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Updated 10/1/10 Baltimore City Schools Dr. Andrés Alonso Dr. Sonja Santelises Linda Eberhart Chief Executive Officer Chief Academic Officer Executive Director Teaching and Learning Curriculum Writers Thanks to all City Schools teachers who wrote, revised, and provided feedback for this curriculum. A special thanks to the following curriculum writers: Kim Alexander Geneve Garcia Elizabeth Renwick Margo Berish Beth Goldscher Estelito Reyes Julia Bonkowski Andrew Hlavka Katherine Schlee Megan Bovill Gil Laqui Weston Schreiber Thomas Coleman Maggie Lasaga-Flister Levi Straight Megan Cooper Benjamin Lawrence Odessa Tamayo Matthew Damseaux Luis Lima Siriporn Vinijkul Kimberly David Genevieve Mason Smitha Viswanathan Melanie Davison Scott Messinger Shanekwa Winfield Chritian Fisher Kevin Older Math Works Homework Other Useful Links Homework can be an effective part of your math MSA Daily Reviews program - giving students the practice they need to master skills. Below are some Math Works methods for utilizing homework. Mathematics Study Guide Suggested Homework Procedures: o Check homework every night o Give students an opportunity to revise homework Vocabulary Activities o Start the homework assignment together at the beginning or end of class. o Dedicate 10 minutes to going over 2-5 problems that Math Templates students are having trouble with (they pick some, you pick some). Model how you work through the problems on the board. Structuring Your Math Block - o Reward students for doing homework and revising it. Weekly Planning Grid Homework Tips: o Homework should consist primarily of skills that students have already been exposed to. Skills should Sample Lesson Plan Template cycle in and out depending on what your students have been taught AND what they have mastered. o Require students to show their work on homework problems, not just write the answer. Give credit only when there is work. o Circulate throughout the classroom while talking about homework problems to be sure students are writing down what you are talking about and are showing work. o At the beginning of the year, homework should consist of skills taught in the previous grade level. Grade 4 Homework Grade 4 Math Curriculum Sequence School Year 2010-2011 QUARTER 1 (Aug 30 – Nov 5) Suggested Time 45 days Frame BENCHMARK A Sept 7 - Sept 17 (same skills as June Benchmark in previous grade) testing window UNIT 1: Whole Number Concepts (7-12 days) Read, Write, Represent Whole Numbers Represent numbers with models through the millions *COMMON Represent numbers in numeric and word form through the CORE 2 – 4 days millions Create equivalent representations through the millions Represent numbers in expanded form through the millions *COMMON Place Value and Expanded Form of Whole Numbers CORE Identify the value of a digit through the millions using the 3 – 5 days base ten model *COMMON Compare and Order Whole Numbers CORE Compare numbers through the millions 2 – 3 days Order numbers through the millions UNIT 2: Whole Number Computation 1 (7-11 days) Add Whole Numbers *COMMON Add up to 4-digit whole numbers with regrouping CORE 1 – 2 days Subtract Whole Numbers *COMMON Subtract up to 4-digit minus 4-digit regrouping once CORE Subtract up to 4-digit minus 4-digit regrouping twice 3 – 4 days Subtract up to 4-digit minus 4-digit regrouping three times Estimate Sums and Differences *COMMON Rounding whole numbers CORE Estimating sums and differences 2 – 3 days Compare Values of Mixed Currency Identify value of mixed currency 1 – 2 days Compare money sets Unit 3: Number Theory and Computation 2 (10-20 days) Multiples 1 – 2 days Identify multiples Factors Identify factors 1 – 3 days Create and interpret factor arrays Multiply Whole Numbers *COMMON Multiply up to 3-digits by 1 digit no regrouping CORE Multiply up to 3-digits by 1 digit with regrouping 2 – 4 days Multiply up to 4-digits by 1 digit with regrouping Divide Whole Numbers *COMMON Divide 2-digits by 1-digit CORE Divide 3-digits by 1 digit 3 – 5 days Divide 4-digits by 1 digit Estimate Products and Quotients Estimate products 2 – 3 days Estimate quotients Divisibility Rules Identify numbers divisible by 2 Identify numbers divisible by 5 1 – 3 days Identify numbers divisible by 10 Identify numbers divisible by a combination of 2, 5, or 10 UNIT 4: Algebra 1 (7–14 days) Numeric Patterns 1 – 2 days Identify the rule for and extend a number pattern Repeating Patterns 1 - 2 days Identify the rule for and extend a repeating pattern Growing Patterns 1 - 3 days Identify a rule for and extend a growing pattern Solve for Unknown Quantities Find the unknown using addition and subtraction 2 – 3 days Find the unknown using multiplication Function Tables Complete function tables using addition and subtraction 2 - 4 days Complete function tables using multiplication Complete function tables using division Suggested Time QUARTER 2 (Nov 8 – Jan 21) Frame 46 days BENCHMARK B Nov 1 – Nov 12 (all Quarter 1 skills assessed) testing window Unit 5: Fraction Concepts (7-12 days) Proper Fractions and Mixed Numbers Read, write, represent fractions as part of a whole 2 - 3 days Read, write, represent fractions as part of a set Read, write, represent mixed numbers Compare and Order Fractions and Mixed Numbers Compare proper fractions and mixed numbers 1 – 2 days Order proper fractions and mixed numbers Fractional Number Lines Create fractional number lines Write fractions on number lines 2 – 4 days Identify locations on number lines Write and identify mixed numbers on number lines Add and Subtract Proper Fractions and Mixed Numbers *COMMON Add proper fractions CORE Subtract proper fractions 2 – 3 days Add mixed numbers Subtract mixed numbers Unit 6: Statistics and Probability (11-18 days) Probability Express object probability as a fraction 3 - 5 days Express spinner probability as a fraction Express conditional probability as a fraction Median, Mode and Range Determine the range of a set of data 2 – 3 days Determine the mode of a set of data Determine the median of a set of data Line Plots Create line plots 3 – 5 days Interpret line plots Coordinate Grids Identify locations on a coordinate grid given object 1 – 2 days Identify objects on a coordinate grid given location Line Graphs 2 – 3 days Interpret line graphs UNIT 7: Algebra 2 (5-9 days) Write Expressions Write expressions using addition or subtraction 2 – 3 days Write expressions using multiplication or division Equivalent Expressions 1 – 2 days Write equivalent expressions Write Relationships Evaluate relationships with missing relational symbols 2 – 4 days Represent relationships in word problems Unit 8: Geometry 1 (4-8 days) Angles Identify right angles 2 – 4 days Identify acute and obtuse angles Identify angles in shapes and objects Transformations Identify and create translations 2 – 4 days Identify and create reflections Identify and create rotations Suggested Time QUARTER 3 (Jan 25 – Apr 7) Frame 45 days BENCHMARK C – Mock MSA Jan 31 – Feb 11 (all VSC assessed skills) testing window Unit 9: Geometry 2 (6-9 days) Geometric Solids Identify cones and cylinders Identify and describe pyramids by the number of edges, faces, or 4 – 6 days vertices Identify and describe prisms by the number of edges, faces, or vertices Nets for Cubes and Pyramids Identify the number and arrangement of squares needed to create cubes 2 – 3 days Identify the number and arrangement of rectangles/triangles needed to create pyramids Unit 10: Decimals (8-16 days) Read, Write, Represent Decimals Read, write, represent decimals in the tenths 2 – 4 days Read, write, represent decimals in the hundredths Place Value and Expanded Form of Decimals 1 – 3 days Represent decimals in expanded form through the hundredths Compare and Order Decimals Compare decimals through the hundredths 1 – 2 days Order decimals through the hundredths Add Decimals Add decimals through the tenths 1 – 2 days Add decimals through the hundredths Subtract Decimals Subtract decimals through the tenths 1 – 2 days Subtract decimals through the hundredths Estimate Decimal Sums and Differences Round decimals Estimate sums to the tenths 2 – 3 days Estimate sums to the ones place Estimate differences to the tenths Estimate differences to the ones place Unit 11: Measurement 1 (5-9 days) Measure Length Draw length to nearest ¼ inch 2 – 4 days Measure length to nearest ¼ inch Measure length to nearest mm Determine Equivalent Units of Length Convert yards to inches 3 – 5 days Convert inches to yards, feet Unit 12: Measurement 2 (7-11 days) Perimeter Find perimeter given all sides 2 – 3 days Find perimeter with missing sides Area Find area on grid 2 – 3 days Find area using formula Start time, Elapsed Time, and End Time Find end time 3 – 5 days Find start time Find elapsed time March 7 to Maryland State Assessment March 16 Suggested Time POST-MSA CURRICULUM Frame Unit 13: Fraction Concepts 2 (10 - 15 days) Least Common Multiple Identify the least common multiple of 2 numbers 2 - 3 days Identify the least common multiple of 3 numbers Equivalent Forms of Fractions Concrete representations of equivalent fractions using *COMMON visual models with attention to how the number and size of CORE 3 - 5 days the parts differ even though the two fractions themselves are the same size Process of finding equivalent fractions Add and Subtract Proper Fractions with Unlike Denominators *COMMON Add proper fractions with unlike denominators CORE Subtract proper fractions with unlike denominators 5 - 7 days Unit 14: Simplify & Compare Fractions (10 - 14 days) Identify GCF and Simplify Fractions Identify the Greatest Common Factor 5 - 7 days Use the Greatest Common Factor to simplify fractions Compare and Order Fractions with Unlike Denominators Compare fractions with unlike denominators *COMMON Order fractions with unlike denominators Compare mixed CORE 5 - 7 days numbers with unlike denominators Order mixed numbers with unlike denominators Unit 15: Decimal Notation for Fractions 7-13 days *COMMON Express a fraction with denominator 10 as an equivalent CORE 2-4 days fraction with denominator 100 *COMMON Use decimal notation for fractions with denominators 10 or CORE 3-5 days 100 *COMMON Compare two decimals to hundredths by reasoning about their CORE 2-4 days size Unit 16: Whole Number Computation 2 (9 – 15 days) Multiply Whole Numbers *COMMON Multiply 2-digit by 2-digit as multiple of ten CORE Multiply 2-digit by 2-digit 3 – 5 days Divide Whole Numbers *COMMON Divide with 2-digit divisor as multiple of ten with reminders CORE Divide with 2-digit divisor with remainders 3 – 5 days Division word problems BENCHMARK D – End of Year Benchmark May 16 – May 27 (all skills from Quarters 1-4 assessed) testing window *Common Core - This skill will infuse the Maryland State Standards and the Common Core. QUARTER 2 PLANNING CALENDAR* (46 DAYS) Nov 8-Jan 21 SY 2010-2011 MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY 8 Quarter 2 Begins 9 10 11 12 BENCHMARK B 15 16 17 18 (Nov 1-12) 19 NOVEMBER 22 23 24 25 Thanksgiving Holiday 26 Thanksgiving Holiday 29 30 1 2 3 6 7 8 9 10 DECEMBER 13 14 15 16 17 Early Release Day 20 21 22 23 24 Winter Break 27 Winter Break 28 Winter Break 29 Winter Break 30 Winter Break 31 Winter Break 3 4 5 6 7 JANUARY 10 11 12 13 14 17 MLK Holiday 18 19 20 21 Quarter 2 Ends Grade 4: Unit 5 Fraction Concepts Unit Resources Unit Vocabulary Unit Assessment Unit 5: Concept 1 Proper Fractions and Mixed Numbers TIME FRAME: 2-3 days PREREQUISITE SKILLS Proper Fractions and Mixed Numbers Fractions of a region (halves, thirds, fourths) Fractions as part of a set Identify fractional sets (halves, thirds, fourths) Fractions as part of a whole Represent fractional sets (halves, thirds, fourths) Mixed numbers Writing fractions VSC OBJECTIVE (calculators allowed) Knowledge and Skills 4.6.A.2.b Read, write, or represent proper fractions of a set which has the same number of items as the denominator using symbols, words, and models ASSESSMENT LIMIT: Use denominators of 6, 8, and 10 with sets of 6, 8, and 10, respectively 4.6.A.2.a Read, write, and represent proper fractions of a single region using symbols, words, and models ASSESSMENT LIMIT: Use denominators 6, 8, and 10 VOCABULARY ENDURING UNDERSTANDINGS fraction Fractions represent parts of a whole or group. Numerator Fractions can be compared using a variety of models. Denominator Fractions express a relationship between two numbers. fraction bar ESSENTIAL QUESTIONS set How are the numerator and denominator related? region How can the fractional parts of a set be modeled? mixed number How can fractions be modeled using numerals, regions, sets, and number lines? When is it appropriate to use fractions? CONCEPT KNOWLEDGE AND PROCESS A fraction is an EQUAL part of a whole or EQUAL part of a group. The numerator is the number of equal parts you have or want; the denominator is the TOTAL number of equal parts in the whole. A mixed number is a whole number and a fraction. ERROR INTERVENTION IF students confuse the THEN consider using the mnemonic that the denominator numerator and means down. Have students label and count the total denominator number of equal pieces and write that in the denominator first before they write the numerator. Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 14 officeofmath@bcps.k12.md.us Unit 5: Concept 1 Proper Fractions and Mixed Numbers IF students misread what THEN consider requiring that students circle key words that the question is asking identify what the question is asking for (e.g. highlight the for in the numerator difference between “How many pieces are shaded?” and “How many pieces are not shaded?”). IF students do not recall THEN consider showing numerous examples of equal and non- that fractions must equal pieces. have equal pieces Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 15 officeofmath@bcps.k12.md.us Unit 5: Concept 1 Proper Fractions and Mixed Numbers LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials Visual Flagging Conversation The students learn about fractions as a part of a Picture of signal flags with Spatial SF Grade 4 TE Lesson region by looking at boating signal flags. an explanation of their 9-1 (p. 500b) *You can extend this activity by giving the meanings. students a fraction to represent and having them Suggested Learning Plan create their own signal flag with a meaning. Literature Spelling Fractions The students shade parts of a region and Spelling Fractions worksheet Connection determine the fraction of consonants or vowels in List of spelling words from Visual their spelling words. Reading, Science or Social Studies Crayons or colored pencils Visual What’s Your Favorite? The students survey their classmates to find out Crayons Social their favorite pizza and create a pie chart to What’s Your Favorite? determine different fractional parts. worksheet #1 What’s Your Favorite? worksheet #2 Visual Fractions in Paintings The students identify fractional parts in a group Books or magazines with Spatial SF Grade 4 TE Lesson in pictures and in artwork. paintings or pictures 9-2 (p.502b) Social How Many in the Group The students write the fractions for different Cooperative SF Grade 4 TE Lesson characteristics of the students in their tables or 9-2 (p.502b) groups. Visual Food and Fractions The students use food to replicate fractions as a M&M’s, Skittles or Trail Mix Kinesthetic part of a set. Visual Mixed Number Bamboo The students use the integration of art to gain an Water Color Paints Kinesthetic Painting understanding of mixed numbers. The students White Paper create a bamboo painting to represent a mixed Bamboo Paint Brushes number. Bamboo Plant Kinesthetic Different Names, Same The students investigate the concept of mixed 10 x 10 grid paper Number numbers using grid paper and by cutting wholes Teaching Tool 5 SF Grade 4 TE Lesson into parts. Scissors 9-10 (p. 530a) DIFFERENTIATION CROSS-CURRICULAR CONNECTIONS Accommodations* G.A.T.E./Enrichment Artful Teaching Literacy Integration Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 16 officeofmath@bcps.k12.md.us Unit 5: Concept 1 Proper Fractions and Mixed Numbers RESOURCES Suggested Learning Plan Sub-Skills Teacher Created Materials Adopted Textbooks Technology Fractions as part MW Exploring Fractions SF Grade 4 TE Lesson 9-1 (pp. WEB: NLVM - Fraction Naming of a whole MW Exploring Fractions 500A-501) with tiles SF Grade 4 TE Lesson 9-2 (pp. MW Fractional Regions 502A-503) SF Grade 4 TE Lesson 9-10 Fractions as part MW Fractional Sets (pp. 530-533) of a set Mixed numbers MW Exploring Mixed Numbers MW Mixed Numbers Writing in Math Other Resources Assessments CONCEPT MULTIPLE CHOICE OTHER WAYS TO TRACKING SHEET ASSESSMENT QUESTION BANK ASSESS Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 17 officeofmath@bcps.k12.md.us Unit 5: Concept 2 Compare and Order Fractions and Mixed Numbers TIME FRAME: 1 – 2 days PREREQUISITE SKILLS Compare and Order Fractions and Mixed Numbers Comparing numbers Compare proper fractions and mixed numbers Ordering numbers Order proper fractions and mixed numbers Fractional number lines VSC OBJECTIVE (calculators allowed) 4.6.A.2.g Compare and order fractions and mixed numbers with or without using the symbols (<, >, or =) Assessment Limit: Use like denominators and no more than 3 numbers (0 to 20) Knowledge and Skills VOCABULARY ENDURING UNDERSTANDINGS fraction Fractions represent parts of a whole or group. numerator Fractions can be compared using a variety of models. denominator Fractions express a relationship between two numbers. fraction bar ESSENTIAL QUESTIONS mixed number How is the ordering of fractions the same as ordering whole numbers and how is it different? whole number How are the numerator and denominator related? compare How can the fractional parts of a set be modeled? order How can fractions be modeled using numerals, regions, sets, and number lines? greater than When is it appropriate to use fractions? less than CONCEPT KNOWLEDGE AND PROCESS equal to A fraction is an EQUAL part of a whole or EQUAL part of a group. The numerator is the number of equal parts you have or want; the denominator is the TOTAL number of equal parts in the whole. A mixed number is a whole number and a fraction. ERROR INTERVENTION IF students are having trouble THEN consider using fraction tiles and have students compare visualizing the size of and order fractions by laying out the tiles on their desks. fractions IF students overlook the value THEN consider requiring that students circle the whole of the whole number when numbers first and then compare/order the fractions. comparing/ordering fractions They should learn to compare the whole numbers first and mixed numbers and then the numerators when the denominators are the same. IF students read the relational THEN consider having them draw teeth inside the > or < symbol incorrectly symbol because the sign wants to “eat” the greater fraction or mixed number. Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 18 officeofmath@bcps.k12.md.us Unit 5: Concept 2 Compare and Order Fractions and Mixed Numbers LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials Kinesthetic Comparing Fraction Tiles The students use fraction tiles to compare Fraction tiles * Visual fractions and are able to visualize which Blank paper Suggested Learning Plan Spatial fraction is greater or smaller. Pencil Cooperative Place Your Order The students work with their groups to Index cards with fractions Visual represent and order fractions with like written on them Kinesthetic denominators. Pencil or crayons Visual I Spy The students spy on their classmates to I Spy! worksheet determine fractions as a part of a group. Pencil DIFFERENTIATION CROSS-CURRICULAR CONNECTIONS Accommodations* G.A.T.E./Enrichment Artful Teaching Literacy Integration Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 19 officeofmath@bcps.k12.md.us Unit 5: Concept 2 Compare and Order Fractions and Mixed Numbers RESOURCES Suggested Learning Plan Sub-Skills Teacher Created Materials Adopted Textbooks Technology Compare proper MW Exploring Compare & SF Grade 4 TE Lesson 9-9 (pp. WEB: Greater Than, Less Than, fractions and Order Fractions 524A-527) or the Same mixed numbers MW Compare Fractions MW Exploring Compare Mixed Numbers MW Compare Mixed Numbers Order proper MW Order Fractions fractions and MW Order Mixed mixed numbers Numbers Writing in Math Other Resources Assessments CONCEPT MULTIPLE CHOICE OTHER WAYS TO TRACKING SHEET ASSESSMENT QUESTION BANK ASSESS Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 20 officeofmath@bcps.k12.md.us Unit 5: Concept 3 Proper Fractions and Mixed Numbers on a Number Line TIME FRAME: 2-4 days PREREQUISITE SKILLS Proper Fractions and Mixed Numbers on a Finding a fraction on a number line (up to fourths) Number Line Finding a location on a number line (up to Create fractional number lines fourths) Write numbers on number line Identify locations on number line Knowledge and Skills Write and Identify mixed numbers on number line VSC OBJECTIVE (calculators allowed) 4.1.C.1.a Represent mixed numbers and proper fractions on a number line Assessment Line: Use proper fractions with a denominators of 6, 8, or 10 VOCABULARY ENDURING UNDERSTANDINGS fraction Fractions represent parts of a whole or group. numerator Fractions can be compared using a variety of models. denominator ESSENTIAL QUESTIONS fraction bar How are the numerator and denominator related? mixed number How can the fractional parts of a set be modeled? whole number How can fractions be modeled using numerals, regions, set, and number lines? CONCEPT KNOWLEDGE AND PROCESS A fraction is an equal part of a whole or part of a group (set). The numerator is the number of equal parts you have or want; the denominator is the TOTAL number of equal parts in the whole. ERROR INTERVENTION IF students count the number of lines THEN consider having students highlight each instead of the number of spaces space with a different color to find the denominator of the fraction. IF students forget to label the whole THEN consider having students trace each whole number past 1 on a number line number on a number line in a different color (mixed numbers on a number line) and write in the whole number before they actually write the mixed number/fraction. Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 21 officeofmath@bcps.k12.md.us Unit 5: Concept 3 Proper Fractions and Mixed Numbers on a Number Line IF students find the denominator by THEN consider modeling this common mistake and counting all of the equal spaces on emphasizing that the denominator is only the a number line and not just the number of equal spaces between two whole number of spaces between whole numbers. numbers IF students have trouble identifying a THEN consider requiring that students fill in all fraction/mixed number located missing fractions on the number line before between two other fractions choosing the correct answer. Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 22 officeofmath@bcps.k12.md.us Unit 5: Concept 3 Proper Fractions and Mixed Numbers on a Number Line LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials Visual Make a Number Line The students use fraction tiles to create a Fraction tiles * Spatial number line. Suggested Learning Plan Concrete Kinesthetic In the Fold The students create fractional number Strips of paper that are at SF Grade 4 TE Lesson 9-3 lines by folding strips of paper into equal least 11 inches long (p. 504b) sections and by labeling the fractions. Pencils Kinesthetic Pin the Fraction on the The students place Post-it notes on Post-it notes with various Visual Number Line number lines to begin to the connection fractions written on them between the denominator and the equal Blank number lines to number of spaces on a number line. accommodate fractions with different denominators Kinesthetic Number Line on a Floor The students use the floor and create a Fraction cards Visual class-size number line to plot specific Students points Sentence strip DIFFERENTIATION CROSS-CURRICULAR CONNECTIONS Accommodations* G.A.T.E./Enrichment Artful Teaching Literacy Integration Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 23 officeofmath@bcps.k12.md.us Unit 5: Concept 3 Proper Fractions and Mixed Numbers on a Number Line RESOURCES Suggested Learning Sub-Skills Teacher Created Materials Adopted Textbooks Technology Create fractional MW Create Fractional SF Grade 4 TE Lesson 9-3 (pp. WEB: Identify Fractions number lines Number Line 504A-507) WEB: Fractions on a Number Line SF Grade 4 TE Lesson 9-11 – Drag and Drop (pp. 534-535) WEB: Find Grammy Write numbers MW Write Fractions on a WEB: Identify Mixed Fractions on number line Number Line Plan Find locations on MW Identify Locations on number line a Number Line Mixed numbers MW Mixed Numbers on a on number line Number Line Writing in Math Other Resources Assessments CONCEPT MULTIPLE CHOICE OTHER WAYS TO TRACKING SHEET ASSESSMENT QUESTION BANK ASSESS Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 24 officeofmath@bcps.k12.md.us Unit 5: Concept 4 Add and Subtract Proper Fractions and Mixed Numbers TIME FRAME: 2-3 days PREREQUISITE SKILLS Add and Subtract Proper Fractions and Basic addition and subtraction facts Mixed Numbers Add proper fractions Subtract proper fractions Add mixed numbers Subtract mixed numbers Knowledge and Skills VSC OBJECTIVE (calculators not allowed) 4.6.C.1.e Add and subtract proper fractions and mixed numbers Assessment Limits: Use 2 proper fractions with a single digit like denominators, 2 mixed numbers with a single digit, like denominators a whole number and a proper fraction with a single digit denominator and numbers (0 to 20) VOCABULARY ENDURING UNDERSTANDINGS fraction Operation strategies with fractions are similar to those used with whole numbers. numerator Fractions represent parts of a whole or group. denominator Fractions can be compared using a variety of models. fraction bar ESSENTIAL QUESTIONS mixed number What strategies can be developed to show computation with fractions? whole number How are models used to show how fractional parts are combined or separated? proper fraction How can fractions be modeled using numerals, regions, sets, and number lines? CONCEPT KNOWLEDGE AND PROCESS A fraction is an equal part of a whole or part of a group (set). The numerator is the number of equal parts you have or want; the denominator is the TOTAL number of equal parts in the whole. ERROR INTERVENTION IF students add both the THEN consider emphasizing repeatedly that the numerator and denominator denominator stays the same when you are adding and subtracting like denominators. IF students add both the THEN consider having the students show the work with numerator and denominator fraction tiles. Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 25 officeofmath@bcps.k12.md.us Unit 5: Concept 4 Add and Subtract Proper Fractions and Mixed Numbers IF students have trouble adding THEN consider requiring that students draw a picture before and subtracting a whole adding or subtracting. If subtracting, they should number with a fraction (e.g. 3 cross out the part that needs to be taken away. – ½) IF students have trouble knowing THEN consider having students line up the problem what parts of a mixed number vertically with one column for the fraction and one and fraction to add together or column for the whole number. This should help them subtract stay organized. Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 26 officeofmath@bcps.k12.md.us Unit 5: Concept 4 Add and Subtract Proper Fractions and Mixed Numbers LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials Visual Adding Fraction Tiles The students use fraction tiles to visualize Fraction tiles * Concrete the concept of adding fractions with like Suggested Learning Plan denominators. Linguistic Quilt Story The students create stories and illustrate Centimeter grid paper SF Grade 4 TE Lesson 10-2 them to demonstrate adding fractions. (p. 564b) DIFFERENTIATION CROSS-CURRICULAR CONNECTIONS Accommodations* G.A.T.E./Enrichment Artful Teaching Literacy Integration Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 27 officeofmath@bcps.k12.md.us Unit 5: Concept 4 Add and Subtract Proper Fractions and Mixed Numbers RESOURCES Sub-Skills Teacher Created Materials Adopted Textbooks Technology Suggested Learning Add proper MW Exploring Fraction SF Grade 4 TE Lesson 10-2 fractions Computation (pp. 564-567) MW Add Proper Fractions SF Grade 4 TE Lesson 10-4 (pp. 574A-577) Subtract proper MW Subtraction Proper fractions Fractions Plan Add mixed MW Exploring Mixed numbers Number Computation MW Add Mixed Numbers Subtract mixed MW Subtract Mixed numbers Numbers Writing in Math Other Resources Assessments CONCEPT MULTIPLE CHOICE OTHER WAYS TO TRACKING SHEET ASSESSMENT QUESTION BANK ASSESS Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 28 officeofmath@bcps.k12.md.us Grade 4: Unit 6 Statistics Unit Resources Unit Vocabulary Unit Assessment Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 29 officeofmath@bcps.k12.md.us Unit 6: Concept 1 Probability TIME FRAME: 3-5 days PREREQUISITE SKILLS Probability Object probability (describing using words) Express object probability as a fraction Spinner probability (describing using words) Express spinner probability as a fraction Fractions Express conditional probability as a fraction VSC OBJECTIVE (calculators allowed) 4.5.B.1.a Express the probability as a fraction Assessment Limit: Use a sample space of no more than 6 outcomes Knowledge and Skills VOCABULARY ENDURING UNDERSTANDINGS probability The likelihood of an event depends on the possible outcomes. favorable outcomes Probability can be represented numerically and graphically. total outcomes ESSENTIAL QUESTIONS possible outcomes How can the possible outcomes for an event be determined? numerator How is probability represented numerically? denominator How is the likelihood of an event determined and communicated? fraction bar CONCEPT KNOWLEDGE AND PROCESS event Probability is the chance or likelihood of something happening. likely Probability can be written in terms of certain [WILL ALWAYS HAPPEN], impossible [WILL unlikely NEVER HAPPEN], less likely, more likely, or equally likely. equally likely ERROR INTERVENTION impossible certain IF students forget to write probability THEN consider modeling this error for them and fair as a fraction (e.g., they simply create a process chart for finding the unfair write the number of favorable probability with probability itself written as a outcomes) fraction. Example: proba Bility IF students forget that adding or THEN consider requiring that students draw taking away objects changes the pictures to show items that are added or denominator and may change the taken away. numerator IF students write the fraction as the THEN consider requiring that students label and number of favorable outcomes over count the total number of objects and write the number of remaining objects that in the denominator first. Students instead of the number of total should then circle the objects that make up outcomes the favorable outcomes. Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 30 officeofmath@bcps.k12.md.us Unit 6: Concept 1 Probability LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials Kinesthetic Food and Probability The students use food to explore the Skittles, M&Ms, Trail Mix or Visual probability of a certain outcome. The Fruit Loops Suggested Learning Plan Concrete students also discover how conditions can Pencil and paper change the probability of an event. Visual Raffle Jar The students win raffle tickets in class and Raffle jar * Concrete participate in a weekly drawing in order to Raffle tickets or strips of paper learn the concept of events and outcomes. Linguistic Hundred Penny Box The students find the probability of picking Book Hundred Penny Box by Literature SF Grade 4 TE Lesson 12-7 a penny with certain years printed on Sharon Bell Mathis Connection (p. 706b) them after reading the story Hundred Penny Box. Kinesthetic Coin Toss The students flip coins to determine the Play money or SF Grade 4 TE Lesson 12-7 possible outcomes and the probability of Teaching Tool 7 (p. 706b) flipping heads or tails. Coins Social Probability Design The students develop a set of index cards Index Cards Cooperative SF Grade 4 TE Lesson 12-7 and determine the probability of picking (p. 706b) certain favorable outcomes. Visual Fractions = Probability The students create a spinner and express Spinner * Concrete SF Grade 4 TE Lesson 12-7 the probability of landing on different Teaching Tool 20 with six (p. 706b) colors as a fraction. sections Crayons DIFFERENTIATION CROSS-CURRICULAR CONNECTIONS Accommodations* G.A.T.E./Enrichment Artful Teaching Literacy Integration Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 31 officeofmath@bcps.k12.md.us Unit 6: Concept 1 Probability RESOURCES Assessments S u g g e s t e d L e a r n i n g P l a n Sub-Skills Teacher Created Materials Adopted Textbooks Technology Object MW Exploring Probability SF Grade 4 TE Lesson 12-5 US: “Understanding: Probability probability MW Object Probability (pp. 700A-703) and Odds” SF Grade 4 TE Lesson 12-6 WEB: NLVM - Spinners (pp. 704A-705) US: “Discovering Math: SF Grade 4 TE Lesson 12-7 Probability” Spinner MW Spinner Probability (pp. 706-709) probability Conditional MW Conditional probability Probability Writing in Math Other Resources CONCEPT MULTIPLE CHOICE OTHER WAYS TO TRACKING SHEET ASSESSMENT QUESTION BANK ASSESS Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 32 officeofmath@bcps.k12.md.us Unit 6: Concept 2 Median, Mode, and Range TIME FRAME: 2 -3 days PREREQUISITE SKILLS Median, Mode, and Range Interpreting tables Determine the range of a set of data Ordering numbers Determine mode of a set of data Determine median of a set of data VSC OBJECTIVE (calculators allowed) 4.4.B.2.a Determine median, mode, and range ASSESSMENT LIMIT: Use no more than 8 pieces of data and whole numbers (0 to 100) Knowledge and Skills VOCABULARY ENDURING UNDERSTANDINGS statistics The type of data determines how data sets can be organized, displayed, and analyzed. data Statistical measures provide a numeric picture of the shape of the data. median ESSENTIAL QUESTIONS mode In what ways can sets of data be represented by statistical measures? range How can the mean, median, mode, and range be used to describe the shape of the data? How can range, median, and mode be computed and compared? CONCEPT KNOWLEDGE AND PROCESS Median is the middle number in a set of ordered data. Mode is the number that occurs the most often in a set of data. Range is the difference between the greatest number and the least number in a set of data. ERROR INTERVENTION IF students attempt to find the THEN consider requiring that they order the numbers from median, mode, and range least to greatest before they solve the problem. without ordering the numbers from least to greatest IF students do not remember the THEN consider thinking of creative ways to teach the definitions of median, mode, meanings of the words: and range Median: the median is the middle barrier on a street; draw three shirts (small, medium, and large) and label the middle one with an M for median and middle. Mode: most often in data; relate the mode to what’s in style. Median, mode, and range rap IF students have trouble finding THEN consider having them “spread out” the missing the median when there is an numbers between the two middle numbers and then event amount of data find the median. Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 33 officeofmath@bcps.k12.md.us Unit 6: Concept 2 Median, Mode, and Range LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials Social Pet Summary The students are introduced to mode, Index cards Kinesthetic SF Grade 4 TE Lesson 4-12 median, and range by taking a survey of Suggested Learning Plan (p. 226A) how many pets that they have. Kinesthetic Comparing Cubits The students work in groups to visualize Adding machine tape or other Visual SF Grade 4 TE Lesson 4-12 what mode, median, and range look like. strips of paper (p. 226B) Scissors Kinesthetic Hands-on Activity The students use data that is relevant to Scissors Visual them and complete a hands-on activity in Construction paper Concrete order to find the mode, median, and Crayons range of the data. 1-inch graph paper Data on a transparency Auditory Mode, Median, Range Rap The students learn the meaning of mode, Song on overhead median, and range by learning a rap. Teacher copy of the rap Student copy of the rap DIFFERENTIATION CROSS-CURRICULAR CONNECTIONS Accommodations* G.A.T.E./Enrichment Artful Teaching Literacy Integration Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 34 officeofmath@bcps.k12.md.us Unit 6: Concept 2 Median, Mode, and Range RESOURCES Suggested Learning Plan Sub-Skills Teacher Created Materials Adopted Textbooks Technology Determine the MW Exploring Median, SF Grade 4 TE Lesson 4-12 US: “Estimating a Range" range of a group Mode, and Range (pp. 226A-229) WEB: "Rags to Riches" of data MW Range US: "Mean, Median, Mode, Range, and Overall Distribution" WEB: Maths: Handling Data - Determine mode MW Mode Mode, median, and mean of a group of US: Math Mastery: Graphs and data Statistics WEB: BrainPOP: Spelling Test Scores Determine MW Median median of a group of data Writing in Math Other Resources Assessments CONCEPT MULTIPLE CHOICE OTHER WAYS TO TRACKING SHEET ASSESSMENT QUESTION BANK ASSESS Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 35 officeofmath@bcps.k12.md.us Unit 6: Concept 3 Line Plots TIME FRAME: 3-5 days PREREQUISITE SKILLS Line Plots Interpreting tables Create line plots Ordering numbers Interpret line plots Range, median, and mode VSC OBJECTIVE (calculators allowed) 4.4.B.1.a Interpret line plots ASSESSMENT LIMIT: Use no more than 20 pieces of data with a range no more than 10 and whole numbers (0 to 100) Knowledge and Skills 4.4.A.1.b Organize and display data in line plots and frequency tables using a variety of categories and sets of data ASSESSMENT LIMIT: Use line plots with no more than 20 pieces of unorganized data and a range of no more than 10 and whole numbers (0 – 100) VOCABULARY ENDURING UNDERSTANDINGS statistics Representation of data depends on the characteristics of that data. graph The type of data determines how data sets can be organized, displayed, and analyzed. data ESSENTIAL QUESTIONS title What data display is appropriate for a given set of data? key How does the type of data influence the choice of graph? horizontal axis What kinds of questions can be answered using different data displays? median CONCEPT KNOWLEDGE AND PROCESS mode Line plots show the frequency and spread of data. range outlier ERROR INTERVENTION gap IF students randomly guess an THEN consider requiring that students draw the cluster answer in a multiple choice data in a line plot before matching it with the line plot problem or miss a data point best answer. IF students confuse line plots and line THEN consider making the connection between a graphs line plot and planting seeds in which they plot one or more seeds on a direct line. IF students confuse the meaning of THEN consider having students design a large the Xs class line plot and then place individual cut- out X’s on the plot. They will then see that one X represents one person. Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 36 officeofmath@bcps.k12.md.us Unit 6: Concept 3 Line Plots IF students have trouble finding the THEN consider requiring that they translate the Xs median, mode, and range by into a list of numerical data from least to simply looking at a line plot greatest. IF students have trouble THEN consider having them circle the data on the understanding the difference graph. This helps visual learners understand between “3 or more” and “more the meaning of the question. than 3” IF students do not understand the THEN consider having them underline key words meaning of the question and ask themselves: “Is this question asking me to look at the Xs or to look at the horizontal axis?” Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 37 officeofmath@bcps.k12.md.us Unit 6: Concept 3 Line Plots LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials Social Line Up the Kids The students interpret a line plot that is Chalkboard or white board Cooperative SF Grade 4 TE Lesson 4-7 based on class survey results. Chalk or dry erase markers (p. 206B) Suggested Learning Plan Kinesthetic How Many Breaths per The class collects data and displays it on a Clock with a second hand or Minute? line plot. The students interpret the data stop watch SF Grade 4 TE Lesson 4-7 on the line plot by looking at the number (p. 206B) of “Xs” over each number. Verbal Journal Idea The students demonstrate that they are Pencil SF Grade 4 TE Lesson 4-7 able to create a line plot based on data by Paper or journal notebook (p. 207) completing a journal assignment where they have to describe the steps to create a line plot. Kinesthetic Human Line Plot * The students create a line plot using Chart paper or large poster Visual information based on themselves and board Social place their data on the horizontal axis. 1 paper X per student Tape or glue Markers Crayons Kinesthetic A Handful of Counters The students create a line plot based on Counters or SF Grade 4 TE Lesson 4-7 the number of counters that they grab in Teaching Tool 14 (p. 206A) their hands. DIFFERENTIATION CROSS-CURRICULAR CONNECTIONS Accommodations* G.A.T.E./Enrichment Artful Teaching Literacy Integration Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 38 officeofmath@bcps.k12.md.us Unit 6: Concept 3 Line Plots RESOURCES Assessments S u g g e s t e d L e a r n i n g P l a n Sub-Skills Teacher Created Materials Adopted Textbooks Technology Create line plots MW Create Line Plots SF Grade 4 TE Lesson 4-7 (pp. WEB: Plop It! 206A-207) Interpret line MW Exploring Interpret plots Line Plots MW Interpret Line Plots Writing in Math Other Resources CONCEPT MULTIPLE CHOICE OTHER WAYS TO TRACKING SHEET ASSESSMENT QUESTION BANK ASSESS Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 39 officeofmath@bcps.k12.md.us Unit 6: Concept 4 Coordinate Grids TIME FRAME: 1-2 days PREREQUISITE SKILLS Coordinate Plane Number lines Identify locations on a coordinate grid given object Identifying the X and Y axis Identify objects on a coordinate grid given location VSC OBJECTIVE (calculators allowed) Knowledge and Skills 4.1.C.1.b Identify positions in a coordinate plane ASSESSMENT LIMIT: Use the first quadrant and ordered pairs of whole numbers (0 to 20) VOCABULARY ENDURING UNDERSTANDINGS coordinate grid Ordered pairs show an exact location on a coordinate plane. coordinate plane Functional relationships can be represented graphically and symbolically. ordered pair ESSENTIAL QUESTIONS horizontal How is the location of a point on a grid described? vertical How are graphs, tables, and symbols used to represent relationships? plot CONCEPT KNOWLEDGE AND PROCESS origin A coordinate grid describes the location of an object by its distance from a horizontal and vertical axis. ERROR INTERVENTION IF students mistakenly label THEN consider teaching students a creative mnemonic points by writing the vertical to remember “over, then up.” point first and then the horizontal point Examples: 1.) Superman runs before he flies. 2.) In basketball, you dribble the ball before you shoot. IF students forget to start at THEN consider requiring that they put a star at zero zero before plotting any points. Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 40 officeofmath@bcps.k12.md.us Unit 6: Concept 4 Coordinate Grids LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials Kinesthetic Classroom Coordinate Grid Create a coordinate grid on the classroom Blue painter’s tape * floor and allow the students to slide Deck of cards Suggested Learning Plan horizontally and vertically to the ordered pair that they drew from the deck of cards. Games Treasure Map Bingo The students choose five locations on a 1-inch graph paper coordinate grid treasure map and win Deck of cards BINGO if all of their ordered pairs are Markers called on their Treasure Map. Visual What’s the Location? The students compare a coordinate grid to Chalkboard or whiteboard Spatial SF Grade 4 TE Lesson 4-9 a map and describe the ordered pairs as Chalk or dry erase markers (p. 212A) streets and avenues. Ruler DIFFERENTIATION CROSS-CURRICULAR CONNECTIONS Accommodations* G.A.T.E./Enrichment Artful Teaching Literacy Integration Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 41 officeofmath@bcps.k12.md.us Unit 6: Concept 4 Coordinate Grids RESOURCES Suggested Learning Plan Sub-Skills Teacher Created Materials Adopted Textbooks Technology Identify locations MW Exploring Coordinate SF Grade 4 TE Lesson 4-9 (pp. US: "Coordinate Mapping" on a coordinate Grid 212A-215) WEB: Plot Points on a Coordinate grid given object MW Identify Locations Grid Coordinate Grid Identify objects MW Identify Objects on a coordinate Coordinate Grid grid given location Writing in Math Other Resources Assessments CONCEPT MULTIPLE CHOICE OTHER WAYS TO TRACKING SHEET ASSESSMENT QUESTION BANK ASSESS Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 42 officeofmath@bcps.k12.md.us Unit 6: Concept 5 Interpret Line Graphs TIME FRAME: 2 - 3 days PREREQUISITE SKILLS Interpret Line Graphs Addition Interpret line graphs Subtraction Range, median, mode VSC OBJECTIVE (calculators allowed) 4.4.B.1.b Interpret line graphs Knowledge and Skills ASSESSMENT LIMIT: Use the x-axis representing no more than 6 time intervals, the y-axis consisting of no more than 10 intervals with scales as factors of 100 using whole numbers (0 to 100) VOCABULARY ENDURING UNDERSTANDINGS statistics Representation of data depends on the characteristics of that data. graph The type of data determines how data sets can be organized, displayed, and analyzed. data ESSENTIAL QUESTIONS title What data display is appropriate for a given set of data? scale How does the type of data influence the choice of graph? Interval What kinds of questions can be answered using different data displays? horizontal axis CONCEPT KNOWLEDGE AND PROCESS vertical axis Line graphs show how data changes over time. Increase Horizontal axis will always be time. decrease no change ERROR INTERVENTION line graph IF students do not see where the THEN consider having them subtract between each greatest increase or decrease is data point to show the change. IF students do not recognize where a THEN consider using arm signals for up, down, and line graph increases, decreases, or no change and having students draw arrows stays the same on each segment of the line graph. IF students don’t understand the THEN make a list of typical questions and question operations that could be used to answer a question. Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 43 officeofmath@bcps.k12.md.us Unit 6: Concept 5 Interpret Line Graphs LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials Linguistic What Story Does the Graph The students look at a line graph and Paper or journal notebook Tell? create a story to describe how the data in Pencil Suggested Learning Plan SF Grade 4 TE Lesson 4-10 the graph changed over time. (p. 216B) Concrete How Am I Doing? Students look at their own class work or Student work samples Visual tests to create a line graph and determine Graph paper how their grades have changed over the Rulers school year. Pencils Kinesthetic Arm Signals The students use movements of their Example of a line graph on the Visual arms to indicate whether the data overhead increases, decreases or remains the same Overhead projector as time progresses. Linguistic What Story Does the Graph The students look at a line graph and Paper or journal notebook Tell? create a story to describe how the data in Pencil SF Grade 4 TE Lesson 4-10 the graph changed over time. (p. 216B) DIFFERENTIATION CROSS-CURRICULAR CONNECTIONS Accommodations* G.A.T.E./Enrichment Artful Teaching Literacy Integration Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 44 officeofmath@bcps.k12.md.us Unit 6: Concept 5 Interpret Line Graphs RESOURCES Suggested Learning Plan Sub-Skills Teacher Created Materials Adopted Textbooks Technology Interpret line MW Interpret Line Graphs SF Grade 4 TE Lesson 4-10 WEB: Create A Graph graphs (pp. 216A-221) WEB: Print Your Own Graph Paper Writing in Math Other Resources Assessments CONCEPT MULTIPLE CHOICE OTHER WAYS TO TRACKING SHEET ASSESSMENT QUESTION BANK ASSESS Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 45 officeofmath@bcps.k12.md.us Grade 4: Unit 7 Algebra 2 Unit Resources Unit Vocabulary Unit Assessment Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 46 officeofmath@bcps.k12.md.us Unit 7: Concept 1 Write Expressions TIME FRAME: 2 - 3 days PREREQUISITE SKILLS Write Expression Writing expressions using addition Write expressions using addition and subtraction Writing expressions using subtraction Write expressions using multiplication and division VSC OBJECTIVE (calculators allowed) 4.1.B.1.a Represent numeric quantities using operational symbols (+, -, ×, ÷ with no remainders) Knowledge and Skills ASSESSMENT LIMIT: Use whole numbers (0 to 100) VOCABULARY ENDURING UNDERSTANDINGS operation Mathematical expressions and equations represent relationships among quantities. operational symbols Symbolic notation is used to represent mathematical relationships. ESSENTIAL QUESTIONS How does a mathematical expression differ from a number sentence? How is a number sentence like a balance scale? How are symbols used to represent mathematical relationships including operations, equality, and inequality? CONCEPT KNOWLEDGE AND PROCESS An expression names an amount. ERROR INTERVENTION IF students do not understand THEN consider making a list of addition, subtraction, which operation to use to multiplication, and division clue words. Students write or solve the problem should then circle important numbers and underline clue words before determining the operation needed. IF students do not understand THEN consider having them draw a picture to represent which operation to use to the problem. They can then usually identify the write or solve the problem correct operation. IF students do not understand THEN consider having them visualize the problem, which operation to use to determine if the answer is increasing (+ or x) or write or solve the problem decreasing (- or ÷) in equal groups or non-equal groups, and then identify the correct operation. Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 47 officeofmath@bcps.k12.md.us Unit 7: Concept 1 Write Expressions LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials Verbal Develop Clue Words * The students create an ongoing list of clue Chart paper words that will aid them in choosing the Markers Suggested Learning Plan appropriate operational symbol to Teacher clue word sheet complete the expression. Student clue words sheets Auditory Name That Expression The students use clue words to determine White board Kinesthetic if the solution to an expression will be White board markers Visual bigger or smaller and to determine the Overhead appropriate operational symbol to use in Pre-prepared word problems the expression. Linguistic Read to Understand Students identify clue words and record Chart paper Auditory SF Grade 4 TE Lesson 2-10 them on a chart as they read different (p. 94B) phrases. DIFFERENTIATION CROSS-CURRICULAR CONNECTIONS Accommodations* G.A.T.E./Enrichment Artful Teaching Literacy Integration Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 48 officeofmath@bcps.k12.md.us Unit 7: Concept 1 Write Expressions RESOURCES Suggested Learning Plan Sub-Skills Teacher Created Materials Adopted Textbooks Technology Write MW Exploring Write SF Grade 4 TE Lesson 2-10 WEB: Math Playground: Various expressions Expression (pp. 94A-95) Word Problems using addition MW Write Expressions SF Grade 4 TE lesson 3-12 WEB: Four Square for Story and subtraction Addition and Subtraction (pp. 160A-163) Problems Write MW Write Expressions expressions Multiplication and using Division multiplication and division Writing in Math Other Resources Assessments CONCEPT MULTIPLE CHOICE OTHER WAYS TO TRACKING SHEET ASSESSMENT QUESTION BANK ASSESS Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 49 officeofmath@bcps.k12.md.us Unit 7: Concept 2 Equivalent Expressions TIME FRAME: 1 - 2 days PREREQUISITE SKILLS Equivalent Expressions Writing expressions for addition Write equivalent expressions Writing expressions for subtraction VSC OBJECTIVE (calculators allowed) Knowledge and Skills 4.1.B.1.b Determine equivalent expressions ASSESSMENT LIMIT: Use whole numbers (0 to 100) VOCABULARY ENDURING UNDERSTANDINGS equivalent Mathematical expressions and equations represent relationships among quantities. expression Symbolic notation is used to represent mathematical relationships. equal ESSENTIAL QUESTIONS fact family How does a mathematical expression differ from a number sentence? How is a number sentence like a balance scale? How are symbols used to represent mathematical relationships including operations, equality, and inequality? CONCEPT KNOWLEDGE AND PROCESS An expression names an amount. ERROR INTERVENTION IF students assume that because THEN consider requiring students to solve each two problems have the same expression before determining the correct numbers, they are equivalent answer. They will then see that 5 + 3 ≠ 5 x 3. (Example: students think that 5 + 3 = 5 x 3) IF students do not understand THEN consider underlining the “equ” in equivalent, what equivalent means equal, and equation. Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 50 officeofmath@bcps.k12.md.us Unit 7: Concept 2 Equivalent Expressions LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials Visual Balancing Act The students use a number balance to Number balance * Kinesthetic determine whether their expressions are Calculator * Suggested Learning Plan Cooperative equivalent to their partner’s expression. Kinesthetic Equal Expressions The students use white boards to compose Whiteboards Visual an expression equivalent to an expression Dry erase markers that is given. Concrete How Many Ways to 12 The students learn about writing Pencil equivalent expressions by finding how Paper many different ways they can make 12 Calculator * using addition, subtraction, multiplication and division. DIFFERENTIATION CROSS-CURRICULAR CONNECTIONS Accommodations* G.A.T.E./Enrichment Artful Teaching Literacy Integration Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 51 officeofmath@bcps.k12.md.us Unit 7: Concept 2 Equivalent Expressions RESOURCES Suggested Learning Plan Sub-Skills Teacher Created Materials Adopted Textbooks Technology Write equivalent MW Exploring Write SF Grade 4 TE Lesson 2-11 WEB: Can You Balance? expressions Equivalent Expressions (pp. 96A-97) WEB: Match Equivalent MW Write Equivalent SF Grade 4 TE Lesson 2-12 Expressions Expressions (pp. 98A-99) WEB: Cyberchase – Poodle Weigh In Writing in Math Other Resources Assessments CONCEPT MULTIPLE CHOICE OTHER WAYS TO TRACKING SHEET ASSESSMENT QUESTION BANK ASSESS Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 52 officeofmath@bcps.k12.md.us Unit 7: Concept 3 Write Relationships TIME FRAME: 2 – 4 days PREREQUISITE SKILLS Write Relationships Comparing expressions Evaluate relationships with missing relational symbols Evaluate relationships with addition and Represent relationships in word problems subtraction Represent relationships in addition and subtraction word problems VSC OBJECTIVE (calculators allowed) 4.1.B.2.a Represent relationships using relational symbols (>, <, =) and operational symbols (+, -, ×, ÷) on either side Knowledge and Skills Assessment Limit: Use operational symbols (+, -, ×) and whole numbers (0 to 200) VOCABULARY ENDURING UNDERSTANDINGS expression Mathematical expressions and equations represent relationships among quantities. relational symbols Symbolic notation is used to represent mathematical relationships. operational symbols ESSENTIAL QUESTIONS equal How does a mathematical expression differ from a number sentence? balance How is a number sentence like a balance scale? not equal How are symbols used to represent mathematical relationships including operations, Inequality equality, and inequality? equivalent CONCEPT KNOWLEDGE AND PROCESS A relationship where two expressions have the same value has an = sign. A relationship where two expressions do not have the same value has a > or < sign. ERROR INTERVENTION IF students become overwhelmed by THEN consider having them highlight the first the wordiness of the problem expression in one color and the second expression in another color; write the first expression, then write the second expression; finally, compare the expressions. IF students rush to input operational THEN consider requiring that they plug in all symbols possible operational symbols before determining the correct answer. IF students choose a relationship as THEN consider requiring that they solve each correct just by looking at the expression before determining the correct numbers answer. Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 53 officeofmath@bcps.k12.md.us Unit 7: Concept 3 Write Relationships LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials Verbal Develop Clue Words The students create an ongoing list of clue Chart paper words that will aid them in choosing the Markers appropriate operational symbol to Student clue words sheets Suggested Learning Plan complete the expression. Auditory Name That Expression The students use clue words to determine White board Kinesthetic if the solution to an expression will be White board markers Visual bigger or smaller and to determine the Overhead appropriate operational symbol to use in Pre-prepared word problems the expression. Linguistic Read to Understand Students identify clue words and record Chart paper Auditory SF Grade 4 TE Lesson 2-10 them on a chart as they read different (p. 94B) phrases. Kinesthetic Pinch Cards The students use an index card with Index Cards with > < = on Visual relational symbols on it to indicate the them appropriate relationship between two Markers expressions. DIFFERENTIATION CROSS-CURRICULAR CONNECTIONS Accommodations* G.A.T.E./Enrichment Artful Teaching Literacy Integration Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 54 officeofmath@bcps.k12.md.us Unit 7: Concept 3 Write Relationships RESOURCES Suggested Learning Sub-Skills Teacher Created Materials Adopted Textbooks Technology Evaluate MW Exploring Relationships SF Grade 4 TE Lesson WEB: BrainPOP: Inequalities relationships with MW Evaluate Relationships 2-11 (pp. 96A-97) Movie missing relational Missing Relationships symbols Represent MW Represent Relationships Plan relationships in word in word problems problems Writing in Math Other Resources Assessments CONCEPT MULTIPLE CHOICE OTHER WAYS TO TRACKING SHEET ASSESSMENT QUESTION BANK ASSESS Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 55 officeofmath@bcps.k12.md.us Grade 4: Unit 8 Geometry 1 Unit Resources Unit Vocabulary Unit Assessment Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 56 officeofmath@bcps.k12.md.us Unit 8: Concept 1 Angles TIME FRAME: 2-4 days PREREQUISITE SKILLS Angles Rays, lines, and line segments Identify right angles Identify acute and obtuse angles Identify angles in shapes and objects VSC OBJECTIVE (calculators allowed) 4.2.A.1.b Identify, compare, classify, and describe angles in relationship to another angle Knowledge and Skills ASSESSMENT LIMIT: Use acute, right, or obtuse angles VOCABULARY ENDURING UNDERSTANDINGS geometry Objects can be described and compared using geometric attributes. point A three dimensional figure can be analyzed in terms of its two-dimensional parts. Line ESSENTIAL QUESTIONS ray How are angles classified? line segment What makes one angle different from another? vertex CONCEPT KNOWLEDGE AND PROCESS angle An angle is created from two rays that share an endpoint. endpoint A right angle forms the corner of a square. right angle An acute angle is smaller than a right angle. acute angle An obtuse angle is bigger than a right angle. obtuse angle ERROR INTERVENTION IF students confuse acute angles, THEN consider using a mnemonic to distinguish between right angles, and obtuse angles the types of angles: An acute angle is “a cute” little baby angle. An obtuse angle looks like an open book. A right angle is “just right.” It makes a perfect L. IF students have trouble identifying THEN consider having students highlight the rays to angles within shapes better see the angle. IF students have trouble identifying THEN consider having them put a square in the angle. angles within shapes IF students have trouble identifying THEN consider encouraging students to turn their paper angles that are turned so that the angle looks “right side up.” Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 57 officeofmath@bcps.k12.md.us Unit 8: Concept 1 Angles LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials Visual Geometry on the The students use Geoboards to represent Geoboard or Spatial Geoboard different types of angles by intersecting Geoboard paper Suggested Learning Plan SF Grade 4 TE Lesson 8-3 lines. Rubber bands (p. 440a) Visual Angles on the Floor The students work in pairs to identify Blue painter’s tape Kinesthetic types of angles using a index card to see Index cards * Cooperative if the angle is bigger, smaller, or equal to a right angle. Visual I Spy Right Angles The students identify right angles that Blue painters tape Kinesthetic they see within the classroom and mark them by creating a square inside the angle with blue painter’s tape. Visual Geometry Simon Says The students play a game of Simon Says Kinesthetic where they have to create angles and Game lines using arm signals. DIFFERENTIATION CROSS-CURRICULAR CONNECTIONS Accommodations* G.A.T.E./Enrichment Artful Teaching Literacy Integration Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 58 officeofmath@bcps.k12.md.us Unit 8: Concept 1 Angles RESOURCES Suggested Learning Plan Sub-Skills Teacher Created Materials Adopted Textbooks Technology Identify right MW Exploring Angles SF Grade 4 TE Lesson 8-3 (pp. WEB: Alphabet Geometry: Right angles MW Identify Right Angles 440A-443) Angles WEB: Alphabet Geometry: Acute Angles WEB: Alphabet Geometry: Obtuse Identify acute MW Identify Acute Angles and obtuse Obtuse Angles angles Identify angles in MW Identify Angles in shapes and Objects objects Writing in Math Other Resources Assessments CONCEPT MULTIPLE CHOICE OTHER WAYS TO TRACKING SHEET ASSESSMENT QUESTION BANK ASSESS Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 59 officeofmath@bcps.k12.md.us Unit 8: Concept 2 Transformations TIME FRAME: 2-4 days PREREQUISITE SKILLS Transformations Flips Identify translations Turns Identify reflections Slides Identify rotations Congruence Symmetry VSC OBJECTIVE (calculators allowed) 4.2.E. 1.a Identify and describe the results of translations, reflections, and rotations ASSESSMENT LIMIT: Use a horizontal line translation, reflection over a vertical line, or rotation of 90° clockwise around a Knowledge and Skills given point of a geometric figure or picture 4.2.D.1.a Identify and describe geometric figures as congruent ASSESSMENT LIMIT: Identify the result in a transformation as being congruent to the original figure VOCABULARY ENDURING UNDERSTANDINGS geometry A transformation is a specific movement of an object. congruent Changing the position of an object does not affect its attributes. transformation ESSENTIAL QUESTIONS translation In what ways can the position of geometric figures be changed? reflection What are translations, rotations, and reflections? rotation CONCEPT KNOWLEDGE AND PROCESS A transformation moves a shape to a new spot without changing its size or shape You can transform (move) a shape three ways: by flipping it, sliding it, or turning it. A flip, or reflection, is a mirror image of a figure on the opposite side of a line. A slide, or translation, is a figure moved a certain distance in a given direction. A turn, or rotation, moves a figure around a point. ERROR INTERVENTION IF students confuse translations, THEN consider emphasizing the similar letters reflections, and rotations SLide is a tranSLation. TuRn is a RoTation. FLip is a reFLection. IF students confuse translations, THEN consider doing hand movements to help them identify reflections, and rotations the transformations. IF students have trouble identifying a THEN consider having them actually turn their paper and rotation observe how the figure looks as it turns. IF students forget that transformations THEN consider requiring that they trace the initial figure and must be congruent then translate, rotate, or reflect it to check their work Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 60 officeofmath@bcps.k12.md.us Unit 8: Concept 2 Transformations LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials Visual Finger Painting * The students learn about translations by Three large pieces of paper Kinesthetic using finger paints and their hands as folded in half (per student) Suggested Learning Plan the object being transformed. Finger paints Visual Letter Cut Outs * The students use letter cut-outs to Large pieces of construction Kinesthetic translate, reflect, and rotate over a paper Spatial dotted line. Letter cut outs of the first letter of the first name of each student in the class. Kinesthetic “Transformation Shuffle” The students translate, reflect and rotate Words to transformation Auditory to the tune of a popular hip-hop song. shuffle Song “Cupid Shuffle” by Cupid DIFFERENTIATION CROSS-CURRICULAR CONNECTIONS Accommodations* G.A.T.E./Enrichment Artful Teaching Literacy Integration Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 61 officeofmath@bcps.k12.md.us Unit 8: Concept 2 Transformations RESOURCES Suggested Learning Plan Sub-Skills Teacher Created Materials Adopted Textbooks Technology Identify MW Identify Translations SF Grade 4 TE Lesson 8-6 (pp. WEB: NLVM - Playing with translations 452A-455) Translations WEB: NLVM - Playing with Reflections WEB: NLVM - Playing with Identify MW Identify Reflections Rotations reflections WEB: Alphabet Geometry: Transformations Identify rotations MW Identify Rotations Writing in Math Other Resources Assessments CONCEPT MULTIPLE CHOICE OTHER WAYS TO TRACKING SHEET ASSESSMENT QUESTION BANK ASSESS Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 62 officeofmath@bcps.k12.md.us

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