affixes as a clue to the meaning of a word. CC.1.L.4.c Vocabulary Acquisition and Use: Identify frequently occurring root words (e.g., look) and their inflectional forms (e.g., looks, looked, looking). CC.1.L.5 Vocabulary Acquisition and Use: With guidance and support from adults, demonstrate understanding of word relationships and nuances in word meanings. CC.1.L.5.a Vocabulary Acquisition and Use: Sort words into categories (e.g., colors, clothing) to gain a sense of the concepts the categories represent. CC.1.L.5.b Vocabulary Acquisition and Use: Define words by category and by one or more key attributes (e.g., a duck is a bird that swims; a tiger is a large cat with stripes). CC.1.L.5.c Vocabulary Acquisition and Use: Identify real-life connections between words and their use (e.g., note places at home that are cozy). CC.1.L.5.d Vocabulary Acquisition and Use: Distinguish shades of meaning among verbs differing in manner (e.g., look, peek, glance, stare, glare, scowl) and adjectives differing in intensity (e.g., large, gigantic) by defining or choosing them or by acting out the meanings. CC.1.L.6 Vocabulary Acquisition and Use: Use words and phrases acquired through conversations, reading and being read to, and responding to texts, including using frequently occurring conjunctions to signal simple relationships (e.g., I named my hamster Nibblet because she nibbles too much because she likes that). Mathematics 1st Grade Standard CC.1.OA.1 Represent and solve problems involving addition and subtraction. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. CC.1.OA.2 Represent and solve problems involving addition and subtraction. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. CC.1.OA.3 Understand and apply properties of operations and the relationship between addition and subtraction. Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) (Students need not use formal terms for these properties.) CC.1.OA.4 Understand and apply properties of operations and the relationship between addition and subtraction. Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. CC.1.OA.5 Add and subtract within 20. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). CC.1.OA.6 Add and subtract within 20. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). CC.1.OA.7 Work with addition and subtraction equations. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. CC.1.OA.8 Work with addition and subtraction equations. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ＿ – 3, 6 + 6 = ＿. CC.1.NBT.1 Extend the counting sequence. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. CC.1.NBT.2 Understand place value. Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: -- a. 10 can be thought of as a bundle of ten ones — called a “ten.” -- b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. -- c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). CC.1.NBT.3 Understand place value. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. CC.1.NBT.4 Use place value understanding and properties of operations to add and subtract. Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. CC.1.NBT.5 Use place value understanding and properties of operations to add and subtract. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. CC.1.NBT.6 Use place value understanding and properties of operations to add and subtract. Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. CC.1.MD.1 Measure lengths indirectly and by iterating length units. Order three objects by length; compare the lengths of two objects indirectly by using a third object. CC.1.MD.2 Measure lengths indirectly and by iterating length units. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. CC.1.MD.3 Tell and write time. Tell and write time in hours and half-hours using analog and digital clocks. CC.1.MD.4 Represent and interpret data. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. CC.1.G.1 Reason with shapes and their attributes. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); for a wide variety of shapes; build and draw shapes to possess defining attributes. CC.1.G.2 Reason with shapes and their attributes. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names such as “right rectangular prism.”) CC.1.G.3 Reason with shapes and their attributes. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. English/Language Arts 2nd Grade Standards Standard CC.2.R.L.1 Key Ideas and Details: Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text. CC.2.R.L.2 Key Ideas and Details: Recount stories, including fables and folktales from diverse cultures, and determine their central message, lesson, or moral. CC.2.R.L.3 Key Ideas and Details: Describe how characters in a story respond to major events and challenges. CC.2.R.L.4 Craft and Structure: Describe how words and phrases (e.g., regular beats, alliteration, rhymes, repeated lines) supply rhythm and meaning in a story, poem, or song. CC.2.R.L.5 Craft and Structure: Describe the overall structure of a story, including describing how the beginning introduces the story and the ending concludes the action. CC.2.R.L.6 Craft and Structure: Acknowledge differences in the points of view of characters, including by speaking in a different voice for each character when reading dialogue aloud. CC.2.R.L.7 Integration of Knowledge and Ideas: Use information gained from the illustrations and words in a print or digital text to demonstrate understanding of its characters, setting, or plot. CC.2.R.L.9 Integration of Knowledge and Ideas: Compare and contrast two or more versions of the same story (e.g., Cinderella stories) by different authors or from different cultures. CC.2.R.L.10 Range of Reading and Level of Text Complexity: By the end of the year, read and comprehend literature, including prose and poetry, in the grades 2–3 text complexity band proficiently, with scaffolding as needed at the high end of the range. CC.2.R.I.1 Key Ideas and Details: Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text. CC.2.R.I.2 Key Ideas and Details: Identify the main topic of a multiparagraph text as well as the focus of specific paragraphs within the text. CC.2.R.I.3 Key Ideas and Details: Describe the connection between a series of historical events, scientific ideas or concepts, or steps in technical procedures in a text. CC.2.R.I.4 Craft and Structure: Determine the meaning of words and phrases in a text relevant to a grade 2 topic or subject area. CC.2.R.I.5 Craft and Structure: Know and use various text features (e.g., captions, bold print, subheadings, glossaries, indexes, electronic menus, icons) to locate key facts or information in a text efficiently. CC.2.R.I.6 Craft and Structure: Identify the main purpose of a text, including what the author wants to answer, explain, or describe. CC.2.R.I.7 Integration of Knowledge and Ideas: Explain how specific images (e.g., a diagram showing how a machine works) contribute to and clarify a text. CC.2.R.I.8 Integration of Knowledge and Ideas: Describe how reasons support specific points the author makes in a text. CC.2.R.I.9 Integration of Knowledge and Ideas: Compare and contrast the most important points presented by two texts on the same topic. CC.2.R.I.10 Range of Reading and Level of Text Complexity: By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 2–3 text complexity band proficiently, with scaffolding as needed at the high end of the range. CC.2.R.F.3 Phonics and Word Recognition: Know and apply grade-level phonics and word analysis skills in decoding words. CC.2.R.F.3.a Phonics and Word Recognition: Distinguish long and short vowels when reading regularly spelled one-syllable words. CC.2.R.F.3.b Phonics and Word Recognition: Know spelling-sound correspondences for additional common vowel teams. CC.2.R.F.3.c Phonics and Word Recognition: Decode regularly spelled two-syllable words with long vowels. CC.2.R.F.3.d Phonics and Word Recognition: Decode words with common prefixes and suffixes. CC.2.R.F.3.e Phonics and Word Recognition: Identify words with inconsistent but common spelling- sound correspondences. CC.2.R.F.3.f Phonics and Word Recognition: Recognize and read grade-appropriate irregularly spelled words. CC.2.R.F.4 Fluency: Read with sufficient accuracy and fluency to support comprehension. CC.2.R.F.4.a Read on-level text with purpose and understanding. CC.2.R.F.4.b Read on-level text orally with accuracy, appropriate rate, and expression. CC.2.R.F.4.c Use context to confirm or self-correct word recognition and understanding, rereading as necessary. CC.2.W.1 Text Types and Purposes: Write opinion pieces in which they introduce the topic or book they are writing about, state an opinion, supply reasons that support the opinion, use linking words (e.g., because, and, also) to connect opinion and reasons, and provide a concluding statement or section. CC.2.W.2 Text Types and Purposes: Write informative/explanatory texts in which they introduce a topic, use facts and definitions to develop points, and provide a concluding statement or section. CC.2.W.3 Text Types and Purposes: Write narratives in which they recount a well-elaborated event or short sequence of events, include details to describe actions, thoughts, and feelings, use temporal words to signal event order, and provide a sense of closure. CC.2.W.5 Production and Distribution of Writing: With guidance and support from adults and peers, focus on a topic and strengthen writing as needed by revising and editing. CC.2.W.6 Production and Distribution of Writing: With guidance and support from adults, use a variety of digital tools to produce and publish writing, including in collaboration with peers. CC.2.W.7 Research to Build and Present Knowledge: Participate in shared research and writing projects (e.g., read a number of books on a single topic to produce a report; record science observations). CC.2.W.8 Research to Build and Present Knowledge: Recall information from experiences or gather information from provided sources to answer a question. CC.2.SL.1 Comprehension and Collaboration: Participate in collaborative conversations with diverse partners about grade 2 topics and texts with peers and adults in small and larger groups. CC.2.SL.1.a Comprehension and Collaboration: Follow agreed-upon rules for discussions (e.g., gaining the floor in respectful ways, listening to others with care, speaking one at a time about the topics and texts under discussion). CC.2.SL.1.b Comprehension and Collaboration: Build on others’ talk in conversations by linking their comments to the remarks of others. CC.2.SL.1.c Comprehension and Collaboration: Ask for clarification and further explanation as needed about the topics and texts under discussion. CC.2.SL.2 Comprehension and Collaboration: Recount or describe key ideas or details from a text read aloud or information presented orally or through other media. CC.2.SL.3 Comprehension and Collaboration: Ask and answer questions about what a speaker says in order to clarify comprehension, gather additional information, or deepen understanding of a topic or issue. CC.2.SL.4 Presentation of Knowledge and Ideas: Tell a story or recount an experience with appropriate facts and relevant, descriptive details, speaking audibly in coherent sentences. CC.2.SL.5 Presentation of Knowledge and Ideas: Create audio recordings of stories or poems; add drawings or other visual displays to stories or recounts of experiences when appropriate to clarify ideas, thoughts, and feelings. CC.2.SL.6 Presentation of Knowledge and Ideas: Produce complete sentences when appropriate to task and situation in order to provide requested detail or clarification. (See grade 2 Language standards 1and 3 on page 26 for specific expectations.) CC.2.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. CC.2.L.1.a Conventions of Standard English: Use collective nouns (e.g., group). CC.2.L.1.b Conventions of Standard English: Form and use frequently occurring irregular plural nouns (e.g., feet, children, teeth, mice, fish). CC.2.L.1.c Conventions of Standard English: Use reflexive pronouns (e.g., myself, ourselves). CC.2.L.1.d Conventions of Standard English: Form and use the past tense of frequently occurring irregular verbs (e.g., sat, hid, told). CC.2.L.1.e Conventions of Standard English: Use adjectives and adverbs, and choose between them depending on what is to be modified. CC.2.L.1.f Conventions of Standard English: Produce, expand, and rearrange complete simple and compound sentences (e.g., The boy watched the movie; The little boy watched the movie; The action movie was watched by the little boy). CC.2.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. CC.2.L.2.a Conventions of Standard English: Capitalize holidays, product names, and geographic names. CC.2.L.2.b Conventions of Standard English: Use commas in greetings and closings of letters. CC.2.L.2.c Conventions of Standard English: Use an apostrophe to form contractions and frequently occurring possessives. CC.2.L.2.d Conventions of Standard English: Generalize learned spelling patterns when writing words (e.g., cage → badge; boy → boil). CC.2.L.2.e Conventions of Standard English: Consult reference materials, including beginning dictionaries, as needed to check and correct spellings CC.2.L.3 Knowledge of Language: Use knowledge of language and its conventions when writing, speaking, reading, or listening. CC.2.L.3.a Knowledge of Language: Compare formal and informal uses of English. CC.2.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple- meaning words and phrases based on grade 2 reading and content, choosing flexibly from an array of strategies. CC.2.L.4.a Vocabulary Acquisition and Use: Use sentence-level context as a clue to the meaning of a word or phrase. CC.2.L.4.b Vocabulary Acquisition and Use: Determine the meaning of the new word formed when a known prefix is added to a known word (e.g., happy/unhappy, tell/retell). CC.2.L.4.c Vocabulary Acquisition and Use: Use a known root word as a clue to the meaning of an unknown word with the same root (e.g., addition, additional). CC.2.L.4.d Vocabulary Acquisition and Use: Use knowledge of the meaning of individual words to predict the meaning of compound words (e.g., birdhouse, lighthouse, housefly; bookshelf, notebook, bookmark). CC.2.L.4.e Vocabulary Acquisition and Use: Use glossaries and beginning dictionaries, both print and digital, to determine or clarify the meaning of words and phrases. CC.2.L.5 Vocabulary Acquisition and Use: Demonstrate understanding of word relationships and nuances in word meanings. CC.2.L.5.a Vocabulary Acquisition and Use: Identify real-life connections between words and their use (e.g., describe foods that are spicy or juicy). CC.2.L.5.b Vocabulary Acquisition and Use: Distinguish shades of meaning among closely related verbs (e.g., toss, throw, hurl) and closely related adjectives (e.g., thin, slender, skinny, scrawny). CC.2.L.6 Vocabulary Acquisition and Use: Use words and phrases acquired through conversations, reading and being read to, and responding to texts, including using adjectives and adverbs to describe (e.g., When other kids are happy that makes me happy). Mathematics 2nd Grade Standards Standard CC.2.OA.1 Represent and solve problems involving addition and subtraction. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. CC.2.OA.2 Add and subtract within 20. Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. CC.2.OA.3 Work with equal groups of objects to gain foundations for multiplication. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. CC.2.OA.4 Work with equal groups of objects to gain foundations for multiplication. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. CC.2.NBT.1 Understand place value. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: -- a. 100 can be thought of as a bundle of ten tens — called a “hundred.” -- b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). CC.2.NBT.2 Understand place value. Count within 1000; skip-count by 5s, 10s, and 100s. CC.2.NBT.3 Understand place value. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. CC.2.NBT.4 Understand place value. Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. CC.2.NBT.5 Use place value understanding and properties of operations to add and subtract. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. CC.2.NBT.6 Use place value understanding and properties of operations to add and subtract. Add up to four two-digit numbers using strategies based on place value and properties of operations. CC.2.NBT.7 Use place value understanding and properties of operations to add and subtract. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. CC.2.NBT.8 Use place value understanding and properties of operations to add and subtract. Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100- 900. CC.2.NBT.9 Use place value understanding and properties of operations to add and subtract. Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.) CC.2.MD.1 Measure and estimate lengths in standard units. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. CC.2.MD.2 Measure and estimate lengths in standard units. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. CC.2.MD.3 Measure and estimate lengths in standard units. Estimate lengths using units of inches, feet, centimeters, and meters. CC.2.MD.4 Measure and estimate lengths in standard units. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. CC.2.MD.5 Relate addition and subtraction to length. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. CC.2.MD.6 Relate addition and subtraction to length. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, … , and represent whole-number sums and differences within 100 on a number line diagram. CC.2.MD.7 Work with time and money. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. CC.2.MD.8 Work with time and money. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ (dollars) and ¢ (cents) symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? CC.2.MD.9 Represent and interpret data. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. CC.2.MD.10 Represent and interpret data. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. CC.2.G.1 Reason with shapes and their attributes. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. (Sizes are compared directly or visually, not compared by measuring.) CC.2.G.2 Reason with shapes and their attributes. Partition a rectangle into rows and columns of same- size squares and count to find the total number of them. CC.2.G.3 Reason with shapes and their attributes. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. English/Language Arts 3rd Grade Standards Standard CC.3.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. CC.3.L.1.a Conventions of Standard English: Explain the function of nouns, pronouns, verbs, adjectives, and adverbs in general and their functions in particular sentences. CC.3.L.1.b Conventions of Standard English: Form and use regular and irregular plural nouns. CC.3.R.L.1 Key Ideas and Details: Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers. CC.3.R.L.2 Key Ideas and Details: Recount stories, including fables, folktales, and myths from diverse cultures; determine the central message, lesson, or moral and explain how it is conveyed through key details in the text. CC.3.R.L.3 Key Ideas and Details: Describe characters in a story (e.g., their traits, motivations, or feelings) and explain how their actions contribute to the sequence of events. CC.3.R.L.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, distinguishing literal from nonliteral language. CC.3.R.L.5 Craft and Structure: Refer to parts of stories, dramas, and poems when writing or speaking about a text, using terms such as chapter, scene, and stanza; describe how each successive part builds on earlier sections. CC.3.R.L.6 Craft and Structure: Distinguish their own point of view from that of the narrator or those of the characters. CC.3.R.L.7 Integration of Knowledge and Ideas: Explain how specific aspects of a text’s illustrations contribute to what is conveyed by the words in a story (e.g., create mood, emphasize aspects of a character or setting). CC.3.R.L.9 Integration of Knowledge and Ideas: Compare and contrast the themes, settings, and plots of stories written by the same author about the same or similar characters (e.g., in books from a series). CC.3.R.L.10 Range of Reading and Complexity of Text: 10. By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 2–3 text complexity band independently and proficiently. CC.3.R.I.1 Key Ideas and Details: Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers. CC.3.R.I.2 Key Ideas and Details: Determine the main idea of a text; recount the key details and explain how they support the main idea. CC.3.R.I.3 Key Ideas and Details: Describe the relationship between a series of historical events, scientific ideas or concepts, or steps in technical procedures in a text, using language that pertains to time, sequence, and cause/effect. CC.3.R.I.4 Craft and Structure: Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 3 topic or subject area. CC.3.R.I.5 Craft and Structure: Use text features and search tools (e.g., key words, sidebars, hyperlinks) to locate information relevant to a given topic efficiently. CC.3.R.I.6 Craft and Structure: Distinguish their own point of view from that of the author of a text. CC.3.R.I.7 Integration of Knowledge and Ideas: Use information gained from illustrations (e.g., maps, photographs) and the words in a text to demonstrate understanding of the text (e.g., where, when, why, and how key events occur). CC.3.R.I.8 Integration of Knowledge and Ideas: Describe the logical connection between particular sentences and paragraphs in a text (e.g., comparison, cause/effect, first/second/third in a sequence). CC.3.R.I.9 Integration of Knowledge and Ideas: Compare and contrast the most important points and key details presented in two texts on the same topic. CC.3.R.I.10 Range of Reading and Level of Text Complexity: By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 2–3 text complexity band independently and proficiently. CC.3.R.F.3 Phonics and Word Recognition: Know and apply grade-level phonics and word analysis skills in decoding words. CC.3.R.F.3.a Phonics and Word Recognition: Identify and know the meaning of the most common prefixes and derivational suffixes. CC.3.R.F.3.b Phonics and Word Recognition: Decode words with common Latin suffixes. CC.3.R.F.3.c Phonics and Word Recognition: Decode multisyllable words. CC.3.R.F.3.d Phonics and Word Recognition: Read grade-appropriate irregularly spelled words. CC.3.R.F.4 Fluency: Read with sufficient accuracy and fluency to support comprehension. CC.3.R.F.4.a Fluency: Read on-level text with purpose and understanding. CC.3.R.F.4.b Fluency: Read grade-level prose and poetry orally with accuracy, appropriate rate, and expression. CC.3.R.F.4.c Fluency: Use context to confirm or self-correct word recognition and understanding, rereading as necessary. CC.3.W.1 Text Types and Purposes: Write opinion pieces on familiar topics or texts, supporting a point of view with reasons. CC.3.W.1.a Text Types and Purposes: Introduce the topic or text they are writing about, state an opinion, and create an organizational structure that lists reasons. CC.3.W.1.b Text Types and Purposes: Provide reasons that support the opinion. CC.3.W.1.c Text Types and Purposes: Use linking words and phrases (e.g., because, therefore, since, for example) to connect opinion and reasons. CC.3.W.1.d Text Types and Purposes: Provide a concluding statement or section. CC.3.W.2 Text Types and Purposes: Write informative/explanatory texts to examine a topic and convey ideas and information clearly. CC.3.W.2.a Text Types and Purposes: Introduce a topic and group related information together; include illustrations when useful to aiding comprehension. CC.3.W.2.b Text Types and Purposes: Develop the topic with facts, definitions, and details. CC.3.W.2.c Text Types and Purposes: Use linking words and phrases (e.g., also, another, and, more, but) to connect ideas within categories of information. CC.3.W.2.d Text Types and Purposes: Provide a concluding statement or section. CC.3.W.3 Text Types and Purposes: Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences. CC.3.W.3.a Text Types and Purposes: Establish a situation and introduce a narrator and/or characters; organize an event sequence that unfolds naturally. CC.3.W.3.b Text Types and Purposes: Use dialogue and descriptions of actions, thoughts, and feelings to develop experiences and events or show the response of characters to situations. CC.3.W.3.c Text Types and Purposes: Use temporal words and phrases to signal event order. CC.3.W.3.d Text Types and Purposes: Provide a sense of closure. CC.3.W.4 Production and Distribution of Writing: With guidance and support from adults, produce writing in which the development and organization are appropriate to task and purpose. (Grade-specific expectations for writing types are defined in standards 1–3 above.) CC.3.W.5 Production and Distribution of Writing: With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing. (Editing for conventions should demonstrate command of Language standards 1–3 up to and including grade 3 on page 29.) CC.3.W.6 Production and Distribution of Writing: With guidance and support from adults, use technology to produce and publish writing (using keyboarding skills) as well as to interact and collaborate with others. CC.3.W.7 Research to Build and Present Knowledge: Conduct short research projects that build knowledge about a topic. CC.3.W.8 Research to Build and Present Knowledge: Recall information from experiences or gather information from print and digital sources; take brief notes on sources and sort evidence into provided categories. CC.3.W.10 Range of Writing: Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. CC.3.SL.1 Comprehension and Collaboration: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 3 topics and texts, building on others’ ideas and expressing their own clearly. CC.3.SL.1.a Comprehension and Collaboration: Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. CC.3.SL.1.b Comprehension and Collaboration: Follow agreed-upon rules for discussions (e.g., gaining the floor in respectful ways, listening to others with care, speaking one at a time about the topics and texts under discussion). CC.3.SL.1.c Comprehension and Collaboration: Ask questions to check understanding of information presented, stay on topic, and link their comments to the remarks of others. CC.3.SL.1.d Comprehension and Collaboration: Explain their own ideas and understanding in light of the discussion. CC.3.SL.2 Comprehension and Collaboration: Determine the main ideas and supporting details of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. CC.3.SL.3 Comprehension and Collaboration: Ask and answer questions about information from a speaker, offering appropriate elaboration and detail. CC.3.SL.4 Presentation of Knowledge and Ideas: Report on a topic or text, tell a story, or recount an experience with appropriate facts and relevant, descriptive details, speaking clearly at an understandable pace. CC.3.SL.5 Presentation of Knowledge and Ideas: Create engaging audio recordings of stories or poems that demonstrate fluid reading at an understandable pace; add visual displays when appropriate to emphasize or enhance certain facts or details. CC.3.SL.6 Presentation of Knowledge and Ideas: Speak in complete sentences when appropriate to task and situation in order to provide requested detail or clarification. (See grade 3 Language standards 1 and 3 on page 26 for specific expectations.) CC.3.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. CC.3.L.1.a Conventions of Standard English: Explain the function of nouns, pronouns, verbs, adjectives, and adverbs in general and their functions in particular sentences. CC.3.L.1.b Conventions of Standard English: Form and use regular and irregular plural nouns CC.3.L.1.c Conventions of Standard Engligh: Use abstract nouns (e.g., childhood). CC.3.L.1.d Conventions of Standard English: Form and use regular and irregular verbs. CC.3.L.1.e Conventions of Standard English: Form and use the simple (e.g., I walked; I walk; I will walk) verb tenses. CC.3.L.1.f Conventions of Standard English: Ensure subject-verb and pronoun-antecedent agreement.* CC.3.L.1.g Conventions of Standard English: Form and use comparative and superlative adjectives and adverbs, and choose between them depending on what is to be modified. CC.3.L.1.h Conventions of Standard English: Use coordinating and subordinating conjunctions. CC.3.L.1.i Conventions of Standard English: Produce simple, compound, and complex sentences. CC.3.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. CC.3.L.2.a Conventions of Standard English: Capitalize appropriate words in titles. CC.3.L.2.b Conventions of Standard English: Use commas in addresses. CC.3.L.2.c Conventions of Standard English: Use commas and quotation marks in dialogue. CC.3.L.2.d Conventions of Standard English: Form and use possessives. CC.3.L.2.e Conventions of Standard English: Use conventional spelling for high-frequency and other studied words and for adding suffixes to base words (e.g., sitting, smiled, cries, happiness). CC.3.L.2.f Conventions of Standard English: Use spelling patterns and generalizations (e.g., word families, position-based spellings, syllable patterns, ending rules, meaningful word parts) in writing words. CC.3.L.2.g Conventions of Standard English: Consult reference materials, including beginning dictionaries, as needed to check and correct spellings. CC.3.L.3 Knowledge of Language: Use knowledge of language and its conventions when writing, speaking, reading, or listening. CC.3.L.3.a Knowledge of Language: Choose words and phrases for effect.* CC.3.L.3.b Knowledge of Language: Recognize and observe differences between the conventions of spoken and written standard English. CC.3.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple- meaning word and phrases based on grade 3 reading and content, choosing flexibly from a range of strategies. CC.3.L.4.a Vocabulary Acquisition and Use: Use sentence-level context as a clue to the meaning of a word or phrase. CC.3.L.4.b Vocabulary Acquisition and Use: Determine the meaning of the new word formed when a known affix is added to a known word (e.g., agreeable/disagreeable, comfortable/uncomfortable, care/careless, heat/preheat). CC.3.L.4.c Vocabulary Acquisition and Use: Use a known root word as a clue to the meaning of an unknown word with the same root (e.g., company, companion). CC.3.L.4.d Vocabulary Acquisition and Use: Use glossaries or beginning dictionaries, both print and digital, to determine or clarify the precise meaning of key words and phrases. CC.3.L.5 Vocabulary Acquisition and Use: Demonstrate understanding of word relationships and nuances in word meanings. CC.3.L.5.a Vocabulary Acquisition and Use: Distinguish the literal and nonliteral meanings of words and phrases in context (e.g., take steps). CC.3.L.5.b Vocabulary Acquisition and Use: Identify real-life connections between words and their use (e.g., describe people who are friendly or helpful). CC.3.L.5.c Vocabulary Acquisition and Use: Distinguish shades of meaning among related words that describe states of mind or degrees of certainty (e.g., knew, believed, suspected, heard, wondered). CC.3.L.6 Vocabulary Acquisition and Use: Acquire and use accurately grade-appropriate conversational, general academic, and domain-specific words and phrases, including those that signal spatial and temporal relationships (e.g., After dinner that night we went looking for them). Mathematics 3rd Grade Standards Standard CC.3.OA.1 Represent and solve problems involving multiplication and division. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. CC.3.OA.2 Represent and solve problems involving multiplication and division. Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. CC.3.OA.3 Represent and solve problems involving multiplication and division. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. CC.3.OA.4 Represent and solve problems involving multiplication and division. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = __÷ 3, 6 × 6 = ?. CC.3.OA.5 Understand properties of multiplication and the relationship between multiplication and division. Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15 then 15 × 2 = 30, or by 5 × 2 = 10 then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) (Students need not use formal terms for these properties.) CC.3.OA.6 Understand properties of multiplication and the relationship between multiplication and division. Understand division as an unknown-factor problem. For example, divide 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. CC.3.OA.7 Multiply and divide within 100. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of one-digit numbers. CC.3.OA.8 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) CC.3.OA.9 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. CC.3.NBT.1 Use place value understanding and properties of operations to perform multi-digit arithmetic. Use place value understanding to round whole numbers to the nearest 10 or 100. CC.3.NBT.2 Use place value understanding and properties of operations to perform multi-digit arithmetic. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. (A range of algorithms may be used.) CC.3.NBT.3 Use place value understanding and properties of operations to perform multi-digit arithmetic. Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. (A range of algorithms may be used.) CC.3.NF.1 Develop understanding of fractions as numbers. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) CC.3.NF.2 Develop understanding of fractions as numbers. Understand a fraction as a number on the number line; represent fractions on a number line diagram. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) CC.3.NF.2a Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) CC.3.NF.2b Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) CC.3.NF.3 Develop understanding of fractions as numbers. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) CC.3.NF.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) CC.3.NF.3b Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3), Explain why the fractions are equivalent, e.g., by using a visual fraction model. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) CC.3.NF.3c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) CC.3.NF.3d Compare two fractions with the same numerator or the same denominator, by reasoning about their size, Recognize that valid comparisons rely on the two fractions referring to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) CC.3.MD.1 Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. CC.3.MD.2 Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^3 and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems (problems involving notions of “times as much.”) CC.3.MD.3 Represent and interpret data. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. CC.3.MD.4 Represent and interpret data. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters. CC.3.MD.5 Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Recognize area as an attribute of plane figures and understand concepts of area measurement. -- a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. -- b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. CC.3.MD.6 Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). CC.3.MD.7 Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Relate area to the operations of multiplication and addition. CC.3.MD.7a Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. CC.3.MD.7b Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. CC.3.MD.7c Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. CC.3.MD.7d Recognize area as additive. Find areas of rectilinear figures by decomposing them into non- overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. CC.3.MD.8 Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different area or with the same area and different perimeter. CC.3.G.1 Reason with shapes and their attributes. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. CC.3.G.2 Reason with shapes and their attributes. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part is 1/4 of the area of the shape. English/Language Arts 4th Grade Standards Standard CC.4.R.L.1 Key Ideas and Details: Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text. CC.4.R.L.2 Key Ideas and Details: Determine a theme of a story, drama, or poem from details in the text; summarize the text. CC.4.R.L.3 Key Ideas and Details: Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text (e.g., a character’s thoughts, words, or actions). CC.4.R.L.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, including those that allude to significant characters found in mythology (e.g., Herculean). CC.4.R.L.5 Craft and Structure: Explain major differences between poems, drama, and prose, and refer to the structural elements of poems (e.g., verse, rhythm, meter) and drama (e.g., casts of characters, setting descriptions, dialogue, stage directions) when writing or speaking about a text. CC.4.R.L.6 Craft and Structure: Compare and contrast the point of view from which different stories are narrated, including the difference between first- and third-person narrations. CC.4.R.L.7 Integration of Knowledge and Ideas: Make connections between the text of a story or drama and a visual or oral presentation of the text, identifying where each version reflects specific descriptions and directions in the text. CC.4.R.L.9 Integration of Knowledge and Ideas: Compare and contrast the treatment of similar themes and topics (e.g., opposition of good and evil) and patterns of events (e.g., the quest) in stories, myths, and traditional literature from different cultures. CC.4.R.L.10 Range of Reading and Complexity of Text: By the end of the year, read and comprehend literature, including stories, dramas, and poetry, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range. CC.4.R.I.1 Key Ideas and Details: Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text. CC.4.R.I.2 Key Ideas and Details: Determine the main idea of a text and explain how it is supported by key details; summarize the text. CC.4.R.I.3 Key Ideas and Details: Explain events, procedures, ideas, or concepts in a historical, scientific, or technical text, including what happened and why, based on specific information in the text. CC.4.R.I.4 Craft and Structure: Determine the meaning of general academic and domain-specific words or phrases in a text relevant to a grade 4 topic or subject area. CC.4.R.I.5 Craft and Structure: Describe the overall structure (e.g., chronology, comparison, cause/effect, problem/solution) of events, ideas, concepts, or information in a text or part of a text. CC.4.R.I.6 Craft and Structure: Compare and contrast a firsthand and secondhand account of the same event or topic; describe the differences in focus and the information provided. CC.4.R.I.7 Integration of Knowledge and Ideas: Interpret information presented visually, orally, or quantitatively (e.g., in charts, graphs, diagrams, time lines, animations, or interactive elements on Web pages) and explain how the information contributes to an understanding of the text in which it appears. CC.4.R.I.8 Integration of Knowledge and Ideas: Explain how an author uses reasons and evidence to support particular points in a text. CC.4.R.I.9 Integration of Knowledge and Ideas: Integrate information from two texts on the same topic in order to write or speak about the subject knowledgeably. CC.4.R.I.10 Range of Reading and Complexity of Text: By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 4–5 text complexity band proficiently, with scaffolding as necessary at the high end of the range. CC.4.R.F.3 Phonics and Word Recognition: Know and apply grade-level phonics and word analysis skills in decoding words. CC.4.R.F.3.a Phonics and Word Recognition: Use combined knowledge of all letter-sound correspondences, syllabication patterns, and morphology (e.g., roots and affixes) to read accurately unfamiliar multisyllabic words in context and out of context. CC.4.R.F.4 Fluency: Read with sufficient accuracy and fluency to support comprehension. CC.4.R.F.4.a Fluency: Read on-level text with purpose and understanding. CC.4.R.F.4.b Fluency: Read on-level prose and poetry orally with accuracy, appropriate rate, and expression. CC.4.R.F.4.c Fluency: Use context to confirm or self-correct word recognition and understanding, rereading as necessary. CC.4.W.1 Text Types and Purposes: Write opinion pieces on topics or texts, supporting a point of view with reasons and information. CC.4.W.1.a Text Types and Purposes: Introduce a topic or text clearly, state an opinion, and create an organizational structure in which related ideas are grouped to support the writer’s purpose. CC.4.W.1.b Text Types and Purposes: Provide reasons that are supported by facts and details. CC.4.W.1.c Text Types and Purposes: Link opinion and reasons using words and phrases (e.g., for instance, in order to, in addition). CC.4.W.1.d Text Types and Purposes: Provide a concluding statement or section related to the opinion presented. CC.4.W.2 Text Types and Purposes: Write informative/explanatory texts to examine a topic and convey ideas and information clearly. CC.4.W.2.a Text Types and Purposes: Introduce a topic clearly and group related information in paragraphs and sections; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. CC.4.W.2.b Text Types and Purposes: Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. CC.4.W.2.c Text Types and Purposes: Link ideas within categories of information using words and phrases (e.g., another, for example, also, because). CC.4.W.2.d Text Types and Purposes: Use precise language and domain-specific vocabulary to inform about or explain the topic. CC.4.W.2.e Text Types and Purposes: Provide a concluding statement or section related to the information or explanation presented. CC.4.W.3 Text Types and Purposes: Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences. CC.4.W.3.a Text Types and Purposes: Orient the reader by establishing a situation and introducing a narrator and/or characters; organize an event sequence that unfolds naturally. CC.4.W.3.b Text Types and Purposes: Use dialogue and description to develop experiences and events or show the responses of characters to situations. CC.4.W.3.c Text Types and Purposes: Use a variety of transitional words and phrases to manage the sequence of events. CC.4.W.3.d Text Types and Purposes: Use concrete words and phrases and sensory details to convey experiences and events precisely. CC.4.W.3.e Text Types and Purposes: Provide a conclusion that follows from the narrated experiences or events. CC.4.W.4 Production and Distribution of Writing: Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) CC.4.W.5 Production and Distribution of Writing: With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing.(Editing for conventions should demonstrate command of Language standards 1–3up to and including grade 4 on page 29.) CC.4.W.6 Production and Distribution of Writing: With some guidance and support from adults, use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of one page in a single sitting. CC.4.W.7 Research to Build and Present Knowledge: Conduct short research projects that build knowledge through investigation of different aspects of a topic. CC.4.W.8 Research to Build and Present Knowledge: Recall relevant information from experiences or gather relevant information from print and digital sources; take notes and categorize information, and provide a list of sources. CC.4.W.9 Research to Build and Present Knowledge: Draw evidence from literary or informational texts to support analysis, reflection, and research. CC.4.W.9.a Research to Build and Present Knowledge: Apply grade 4 Reading standards to literature (e.g., “Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text [e.g., a character’s thoughts, words, or actions].”). CC.4.W.9.b Research to Build and Present Knowledge: Apply grade 4 Reading standards to informational texts (e.g., “Explain how an author uses reasons and evidence to support particular points in a text”). CC.4.W.10 Range of Writing: Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. CC.4.SL.1 Comprehension and Collaboration: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led)with diverse partners on grade 4 topics and texts, building on others’ ideas and expressing their own clearly. CC.4.SL.1.a Comprehension and Collaboration: Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. CC.4.SL.1.b Comprehension and Collaboration: Follow agreed-upon rules for discussions and carry out assigned roles. CC.4.SL.1.c Comprehension and Collaboration: Pose and respond to specific questions to clarify or follow up on information, and make comments that contribute to the discussion and link to the remarks of others. CC.4.SL.1.d Comprehension and Collaboration: Review the key ideas expressed and explain their own ideas and understanding in light of the discussion. CC.4.SL.2 Comprehension and Collaboration: Paraphrase portions of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. CC.4.SL.3 Comprehension and Collaboration: Identify the reasons and evidence a speaker provides to support particular points. CC.4.SL.4 Presentation of Knowledge and Ideas: Report on a topic or text, tell a story, or recount an experience in an organized manner, using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace. CC.4.SL.5 Presentation of Knowledge and Ideas: Add audio recordings and visual displays to presentations when appropriate to enhance the development of main ideas or themes. CC.4.SL.6 Presentation of Knowledge and Ideas: Differentiate between contexts that call for formal English (e.g., presenting ideas) and situations where informal discourse is appropriate (e.g., small-group discussion); use formal English when appropriate to task and situation. (See grade 4 Language standards 1 and 3 on page 28 for specific expectations.) CC.4.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. CC.4.L.1.a Conventions of Standard English: Use relative pronouns (who, whose, whom, which, that) and relative adverbs (where, when, why). CC.4.L.1.b Conventions of Standard English: Form and use the progressive (e.g., I was walking; I am walking; I will be walking) verb tenses. CC.4.L.1.c Conventions of Standard English: Use modal auxiliaries (e.g., can, may, must) to convey various conditions. CC.4.L.1.d Conventions of Standard English: Order adjectives within sentences according to conventional patterns (e.g., a small red bag rather than a red small bag). CC.4.L.1.e Conventions of Standard English: Form and use prepositional phrases. CC.4.L.1.f Conventions of Standard English: Produce complete sentences, recognizing and correcting inappropriate fragments and run-ons.* CC.4.L.1.g Conventions of Standard English: Correctly use frequently confused words (e.g., to, too, two; there, their).* CC.4.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. CC.4.L.2.a Conventions of Standard English: Use correct capitalization. CC.4.L.2.b Conventions of Standard English: Use commas and quotation marks to mark direct speech and quotations from a text. CC.4.L.2.c Conventions of Standard English: Use a comma before a coordinating conjunction in a compound sentence. CC.4.L.2.d Conventions of Standard English: Spell grade-appropriate words correctly, consulting references as needed. CC.4.L.3 Knowledge of Language: Use knowledge of language and its conventions when writing, speaking, reading, or listening. CC.4.L.3.a Knowledge of Language: Choose words and phrases to convey ideas precisely.* CC.4.L.3.b Knowledge of Language: Choose punctuation for effect.* CC.4.L.3.c Knowledge of Language: Differentiate between contexts that call for formal English (e.g., presenting ideas) and situations where informal discourse is appropriate (e.g., small-group discussion). CC.4.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple- meaning words and phrases based on grade 4 reading and content, choosing flexibly from a range of strategies. CC.4.L.4.a Vocabulary Acquisition and Use: Use context (e.g., definitions, examples, or restatements in text) as a clue to the meaning of a word or phrase. CC.4.L.4.b Vocabulary Acquisition and Use: Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., telegraph, photograph, autograph). CC.4.L.4.c Vocabulary Acquisition and Use: Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases. CC.4.L.5 Vocabulary Acquisition and Use: Demonstrate understanding of figurative language, word relationships, and nuances in word meanings. CC.4.L.5.a Vocabulary Acquisition and Use: Explain the meaning of simple similes and metaphors (e.g., as pretty as a picture) in context. CC.4.L.5.b Vocabulary Acquisition and Use: Recognize and explain the meaning of common idioms, adages, and proverbs. CC.4.L.5.c Vocabulary Acquisition and Use: Demonstrate understanding of words by relating them to their opposites (antonyms) and to words with similar but not identical meanings (synonyms). CC.4.L.6 Vocabulary Acquisition and Use: Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal precise actions, emotions, or states of being (e.g., quizzed, whined, stammered) and that are basic to a particular topic (e.g., wildlife, conservation, and endangered when discussing animal preservation). Mathematics 4th Grade Standards Standard CC.4.OA.1 Use the four operations with whole numbers to solve problems. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. CC.4.OA.2 Use the four operations with whole numbers to solve problems. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. CC.4.OA.3 Use the four operations with whole numbers to solve problems. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. CC.4.OA.4 Gain familiarity with factors and multiples. Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. CC.4.OA.5 Generate and analyze patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. CC.4.NBT.1 Generalize place value understanding for multi-digit whole numbers. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.) CC.4.NBT.2 Generalize place value understanding for multi-digit whole numbers. Read and write multi- digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi- digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.) CC.4.NBT.3 Generalize place value understanding for multi-digit whole numbers. Use place value understanding to round multi-digit whole numbers to any place. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.) CC.4.NBT.4 Use place value understanding and properties of operations to perform multi-digit arithmetic. Fluently add and subtract multi-digit whole numbers using the standard algorithm. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.) CC.4.NBT.5 Use place value understanding and properties of operations to perform multi-digit arithmetic. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.) CC.4.NBT.6 Use place value understanding and properties of operations to perform multi-digit arithmetic. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.) CC.4.NF.1 Extend understanding of fraction equivalence and ordering. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.) CC.4.NF.2 Extend understanding of fraction equivalence and ordering. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.) CC.4.NF.3 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.) CC.4.NF.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. CC.4.NF.3b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. CC.4.NF.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. CC.4.NF.3d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. CC.4.NF.4 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.) CC.4.NF.4a Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4). CC.4.NF.4b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) CC.4.NF.4c Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? CC.4.NF.5 Understand decimal notation for fractions, and compare decimal fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100 and add 3/10 + 4/100 = 34/100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.) CC.4.NF.6 Understand decimal notation for fractions, and compare decimal fractions. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 meters; locate 0.62 on a number line diagram. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.) CC.4.NF.7 Understand decimal notation for fractions, and compare decimal fractions. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons comparisons are valid only when two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.) CC.4.MD.1 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example: Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …. CC.4.MD.2 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. CC.4.MD.3 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. CC.4.MD.4 Represent and interpret data. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. CC.4.MD.5 Geometric measurement: understand concepts of angle and measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: -- a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. -- b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. CC.4.MD.6 Geometric measurement: understand concepts of angle and measure angles. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. CC.4.MD.7 Geometric measurement: understand concepts of angle and measure angles. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. CC.4.G.1 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. CC.4.G.2 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. CC.4.G.3 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. English/Language Arts 5th Grade Standards Standard CC.5.R.L.1 Key Ideas and Details: Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text. CC.5.R.L.2 Key Ideas and Details: Determine a theme of a story, drama, or poem from details in the text, including how characters in a story or drama respond to challenges or how the speaker in a poem reflects upon a topic; summarize the text. CC.5.R.L.3 Key Ideas and Details: Compare and contrast two or more characters, settings, or events in a story or drama, drawing on specific details in the text (e.g., how characters interact). CC.5.R.L.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, including figurative language such as metaphors and similes. CC.5.R.L.5 Craft and Structure: Explain how a series of chapters, scenes, or stanzas fits together to provide the overall structure of a particular story, drama, or poem. CC.5.R.L.6 Craft and Structure: Describe how a narrator’s or speaker’s point of view influences how events are described. CC.5.R.L.7 Integration of Knowledge and Ideas: Analyze how visual and multimedia elements contribute to the meaning, tone, or beauty of a text (e.g., graphic novel; multimedia presentation of fiction, folktale, myth, poem). CC.5.R.L.9 Integration of Knowledge and Ideas: Compare and contrast stories in the same genre (e.g., mysteries and adventure stories) on their approaches to similar themes and topics. CC.5.R.L.10 Range of Reading and Complexity of Text: By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 4–5 text complexity band independently and proficiently. CC.5.R.I.1 Key Ideas and Details: Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text. CC.5.R.I.2 Key Ideas and Details: Determine two or more main ideas of a text and explain how they are supported by key details; summarize the text. CC.5.R.I.3 Key Ideas and Details: Explain the relationships or interactions between two or more individuals, events, ideas, or concepts in a historical, scientific, or technical text based on specific information in the text. CC.5.R.I.4 Craft and Structure: Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 5 topic or subject area. CC.5.R.I.5 Craft and Structure: Compare and contrast the overall structure (e.g., chronology, comparison, cause/effect, problem/solution) of events, ideas, concepts, or information in two or more texts. CC.5.R.I.6 Craft and Structure: Analyze multiple accounts of the same event or topic, noting important similarities and differences in the point of view they represent. CC.5.R.I.7 Integration of Knowledge and Ideas: Draw on information from multiple print or digital sources, demonstrating the ability to locate an answer to a question quickly or to solve a problem efficiently. CC.5.R.I.8 Integration of Knowledge and Ideas: Explain how an author uses reasons and evidence to support particular points in a text, identifying which reasons and evidence support which point(s). CC.5.R.I.9 Integration of Knowledge and Ideas: Integrate information from several texts on the same topic in order to write or speak about the subject knowledgeably. CC.5.R.I.10 Range of Reading and Complexity of Text: By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 4–5 text complexity band independently and proficiently. CC.5.R.F.3 Phonics and Word Recognition: Know and apply grade-level phonics and word analysis skills in decoding words. CC.5.R.F.3.a Phonics and Word Recognition: Use combined knowledge of all letter-sound correspondences, syllabication patterns, and morphology (e.g., roots and affixes) to read accurately unfamiliar multisyllabic words in context and out of context. CC.5.R.F.4 Fluency: Read with sufficient accuracy and fluency to support comprehension. CC.5.R.F.4.a Fluency: Read grade-level text with purpose and understanding. CC.5.R.F.4.b Fluency: Read grade-level prose and poetry orally with accuracy, appropriate rate, and expression. CC.5.R.F.4.c Fluency: Use context to confirm or self-correct word recognition and understanding, rereading as necessary. CC.5.W.1 Text Types and Purposes: Write opinion pieces on topics or texts, supporting a point of view with reasons and information. CC.5.W.1.a Text Types and Purposes: Introduce a topic or text clearly, state an opinion, and create an organizational structure in which ideas are logically grouped to support the writer’s purpose. CC.5.W.1.b Text Types and Purposes: Provide logically ordered reasons that are supported by facts and details. CC.5.W.1.c Text Types and Purposes: Link opinion and reasons using words, phrases, and clauses (e.g., consequently, specifically). CC.5.W.1.d Text Types and Purposes: Provide a concluding statement or section related to the opinion presented. CC.5.W.2 Text Types and Purposes: Write informative/explanatory texts to examine a topic and convey ideas and information clearly. CC.5.W.2.a Text Types and Purposes: Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. CC.5.W.2.b Text Types and Purposes: Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. CC.5.W.2.c Text Types and Purposes: Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). CC.5.W.2.d Text Types and Purposes: Use precise language and domain-specific vocabulary to inform about or explain the topic. CC.5.W.2.e Text Types and Purposes: Provide a concluding statement or section related to the information or explanation presented. CC.5.W.3 Text Types and Purposes: Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences. CC.5.W.3.a Text Types and Purposes: Orient the reader by establishing a situation and introducing a narrator and/or characters; organize an event sequence that unfolds naturally. CC.5.W.3.b Text Types and Purposes: Use narrative techniques, such as dialogue, description, and pacing, to develop experiences and events or show the responses of characters to situations. CC.5.W.3.c Text Types and Purposes: Use a variety of transitional words, phrases, and clauses to manage the sequence of events. CC.5.W.3.d Text Types and Purposes: Use concrete words and phrases and sensory details to convey experiences and events precisely. CC.5.W.3.e Text Types and Purposes: Provide a conclusion that follows from the narrated experiences or events. CC.5.W.4 Production and Distribution of Writing: Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) CC.5.W.5 Production and Distribution of Writing: With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.(Editing for conventions should demonstrate command of Language standards 1–3up to and including grade 5 on page 29.) CC.5.W.6 Production and Distribution of Writing: With some guidance and support from adults, use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of two pages in a single sitting. CC.5.W.7 Research to Build and Present Knowledge: Conduct short research projects that use several sources to build knowledge through investigation of different aspects of a topic. CC.5.W.8 Research to Build and Present Knowledge: Recall relevant information from experiences or gather relevant information from print and digital sources; summarize or paraphrase information in notes and finished work, and provide a list of sources. CC.5.W.9 Research to Build and Present Knowledge: Draw evidence from literary or informational texts to support analysis, reflection, and research. CC.5.W.9.a Research to Build and Present Knowledge: Apply grade 5 Reading standards to literature (e.g., “Compare and contrast two or more characters, settings, or events in a story or a drama, drawing on specific details in the text [e.g., how characters interact]”). CC.5.W.9.b Research to Build and Present Knowledge: Apply grade 5 Reading standards to informational texts (e.g., “Explain how an author uses reasons and evidence to support particular points in a text, identifying which reasons and evidence support which point[s]”). CC.5.W.10 Range of Writing: Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. CC.5.SL.1 Comprehension and Collaboration: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. CC.5.SL.1.a Comprehension and Collaboration: Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. CC.5.SL.1.b Comprehension and Collaboration: Follow agreed-upon rules for discussions and carry out assigned roles. CC.5.SL.1.c Comprehension and Collaboration: Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. CC.5.SL.1.d Comprehension and Collaboration: Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. CC.5.SL.2 Comprehension and Collaboration: Summarize written a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. CC.5.SL.3 Comprehension and Collaboration: Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. CC.5.SL.4 Presentation of Knowledge and Ideas: Report on a topic or text or present an opinion, sequencing ideas logically and using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace. CC.5.SL.5 Presentation of Knowledge and Ideas: Include multimedia components (e.g., graphics, sound) and visual displays in presentations when appropriate to enhance the development of main ideas or themes. CC.5.SL.6 Presentation of Knowledge and Ideas: Adapt speech to a variety of contexts and tasks, using formal English when appropriate to task and situation. (See grade 5 Language standards 1 and 3 on page 28 for specific expectations.) CC.5.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. CC.5.L.1.a Conventions of Standard English: Explain the function of conjunctions, prepositions, and interjections in general and their function in particular sentences. CC.5.L.1.b Conventions of Standard English: Form and use the perfect (e.g., I had walked; I have walked; I will have walked) verb tenses. CC.5.L.1.c Conventions of Standard English: Use verb tense to convey various times, sequences, states, and conditions. CC.5.L.1.d Conventions of Standard English: Recognize and correct inappropriate shifts in verb tense.* CC.5.L.1.e Conventions of Standard English: Use correlative conjunctions (e.g., either/or, neither/nor). CC.5.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. CC.5.L.2.a Conventions of Standard English: Use punctuation to separate items in a series.* CC.5.L.2.b Conventions of Standard English: Use a comma to separate an introductory element from the rest of the sentence. CC.5.L.2.c Conventions of Standard English: Use a comma to set off the words yes and no (e.g., Yes, thank you), to set off a tag question from the rest of the sentence (e.g., It’s true, isn’t it?), and to indicate direct address (e.g., Is that you, Steve?). CC.5.L.2.d Conventions of Standard English: Use underlining, quotation marks, or italics to indicate titles of works. CC.5.L.2.e Conventions of Standard English: Spell grade-appropriate words correctly, consulting references as needed. CC.5.L.3 Knowledge of Language: Use knowledge of language and its conventions when writing, speaking, reading, or listening. CC.5.L.3.a Knowledge of Language: Expand, combine, and reduce sentences for meaning, reader/listener interest, and style. CC.5.L.3.b Knowledge of Language: Compare and contrast the varieties of English (e.g., dialects, registers) used in stories, dramas, or poems. CC.5.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple- meaning words and phrases based on grade 5 reading and content, choosing flexibly from a range of strategies. CC.5.L.4.a Vocabulary Acquisition and Use: Use context (e.g., cause/effect relationships and comparisons in text) as a clue to the meaning of a word or phrase. CC.5.L.4.b Vocabulary Acquisition and Use: Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., photograph, photosynthesis). CC.5.L.4.c Vocabulary Acquisition and Use: Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases. CC.5.L.5 Vocabulary Acquisition and Use: Demonstrate understanding of figurative language, word relationships, and nuances in word meanings. CC.5.L.5.a Vocabulary Acquisition and Use: Interpret figurative language, including similes and metaphors, in context. CC.5.L.5.b Vocabulary Acquisition and Use: Recognize and explain the meaning of common idioms, adages, and proverbs. CC.5.L.5.c Vocabulary Acquisition and Use: Use the relationship between particular words (e.g., synonyms, antonyms, homographs) to better understand each of the words. CC.5.L.6 Vocabulary Acquisition and Use: Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal contrast, addition, and other logical relationships (e.g., however, although, nevertheless, similarly, moreover, in addition). Mathematics 5th Grade Standards Standard CC.5.OA.1 Write and interpret numerical expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. CC.5.OA.2 Write and interpret numerical expressions. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. CC.5.OA.3 Analyze patterns and relationships. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. CC.5.NBT.1 Understand the place value system. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. CC.5.NBT.2 Understand the place value system. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10. CC.5.NBT.3 Understand the place value system. Read, write, and compare decimals to thousandths. CC.5.NBT.3a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). CC.5.NBT.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. CC.5.NBT.4 Understand the place value system. Use place value understanding to round decimals to any place. CC.5.NBT.5 Perform operations with multi-digit whole numbers and with decimals to hundredths. Fluently multiply multi-digit whole numbers using the standard algorithm. CC.5.NBT.6 Perform operations with multi-digit whole numbers and with decimals to hundredths. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. CC.5.NBT.7 Perform operations with multi-digit whole numbers and with decimals to hundredths. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. CC.5.NF.1 Use equivalent fractions as a strategy to add and subtract fractions. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) CC.5.NF.2 Use equivalent fractions as a strategy to add and subtract fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 by observing that 3/7 < 1/2. CC.5.NF.3 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3 and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? CC.5.NF.4 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. CC.5.NF.4a Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) CC.5.NF.4b Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. CC.5.NF.5 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Interpret multiplication as scaling (resizing) by: -- a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. -- b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a) / (n×b) to the effect of multiplying a/b by 1. CC.5.NF.6 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. CC.5.NF.7 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.) CC.5.NF.7a Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4 and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. CC.5.NF.7b Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5) and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. CC.5.NF.7c Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? CC.5.MD.1 Convert like measurement units within a given measurement system. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step real world problems. CC.5.MD.2 Represent and interpret data. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. CC.5.MD.3 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. -- a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. -- b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. CC.5.MD.4 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. CC.5.MD.5 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. CC.5.MD.5a Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent three-fold whole- number products as volumes, e.g., to represent the associative property of multiplication. CC.5.MD.5b Apply the formulas V =(l)(w)(h) and V = (b)(h) for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. CC.5.MD.5c Recognize volume as additive. Find volumes of solid figures composed of two non- overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. CC.5.G.1 Graph points on the coordinate plane to solve real-world and mathematical problems. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). CC.5.G.2 Graph points on the coordinate plane to solve real-world and mathematical problems. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. CC.5.G.3 Classify two-dimensional figures into categories based on their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. CC.5.G.4 Classify two-dimensional figures into categories based on their properties. Classify two- dimensional figures in a hierarchy based on properties. English/Language Arts 6th Grade Standards Standard CC.6.R.L.1 Key Ideas and Details: Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. CC.6.R.L.2 Key Ideas and Details: Determine a theme or central idea of a text and how it is conveyed through particular details; provide a summary of the text distinct from personal opinions or judgments. CC.6.R.L.3 Key Ideas and Details: Describe how a particular story’s or drama’s plot unfolds in a series of episodes as well as how the characters respond or change as the plot moves toward a resolution. CC.6.R.L.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of a specific word choice on meaning and tone. CC.6.R.L.5 Craft and Structure: Analyze how a particular sentence, chapter, scene, or stanza fits into the overall structure of a text and contributes to the development of the theme, setting, or plot. CC.6.R.L.6 Craft and Structure: Explain how an author develops the point of view of the narrator or speaker in a text. CC.6.R.L.7 Integration of Knowledge and Ideas: Compare and contrast the experience of reading a story, drama, or poem to listening to or viewing an audio, video, or live version of the text, including contrasting what they “see” and “hear” when reading the text to what they perceive when they listen or watch. CC.6.R.L.9 Integration of Knowledge and Ideas: Compare and contrast texts in different forms or genres (e.g., stories and poems; historical novels and fantasy stories) in terms of their approaches to similar themes and topics. CC.6.R.L.10 Range of Reading and Level of Text Complexity: By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range. CC.6.R.I.1 Key Ideas and Details: Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. CC.6.R.I.2 Key Ideas and Details: Determine a central idea of a text and how it is conveyed through particular details; provide a summary of the text distinct from personal opinions or judgments. CC.6.R.I.3 Key Ideas and Details: Analyze in detail how a key individual, event, or idea is introduced, illustrated, and elaborated in a text (e.g., through examples or anecdotes). CC.6.R.I.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings. CC.6.R.I.5 Craft and Structure: Analyze how a particular sentence, paragraph, chapter, or section fits into the overall structure of a text and contributes to the development of the ideas. CC.6.R.I.6 Craft and Structure: Determine an author’s point of view or purpose in a text and explain how it is conveyed in the text. CC.6.R.I.7 Integration of Knowledge and Ideas: Integrate information presented in different media or formats (e.g., visually, quantitatively) as well as in words to develop a coherent understanding of a topic or issue. CC.6.R.I.8 Integration of Knowledge and Ideas: Trace and evaluate the argument and specific claims in a text, distinguishing claims that are supported by reasons and evidence from claims that are not. CC.6.R.I.9 Integration of Knowledge and Ideas: Compare and contrast one author’s presentation of events with that of another (e.g., a memoir written by and a biography on the same person). CC.6.R.I.10 Range of Reading and Level of Text Complexity: By the end of the year, read and comprehend literary nonfiction in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range. CC.6.W.1 Text Types and Purposes: Write arguments to support claims with clear reasons and relevant evidence. CC.6.W.1.a Text Types and Purposes: Introduce claim(s) and organize the reasons and evidence clearly. CC.6.W.1.b Text Types and Purposes: Support claim(s) with clear reasons and relevant evidence, using credible sources and demonstrating an understanding of the topic or text. CC.6.W.1.c Text Types and Purposes: Use words, phrases, and clauses to clarify the relationships among claim(s) and reasons. CC.6.W.1.d Text Types and Purposes: Establish and maintain a formal style. CC.6.W.1.e Text Types and Purposes: Provide a concluding statement or section that follows from the argument presented. CC.6.W.2 Text Types and Purposes: Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content. CC.6.W.2.a Text Types and Purposes: Introduce a topic; organize ideas, concepts, and information, using strategies such as definition, classification, comparison/contrast, and cause/effect; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension. CC.6.W.2.b Text Types and Purposes: Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples. CC.6.W.2.c Text Types and Purposes: Use appropriate transitions to clarify the relationships among ideas and concepts. CC.6.W.2.d Text Types and Purposes: Use precise language and domain-specific vocabulary to inform about or explain the topic. CC.6.W.2.e Text Types and Purposes: Establish and maintain a formal style. CC.6.W.2.f Text Types and Purposes: Provide a concluding statement or section that follows from the information or explanation presented. CC.6.W.3 Text Types and Purposes: Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences. CC.6.W.3.a Text Types and Purposes: Engage and orient the reader by establishing a context and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically. CC.6.W.3.b Text Types and Purposes: Use narrative techniques, such as dialogue, pacing, and description, to develop experiences, events, and/or characters. CC.6.W.3.c Text Types and Purposes: Use a variety of transition words, phrases, and clauses to convey sequence and signal shifts from one time frame or setting to another. CC.6.W.3.d Text Types and Purposes: Use precise words and phrases, relevant descriptive details, and sensory language to convey experiences and events. CC.6.W.3.e Text Types and Purposes: Provide a conclusion that follows from the narrated experiences or events. CC.6.W.4 Production and Distribution of Writing: Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) CC.6.W.5 Production and Distribution of Writing: With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.(Editing for conventions should demonstrate command of Language standards 1–3up to and including grade 6 on page53.) CC.6.W.6 Production and Distribution of Writing: Use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of three pages in a single sitting. CC.6.W.7 Research to Build and Present Knowledge: Conduct short research projects to answer a question, drawing on several sources and refocusing the inquiry when appropriate. CC.6.W.8 Research to Build and Present Knowledge: Gather relevant information from multiple print and digital sources; assess the credibility of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and providing basic bibliographic information for sources. CC.6.W.9 Research to Build and Present Knowledge: Draw evidence from literary or informational texts to support analysis, reflection, and research. CC.6.W.9.a Research to Build and Present Knowledge: Apply grade 6 Reading standards to literature (e.g., “Compare and contrast texts in different forms or genres [e.g., stories and poems; historical novels and fantasy stories]in terms of their approaches to similar themes and topics”). CC.6.W.9.b Research to Build and Present Knowledge: Apply grade 6 Reading standards to literary nonfiction (e.g., “Trace and evaluate the argument and specific claims in a text, distinguishing claims that are supported by reasons and evidence from claims that are not”). CC.6.W.10 Range of Writing: Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. CC.6.SL.1 Comprehension and Collaboration: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 6 topics, texts, and issues, building on others’ ideas and expressing their own clearly. CC.6.SL.1.a Comprehension and Collaboration: Come to discussions prepared, having read or studied required material; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion. CC.6.SL.1.b Comprehension and Collaboration: Follow rules for collegial discussions, set specific goals and deadlines, and define individual roles as needed. CC.6.SL.1.c Comprehension and Collaboration: Pose and respond to specific questions with elaboration and detail by making comments that contribute to the topic, text, or issue under discussion. CC.6.SL.1.d Comprehension and Collaboration: Review the key ideas expressed and demonstrate understanding of multiple perspectives through reflection and paraphrasing. CC.6.SL.2 Comprehension and Collaboration: Interpret information presented in diverse media and formats (e.g., visually, quantitatively, orally) and explain how it contributes to a topic, text, or issue under study. CC.6.SL.3 Comprehension and Collaboration: Delineate a speaker’s argument and specific claims, distinguishing claims that are supported by reasons and evidence from claims that are not. CC.6.SL.4 Presentation of Knowledge and Ideas: Present claims and findings, sequencing ideas logically and using pertinent descriptions, facts, and details to accentuate main ideas or themes; use appropriate eye contact, adequate volume, and clear pronunciation. CC.6.SL.5 Presentation of Knowledge and Ideas: Include multimedia components (e.g., graphics, images, music, sound) and visual displays in presentations to clarify information. CC.6.SL.6 Presentation of Knowledge and Ideas: Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate. (See grade 6 Language standards 1 and 3 on page 53 for specific expectations.) CC.6.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. CC.6.L.1.a Conventions of Standard English: Ensure that pronouns are in the proper case (subjective, objective, possessive). CC.6.L.1.b Conventions of Standard English: Use intensive pronouns (e.g., myself, ourselves). CC.6.L.1.c Conventions of Standard English: Recognize and correct inappropriate shifts in pronoun number and person.* CC.6.L.1.d Conventions of Standard English: Recognize and correct vague pronouns (i.e., ones with unclear or ambiguous antecedents).* CC.6.L.1.e Conventions of Standard English: Recognize variations from standard English in their own and others' writing and speaking, and identify and use strategies to improve expression in conventional language.* CC.6.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. CC.6.L.2.a Conventions of Standard English: Use punctuation (commas, parentheses, dashes) to set off nonrestrictive/parenthetical elements.* CC.6.L.2.b Conventions of Standard English: Spell correctly. CC.6.L.3 Knowledge of Language: Use knowledge of language and its conventions when writing, speaking, reading, or listening. CC.6.L.3.a Knowledge of Language: Vary sentence patterns for meaning, reader/listener interest, and style.* CC.6.L.3.b Knowledge of Language: Maintain consistency in style and tone.* CC.6.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple- meaning words and phrases based on grade 6 reading and content, choosing flexibly from a range of strategies. CC.6.L.4.a Vocabulary Acquisition and Use: Use context (e.g., the overall meaning of a sentence or paragraph; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. CC.6.L.4.b Vocabulary Acquisition and Use: Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., audience, auditory, audible). CC.6.L.4.c Vocabulary Acquisition and Use: Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech. CC.6.L.4.d Vocabulary Acquisition and Use: Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary). CC.6.L.5 Vocabulary Acquisition and Use: Demonstrate understanding of figurative language, word relationships, and nuances in word meanings. CC.6.L.5.a Vocabulary Acquisition and Use: Interpret figures of speech (e.g., personification) in context. CC.6.L.5.b Vocabulary Acquisition and Use: Use the relationship between particular words (e.g., cause/effect, part/whole, item/category) to better understand each of the words. CC.6.L.5.c Vocabulary Acquisition and Use: Distinguish among the connotations (associations) of words with similar denotations (definitions) (e.g., stingy, scrimping, economical, unwasteful, thrifty). CC.6.L.6 Vocabulary Acquisition and Use: Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression. Mathematics 6th Grade Standards Standard CC.6.RP.1 Understand ratio concepts and use ratio reasoning to solve problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” CC.6.RP.2 Understand ratio concepts and use ratio reasoning to solve problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0 (b not equal to zero), and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." (Expectations for unit rates in this grade are limited to non- complex fractions.) CC.6.RP.3 Understand ratio concepts and use ratio reasoning to solve problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. CC.6.RP.3a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. CC.6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed. For example, If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? CC.6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole given a part and the percent. CC.6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. CC.6.NS.1 Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? CC.6.NS.2 Compute fluently with multi-digit numbers and find common factors and multiples. Fluently divide multi-digit numbers using the standard algorithm. CC.6.NS.3 Compute fluently with multi-digit numbers and find common factors and multiples. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. CC.6.NS.4 Compute fluently with multi-digit numbers and find common factors and multiples. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). CC.6.NS.5 Apply and extend previous understandings of numbers to the system of rational numbers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. CC.6.NS.6 Apply and extend previous understandings of numbers to the system of rational numbers. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. CC.6.NS.6a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. CC.6.NS.6b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. CC.6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. CC.6.NS.7 Apply and extend previous understandings of numbers to the system of rational numbers. Understand ordering and absolute value of rational numbers. CC.6.NS.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. CC.6.NS.7b Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3°C > –7°C to express the fact that –3°C is warmer than –7°C. CC.6.NS.7c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. CC.6.NS.7d Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. CC.6.NS.8 Apply and extend previous understandings of numbers to the system of rational numbers. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. CC.6.EE.1 Apply and extend previous understandings of arithmetic to algebraic expressions. Write and evaluate numerical expressions involving whole-number exponents. CC.6.EE.2 Apply and extend previous understandings of arithmetic to algebraic expressions. Write, read, and evaluate expressions in which letters stand for numbers. CC.6.EE.2a Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. CC.6.EE.2b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. CC.6.EE.2c Evaluate expressions at specific values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, including those involving whole- number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s^3 and A = 6 s^2 to find the volume and surface area of a cube with sides of length s = 1/2. CC.6.EE.3 Apply and extend previous understandings of arithmetic to algebraic expressions. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. CC.6.EE.4 Apply and extend previous understandings of arithmetic to algebraic expressions. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. CC.6.EE.5 Reason about and solve one-variable equations and inequalities. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. CC.6.EE.6 Reason about and solve one-variable equations and inequalities. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. CC.6.EE.7 Reason about and solve one-variable equations and inequalities. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. CC.6.EE.8 Reason about and solve one-variable equations and inequalities. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. CC.6.EE.9 Represent and analyze quantitative relationships between dependent and independent variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. CC.6.G.1 Solve real-world and mathematical problems involving area, surface area, and volume. Find area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real- world and mathematical problems. CC.6.G.2 Solve real-world and mathematical problems involving area, surface area, and volume. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. CC.6.G.3 Solve real-world and mathematical problems involving area, surface area, and volume. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. CC.6.G.4 Solve real-world and mathematical problems involving area, surface area, and volume. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. CC.6.SP.1 Develop understanding of statistical variability. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. CC.6.SP.2 Develop understanding of statistical variability. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. CC.6.SP.3 Develop understanding of statistical variability. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. CC.6.SP.4 Summarize and describe distributions. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. CC.6.SP.5 Summarize and describe distributions. Summarize numerical data sets in relation to their context, such as by: -- a. Reporting the number of observations. -- b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. -- c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data was gathered. -- d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered. English/Language Arts 7th Grade Standards Standard CC.7.R.L.1 Key Ideas and Details: Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. CC.7.R.L.2 Key Ideas and Details: Determine a theme or central idea of a text and analyze its development over the course of the text; provide an objective summary of the text. CC.7.R.L.3 Key Ideas and Details: Analyze how particular elements of a story or drama interact (e.g., how setting shapes the characters or plot). CC.7.R.L.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of rhymes and other repetitions of sounds (e.g., alliteration) on a specific verse or stanza of a poem or section of a story or drama. CC.7.R.L.5 Craft and Structure: Analyze how a drama’s or poem’s form or structure (e.g., soliloquy, sonnet) contributes to its meaning. CC.7.R.L.6 Craft and Structure: Analyze how an author develops and contrasts the points of view of different characters or narrators in a text. CC.7.R.L.7 Integration of Knowledge and Ideas: Compare and contrast a written story, drama, or poem to its audio, filmed, staged, or multimedia version, analyzing the effects of techniques unique to each medium (e.g., lighting, sound, color, or camera focus and angles in a film). CC.7.R.L.9 Integration of Knowledge and Ideas: Compare and contrast a fictional portrayal of a time, place, or character and a historical account of the same period as a means of understanding how authors of fiction use or alter history. CC.7.R.L.10 Range of Reading and Level of Text Complexity: By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range. CC.7.R.I.1 Key Ideas and Details: Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. CC.7.R.I.2 Key Ideas and Details: Determine two or more central ideas in a text and analyze their development over the course of the text; provide an objective summary of the text. CC.7.R.I.3 Key Ideas and Details: Analyze the interactions between individuals, events, and ideas in a text (e.g., how ideas influence individuals or events, or how individuals influence ideas or events). CC.7.R.I.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of a specific word choice on meaning and tone. CC.7.R.I.5 Craft and Structure: Analyze the structure an author uses to organize a text, including how the major sections contribute to the whole and to the development of the ideas. CC.7.R.I.6 Craft and Structure: Determine an author’s point of view or purpose in a text and analyze how the author distinguishes his or her position from that of others. CC.7.R.I.7 Integration of Knowledge and Ideas: Compare and contrast a text to an audio, video, or multimedia version of the text, analyzing each medium’s portrayal of the subject (e.g., how the delivery of a speech affects the impact of the words). CC.7.R.I.8 Integration of Knowledge and Ideas: Trace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient to support the claims. CC.7.R.I.9 Integration of Knowledge and Ideas: Analyze how two or more authors writing about the same topic shape their presentations of key information by emphasizing different evidence or advancing different interpretations of facts. CC.7.R.I.10 Range of Reading and Level of Text Complexity: By the end of the year, read and comprehend literary nonfiction in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range. CC.7.W.1 Text Types and Purposes: Write arguments to support claims with clear reasons and relevant evidence. CC.7.W.1.a Text Types and Purposes: Introduce claim(s), acknowledge alternate or opposing claims, and organize the reasons and evidence logically. CC.7.W.1.b Text Types and Purposes: Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text. CC.7.W.1.c Text Types and Purposes: Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), reasons, and evidence. CC.7.W.1.d Text Types and Purposes: Establish and maintain a formal style. CC.7.W.1.e Text Types and Purposes: Provide a concluding statement or section that follows from and supports the argument presented. CC.7.W.2 Text Types and Purposes: Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content. CC.7.W.2.a Text Types and Purposes: Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information, using strategies such as definition, classification, comparison/contrast, and cause/effect; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension. CC.7.W.2.b Text Types and Purposes: Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples. CC.7.W.2.c Text Types and Purposes: Use appropriate transitions to create cohesion and clarify the relationships among ideas and concepts. CC.7.W.2.d Text Types and Purposes: Use precise language and domain-specific vocabulary to inform about or explain the topic. CC.7.W.2.e Text Types and Purposes: Establish and maintain a formal style. CC.7.W.2.f Text Types and Purposes: Provide a concluding statement or section that follows from and supports the information or explanation presented. CC.7.W.3 Text Types and Purposes: Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences. CC.7.W.3.a Text Types and Purposes: Engage and orient the reader by establishing a context and point of view and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically. CC.7.W.3.b Text Types and Purposes: Use narrative techniques, such as dialogue, pacing, and description, to develop experiences, events, and/or characters. CC.7.W.3.c Text Types and Purposes: Use a variety of transition words, phrases, and clauses to convey sequence and signal shifts from one time frame or setting to another. CC.7.W.3.d Text Types and Purposes: Use precise words and phrases, relevant descriptive details, and sensory language to capture the action and convey experiences and events. CC.7.W.3.e Text Types and Purposes: Provide a conclusion that follows from and reflects on the narrated experiences or events. CC.7.W.4 Production and Distribution of Writing: Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) CC.7.W.5 Production and Distribution of Writing: With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on how well purpose and audience have been addressed. (Editing for conventions should demonstrate command of Language standards 1–3 up to and including grade 7 on page 53.) CC.7.W.6 Production and Distribution of Writing: Use technology, including the Internet, to produce and publish writing and link to and cite sources as well as to interact and collaborate with others, including linking to and citing sources. CC.7.W.7 Research to Build and Present Knowledge: Conduct short research projects to answer a question, drawing on several sources and generating additional related, focused questions for further research and investigation. CC.7.W.8 Research to Build and Present Knowledge: Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation. CC.7.W.9 Research to Build and Present Knowledge: Draw evidence from literary or informational texts to support analysis, reflection, and research. CC.7.W.9.a Research to Build and Present Knowledge: Apply grade 7 Reading standards to literature (e.g., “Compare and contrast a fictional portrayal of a time, place, or character and a historical account of the same period as a means of understanding how authors of fiction use or alter history”). CC.7.W.9.b Research to Build and Present Knowledge: Apply grade 7 Reading standards to literary nonfiction (e.g. “Trace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient to support the claims”). CC.7.W.10 Range of Writing: Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. CC.7.SL.1 Comprehension and Collaboration: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 7 topics, texts, and issues, building on others’ ideas and expressing their own clearly. CC.7.SL.1.a Comprehension and Collaboration: Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion. CC.7.SL.1.b Comprehension and Collaboration: Follow rules for collegial discussions, track progress toward specific goals and deadlines, and define individual roles as needed. CC.7.SL.1.c Comprehension and Collaboration: Pose questions that elicit elaboration and respond to others’ questions and comments with relevant observations and ideas that bring the discussion back on topic as needed. CC.7.SL.1.d Comprehension and Collaboration: Acknowledge new information expressed by others and, when warranted, modify their own views. CC.7.SL.2 Comprehension and Collaboration: Analyze the main ideas and supporting details presented in diverse media and formats (e.g., visually, quantitatively, orally) and explain how the ideas clarify a topic, text, or issue under study. CC.7.SL.3 Comprehension and Collaboration: Delineate a speaker’s argument and specific claims, evaluating the soundness of the reasoning and the relevance and sufficiency of the evidence. CC.7.SL.4 Presentation of Knowledge and Ideas: Present claims and findings, emphasizing salient points in a focused, coherent manner with pertinent descriptions, facts, details, and examples; use appropriate eye contact, adequate volume, and clear pronunciation. CC.7.SL.5 Presentation of Knowledge and Ideas: Include multimedia components and visual displays in presentations to clarify claims and findings and emphasize salient points CC.7.SL.6 Presentation of Knowledge and Ideas: Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate. CC.7.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. CC.7.L.1.a Conventions of Standard English: Explain the function of phrases and clauses in general and their function in specific sentences. CC.7.L.1.b Conventions of Standard English: Choose among simple, compound, complex, and compound- complex sentences to signal differing relationships among ideas. CC.7.L.1.c Conventions of Standard English: Place phrases and clauses within a sentence, recognizing and correcting misplaced and dangling modifiers.* CC.7.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. CC.7.L.2.a Conventions of Standard English: Use a comma to separate coordinate adjectives (e.g., It was a fascinating, enjoyable movie but not He wore an old[,] green shirt). CC.7.L.2.b Conventions of Standard English: Spell correctly. CC.7.L.3 Knowledge of Language: Use knowledge of language and its conventions when writing, speaking, reading, or listening. CC.7.L.3.a Knowledge of Language: Choose language that expresses ideas precisely and concisely, recognizing and eliminating wordiness and redundancy.* CC.7.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple- meaning words and phrases based on grade 7 reading and content, choosing flexibly from a range of strategies. CC.7.L.4.a Vocabulary Acquisition and Use: Use context (e.g., the overall meaning of a sentence or paragraph; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. CC.7.L.4.b Vocabulary Acquisition and Use: Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., belligerent, bellicose, rebel). CC.7.L.4.c Vocabulary Acquisition and Use: Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech. CC.7.L.4.d Vocabulary Acquisition and Use: Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary). CC.7.L.5 Vocabulary Acquisition and Use: Demonstrate understanding of figurative language, word relationships, and nuances in word meanings. CC.7.L.5.a Vocabulary Acquisition and Use: Interpret figures of speech (e.g., literary, biblical, and mythological allusions) in context. CC.7.L.5.b Vocabulary Acquisition and Use: Use the relationship between particular words (e.g., synonym/antonym, analogy) to better understand each of the words. CC.7.L.5.c Vocabulary Acquisition and Use: Distinguish among the connotations (associations) of words with similar denotations (definitions) (e.g., refined, respectful, polite, diplomatic, condescending). CC.7.L.6 Vocabulary Acquisition and Use: Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression. Mathematics 7th Grade Standards Standard CC.7.RP.1 Analyze proportional relationships and use them to solve real-world and mathematical problems. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour. CC.7.RP.2 Analyze proportional relationships and use them to solve real-world and mathematical problems. Recognize and represent proportional relationships between quantities. CC.7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. CC.7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. CC.7.RP.2c Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. CC.7.RP.2d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. CC.7.RP.3 Analyze proportional relationships and use them to solve real-world and mathematical problems. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. CC.7.NS.1 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. CC.7.NS.1a Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. CC.7.NS.1b Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. CC.7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. CC.7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers. CC.7.NS.2 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. CC.7.NS.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. CC.7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts. CC.7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers. CC.7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. CC.7.NS.3 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) CC.7.EE.1 Use properties of operations to generate equivalent expressions. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. CC.7.EE.2 Use properties of operations to generate equivalent expressions. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.” CC.7.EE.3 Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. CC.7.EE.4 Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. CC.7.EE.4a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? CC.7.EE.4b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example, As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. CC.7.G.1 Draw, construct, and describe geometrical figures and describe the relationships between them. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. CC.7.G.2 Draw, construct, and describe geometrical figures and describe the relationships between them. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. CC.7.G.3 Draw, construct, and describe geometrical figures and describe the relationships between them. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. CC.7.G.4 Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. CC.7.G.5 Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. CC.7.G.6 Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. CC.7.SP.1 Use random sampling to draw inferences about a population. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. CC.7.SP.2 Use random sampling to draw inferences about a population. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. CC.7.SP.3 Draw informal comparative inferences about two populations. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. CC.7.SP.4 Draw informal comparative inferences about two populations. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh- grade science book are generally longer than the words in a chapter of a fourth-grade science book. CC.7.SP.5 Investigate chance processes and develop, use, and evaluate probability models. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. CC.7.SP.6 Investigate chance processes and develop, use, and evaluate probability models. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. CC.7.SP.7 Investigate chance processes and develop, use, and evaluate probability models. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. CC.7.SP.7a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. CC.7.SP.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? CC.7.SP.8 Investigate chance processes and develop, use, and evaluate probability models. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. CC.7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. CC.7.SP.8b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. CC.7.SP.8c Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? English/Language Arts 8th Grade Standards Standard CC.8.R.L.1 Key Ideas and Details: Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text. CC.8.R.L.2 Key Ideas and Details: Determine a theme or central idea of a text and analyze its development over the course of the text, including its relationship to the characters, setting, and plot; provide an objective summary of the text. CC.8.R.L.3 Key Ideas and Details: Analyze how particular lines of dialogue or incidents in a story or drama propel the action, reveal aspects of a character, or provoke a decision. CC.8.R.L.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts. CC.8.R.L.5 Craft and Structure: Compare and contrast the structure of two or more texts and analyze how the differing structure of each text contributes to its meaning and style. CC.8.R.L.6 Craft and Structure: Analyze how differences in the points of view of the characters and the audience or reader (e.g., created through the use of dramatic irony) create such effects as suspense or humor. CC.8.R.L.7 Integration of Knowledge and Ideas: Analyze the extent to which a filmed or live production of a story or drama stays faithful to or departs from the text or script, evaluating the choices made by the director or actors. CC.8.R.L.9 Integration of Knowledge and Ideas: Analyze how a modern work of fiction draws on themes, patterns of events, or character types from myths, traditional stories, or religious works such as the Bible, including describing how the material is rendered new. CC.8.R.L.10 Range of Reading and Level of Text Complexity: By the end of the year, read and comprehend literature, including stories, dramas, and poems, at the high end of grades 6–8 text complexity band independently and proficiently. CC.8.R.I.1 Key Ideas and Details: Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text. CC.8.R.I.2 Key Ideas and Details: Determine a central idea of a text and analyze its development over the course of the text, including its relationship to supporting ideas; provide an objective summary of the text. CC.8.R.I.3 Key Ideas and Details: Analyze how a text makes connections among and distinctions between individuals, ideas, or events (e.g., through comparisons, analogies, or categories). CC.8.R.I.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts. CC.8.R.I.5 Craft and Structure: Analyze in detail the structure of a specific paragraph in a text, including the role of particular sentences in developing and refining a key concept. CC.8.R.I.6 Craft and Structure: Determine an author’s point of view or purpose in a text and analyze how the author acknowledges and responds to conflicting evidence or viewpoints. CC.8.R.I.7 Integration of Knowledge and Ideas: Evaluate the advantages and disadvantages of using different mediums (e.g., print or digital text, video, multimedia) to present a particular topic or idea. CC.8.R.I.8 Integration of Knowledge and Ideas: Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient; recognize when irrelevant evidence is introduced. CC.8.R.I.9 Integration of Knowledge and Ideas: Analyze a case in which two or more texts provide conflicting information on the same topic and identify where the texts disagree on matters of fact or interpretation. CC.8.R.I.10 Range of Reading and Level of Text Complexity: By the end of the year, read and comprehend literary nonfiction at the high end of the grades 6–8 text complexity band independently and proficiently. CC.8.W.1 Text Types and Purposes: Write arguments to support claims with clear reasons and relevant evidence. CC.8.W.1.a Text Types and Purposes: Introduce claim(s), acknowledge and distinguish the claim(s) from alternate or opposing claims, and organize the reasons and evidence logically. CC.8.W.1.b Text Types and Purposes: Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text. CC.8.W.1.c Text Types and Purposes: Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), counterclaims, reasons, and evidence. CC.8.W.1.d Text Types and Purposes: Establish and maintain a formal style. CC.8.W.1.e Text Types and Purposes: Provide a concluding statement or section that follows from and supports the argument presented. CC.8.W.2 Text Types and Purposes: Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content. CC.8.W.2.a Text Types and Purposes: Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information into broader categories; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension. CC.8.W.2.b Text Types and Purposes: Develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other information and examples. CC.8.W.2.c Text Types and Purposes: Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and concepts. CC.8.W.2.d Text Types and Purposes: Use precise language and domain-specific vocabulary to inform about or explain the topic. CC.8.W.2.e Text Types and Purposes: Establish and maintain a formal style. CC.8.W.2.f Text Types and Purposes: Provide a concluding statement or section that follows from and supports the information or explanation presented. CC.8.W.3 Text Types and Purposes: Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences. CC.8.W.3.a Text Types and Purposes: Engage and orient the reader by establishing a context and point of view and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically. CC.8.W.3.b Text Types and Purposes: Use narrative techniques, such as dialogue, pacing, description, and reflection, to develop experiences, events, and/or characters. CC.8.W.3.c Text Types and Purposes: Use a variety of transition words, phrases, and clauses to convey sequence, signal shifts from one time frame or setting to another, and show the relationships among experiences and events. CC.8.W.3.d Text Types and Purposes: Use precise words and phrases, relevant descriptive details, and sensory language to capture the action and convey experiences and events. CC.8.W.3.e Text Types and Purposes: Provide a conclusion that follows from and reflects on the narrated experiences or events. CC.8.W.4 Production and Distribution of Writing: Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) CC.8.W.5 Production and Distribution of Writing: With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on how well purpose and audience have been addressed. (Editing for conventions should demonstrate command of Language standards 1–3 up to and including grade 8 on page 53.) CC.8.W.6 Production and Distribution of Writing: Use technology, including the Internet, to produce and publish writing and present the relationships between information and ideas efficiently as well as to interact and collaborate with others. CC.8.W.7 Research to Build and Present Knowledge: Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration. CC.8.W.8 Research to Build and Present Knowledge: Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation. CC.8.W.9 Research to Build and Present Knowledge: Draw evidence from literary or informational texts to support analysis, reflection, and research. CC.8.W.9.a Research to Build and Present Knowledge: Apply grade 8 Reading standards to literature (e.g., “Analyze how a modern work of fiction draws on themes, patterns of events, or character types from myths, traditional stories, or religious works such as the Bible, including describing how the material is rendered new”). CC.8.W.9.b Research to Build and Present Knowledge: Apply grade 8 Reading standards to literary nonfiction (e.g., “Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient; recognize when irrelevant evidence is introduced”). CC.8.W.10 Range of Writing: Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. CC.8.SL.1 Comprehension and Collaboration: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 8 topics, texts, and issues, building on others’ ideas and expressing their own clearly. CC.8.SL.1.a Comprehension and Collaboration: Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion. CC.8.SL.1.b Comprehension and Collaboration: Follow rules for collegial discussions and decision- making, track progress toward specific goals and deadlines, and define individual roles as needed. CC.8.SL.1.c Comprehension and Collaboration: Pose questions that connect the ideas of several speakers and respond to others’ questions and comments with relevant evidence, observations, and ideas. CC.8.SL.1.d Comprehension and Collaboration: Acknowledge new information expressed by others, and, when warranted, qualify or justify their own views in light of the evidence presented. CC.8.SL.2 Comprehension and Collaboration: Analyze the purpose of information presented in diverse media and formats (e.g., visually, quantitatively, orally) and evaluate the motives (e.g., social, commercial, political) behind its presentation. CC.8.SL.3 Comprehension and Collaboration: Delineate a speaker’s argument and specific claims, evaluating the soundness of the reasoning and relevance and sufficiency of the evidence and identifying when irrelevant evidence is introduced. CC.8.SL.4 Presentation of Knowledge and Ideas: Present claims and findings, emphasizing salient points in a focused, coherent manner with relevant evidence, sound valid reasoning, and well-chosen details; use appropriate eye contact, adequate volume, and clear pronunciation. CC.8.SL.5 Presentation of Knowledge and Ideas: Integrate multimedia and visual displays into presentations to clarify information, strengthen claims and evidence, and add interest. CC.8.SL.6 Presentation of Knowledge and Ideas: Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate. (See grade 8 Language standards 1 and 3 on page 53 for specific expectations.) CC.8.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. CC.8.L.1.a Conventions of Standard English: Explain the function of verbals (gerunds, participles, infinitives) in general and their function in particular sentences. CC.8.L.1.b Conventions of Standard English: Form and use verbs in the active and passive voice. CC.8.L.1.c Conventions of Standard English: Form and use verbs in the indicative, imperative, interrogative, conditional, and subjunctive mood. CC.8.L.1.d Conventions of Standard English: Recognize and correct inappropriate shifts in verb voice and mood.* CC.8.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. CC.8.L.2.a Conventions of Standard English: Use punctuation (comma, ellipsis, dash) to indicate a pause or break. CC.8.L.2.b Conventions of Standard English: Use an ellipsis to indicate an omission. CC.8.L.2.c Conventions of Standard English: Spell correctly. CC.8.L.3 Knowledge of Language: Use knowledge of language and its conventions when writing, speaking, reading, or listening. CC.8.L.3.a Knowledge of Language: Use verbs in the active and passive voice and in the conditional and subjunctive mood to achieve particular effects (e.g., emphasizing the actor or the action; expressing uncertainty or describing a state contrary to fact). CC.8.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple- meaning words or phrases based on grade 8 reading and content, choosing flexibly from a range of strategies. CC.8.L.4.a Vocabulary Acquisition and Use: Use context (e.g., the overall meaning of a sentence or paragraph; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. CC.8.L.4.b Vocabulary Acquisition and Use: Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., precede, recede, secede). CC.8.L.4.c Vocabulary Acquisition and Use: Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech. CC.8.L.4.d Vocabulary Acquisition and Use: Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary). CC.8.L.5 Vocabulary Acquisition and Use: Demonstrate understanding of figurative language, word relationships, and nuances in word meanings. CC.8.L.5.a Vocabulary Acquisition and Use: Interpret figures of speech (e.g. verbal irony, puns) in context. CC.8.L.5.b Vocabulary Acquisition and Use: Use the relationship between particular words to better understand each of the words. CC.8.L.5.c Vocabulary Acquisition and Use: Distinguish among the connotations (associations) of words with similar denotations (definitions) (e.g., bullheaded, willful, firm, persistent, resolute). CC.8.L.6 Vocabulary Acquisition and Use: Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression. Mathematics 8th Grade Standards Standard CC.8.NS.1.Understand informally that evey number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0's or eventually repeat. Know that other numbers are call irrational. CC.8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example,by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. CC.8.EE.1 Work with radicals and integer exponents. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 × 3^(–5) = 3^(–3) = 1/(3^3) = 1/27. CC.8.EE.2 Work with radicals and integer exponents. Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. CC.8.EE.3 Work with radicals and integer exponents. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 10^8 and the population of the world as 7 × 10^9, and determine that the world population is more than 20 times larger. CC.8.EE.4 Work with radicals and integer exponents. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. CC.8.EE.5 Understand the connections between proportional relationships, lines, and linear equations. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance- time graph to a distance-time equation to determine which of two moving objects has greater speed. CC.8.EE.6 Understand the connections between proportional relationships, lines, and linear equations. Use similar triangles to explain why the slope m is the same between any two distinct points on a non- vertical line in the coordinate plane; derive the equation y =mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. CC.8.EE.7 Analyze and solve linear equations and pairs of simultaneous linear equations. Solve linear equations in one variable. CC.8.EE.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). CC.8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. CC.8.EE.8 Analyze and solve linear equations and pairs of simultaneous linear equations. Analyze and solve pairs of simultaneous linear equations. CC.8.EE.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. CC.8.EE.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. CC.8.EE.8c Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. CC.8.F.1 Define, evaluate, and compare functions. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.) CC.8.F.2 Define, evaluate, and compare functions. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. CC.8.F.3 Define, evaluate, and compare functions. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. CC.8.F.4 Use functions to model relationships between quantities. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. CC.8.F.5 Use functions to model relationships between quantities. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. CC.8.G.1 Understand congruence and similarity using physical models, transparencies, or geometry software. Verify experimentally the properties of rotations, reflections, and translations: -- a. Lines are taken to lines, and line segments to line segments of the same length. -- b. Angles are taken to angles of the same measure. -- c. Parallel lines are taken to parallel lines. CC.8.G.2 Understand congruence and similarity using physical models, transparencies, or geometry software. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. CC.8.G.3 Understand congruence and similarity using physical models, transparencies, or geometry software. Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. CC.8.G.4 Understand congruence and similarity using physical models, transparencies, or geometry software. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them. CC.8.G.5 Understand congruence and similarity using physical models, transparencies, or geometry software. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the three angles appear to form a line, and give an argument in terms of transversals why this is so. CC.8.G.6 Understand and apply the Pythagorean Theorem. Explain a proof of the Pythagorean Theorem and its converse. CC.8.G.7 Understand and apply the Pythagorean Theorem. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. CC.8.G.8 Understand and apply the Pythagorean Theorem. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. CC.8.G.9 Solve real-world and mathematical problems involving volume of cylinders, cones and spheres. Know the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. CC.8.SP.1 Investigate patterns of association in bivariate data. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. CC.8.SP.2 Investigate patterns of association in bivariate data. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. CC.8.SP.3 Investigate patterns of association in bivariate data. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. CC.8.SP.4 Investigate patterns of association in bivariate data. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two- way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? English/Language Arts 9 - 10th Grade Standards Standard CC.9-10.R.L.1 Key Ideas and Details: Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. CC.9-10.R.L.2 Key Ideas and Details: Determine a theme or central idea of a text and analyze in detail its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text. CC.9-10.R.L.3 Key Ideas and Details: Analyze how complex characters (e.g., those with multiple or conflicting motivations) develop over the course of a text, interact with other characters, and advance the plot or develop the theme. CC.9-10.R.L.4 Craft and Structure: Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language evokes a sense of time and place; how it sets a formal or informal tone). CC.9-10.R.L.5 Craft and Structure: Analyze how an author’s choices concerning how to structure a text, order events within it (e.g., parallel plots), and manipulate time (e.g., pacing, flashbacks) create such effects as mystery, tension, or surprise. CC.9-10.R.L.6 Craft and Structure: Analyze a particular point of view or cultural experience reflected in a work of literature from outside the United States, drawing on a wide reading of world literature. CC.9-10.R.L.7 Integration of Knowledge and Ideas: Analyze the representation of a subject or a key scene in two different artistic mediums, including what is emphasized or absent in each treatment (e.g., Auden’s “Musée des Beaux Arts” and Breughel’s Landscape with the Fall of Icarus). CC.9-10.R.L.9 Integration of Knowledge and Ideas: Analyze how an author draws on and transforms source material in a specific work (e.g., how Shakespeare treats a theme or topic from Ovid or the Bible or how a later author draws on a play by Shakespeare). CC.9-10.R.L.10 Range of Reading and Level of Text Complexity: By the end of grade 9, read and comprehend literature, including stories, dramas, and poems, in the grades 9–10 text complexity band proficiently, with scaffolding as needed at the high end of the range. By the end of grade 10, read and comprehend literature, including stories, dramas, and poems, at the high end of the grades 9–10 text complexity band independently and proficiently. CC.9-10.R.I.1 Key Ideas and Details: Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. CC.9-10.R.I.2 Key Ideas and Details: Determine a central idea of a text and analyze its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text. CC.9-10.R.I.3 Key Ideas and Details: Analyze how the author unfolds an analysis or series of ideas or events, including the order in which the points are made, how they are introduced and developed, and the connections that are drawn between them. CC.9-10.R.I.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language of a court opinion differs from that of a newspaper). CC.9-10.R.I.5 Craft and Structure: Analyze in detail how an author’s ideas or claims are developed and refined by particular sentences, paragraphs, or larger portions of a text (e.g., a section or chapter). CC.9-10.R.I.6 Craft and Structure: Determine an author’s point of view or purpose in a text and analyze how an author uses rhetoric to advance that point of view or purpose. CC.9-10.R.I.7 Integration of Knowledge and Ideas: Analyze various accounts of a subject told in different mediums (e.g., a person’s life story in both print and multimedia), determining which details are emphasized in each account. CC.9-10.R.I.8 Integration of Knowledge and Ideas: Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is valid and the evidence is relevant and sufficient; identify false statements and fallacious reasoning. CC.9-10.R.I.9 Integration of Knowledge and Ideas: Analyze seminal U.S. documents of historical and literary significance (e.g., Washington’s Farewell Address, the Gettysburg Address, Roosevelt’s Four Freedoms speech, King’s "Letter From Birmingham Jail"), including how they address related themes and concepts. CC.9-10.R.I.10 Range of Reading and Level of Text Complexity: By the end of grade 9, read and comprehend literary nonfiction in the grades 9–10 text complexity band proficiently, with scaffolding as needed at the high end of the range. By the end of grade 10, read and comprehend literary nonfiction at the high end of the grades 9–10 text complexity band independently and proficiently. CC.9-10.W.1 Text Types and Purposes: Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence. CC.9-10.W.1.a Text Types and Purposes: Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among claim(s), counterclaims, reasons, and evidence. CC.9-10.W.1.b Text Types and Purposes: Develop claim(s) and counterclaims fairly, supplying evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audience’s knowledge level and concerns. CC.9-10.W.1.c Text Types and Purposes: Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims. CC.9-10.W.1.d Text Types and Purposes: Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. CC.9-10.W.1.e Text Types and Purposes: Provide a concluding statement or section that follows from and supports the argument presented. CC.9-10.W.2 Text Types and Purposes: Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content. CC.9-10.W.2.a Text Types and Purposes: Introduce a topic; organize complex ideas, concepts, and information to make important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension. CC.9-10.W.2.b Text Types and Purposes: Develop the topic with well-chosen, relevant, and sufficient facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic. CC.9-10.W.2.c Text Types and Purposes: Use appropriate and varied transitions to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts. CC.9-10.W.2.d Text Types and Purposes: Use precise language and domain-specific vocabulary to manage the complexity of the topic. CC.9-10.W.2.e Text Types and Purposes: Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. CC.9-10.W.2.f Text Types and Purposes: Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic). CC.9-10.W.3 Text Types and Purposes: Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details, and well-structured event sequences. CC.9-10.W.3.a Text Types and Purposes: Engage and orient the reader by setting out a problem, situation, or observation, establishing one or multiple point(s) of view, and introducing a narrator and/or characters; create a smooth progression of experiences or events. CC.9-10.W.3.b Text Types and Purposes: Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, events, and/or characters. CC.9-10.W.3.c Text Types and Purposes: Use a variety of techniques to sequence events so that they build on one another to create a coherent whole. CC.9-10.W.3.d Text Types and Purposes: Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and/or characters. CC.9-10.W.3.e Text Types and Purposes: Provide a conclusion that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative. CC.9-10.W.4 Production and Distribution of Writing: Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) CC.9-10.W.5 Production and Distribution of Writing: Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience. (Editing for conventions should demonstrate command of Language standards 1–3 on up to and including grades 9-10 page 55.) CC.9-10.W.6 Production and Distribution of Writing: Use technology, including the Internet, to produce, publish, and update individual or shared writing products, taking advantage of technology’s capacity to link to other information and to display information flexibly and dynamically. CC.9-10.W.7 Research to Build and Present Knowledge: Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation. CC.9-10.W.8 Research to Build and Present Knowledge: Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the usefulness of each source in answering the research question; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and following a standard format for citation. CC.9-10.W.9 Research to Build and Present Knowledge: Draw evidence from literary or informational texts to support analysis, reflection, and research. CC.9-10.W.9.a Research to Build and Present Knowledge: Apply grades 9–10 Reading standards to literature(e.g., “Analyze how an author draws on and transforms source material in a specific work [e.g., how Shakespeare treats a theme or topic from Ovid or the Bible or how a later author draws on a play by Shakespeare]”). CC.9-10.W.9.b Research to Build and Present Knowledge: Apply grades 9–10 Reading standards to literary nonfiction (e.g., “Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is valid and the evidence is relevant and sufficient; identify false statements and fallacious reasoning”). CC.9-10.W.10 Range of Writing: Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences. CC.9-10.SL.1 Comprehension and Collaboration: Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grades 9–10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively. CC.9-10.SL.1.a Comprehension and Collaboration: Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas. CC.9-10.SL.1.b Comprehension and Collaboration: Work with peers to set rules for collegial discussions and decision-making (e.g., informal consensus, taking votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed. CC.9-10.SL.1.c Comprehension and Collaboration: Propel conversations by posing and responding to questions that relate the current discussion to broader themes or larger ideas; actively incorporate others into the discussion; and clarify, verify, or challenge ideas and conclusions. CC.9-10.SL.1.d Comprehension and Collaboration: Respond thoughtfully to diverse perspectives, summarize points of agreement and disagreement, and, when warranted, qualify or justify their own views and understanding and make new connections in light of the evidence and reasoning presented. CC.9-10.SL.2 Comprehension and Collaboration: Integrate multiple sources of information presented in diverse media or formats (e.g., visually, quantitatively, orally) evaluating the credibility and accuracy of each source. CC.9-10.SL.3 Comprehension and Collaboration: Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric, identifying any fallacious reasoning or exaggerated or distorted evidence. CC.9-10.SL.4 Presentation of Knowledge and Ideas: Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task. CC.9-10.SL.5 Presentation of Knowledge and Ideas: Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest. CC.9-10.SL.6 Presentation of Knowledge and Ideas: Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate. (See grades 9-10 Language standards 1 and 3 on pages 54 for specific expectations.) CC.9-10.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. CC.9-10.L.1.a Conventions of Standard English: Use parallel structure.* CC.9-10.L.1.b Conventions of Standard English: Use various types of phrases (noun, verb, adjectival, adverbial, participial, prepositional, absolute) and clauses (independent, dependent; noun, relative, adverbial) to convey specific meanings and add variety and interest to writing or presentations. CC.9-10.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. CC.9-10.L.2.a Conventions of Standard English: Use a semicolon (and perhaps a conjunctive adverb) to link two or more closely related independent clauses. CC.9-10.L.2.b Conventions of Standard English: Use a colon to introduce a list or quotation. CC.9-10.L.2.c Conventions of Standard English: Spell correctly. CC.9-10.L.3 Knowledge of Language: Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening. CC.9-10.L.3.a Knowledge of Language: Write and edit work so that it conforms to the guidelines in a style manual (e.g., MLA Handbook, Turabian’s Manual for Writers) appropriate for the discipline and writing type. CC.9-10.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple- meaning words and phrases based on grades 9–10 reading and content, choosing flexibly from a range of strategies. CC.9-10.L.4.a Vocabulary Acquisition and Use: Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. CC.9-10.L.4.b Vocabulary Acquisition and Use: Identify and correctly use patterns of word changes that indicate different meanings or parts of speech (e.g., analyze, analysis, analytical; advocate, advocacy). CC.9-10.L.4.c Vocabulary Acquisition and Use: Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, or its etymology. CC.9-10.L.4.d Vocabulary Acquisition and Use: Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary). CC.9-10.L.5 Vocabulary Acquisition and Use: Demonstrate understanding of figurative language, word relationships, and nuances in word meanings. CC.9-10.L.5.a Vocabulary Acquisition and Use: Interpret figures of speech (e.g., satire, sarcasm) in context and analyze their role in the text. CC.9-10.L.5.b Vocabulary Acquisition and Use: Analyze nuances in the meaning of words with similar denotations. CC.9-10.L.6 Vocabulary Acquisition and Use: Acquire and use accurately general academic and domain- specific words and phrases, sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression CC.9-10.R.H.1 Key Ideas and Details: Cite specific textual evidence to support analysis of primary and secondary sources, attending to such features as the date and origin of the information. CC.9-10.R.H.2 Key Ideas and Details: Determine the central ideas or information of a primary or secondary source; provide an accurate summary of how key events or ideas develop over the course of the text. CC.9-10.R.H.3 Key Ideas and Details: Analyze in detail a series of events described in a text; determine whether earlier events caused later ones or simply preceded them. CC.9-10.R.H.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, including vocabulary describing political, social, or economic aspects of history/social science. CC.9-10.R.H.5 Craft and Structure: Analyze how a text uses structure to emphasize key points or advance an explanation or analysis CC.9-10.R.H.6 Craft and Structure: Compare the point of view of two or more authors for how they treat the same or similar topics, including which details they include and emphasize in their respective accounts. CC.9-10.R.H.7 Integration of Knowledge and Ideas: Integrate quantitative or technical analysis (e.g., charts, research data) with qualitative analysis in print or digital text. CC.9-10.R.H.8 Integration of Knowledge and Ideas: Assess the extent to which the reasoning and evidence in a text support the author’s claims. CC.9-10.R.H.9 Integration of Knowledge and Ideas: Compare and contrast treatments of the same topic in several primary and secondary sources. CC.9-10.R.H.10 Range of Reading and Level of Text Complexity: By the end of grade 10, read and comprehend history/social studies texts in the grades 9–10 text complexity band independently and proficiently. CC.9-10.R.ST.1 Key Ideas and Details: Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions. CC.9-10.R.ST.2 Key Ideas and Details: Determine the central ideas or conclusions of a text; trace the text’s explanation or depiction of a complex process, phenomenon, or concept; provide an accurate summary of the text. CC.9-10.R.ST.3 Key Ideas and Details: Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks attending to special cases or exceptions defined in the text. CC.9-10.R.ST.4 Craft and Structure: Determine the meaning of symbols, key terms, and other domain- specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics. CC.9-10.R.ST.5 Craft and Structure: Analyze the structure of the relationships among concepts in a text, including relationships among key terms (e.g., force, friction, reaction force, energy). CC.9-10.R.ST.6 Craft and Structure: Analyze the author’s purpose in providing an explanation, describing a procedure, or discussing an experiment in a text, defining the question the author seeks to address. CC.9-10.R.ST.7 Integration of Knowledge and Ideas: Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words. CC.9-10.R.ST.8 Integration of Knowledge and Ideas: Assess the extent to which the reasoning and evidence in a text support the author’s claim or a recommendation for solving a scientific or technical problem. CC.9-10.R.ST.9 Integration of Knowledge and Ideas: Compare and contrast findings presented in a text to those from other sources (including their own experiments), noting when the findings support or contradict previous explanations or accounts. CC.9-10.R.ST.10 Range of Reading and Level of Text Complexity: By the end of grade 10, read and comprehend science/technical texts in the grades 9–10 text complexity band independently and proficiently CC.9-10.W.HST.1 Text Types and Purposes: Write arguments focused on discipline-specific content. CC.9-10.W.HST.1.a Text Types and Purposes: Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among the claim(s), counterclaims, reasons, and evidence. CC.9-10.W.HST.1.b Text Types and Purposes: Develop claim(s) and counterclaims fairly, supplying data and evidence for each while pointing out the strengths and limitations of both claim(s) and counterclaims in a discipline-appropriate form and in a manner that anticipates the audience’s knowledge level and concerns. CC.9-10.W.HST.1.c Text Types and Purposes: Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims. CC.9-10.W.HST.1.d Text Types and Purposes: Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. CC.9-10.W.HST.1.e Text Types and Purposes: Provide a concluding statement or section that follows from or supports the argument presented. CC.9-10.W.HST.2 Text Types and Purposes: Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes. CC.9-10.W.HST.2.a Text Types and Purposes: Introduce a topic and organize ideas, concepts, and information to make important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension. CC.9-10.W.HST.2.b Text Types and Purposes: Develop the topic with well-chosen, relevant, and sufficient facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic. CC.9-10.W.HST.2.c Text Types and Purposes: Use varied transitions and sentence structures to link the major sections of the text, create cohesion, and clarify the relationships among ideas and concepts. CC.9-10.W.HST.2.d Text Types and Purposes: Use precise language and domain-specific vocabulary to manage the complexity of the topic and convey a style appropriate to the discipline and context as well as to the expertise of likely readers. CC.9-10.W.HST.2.e Text Types and Purposes: Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. CC.9-10.W.HST.2.f Text Types and Purposes: Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic). CC.9-10.W.HST.4 Production and Distribution of Writing: Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. CC.9-10.W.HST.5 Production and Distribution of Writing: Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience. CC.9-10.W.HST.6 Production and Distribution of Writing: Use technology, including the Internet, to produce, publish, and update individual or shared writing products, taking advantage of technology’s capacity to link to other information and to display information flexibly and dynamically. CC.9-10.W.HST.7 Research to Build and Present Knowledge: Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation. CC.9-10.W.HST.8 Research to Build and Present Knowledge: Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the usefulness of each source in answering the research question; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and following a standard format for citation. CC.9-10.W.HST.9 Research to Build and Present Knowledge: Draw evidence from informational texts to support analysis, reflection, and research. CC.9-10.W.HST.10 Range of Writing: Write routinely over extended time frames (time for reflection and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. Mathematics 9 - 12th Grade Standards Standard CC.9-12.N.RN.1 Extend the properties of exponents to rational exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want [5^(1/3)]^3 = 5^[(1/3) x 3] to hold, so [5^(1/3)]^3 must equal 5. CC.9-12.N.RN.2 Extend the properties of exponents to rational exponents. Rewrite expressions involving radicals and rational exponents using the properties of exponents. CC.9-12.N.RN.3 Use properties of rational and irrational numbers. Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. CC.9-12.N.Q.1 Reason quantitatively and use units to solve problems. Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.* CC.9-12.N.Q.2 Reason quantitatively and use units to solve problems. Define appropriate quantities for the purpose of descriptive modeling.* CC.9-12.N.Q.3 Reason quantitatively and use units to solve problems. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.* CC.9-12.N.CN.1 Perform arithmetic operations with complex numbers. Know there is a complex number i such that i^2 = −1, and every complex number has the form a + bi with a and b real. CC.9-12.N.CN.2 Perform arithmetic operations with complex numbers. Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. CC.9-12.N.CN.3 (+) Perform arithmetic operations with complex numbers. Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. CC.9-12.N.CN.4 (+) Represent complex numbers and their operations on the complex plane. Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. CC.9-12.N.CN.5 (+) Represent complex numbers and their operations on the complex plane. Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + √3i)^3 = 8 because (-1 + √3i) has modulus 2 and argument 120°. CC.9-12.N.CN.6 (+) Represent complex numbers and their operations on the complex plane. Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. CC.9-12.N.CN.7 Use complex numbers in polynomial identities and equations. Solve quadratic equations with real coefficients that have complex solutions. CC.9-12.N.CN.8 (+) Use complex numbers in polynomial identities and equations. Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i). CC.9-12.N.CN.9 (+) Use complex numbers in polynomial identities and equations. Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. CC.9-12.N.VM.1 (+) Represent and model with vector quantities. Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v(bold), |v|, ||v||, v(not bold)). CC.9-12.N.VM.2 (+) Represent and model with vector quantities. Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. CC.9-12.N.VM.3 (+) Represent and model with vector quantities. Solve problems involving velocity and other quantities that can be represented by vectors. CC.9-12.N.VM.4 (+) Perform operations on vectors. Add and subtract vectors. CC.9-12.N.VM.4a (+) Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. CC.9-12.N.VM.4b (+) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. CC.9-12.N.VM.4c (+) Understand vector subtraction v – w as v + (–w), where (–w) is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise. CC.9-12.N.VM.5 (+) Perform operations on vectors. Multiply a vector by a scalar. CC.9-12.N.VM.5a (+) Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(v(sub x), v(sub y)) = (cv(sub x), cv(sub y)). CC.9-12.N.VM.5b (+) Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0). CC.9-12.N.VM.6 (+) Perform operations on matrices and use matrices in applications. Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. CC.9-12.N.VM.7 (+) Perform operations on matrices and use matrices in applications. Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. CC.9-12.N.VM.8 (+) Perform operations on matrices and use matrices in applications. Add, subtract, and multiply matrices of appropriate dimensions. CC.9-12.N.VM.9 (+) Perform operations on matrices and use matrices in applications. Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. CC.9-12.N.VM.10 (+) Perform operations on matrices and use matrices in applications. Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. CC.9-12.N.VM.11 (+) Perform operations on matrices and use matrices in applications. Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. CC.9-12.N.VM.12 (+) Perform operations on matrices and use matrices in applications. Work with 2 X 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. CC.9-12.A.SSE.1 Interpret the structure of expressions. Interpret expressions that represent a quantity in terms of its context.* CC.9-12.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients.* CC.9-12.A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as the product of P and a factor not depending on P.* CC.9-12.A.SSE.2 Interpret the structure of expressions. Use the structure of an expression to identify ways to rewrite it. For example, see x^4 – y^4 as (x^2)^2 – (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 – y^2)(x^2 + y^2). CC.9-12.A.SSE.3 Write expressions in equivalent forms to solve problems. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* CC.9-12.A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines.* CC.9-12.A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.* CC.9-12.A.SSE.3c Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15^t can be rewritten as [1.15^(1/12)]^(12t) ≈ 1.012^(12t) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.* CC.9-12.A.SSE.4 Write expressions in equivalent forms to solve problems. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.* CC.9-12.A.APR.1 Perform arithmetic operations on polynomials. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. CC.9-12.A.APR.2 Understand the relationship between zeros and factors of polynomial. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). CC.9-12.A.APR.3 Understand the relationship between zeros and factors of polynomials. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. CC.9-12.A.APR.4 Use polynomial identities to solve problems. Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^2 + y^2)^2 = (x^2 – y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples. CC.9-12.A.APR.5 (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.1 CC.9-12.A.APR.6 Rewrite rational expressions. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. CC.9-12.A.APR.7 (+) Rewrite rational expressions. Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. CC.9-12.A.CED.1 Create equations that describe numbers or relationship. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.* CC.9-12.A.CED.2 Create equations that describe numbers or relationship. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.* CC.9-12.A.CED.3 Create equations that describe numbers or relationship. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.* CC.9-12.A.CED.4 Create equations that describe numbers or relationship. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.* CC.9-12.A.REI.1 Understand solving equations as a process of reasoning and explain the reasoning. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. CC.9-12.A.REI.2 Understand solving equations as a process of reasoning and explain the reasoning. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. CC.9-12.A.REI.3 Solve equations and inequalities in one variable. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. CC.9-12.A.REI.4 Solve equations and inequalities in one variable. Solve quadratic equations in one variable. CC.9-12.A.REI.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)^2 = q that has the same solutions. Derive the quadratic formula from this form. CC.9-12.A.REI.4b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. CC.9-12.A.REI.5 Solve systems of equations. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. CC.9-12.A.REI.6 Solve systems of equations. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. CC.9-12.A.REI.7 Solve systems of equations. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x^2 + y^2 = 3. CC.9-12.A.REI.8 (+) Solve systems of equations. Represent a system of linear equations as a single matrix equation in a vector variable. CC.9-12.A.REI.9 (+) Solve systems of equations. Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater). CC.9-12.A.REI.10 Represent and solve equations and inequalities graphically. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). CC.9-12.A.REI.11 Represent and solve equations and inequalities graphically. Explain why the x- coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* CC.9-12.A.REI.12 Represent and solve equations and inequalities graphically. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. CC.9-12.F.IF.1 Understand the concept of a function and use function notation. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). CC.9-12.F.IF.2 Understand the concept of a function and use function notation. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. CC.9-12.F.IF.3 Understand the concept of a function and use function notation. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1 (n is greater than or equal to 1). CC.9-12.F.IF.4 Interpret functions that arise in applications in terms of the context. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* CC.9-12.F.IF.5 Interpret functions that arise in applications in terms of the context. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.* CC.9-12.F.IF.6 Interpret functions that arise in applications in terms of the context. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* CC.9-12.F.IF.7 Analyze functions using different representations. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* CC.9-12.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.* CC.9-12.F.IF.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.* CC.9-12.F.IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.* CC.9-12.F.IF.7d (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.* CC.9-12.F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.* CC.9-12.F.IF.8 Analyze functions using different representations. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. CC.9-12.F.IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. CC.9-12.F.IF.8b Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^(12t), y = (1.2)^(t/10), and classify them as representing exponential growth and decay. CC.9-12.F.IF.9 Analyze functions using different representations. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. CC.9-12.F.BF.1 Build a function that models a relationship between two quantities. Write a function that describes a relationship between two quantities.* CC.9-12.F.BF.1a Determine an explicit expression, a recursive process, or steps for calculation from a context. CC.9-12.F.BF.1b Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. CC.9-12.F.BF.1c (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. CC.9-12.F.BF.2 Build a function that models a relationship between two quantities. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* CC.9-12.F.BF.3 Build new functions from existing functions. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. CC.9-12.F.BF.4 Build new functions from existing functions. Find inverse functions. CC.9-12.F.BF.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2(x^3) or f(x) = (x+1)/(x-1) for x ≠ 1 (x not equal to 1). CC.9-12.F.BF.4b (+) Verify by composition that one function is the inverse of another. CC.9-12.F.BF.4c (+) Read values of an inverse function from a graph or a table, given that the function has an inverse. CC.9-12.F.BF.4d (+) Produce an invertible function from a non-invertible function by restricting the domain. CC.9-12.F.BF.5 (+) Build new functions from existing functions. Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. CC.9-12.F.LE.1 Construct and compare linear, quadratic, and exponential models and solve problems. Distinguish between situations that can be modeled with linear functions and with exponential functions.* CC.9-12.F.LE.1a Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.* CC.9-12.F.LE.1b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.* CC.9-12.F.LE.1c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.* CC.9-12.F.LE.2 Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).* CC.9-12.F.LE.3 Construct and compare linear, quadratic, and exponential models and solve problems. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.* CC.9-12.F.LE.4 Construct and compare linear, quadratic, and exponential models and solve problems. For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.* CC.9-12.F.LE.5 Interpret expressions for functions in terms of the situation they model. Interpret the parameters in a linear or exponential function in terms of a context.* CC.9-12.F.TF.1 Extend the domain of trigonometric functions using the unit circle. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. CC.9-12.F.TF.2 Extend the domain of trigonometric functions using the unit circle. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. CC.9-12.F.TF.3 (+) Extend the domain of trigonometric functions using the unit circle. Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π - x, π + x, and 2π - x in terms of their values for x, where x is any real number. CC.9-12.F.TF.4 (+) Extend the domain of trigonometric functions using the unit circle. Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. CC.9-12.F.TF.5 Model periodic phenomena with trigonometric functions. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* CC.9-12.F.TF.6 (+) Model periodic phenomena with trigonometric functions. Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. CC.9-12.F.TF.7 (+) Model periodic phenomena with trigonometric functions. Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.* CC.9-12.F.TF.8 Prove and apply trigonometric identities. Prove the Pythagorean identity (sin A)^2 + (cos A)^2 = 1 and use it to find sin A, cos A, or tan A, given sin A, cos A, or tan A, and the quadrant of the angle. CC.9-12.F.TF.9 (+) Prove and apply trigonometric identities. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. CC.9-12.G.CO.1 Experiment with transformations in the plane. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. CC.9-12.G.CO.2 Experiment with transformations in the plane. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). CC.9-12.G.CO.3 Experiment with transformations in the plane. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. CC.9-12.G.CO.4 Experiment with transformations in the plane. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. CC.9-12.G.CO.5 Experiment with transformations in the plane. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. CC.9-12.G.CO.6 Understand congruence in terms of rigid motions. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. CC.9-12.G.CO.7 Understand congruence in terms of rigid motions. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. CC.9-12.G.CO.8 Understand congruence in terms of rigid motions. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. CC.9-12.G.CO.9 Prove geometric theorems. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. CC.9-12.G.CO.10 Prove geometric theorems. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. CC.9-12.G.CO.11 Prove geometric theorems. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. CC.9-12.G.CO.12 Make geometric constructions. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. CC.9-12.G.CO.13 Make geometric constructions. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. CC.9-12.G.SRT.1 Understand similarity in terms of similarity transformations. Verify experimentally the properties of dilations given by a center and a scale factor: -- a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. -- b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. CC.9-12.G.SRT.2 Understand similarity in terms of similarity transformations. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. CC.9-12.G.SRT.3 Understand similarity in terms of similarity transformations. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. CC.9-12.G.SRT.4 Prove theorems involving similarity. Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. CC.9-12.G.SRT.5 Prove theorems involving similarity. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. CC.9-12.G.SRT.6 Define trigonometric ratios and solve problems involving right triangles. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. CC.9-12.G.SRT.7 Define trigonometric ratios and solve problems involving right triangles. Explain and use the relationship between the sine and cosine of complementary angles. CC.9-12.G.SRT.8 Define trigonometric ratios and solve problems involving right triangles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. CC.9-12.G.SRT.9 (+) Apply trigonometry to general triangles. Derive the formula A = (1/2)ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. CC.9-12.G.SRT.10 (+) Apply trigonometry to general triangles. Prove the Laws of Sines and Cosines and use them to solve problems. CC.9-12.G.SRT.11 (+) Apply trigonometry to general triangles. Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). CC.9-12.G.C.1 Understand and apply theorems about circles. Prove that all circles are similar. CC.9-12.G.C.2 Understand and apply theorems about circles. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. CC.9-12.G.C.3 Understand and apply theorems about circles. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. CC.9-12.G.C.4 (+) Understand and apply theorems about circles. Construct a tangent line from a point outside a given circle to the circle. CC.9-12.G.C.5 Find arc lengths and areas of sectors of circles. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. CC.9-12.G.GPE.1 Translate between the geometric description and the equation for a conic section. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. CC.9-12.G.GPE.2 Translate between the geometric description and the equation for a conic section. Derive the equation of a parabola given a focus and directrix. CC.9-12.G.GPE.3 (+) Translate between the geometric description and the equation for a conic section. Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. CC.9-12.G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). CC.9-12.G.GPE.5 Use coordinates to prove simple geometric theorems algebraically. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). CC.9-12.G.GPE.6 Use coordinates to prove simple geometric theorems algebraically. Find the point on a directed line segment between two given points that partitions the segment in a given ratio. CC.9-12.G.GPE.7 Use coordinates to prove simple geometric theorems algebraically. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.* CC.9-12.G.GMD.1 Explain volume formulas and use them to solve problems. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. CC.9-12.G.GMD.2 (+) Explain volume formulas and use them to solve problems. Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures. CC.9-12.G.GMD.3 Explain volume formulas and use them to solve problems. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* CC.9-12.G.GMD.4 Visualize relationships between two-dimensional and three-dimensional objects. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three- dimensional objects generated by rotations of two-dimensional objects. CC.9-12.G.MG.1 Apply geometric concepts in modeling situations. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* CC.9-12.G.MG.2 Apply geometric concepts in modeling situations. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).* CC.9-12.G.MG.3 Apply geometric concepts in modeling situations. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).* CC.9-12.S.ID.1 Summarize, represent, and interpret data on a single count or measurement variable. Represent data with plots on the real number line (dot plots, histograms, and box plots).* CC.9-12.S.ID.2 Summarize, represent, and interpret data on a single count or measurement variable. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.* CC.9-12.S.ID.3 Summarize, represent, and interpret data on a single count or measurement variable. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).* CC.9-12.S.ID.4 Summarize, represent, and interpret data on a single count or measurement variable. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.* CC.9-12.S.ID.5 Summarize, represent, and interpret data on two categorical and quantitative variables. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.* ns and Algebraic Thinking, NBT=Number and Operations in Base 10, MD=Measurements and Data, G=Geometry, CC.9-12.S.ID.6 Summarize, represent, and interpret data on two categorical and quantitative variables. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.* CC.9-12.S.ID.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.* CC.9-12.S.ID.6b Informally assess the fit of a function by plotting and analyzing residuals.* CC.9-12.S.ID.6c Fit a linear function for a scatter plot that suggests a linear association.* CC.9-12.S.ID.7 Interpret linear models. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.* CC.9-12.S.ID.8 Interpret linear models. Compute (using technology) and interpret the correlation coefficient of a linear fit.* CC.9-12.S.ID.9 Interpret linear models. Distinguish between correlation and causation.* CC.9-12.S.IC.1 Understand and evaluate random processes underlying statistical experiments. Understand statistics as a process for making inferences about population parameters based on a random sample from that population.* CC.9-12.S.IC.2 Understand and evaluate random processes underlying statistical experiments. Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0. 5. Would a result of 5 tails in a row cause you to question the model?* CC.9-12.S.IC.3 Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.* CC.9-12.S.IC.4 Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.* CC.9-12.S.IC.5 Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.* CC.9-12.S.IC.6 Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Evaluate reports based on data.* CC.9-12.S.CP.2 Understand independence and conditional probability and use them to interpret data. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.* CC.9-12.S.CP.3 Understand independence and conditional probability and use them to interpret data. Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.* CC.9-12.S.CP.4 Understand independence and conditional probability and use them to interpret data. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.* CC.9-12.S.CP.5 Understand independence and conditional probability and use them to interpret data. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.* CC.9-12.S.CP.6 Use the rules of probability to compute probabilities of compound events in a uniform probability model. Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.* CC.9-12.S.CP.7 Use the rules of probability to compute probabilities of compound events in a uniform probability model. Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.* CC.9-12.S.CP.8 (+) Use the rules of probability to compute probabilities of compound events in a uniform probability model. Apply the general Multiplication Rule in a uniform probability model, P(A and B) = [P(A)]x[P(B|A)] =[P(B)]x[P(A|B)], and interpret the answer in terms of the model.* CC.9-12.S.CP.9 (+) Use the rules of probability to compute probabilities of compound events in a uniform probability model. Use permutations and combinations to compute probabilities of compound events and solve problems.* CC.9-12.S.MD.1 (+) Calculate expected values and use them to solve problems. Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.* CC.9-12.S.MD.2 (+) Calculate expected values and use them to solve problems. Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.* CC.9-12.S.MD.3 (+) Calculate expected values and use them to solve problems. Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.* CC.9-12.S.MD.4 (+) Calculate expected values and use them to solve problems. Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?* CC.9-12.S.MD.5 (+) Use probability to evaluate outcomes of decisions. Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.* CC.9-12.S.MD.5a (+) Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant.* CC.9-12.S.MD.5b (+) Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.* CC.9-12.S.MD.6 (+) Use probability to evaluate outcomes of decisions. Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).* CC.9-12.S.MD.7 (+) Use probability to evaluate outcomes of decisions. Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).* English/Language Arts 11 -12th Grade Standards Standard CC.11-12.R.L.1 Key Ideas and Details: Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text, including determining where the text leaves matters uncertain. CC.11-12.R.L.2 Key Ideas and Details: Determine two or more themes or central ideas of a text and analyze their development over the course of the text, including how they interact and build on one another to produce a complex account; provide an objective summary of the text. CC.11-12.R.L.3 Key Ideas and Details: Analyze the impact of the author’s choices regarding how to develop and relate elements of a story or drama (e.g., where a story is set, how the action is ordered, how the characters are introduced and developed). CC.11-12.R.L.4 Craft and Structure: Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, including words with multiple meanings or language that is particularly fresh, engaging, or beautiful. (Include Shakespeare as well as other authors.) CC.11-12.R.L.5 Craft and Structure: Analyze how an author’s choices concerning how to structure specific parts of a text (e.g., the choice of where to begin or end a story, the choice to provide a comedic or tragic resolution) contribute to its overall structure and meaning as well as its aesthetic impact. CC.11-12.R.L.6 Craft and Structure: Analyze a case in which grasping point of view requires distinguishing what is directly stated in a text from what is really meant (e.g., satire, sarcasm, irony, or understatement). CC.11-12.R.L.7 Integration of Knowledge and Ideas: Analyze multiple interpretations of a story, drama, or poem (e.g., recorded or live production of a play or recorded novel or poetry), evaluating how each version interprets the source text. (Include at least one play by Shakespeare and one play by an American dramatist.) CC.11-12.R.L.9 Integration of Knowledge and Ideas: Demonstrate knowledge of eighteenth-, nineteenth- and early-twentieth-century foundational works of American literature, including how two or more texts from the same period treat similar themes or topics. CC.11-12.R.L.10 Range of Reading and Level of Text Complexity: By the end of grade 11, read and comprehend literature, including stories, dramas, and poems, in the grades 11–CCR text complexity band proficiently, with scaffolding as needed at the high end of the range. By the end of grade 12, read and comprehend literature, including stories, dramas, and poems, at the high end of the grades 11–CCR text complexity band independently and proficiently. CC.11-12.R.I.1 Key Ideas and Details: Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text, including determining where the text leaves matters uncertain. CC.11-12.R.I.2 Key Ideas and Details: Determine two or more central ideas of a text and analyze their development over the course of the text, including how they interact and build on one another to provide a complex analysis; provide an objective summary of the text. CC.11-12.R.I.3 Key Ideas and Details: Analyze a complex set of ideas or sequence of events and explain how specific individuals, ideas, or events interact and develop over the course of the text. CC.11-12.R.I.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze how an author uses and refines the meaning of a key term or terms over the course of a text (e.g., how Madison defines faction in Federalist No. 10). CC.11-12.R.I.5 Craft and Structure: Analyze and evaluate the effectiveness of the structure an author uses in his or her exposition or argument, including whether the structure makes points clear, convincing, and engaging. CC.11-12.R.I.6 Craft and Structure: Determine an author’s point of view or purpose in a text in which the rhetoric is particularly effective, analyzing how style and content contribute to the power, persuasiveness, or beauty of the text. CC.11-12.R.I.7 Integration of Knowledge and Ideas: Integrate and evaluate multiple sources of information presented in different media or formats (e.g., visually, quantitatively) as well as in words in order to address a question or solve a problem. CC.11-12.R.I.8 Integration of Knowledge and Ideas: Delineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional principles and use of legal reasoning (e.g., in U.S. Supreme Court majority opinions and dissents) and the premises, purposes, and arguments in works of public advocacy (e.g., The Federalist, presidential addresses). CC.11-12.R.I.9 Integration of Knowledge and Ideas: Analyze seventeenth-, eighteenth-, and nineteenth- century foundational U.S. documents of historical and literary significance (including The Declaration of Independence, the Preamble to the Constitution, the Bill of Rights, and Lincoln’s Second Inaugural Address) for their themes, purposes, and rhetorical features. CC.11-12.R.I.10 Range of Reading and Level of Text Complexity: By the end of grade 11, read and comprehend literary nonfiction in the grades 11–CCR text complexity band proficiently, with scaffolding as needed at the high end of the range. By the end of grade 12, read and comprehend literary nonfiction at the high end of the grades 11–CCR text complexity band independently and proficiently. CC.11-12.W.1 Text Types and Purposes: Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence. CC.11-12.W.1.a Text Types and Purposes: Introduce precise, knowledgeable claim(s), establish the significance of the claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that logically sequences claim(s), counterclaims, reasons, and evidence. CC.11-12.W.1.b Text Types and Purposes: Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audience’s knowledge level, concerns, values, and possible biases. CC.11-12.W.1.c Text Types and Purposes: Use words, phrases, and clauses as well as varied syntax to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims. CC.11-12.W.1.d Text Types and Purposes: Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. CC.11-12.W.1.e Text Types and Purposes: Provide a concluding statement or section that follows from and supports the argument presented. CC.11-12.W.2 Text Types and Purposes: Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content. CC.11-12.W.2.a Text Types and Purposes: Introduce a topic; organize complex ideas, concepts, and information so that each new element builds on that which precedes it to create a unified whole; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension. CC.11-12.W.2.b Text Types and Purposes: Develop the topic thoroughly by selecting the most significant and relevant facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic. CC.11-12.W.2.c Text Types and Purposes: Use appropriate and varied transitions and syntax to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts. CC.11-12.W.2.d Text Types and Purposes: Use precise language, domain-specific vocabulary, and techniques such as metaphor, simile, and analogy to manage the complexity of the topic. CC.11-12.W.2.e Text Types and Purposes: Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. CC.11-12.W.2.f Text Types and Purposes: Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic). CC.11-12.W.3 Text Types and Purposes: Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details, and well-structured event sequences. CC.11-12.W.3.a Text Types and Purposes: Engage and orient the reader by setting out a problem, situation, or observation and its significance, establishing one or multiple point(s) of view, and introducing a narrator and/or characters; create a smooth progression of experiences or events. CC.11-12.W.3.b Text Types and Purposes: Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, events, and/or characters. CC.11-12.W.3.c Text Types and Purposes: Use a variety of techniques to sequence events so that they build on one another to create a coherent whole and build toward a particular tone and outcome (e.g., a sense of mystery, suspense, growth, or resolution). CC.11-12.W.3.d Text Types and Purposes: Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and/or characters. CC.11-12.W.3.e Text Types and Purposes: Provide a conclusion that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative. CC.11-12.W.4 Production and Distribution of Writing: Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) CC.11-12.W.5 Production and Distribution of Writing: Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience. (Editing for conventions should demonstrate command of Language standards 1–3 up to and including grades 11-12 on page 55.) CC.11-12.W.6 Production and Distribution of Writing: Use technology, including the Internet, to produce, publish, and update individual or shared writing products in response to ongoing feedback, including new arguments or information. CC.11-12.W.7 Research to Build and Present Knowledge: Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation. CC.11-12.W.8 Research to Build and Present Knowledge: Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the strengths and limitations of each source in terms of the task, purpose, and audience; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and overreliance on any one source and following a standard format for citation. CC.11-12.W.9 Research to Build and Present Knowledge: Draw evidence form literary or informational texts to support analysis, reflection, and research. CC.11-12.W.9.a Research to Build and Present Knowledge: Apply grades 11–12 Reading standards to literature (e.g., “Demonstrate knowledge of eighteenth-, nineteenth- and early-twentieth-century foundational works of American literature, including how two or more texts from the same period treat similar themes or topics”). CC.11-12.W.9.b Research to Build and Present Knowledge: Apply grades 11–12 Reading standards to literary nonfiction (e.g., “Delineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional principles and use of legal reasoning [e.g., in U.S. Supreme Court Case majority opinions and dissents) and the premises, purposes, and arguments in works of public advocacy (e.g., The Federalist, presidential addresses]”). CC.11-12.W.10 Range of Writing: Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences. CC.11-12.SL.1 Comprehension and Collaboration: Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grades 11–12 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively. CC.11-12.SL.1.a Comprehension and Collaboration: Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas. CC.11-12.SL.1.b Comprehension and Collaboration: Work with peers to promote civil, democratic discussions and decision-making, set clear goals and deadlines, and establish individual roles as needed. CC.11-12.SL.1.c Comprehension and Collaboration: Propel conversations by posing and responding to questions that probe reasoning and evidence; ensure a hearing for a full range of positions on a topic or issue; clarify, verify, or challenge ideas and conclusions; and promote divergent and creative perspectives. CC.11-12.SL.1.d Comprehension and Collaboration: Respond thoughtfully to diverse perspectives; synthesize comments, claims, and evidence made on all sides of an issue; resolve contradictions when possible; and determine what additional information or research is required to deepen the investigation or complete the task. CC.11-12.SL.2 Comprehension and Collaboration: Integrate multiple sources of information presented in diverse formats and media (e.g., visually, quantitatively, orally) in order to make informed decisions and solve problems, evaluating the credibility and accuracy of each source and noting any discrepancies among the data. CC.11-12.SL.3 Comprehension and Collaboration: Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric, assessing the stance, premises, links among ideas, word choice, points of emphasis, and tone used. CC.11-12.SL.4 Presentation of Knowledge and Ideas: Present information, findings, and supporting evidence, conveying a clear and distinct perspective, such that listeners can follow the line of reasoning, alternative or opposing perspectives are addressed, and the organization, development, substance, and style are appropriate to purpose, audience, and a range or formal and informal tasks. CC.11-12.SL.5 Presentation of Knowledge and Ideas: Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest. CC.11-12.SL.6 Presentation of Knowledge and Ideas: Adapt speech to a variety of contexts and tasks, demonstrating a command of formal English when indicated or appropriate. (See grades 11-12 Language standards 1 and 3 on page 54 for specific expectations.) CC.11-12.L.1 Conventions of Standard English: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. CC.11-12.L.1.a Conventions of Standard English: Apply the understanding that usage is a matter of convention, can change over time, and is sometimes contested. CC.11-12.L.1.b Conventions of Standard English: Resolve issues of complex or contested usage, consulting references (e.g., Merriam-Webster’s Dictionary of English Usage, Garner’s Modern American English) as needed. CC.11-12.L.2 Conventions of Standard English: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. CC.11-12.L.2.a Conventions of Standard English: Observe hyphenation conventions. CC.11-12.L.2.b Conventions of Standard English: Spell correctly. CC.11-12.L.3 Knowledge of Language: Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening. CC.11-12.L.3.a Knowledge of Language: Vary syntax for effect, consulting references (e.g., Tufte’s Artful Sentences) for guidance as needed; apply an understanding of syntax to the study of complex texts when reading. CC.11-12.L.4 Vocabulary Acquisition and Use: Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades 11–12 reading and content, choosing flexibly from a range of strategies. CC.11-12.L.4.a Vocabulary Acquisition and Use: Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. CC.11-12.L.4.b Vocabulary Acquisition and Use: Identify and correctly use patterns of word changes that indicate different meanings or parts of speech (e.g., conceive, conception, conceivable). CC.11-12.L.4.c Vocabulary Acquisition and Use: Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, its etymology, or its standard usage. CC.11-12.L.4.d Vocabulary Acquisition and Use: Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary). CC.11-12.L.5 Vocabulary Acquisition and Use: Demonstrate understanding of figurative language, word relationships, and nuances in word meanings. CC.11-12.L.5.a Vocabulary Acquisition and Use: Interpret figures of speech (e.g., hyperbole, paradox) in context and analyze their role in the text. CC.11-12.L.5.b Vocabulary Acquisition and Use: Analyze nuances in the meaning of words with similar denotations. CC.11-12.L.6 Vocabulary Acquisition and Use: Acquire and use accurately general academic and domain- specific words and phrases, sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression. CC.11-12.R.H.1 Key Ideas and Details: Cite specific textual evidence to support analysis of primary and secondary sources, connecting insights gained from specific details to an understanding of the text as a whole. CC.11-12.R.H.2 Key Ideas and Details: Determine the central ideas or information of a primary or secondary source; provide an accurate summary that makes clear the relationships among the key details and ideas. CC.11-12.R.H.3 Key Ideas and Details: Evaluate various explanations for actions or events and determine which explanation best accords with textual evidence, acknowledging where the text leaves matters uncertain. CC.11-12.R.H.4 Craft and Structure: Determine the meaning of words and phrases as they are used in a text, including analyzing how an author uses and refines the meaning of a key term over the course of a text (e.g., how Madison defines faction in Federalist No. 10). CC.11-12.R.H.5 Craft and Structure: Analyze in detail how a complex primary source is structured, including how key sentences, paragraphs, and larger portions of the text contribute to the whole. CC.11-12.R.H.6 Craft and Structure: Evaluate authors’ differing points of view on the same historical event or issue by assessing the authors’ claims, reasoning, and evidence. CC.11-12.R.H.7 Integration of Knowledge and Ideas: Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., visually, quantitatively, as well as in words) in order to address a question or solve a problem. CC.11-12.R.H.8 Integration of Knowledge and Ideas: Evaluate an author’s premises, claims, and evidence by corroborating or challenging them with other information. CC.11-12.R.H.9 Integration of Knowledge and Ideas: Integrate information from diverse sources, both primary and secondary, into a coherent understanding of an idea or event, noting discrepancies among sources. CC.11-12.R.H.10 Range of Reading and Level of Text Complexity: By the end of grade 12, read and comprehend history/social studies texts in the grades 11–12 text complexity band independently and proficiently. CC.11-12.R.ST.1 Key Ideas and Details: Cite specific textual evidence to support analysis of science and technical texts, attending to important distinctions the author makes and to any gaps or inconsistencies in the account. CC.11-12.R.ST.2 Key Ideas and Details: Determine the central ideas or conclusions of a text; summarize complex concepts, processes, or information presented in a text by paraphrasing them in simpler but still accurate terms. CC.11-12.R.ST.3 Key Ideas and Details: Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks; analyze the specific results based on explanations in the text. CC.11-12.R.ST.4 Craft and Structure: Determine the meaning of symbols, key terms, and other domain- specific words and phrases as they are used in a specific scientific or technical context relevant to grades 11–12 texts and topics. CC.11-12.R.ST.5 Craft and Structure: Analyze how the text structures information or ideas into categories or hierarchies, demonstrating understanding of the information or ideas. CC.11-12.R.ST.6 Craft and Structure: Analyze the author’s purpose in providing an explanation, describing a procedure, or discussing an experiment in a text, identifying important issues that remain unresolved. CC.11-12.R.ST.7 Integration of Knowledge and Ideas: Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem. CC.11-12.R.ST.8 Integration of Knowledge and Ideas: Evaluate the hypotheses, data, analysis, and conclusions in a science or technical text, verifying the data when possible and corroborating or challenging conclusions with other sources of information. CC.11-12.R.ST.9 Integration of Knowledge and Ideas: Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of a process, phenomenon, or concept, resolving conflicting information when possible. CC.11-12.R.ST.10 Range of Reading and Level of Text Complexity: By the end of grade 12, read and comprehend science/technical texts in the grades 11–12 text complexity band independently and proficiently. CC.11-12.W.HST.1 Text Types and Purposes: Write arguments focused on discipline-specific content. CC.11-12.W.HST.1.a Text Types and Purposes: Introduce precise, knowledgeable claim(s), establish the significance of the claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that logically sequences the claim(s), counterclaims, reasons, and evidence. CC.11-12.W.HST.1.b Text Types and Purposes: Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant data and evidence for each while pointing out the strengths and limitations of both claim(s) and counterclaims in a discipline-appropriate form that anticipates the audience’s knowledge level, concerns, values, and possible biases. CC.11-12.W.HST.1.c Text Types and Purposes: Use words, phrases, and clauses as well as varied syntax to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims. CC.11-12.W.HST.1.d Text Types and Purposes: Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. CC.11-12.W.HST.1.e Text Types and Purposes: Provide a concluding statement or section that follows from or supports the argument presented. CC.11-12.W.HST.2 Text Types and Purposes: Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes. CC.11-12.W.HST.2.a Text Types and Purposes: Introduce a topic and organize complex ideas, concepts, and information so that each new element builds on that which precedes it to create a unified whole; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension. CC.11-12.W.HST.2.b Text Types and Purposes: Develop the topic thoroughly by selecting the most significant and relevant facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic. CC.11-12.W.HST.2.c Text Types and Purposes: Use varied transitions and sentence structures to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts. CC.11-12.W.HST.2.d Text Types and Purposes: Use precise language, domain-specific vocabulary and techniques such as metaphor, simile, and analogy to manage the complexity of the topic; convey a knowledgeable stance in a style that responds to the discipline and context as well as to the expertise of likely readers. CC.11-12.W.HST.2.e Text Types and Purposes: Provide a concluding statement or section that follows from and supports the information or explanation provided (e.g., articulating implications or the significance of the topic). CC.11-12.W.HST.4 Production and Distribution of Writing: Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. CC.11-12.W.HST.5 Production and Distribution of Writing: Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience. CC.11-12.W.HST.6 Production and Distribution of Writing: Use technology, including the Internet, to produce, publish, and update individual or shared writing products in response to ongoing feedback, including new arguments or information. CC.11-12.W.HST.7 Research to Build and Present Knowledge: Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation. CC.11-12.W.HST.8 Research to Build and Present Knowledge: Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the strengths and limitations of each source in terms of the specific task, purpose, and audience; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and overreliance on any one source and following a standard format for citation. CC.11-12.W.HST.9 Research to Build and Present Knowledge: Draw evidence from informational texts to support analysis, reflection, and research. CC.11-12.W.HST.10 Range of Writing: Write routinely over extended time frames (time for reflection and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. Mathematics 9 - 12th Grade Standards Standard CC.9-12.N.RN.1 Extend the properties of exponents to rational exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want [5^(1/3)]^3 = 5^[(1/3) x 3] to hold, so [5^(1/3)]^3 must equal 5. CC.9-12.N.RN.2 Extend the properties of exponents to rational exponents. Rewrite expressions involving radicals and rational exponents using the properties of exponents. CC.9-12.N.RN.3 Use properties of rational and irrational numbers. Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. CC.9-12.N.Q.1 Reason quantitatively and use units to solve problems. Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.* CC.9-12.N.Q.2 Reason quantitatively and use units to solve problems. Define appropriate quantities for the purpose of descriptive modeling.* CC.9-12.N.Q.3 Reason quantitatively and use units to solve problems. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.* CC.9-12.N.CN.1 Perform arithmetic operations with complex numbers. Know there is a complex number i such that i^2 = −1, and every complex number has the form a + bi with a and b real. CC.9-12.N.CN.2 Perform arithmetic operations with complex numbers. Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. CC.9-12.N.CN.3 (+) Perform arithmetic operations with complex numbers. Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. CC.9-12.N.CN.4 (+) Represent complex numbers and their operations on the complex plane. Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. CC.9-12.N.CN.5 (+) Represent complex numbers and their operations on the complex plane. Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + √3i)^3 = 8 because (-1 + √3i) has modulus 2 and argument 120°. CC.9-12.N.CN.6 (+) Represent complex numbers and their operations on the complex plane. Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. CC.9-12.N.CN.7 Use complex numbers in polynomial identities and equations. Solve quadratic equations with real coefficients that have complex solutions. CC.9-12.N.CN.8 (+) Use complex numbers in polynomial identities and equations. Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i). CC.9-12.N.CN.9 (+) Use complex numbers in polynomial identities and equations. Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. CC.9-12.N.VM.1 (+) Represent and model with vector quantities. Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v(bold), |v|, ||v||, v(not bold)). CC.9-12.N.VM.2 (+) Represent and model with vector quantities. Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. CC.9-12.N.VM.3 (+) Represent and model with vector quantities. Solve problems involving velocity and other quantities that can be represented by vectors. CC.9-12.N.VM.4 (+) Perform operations on vectors. Add and subtract vectors. CC.9-12.N.VM.4a (+) Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. CC.9-12.N.VM.4b (+) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. CC.9-12.N.VM.4c (+) Understand vector subtraction v – w as v + (–w), where (–w) is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise. CC.9-12.N.VM.5 (+) Perform operations on vectors. Multiply a vector by a scalar. CC.9-12.N.VM.5a (+) Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(v(sub x), v(sub y)) = (cv(sub x), cv(sub y)). CC.9-12.N.VM.5b (+) Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0). CC.9-12.N.VM.6 (+) Perform operations on matrices and use matrices in applications. Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. CC.9-12.N.VM.7 (+) Perform operations on matrices and use matrices in applications. Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. CC.9-12.N.VM.8 (+) Perform operations on matrices and use matrices in applications. Add, subtract, and multiply matrices of appropriate dimensions. CC.9-12.N.VM.9 (+) Perform operations on matrices and use matrices in applications. Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. CC.9-12.N.VM.10 (+) Perform operations on matrices and use matrices in applications. Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. CC.9-12.N.VM.11 (+) Perform operations on matrices and use matrices in applications. Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. CC.9-12.N.VM.12 (+) Perform operations on matrices and use matrices in applications. Work with 2 X 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. CC.9-12.A.SSE.1 Interpret the structure of expressions. Interpret expressions that represent a quantity in terms of its context.* CC.9-12.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients.* CC.9-12.A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as the product of P and a factor not depending on P.* CC.9-12.A.SSE.2 Interpret the structure of expressions. Use the structure of an expression to identify ways to rewrite it. For example, see x^4 – y^4 as (x^2)^2 – (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 – y^2)(x^2 + y^2). CC.9-12.A.SSE.3 Write expressions in equivalent forms to solve problems. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* CC.9-12.A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines.* CC.9-12.A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.* CC.9-12.A.SSE.3c Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15^t can be rewritten as [1.15^(1/12)]^(12t) ≈ 1.012^(12t) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.* CC.9-12.A.SSE.4 Write expressions in equivalent forms to solve problems. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.* CC.9-12.A.APR.1 Perform arithmetic operations on polynomials. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. CC.9-12.A.APR.2 Understand the relationship between zeros and factors of polynomial. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). CC.9-12.A.APR.3 Understand the relationship between zeros and factors of polynomials. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. CC.9-12.A.APR.4 Use polynomial identities to solve problems. Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^2 + y^2)^2 = (x^2 – y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples. CC.9-12.A.APR.5 (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.1 CC.9-12.A.APR.6 Rewrite rational expressions. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. CC.9-12.A.APR.7 (+) Rewrite rational expressions. Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. CC.9-12.A.CED.1 Create equations that describe numbers or relationship. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.* CC.9-12.A.CED.2 Create equations that describe numbers or relationship. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.* CC.9-12.A.CED.3 Create equations that describe numbers or relationship. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.* CC.9-12.A.CED.4 Create equations that describe numbers or relationship. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.* CC.9-12.A.REI.1 Understand solving equations as a process of reasoning and explain the reasoning. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. CC.9-12.A.REI.2 Understand solving equations as a process of reasoning and explain the reasoning. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. CC.9-12.A.REI.3 Solve equations and inequalities in one variable. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. CC.9-12.A.REI.4 Solve equations and inequalities in one variable. Solve quadratic equations in one variable. CC.9-12.A.REI.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)^2 = q that has the same solutions. Derive the quadratic formula from this form. CC.9-12.A.REI.4b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. CC.9-12.A.REI.5 Solve systems of equations. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. CC.9-12.A.REI.6 Solve systems of equations. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. CC.9-12.A.REI.7 Solve systems of equations. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x^2 + y^2 = 3. CC.9-12.A.REI.8 (+) Solve systems of equations. Represent a system of linear equations as a single matrix equation in a vector variable. CC.9-12.A.REI.9 (+) Solve systems of equations. Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater). CC.9-12.A.REI.10 Represent and solve equations and inequalities graphically. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). CC.9-12.A.REI.11 Represent and solve equations and inequalities graphically. Explain why the x- coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* CC.9-12.A.REI.12 Represent and solve equations and inequalities graphically. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. CC.9-12.F.IF.1 Understand the concept of a function and use function notation. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). CC.9-12.F.IF.2 Understand the concept of a function and use function notation. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. CC.9-12.F.IF.3 Understand the concept of a function and use function notation. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1 (n is greater than or equal to 1). CC.9-12.F.IF.4 Interpret functions that arise in applications in terms of the context. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* CC.9-12.F.IF.5 Interpret functions that arise in applications in terms of the context. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.* CC.9-12.F.IF.6 Interpret functions that arise in applications in terms of the context. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* CC.9-12.F.IF.7 Analyze functions using different representations. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* CC.9-12.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.* CC.9-12.F.IF.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.* CC.9-12.F.IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.* CC.9-12.F.IF.7d (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.* CC.9-12.F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.* CC.9-12.F.IF.8 Analyze functions using different representations. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. CC.9-12.F.IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. CC.9-12.F.IF.8b Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^(12t), y = (1.2)^(t/10), and classify them as representing exponential growth and decay. CC.9-12.F.IF.9 Analyze functions using different representations. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. CC.9-12.F.BF.1 Build a function that models a relationship between two quantities. Write a function that describes a relationship between two quantities.* CC.9-12.F.BF.1a Determine an explicit expression, a recursive process, or steps for calculation from a context. CC.9-12.F.BF.1b Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. CC.9-12.F.BF.1c (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. CC.9-12.F.BF.2 Build a function that models a relationship between two quantities. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* CC.9-12.F.BF.3 Build new functions from existing functions. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. CC.9-12.F.BF.4 Build new functions from existing functions. Find inverse functions. CC.9-12.F.BF.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2(x^3) or f(x) = (x+1)/(x-1) for x ≠ 1 (x not equal to 1). CC.9-12.F.BF.4b (+) Verify by composition that one function is the inverse of another. CC.9-12.F.BF.4c (+) Read values of an inverse function from a graph or a table, given that the function has an inverse. CC.9-12.F.BF.4d (+) Produce an invertible function from a non-invertible function by restricting the domain. CC.9-12.F.BF.5 (+) Build new functions from existing functions. Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. CC.9-12.F.LE.1 Construct and compare linear, quadratic, and exponential models and solve problems. Distinguish between situations that can be modeled with linear functions and with exponential functions.* CC.9-12.F.LE.1a Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.* CC.9-12.F.LE.1b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.* CC.9-12.F.LE.1c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.* CC.9-12.F.LE.2 Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).* CC.9-12.F.LE.3 Construct and compare linear, quadratic, and exponential models and solve problems. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.* CC.9-12.F.LE.4 Construct and compare linear, quadratic, and exponential models and solve problems. For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.* CC.9-12.F.LE.5 Interpret expressions for functions in terms of the situation they model. Interpret the parameters in a linear or exponential function in terms of a context.* CC.9-12.F.TF.1 Extend the domain of trigonometric functions using the unit circle. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. CC.9-12.F.TF.2 Extend the domain of trigonometric functions using the unit circle. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. CC.9-12.F.TF.3 (+) Extend the domain of trigonometric functions using the unit circle. Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π - x, π + x, and 2π - x in terms of their values for x, where x is any real number. CC.9-12.F.TF.4 (+) Extend the domain of trigonometric functions using the unit circle. Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. CC.9-12.F.TF.5 Model periodic phenomena with trigonometric functions. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* CC.9-12.F.TF.6 (+) Model periodic phenomena with trigonometric functions. Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. CC.9-12.F.TF.7 (+) Model periodic phenomena with trigonometric functions. Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.* CC.9-12.F.TF.8 Prove and apply trigonometric identities. Prove the Pythagorean identity (sin A)^2 + (cos A)^2 = 1 and use it to find sin A, cos A, or tan A, given sin A, cos A, or tan A, and the quadrant of the angle. CC.9-12.F.TF.9 (+) Prove and apply trigonometric identities. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. CC.9-12.G.CO.1 Experiment with transformations in the plane. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. CC.9-12.G.CO.2 Experiment with transformations in the plane. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). CC.9-12.G.CO.3 Experiment with transformations in the plane. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. CC.9-12.G.CO.4 Experiment with transformations in the plane. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. CC.9-12.G.CO.5 Experiment with transformations in the plane. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. CC.9-12.G.CO.6 Understand congruence in terms of rigid motions. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. CC.9-12.G.CO.7 Understand congruence in terms of rigid motions. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. CC.9-12.G.CO.8 Understand congruence in terms of rigid motions. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. CC.9-12.G.CO.9 Prove geometric theorems. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. CC.9-12.G.CO.10 Prove geometric theorems. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. CC.9-12.G.CO.11 Prove geometric theorems. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. CC.9-12.G.CO.12 Make geometric constructions. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. CC.9-12.G.CO.13 Make geometric constructions. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. CC.9-12.G.SRT.1 Understand similarity in terms of similarity transformations. Verify experimentally the properties of dilations given by a center and a scale factor: -- a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. -- b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. CC.9-12.G.SRT.2 Understand similarity in terms of similarity transformations. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. CC.9-12.G.SRT.3 Understand similarity in terms of similarity transformations. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. CC.9-12.G.SRT.4 Prove theorems involving similarity. Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. CC.9-12.G.SRT.5 Prove theorems involving similarity. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. CC.9-12.G.SRT.6 Define trigonometric ratios and solve problems involving right triangles. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. CC.9-12.G.SRT.7 Define trigonometric ratios and solve problems involving right triangles. Explain and use the relationship between the sine and cosine of complementary angles. CC.9-12.G.SRT.8 Define trigonometric ratios and solve problems involving right triangles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. CC.9-12.G.SRT.9 (+) Apply trigonometry to general triangles. Derive the formula A = (1/2)ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. CC.9-12.G.SRT.10 (+) Apply trigonometry to general triangles. Prove the Laws of Sines and Cosines and use them to solve problems. CC.9-12.G.SRT.11 (+) Apply trigonometry to general triangles. Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). CC.9-12.G.C.1 Understand and apply theorems about circles. Prove that all circles are similar. CC.9-12.G.C.2 Understand and apply theorems about circles. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. CC.9-12.G.C.3 Understand and apply theorems about circles. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. CC.9-12.G.C.4 (+) Understand and apply theorems about circles. Construct a tangent line from a point outside a given circle to the circle. CC.9-12.G.C.5 Find arc lengths and areas of sectors of circles. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. CC.9-12.G.GPE.1 Translate between the geometric description and the equation for a conic section. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. CC.9-12.G.GPE.2 Translate between the geometric description and the equation for a conic section. Derive the equation of a parabola given a focus and directrix. CC.9-12.G.GPE.3 (+) Translate between the geometric description and the equation for a conic section. Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. CC.9-12.G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). CC.9-12.G.GPE.5 Use coordinates to prove simple geometric theorems algebraically. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). CC.9-12.G.GPE.6 Use coordinates to prove simple geometric theorems algebraically. Find the point on a directed line segment between two given points that partitions the segment in a given ratio. CC.9-12.G.GPE.7 Use coordinates to prove simple geometric theorems algebraically. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.* CC.9-12.G.GMD.1 Explain volume formulas and use them to solve problems. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. CC.9-12.G.GMD.2 (+) Explain volume formulas and use them to solve problems. Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures. CC.9-12.G.GMD.3 Explain volume formulas and use them to solve problems. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* CC.9-12.G.GMD.4 Visualize relationships between two-dimensional and three-dimensional objects. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three- dimensional objects generated by rotations of two-dimensional objects. CC.9-12.G.MG.1 Apply geometric concepts in modeling situations. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* CC.9-12.G.MG.2 Apply geometric concepts in modeling situations. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).* CC.9-12.G.MG.3 Apply geometric concepts in modeling situations. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).* CC.9-12.S.ID.1 Summarize, represent, and interpret data on a single count or measurement variable. Represent data with plots on the real number line (dot plots, histograms, and box plots).* CC.9-12.S.ID.2 Summarize, represent, and interpret data on a single count or measurement variable. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.* CC.9-12.S.ID.3 Summarize, represent, and interpret data on a single count or measurement variable. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).* CC.9-12.S.ID.4 Summarize, represent, and interpret data on a single count or measurement variable. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.* CC.9-12.S.ID.5 Summarize, represent, and interpret data on two categorical and quantitative variables. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.* ns and Algebraic Thinking, NBT=Number and Operations in Base 10, MD=Measurements and Data, G=Geometry, CC.9-12.S.ID.6 Summarize, represent, and interpret data on two categorical and quantitative variables. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.* CC.9-12.S.ID.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.* CC.9-12.S.ID.6b Informally assess the fit of a function by plotting and analyzing residuals.* CC.9-12.S.ID.6c Fit a linear function for a scatter plot that suggests a linear association.* CC.9-12.S.ID.7 Interpret linear models. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.* CC.9-12.S.ID.8 Interpret linear models. Compute (using technology) and interpret the correlation coefficient of a linear fit.* CC.9-12.S.ID.9 Interpret linear models. Distinguish between correlation and causation.* CC.9-12.S.IC.1 Understand and evaluate random processes underlying statistical experiments. Understand statistics as a process for making inferences about population parameters based on a random sample from that population.* CC.9-12.S.IC.2 Understand and evaluate random processes underlying statistical experiments. Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0. 5. Would a result of 5 tails in a row cause you to question the model?* CC.9-12.S.IC.3 Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.* CC.9-12.S.IC.4 Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.* CC.9-12.S.IC.5 Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.* CC.9-12.S.IC.6 Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Evaluate reports based on data.* CC.9-12.S.CP.2 Understand independence and conditional probability and use them to interpret data. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.* CC.9-12.S.CP.3 Understand independence and conditional probability and use them to interpret data. Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.* CC.9-12.S.CP.4 Understand independence and conditional probability and use them to interpret data. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.* CC.9-12.S.CP.5 Understand independence and conditional probability and use them to interpret data. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.* CC.9-12.S.CP.6 Use the rules of probability to compute probabilities of compound events in a uniform probability model. Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.* CC.9-12.S.CP.7 Use the rules of probability to compute probabilities of compound events in a uniform probability model. Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.* CC.9-12.S.CP.8 (+) Use the rules of probability to compute probabilities of compound events in a uniform probability model. Apply the general Multiplication Rule in a uniform probability model, P(A and B) = [P(A)]x[P(B|A)] =[P(B)]x[P(A|B)], and interpret the answer in terms of the model.* CC.9-12.S.CP.9 (+) Use the rules of probability to compute probabilities of compound events in a uniform probability model. Use permutations and combinations to compute probabilities of compound events and solve problems.* CC.9-12.S.MD.1 (+) Calculate expected values and use them to solve problems. Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.* CC.9-12.S.MD.2 (+) Calculate expected values and use them to solve problems. Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.* CC.9-12.S.MD.3 (+) Calculate expected values and use them to solve problems. Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.* CC.9-12.S.MD.4 (+) Calculate expected values and use them to solve problems. Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?* CC.9-12.S.MD.5 (+) Use probability to evaluate outcomes of decisions. Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.* CC.9-12.S.MD.5a (+) Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant.* CC.9-12.S.MD.5b (+) Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.* CC.9-12.S.MD.6 (+) Use probability to evaluate outcomes of decisions. Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).* CC.9-12.S.MD.7 (+) Use probability to evaluate outcomes of decisions. Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).*