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Grade 2 Mathematics Grade 2 Mathematics Table of Contents Unit 1: Numbers, Numerals, and Data.............................................................................1 Unit 2: Extending Facts and Operations .......................................................................19 Unit 3: Money and Time..................................................................................................37 Unit 4: Place Value and 2-Digit Addition ......................................................................50 Unit 5: Place Value and 2-Digit Subtraction .................................................................64 Unit 6: Shapes and Fractions ..........................................................................................73 Unit 7: Measurement in Our World...............................................................................86 Unit 8: Extending Number Patterns through 100s and 3-Digit Operations ...............99 Louisiana Comprehensive Curriculum, Revised 2008 Course Introduction The Louisiana Department of Education issued the Comprehensive Curriculum in 2005. The curriculum has been revised based on teacher feedback, an external review by a team of content experts from outside the state, and input from course writers. As in the first edition, the Louisiana Comprehensive Curriculum, revised 2008 is aligned with state content standards, as defined by Grade-Level Expectations (GLEs), and organized into coherent, time-bound units with sample activities and classroom assessments to guide teaching and learning. The order of the units ensures that all GLEs to be tested are addressed prior to the administration of iLEAP assessments. District Implementation Guidelines Local districts are responsible for implementation and monitoring of the Louisiana Comprehensive Curriculum and have been delegated the responsibility to decide if units are to be taught in the order presented substitutions of equivalent activities are allowed GLES can be adequately addressed using fewer activities than presented permitted changes are to be made at the district, school, or teacher level Districts have been requested to inform teachers of decisions made. Implementation of Activities in the Classroom Incorporation of activities into lesson plans is critical to the successful implementation of the Louisiana Comprehensive Curriculum. Lesson plans should be designed to introduce students to one or more of the activities, to provide background information and follow-up, and to prepare students for success in mastering the Grade-Level Expectations associated with the activities. Lesson plans should address individual needs of students and should include processes for re- teaching concepts or skills for students who need additional instruction. Appropriate accommodations must be made for students with disabilities. New Features Content Area Literacy Strategies are an integral part of approximately one-third of the activities. Strategy names are italicized. The link (view literacy strategy descriptions) opens a document containing detailed descriptions and examples of the literacy strategies. This document can also be accessed directly at http://www.louisianaschools.net/lde/uploads/11056.doc. A Materials List is provided for each activity and Blackline Masters (BLMs) are provided to assist in the delivery of activities or to assess student learning. A separate Blackline Master document is provided for each course. The Access Guide to the Comprehensive Curriculum is an online database of suggested strategies, accommodations, assistive technology, and assessment options that may provide greater access to the curriculum activities. The Access Guide will be piloted during the 2008-2009 school year in Grades 4 and 8, with other grades to be added over time. Click on the Access Guide icon found on the first page of each unit or by going directly to the url http://mconn.doe.state.la.us/accessguide/default.aspx. Louisiana Comprehensive Curriculum, Revised 2008 Grade 2 Mathematics Unit 1: Numbers, Numerals, and Data Time Frame: Approximately five weeks Unit Description This unit focuses on extending students‟ command of place value, estimation, and collecting and using data to make decisions. Student Understandings Students will demonstrate their understanding of place value using numbers up to 99. They will model, write, compare, and round numbers through 99. They will count forward or backwards from a given number. Using a benchmark, they will be asked to make estimates. Students will also collect, graph, interpret, and analyze data. Guiding Questions 1. Can students count, show expanded and standard notation, and use cardinal number skills through 99? 2. Can students compare and order a set of numbers? 3. Can students round a number to the nearest 10? 4. Can students count forward and backwards from a given number? 5. Can students make reasonable estimates for group sizes through 99 and know when estimations are appropriate? 6. Can students collect and organize data from questionnaires, surveys, and experiments? 7. Can students make and interpret bar graphs, pictographs, and line plots including choice of scale and title? 8. Can students make classifications involving and, or, and is/is not statements and represent outcomes on one- and two-circle Venn diagrams? Unit 1 Grade-Level Expectations (GLEs) GLE # GLE Text and Benchmarks Number and Number Relations 1. Model, read, and write place values for numbers through 999 in word, standard, and expanded form (N-1-E) Grade 2 MathematicsUnit 1Numbers, Numerals, and Data 1 Louisiana Comprehensive Curriculum, Revised 2008 3. Make reasonable estimates of the number of objects in a collection with fewer than 100 objects (N-2-E) 5. Read, write, compare, and order whole numbers through 999 using words, number lines, and models (N-3-E) (N-1-E) 6. From a given number, count forward and backward and count to 100 by 2s (N-3-E) (N-1-E) (N-4-E) 10. Round numbers to the nearest 10 or 100 and identify situations in which rounding is appropriate (N-7-E) (N-9-E) Data Analysis, Probability, and Discrete Math 25. Collect and organize data using observations, surveys, and experiments (D-1-E) 26. Construct and read line plots and tables (D-2-E) 27. Interpret pictographs in which each picture represents more than one object (D-2-E) 28. Generate questions that can be answered by collecting and analyzing data (D- 3-E) 29. Solve logic problems involving two sets by using elementary set logic (i.e., and, or, and is/is not statements) (D-3-E) Sample Activities Activity 1: Counting the Days (GLEs: 1, 5, 6, 10) Materials List: adding machine tape, black marker, monthly calendar, Post-it® notes, Base 10 ® blocks; paper; pencil; a Ziploc® bag containing scissors and a copy of Base 10 Blocks BLM for each student If Base 10® blocks are not available, copy the Base 10 Blocks BLM for each student and have them cut out each piece. Have students use the pieces to model the number of days they have been in school. Store the scissors and the BLM in a Ziploc® bag for future activities. Use a black marker to write the numbers representing the number of school days on adding machine tape and attach it to the walls around the classroom. Circle every multiple of ten. Underline every multiple of 5. Post a monthly calendar. Have students write the date each day. Model the number of days in school with Base 10 ® blocks. Also, have students write the number of days in school in expanded and word form. Each day select an activity from the list below, and have students use the counting tape to locate their answers. Have students practice counting using the counting tape. Cover a number on the counting tape with a Post-it® note. Have students identify the missing number. Grade 2 MathematicsUnit 1Numbers, Numerals, and Data 2 Louisiana Comprehensive Curriculum, Revised 2008 Choose a number and have students count up or down from that number. Select two numbers and have students find the missing number between the two numbers selected. Select a number and have students identify the number that comes before or after the number. Select a number and ask students which ten is closer to it. Select two numbers on the counting tape and have students identify which number is greater and explain why it is greater. Skip count by 2s, 5s, and 10s using the counting tape. Activity 2: Bundles of Ten (GLE: 1) Materials List: Jumbo Popsicle® sticks with each student‟s name on one, rubber bands, paper, pencil Write each student's name on a Jumbo Popsicle® stick. Provide each student with his/her stick, and have class members count-off to see how many students are present. Once the number is determined, write “ ________students are present in our class today.” on the board. Tell students they are going to bundle the sticks into groups of ten. Ask students: “How many bundles of ten do you think we will have? How many sticks will we have that can not be bundled?” Have students count-off again. This time as students count to10, have the10 students come to the front of the class and use a rubber band to make a bundle of ten sticks. Place the bundle where all students can see it. Have the next student start over with 1 while students continue counting-off until another bundle of 10 can be made. Continue this procedure until students cannot make another bundle. Place the unbundled sticks to the right of the bundles. Have students write the sentence, “We have ______students present.” Then have them draw a model to represent the number. See if students can transfer knowledge by asking them, “How many bundles would we need to represent the number 42?” Have them draw the model. Teacher Note: These sticks may be unbundled and placed in a cup/can and pulled one at a time to identify a student who should answer a question during the day’s activities. Do not return the stick to the cup/can unless all the sticks are used. This procedure assures that each student will be given a chance to answer questions throughout the day. Grade 2 MathematicsUnit 1Numbers, Numerals, and Data 3 Louisiana Comprehensive Curriculum, Revised 2008 Activity 3: Modeling Numerals (GLEs: 1, 5) Materials List: Place Value Mat BLM, 40 Popsicle® sticks, rubber bands, Ziploc® bags, Digit Cards BLM, math learning log Teacher Hint: Cut out 2 sets of digit cards for each student prior to the lesson. Put the Popsicle® sticks, rubber bands and 2 sets of digit cards in a Ziploc® bag prior to the lesson. Give each pair of students a Place Value Mat BLM, 40 Popsicle® sticks, and two sets of 0-9 digit cards. Call out the number 13 and have students count out 13 sticks. Have students place three sticks on the ones side of the mat. Have them count how many sticks they have left (10). Have students place the 10 sticks on the mat under the tens side of the mat. Have them group the 10 sticks into 1 bundle. Instruct students to use digit cards to represent the number. Ask students what each digit represents. Have students clear their mats and repeat the procedure using the numbers 12, 18, and 16. Ask students what the 1 represented in 13, 12, 18, and 16? (1 group of 10) Ask students to represent the number 32 on their mats. Have students explain what each digit in the number 32 represents. Repeat the procedure modeling numbers under 41. Give each student a two-digit number between 10 and 40. (Make sure to give someone a multiple of 10.) Have them model the number with Popsicle® sticks and digit cards. Have students compare their number to their neighbor‟s number. Encourage students to use the vocabulary greater than and less than. Make them explain why their number is greater than/less than their neighbor‟s number. Example: One student models 27 and the other models 31. The first student might say, “The number 27 is less than 31 because 27 has 2 tens and 31 has 3 tens. Three tens are more than two tens.” Have students use their math learning logs (view literacy strategy descriptions) to compare and contrast the numbers 23 and 32. A math learning log is a notebook students use to record a problem of the day or an open- ended problem that you want them to solve and explain. Activity 4: Number Words (GLE: 1) Materials List: Vocabulary Self-Awareness Chart BLM, Number Words Chart BLM, scissors, two sets of 0-9 digit cards (see Activity 3-Digit Cards BLM), paper, pencil Introduce students to a vocabulary self-awareness (view literacy strategy descriptions) chart to access their understanding of the meaning of number words. Give each student a Vocabulary Self-Assessment Chart BLM and direct him/her to rate his/her understanding of each word/symbol with either a “+” (understands well), “√ ”(limited understanding), or a “ – ” (don‟t know). Over the course of the activity, students are to return to their chart and add new information. The objective is that students will replace all the check and minus marks with plus signs. Grade 2 MathematicsUnit 1Numbers, Numerals, and Data 4 Louisiana Comprehensive Curriculum, Revised 2008 Give each student a Number Words Chart BLM. Have him/her cut the chart apart and sort words into groups [teens (13-19), ty numbers (20-90), zero-twelve (0-12)]. Review that the word teen means plus ten, and the ending ty stands for ten. 14 - fourteen means 4 plus 10 42 - forty-two means 4 tens plus 2 60 – sixty means 6 tens Flip two digit cards and have students find the number words to represent the two-digit number. Make a big deal about the hyphen. This will help students with expanded form. Twenty-three means 2 tens plus 3 more or, 20 + 3. Repeat the procedure. Circulate to assess students‟ needs. Repeat as many times as possible. Have students reassess their understandings of number words using the self-awareness chart. If any students are still unsure about how number words are connected to numerals, provide the remediation that is necessary. Activity 5: Order It! (GLEs: 5, 6) Materials List: pocket chart, hundreds-chart poster, clock-timer, paper, pencil Cut apart a hundreds chart poster, and allow students to place the cards in correct order in a pocket chart. After about 30 cards have been placed, discuss patterns that are emerging (i.e., skip counting). Play the game, Make 100 Fast. Deal the number cards to the students. Tell the students that they will have 3 minutes (or a specified time determined by you) to fill the 100s chart with their cards. When you say “Go,” the student holding the card with the number 1 places it in the pocket chart; then the student with number 2, and so on. The goal is for students to place all of the cards (1–100) in order as quickly as possible. Remind students to stay seated until the number ahead of theirs is placed in the chart. Allow them to walk fast but not to run. Repeat at various times during the unit as a review with the goal of shortening the time to fill the chart. Take out just the even numbers from 2-100. Give each student an even number and have him/her skip count by 2s to 100 by placing their numbers in the chart. As students become proficient with the numbers through 100, create cards for the numbers from 100 – 999 in sets of 100 (e.g., 201-300). Put students into groups of 4. Give each student a card with a numeral on it. Each member of the group will contribute to a story chain (view literacy strategy descriptions) for each student‟s number. The student writes the first clue for his/her numeral on the back of the card and then passes the card to his/her left. The next student writes another clue for the numeral on the card. Continue passing the card until the card returns to “owner.” The “owner” checks the clues for validity and makes adjustments to false statements. Grade 2 MathematicsUnit 1Numbers, Numerals, and Data 5 Louisiana Comprehensive Curriculum, Revised 2008 Finally, each group exchanges cards and tries to guess the numeral on the card according to the clues that the students listed. Example of a story chain: 47 My number has 4 tens. My one‟s digit is less than 8. My one‟s digit is greater than 6. What am I? Activity 6: Forward – Backwards (GLEs: 1, 5, 6) Material List: Spinner BLM and Hundreds Chart BLM copied on tagboard, large paper clip, pencil Use the Spinner BLM. 1. Place the point of a pencil through a large paper clip. 2. Place the point of the pencil on the center of the spinner. 3. Adjust the paper clip so that the end of the paper clip is on the center of the spinner. 4. “Flick” the paper clip to spin it. Cut apart the Hundreds Chart BLM. Turn the numbers over so that students cannot see the number. A student is selected to come up and choose a number and spin the spinner. According to the spinner he/she must count forward or backwards from his/her number. (You determine if you want him/her to count 1 or 2 numbers forward or backwards.) Play as many rounds as time will permit. A variation is to divide the class in half and make this into a game format, rewarding points to each team when a member completes the task correctly. Teacher note: If the numbers are too small for the students to handle, write the numerals 1-100 on index cards, and substitute them for the Hundreds Chart BLM in the activity. Play a modified version of this game by using just the even numbers. Have students select an even number, and always count forward 2 numbers to find the next even number. Grade 2 MathematicsUnit 1Numbers, Numerals, and Data 6 Louisiana Comprehensive Curriculum, Revised 2008 Activity 7: What’s Missing? (GLEs: 1, 5, 6) ® Materials List: Hundreds Chart BLM per group, 10 x 10 grid BLM, Ziploc bags, glue sticks Cut apart as many Hundreds Chart BLMs as there are groups. As charts are cut apart, place the numerals in a Ziploc® bag. Remove five numerals from each group‟s bag. Give each group a 10 x 10 grid, a bag, and a glue stick. Have students fill in the grids with numerals to find the five missing numerals on their chart. Let each group share their findings. After students have mastered cards from 1-100, create cards for numbers 101- 200, 201-300, and so on. Website of an interactive game http://www.bbc.co.uk/schools/numbertime/games/mend.shtml Activity 8: Families (GLE: 5) Materials List: numeral cards 0-99, word cards 0-19, word cards twenty– ninety, index cards that fit pocket chart, pocket chart, Number Words Chart BLM (see Activity 4 BLM) Make a set of numeral cards representing the numbers 0–99 and set aside. Make a set of word cards for the numerals 0–9. Place the cards for the words for zero to nine horizontally in a pocket chart. Write the words for the multiples of 10 (through 90) on cards. Place them vertically along the left side of the pocket chart. zero one two three four five six etc ten … twenty twenty- three thirty Tell the students that when you point to them, they are to call out any number at random such as 54, 79, etc. Write the students‟ numbers (in word form) on the corresponding numeral card, and ask the students to put them in the pocket chart where they belong. After all students have had a turn, ask them to decide if each number word card has been placed correctly. Make adjustments, as needed. For the numbers that are not yet represented, pass out the number cards (that were set aside) to the students until all cards are distributed, and ask them to write the number words on the back of the card. Check for correct spelling, including the use of the hyphen between words. Direct students to a resource for correct spellings (Number Words Chart BLM from Activity 4). Grade 2 MathematicsUnit 1Numbers, Numerals, and Data 7 Louisiana Comprehensive Curriculum, Revised 2008 When cards are checked and completed, have students place them in the 100-pocket chart correctly. Activity 9: Base 10® Blocks (GLEs: 1, 5) ® ® Materials List: Base 10 blocks, overhead Base 10 blocks, transparency of Place Value Chart BLM, set of cards with numerals 0 – 9 per student, Place Value Chart BLM per student If Base 10® blocks are unavailable, use the Activity 1 BLM to create student sets and transparency of Base 10® blocks. Use the transparency of the Place Value Chart BLM to demonstrate how to use the Base 10® blocks to model a 2-digit number. Give each student a copy of a Place Value Chart BLM. Model a number with the Base 10® blocks on the overhead, and then write the number for your model in standard form, word form, and expanded form. Model about five numbers. Then ask students to choose two numbers to model and write in standard, word and expanded form. Partners can play the High Card game. Give each player a set of cards with the numerals 0–9. Shuffle both sets of cards together. Have each student draw two cards and form the greatest possible number. The student with the greatest number wins a point if he/she can correctly read the number. If the student with the highest number fails to correctly read the number, the next student may earn a point if he/she reads his number correctly. Observe partners playing and discuss strategies they have discovered for making the greatest number. After students have been exposed to 3-digit numbers, let students play High Card using three cards. Activity 10: Spinning Numbers (GLEs: 1, 5, 10) Materials List: Spinners - Number Line BLM and Recording Sheet BLM per pair of students, pencil, large paper clip, 2 counters, (See Activity #6 for explanation of how to make a spinner.) Have students work in pairs. Instruct player 1 to spin a spinner marked 1–8 two times. Record the digits spun on the Recording Sheet BLM. Next, spin a spinner marked larger/smaller to determine if the student is to make the larger or smaller number that can be formed with the two digits. Record the results of spinner on the recording sheet. The student then records the 2-digit number on the recording sheet. Player 2 repeats the process. Next, have students plot their numbers on the number lines at the bottom of the Grade 2 MathematicsUnit 1Numbers, Numerals, and Data 8 Louisiana Comprehensive Curriculum, Revised 2008 Spinners – Number Line BLM using counters. Compare numbers using greater than and less than. Finally, have students round their numbers to the nearest ten. Repeat the process. Collect Recording Sheet BLMs and use them as an informal assessment of what students know about rounding numbers. Rounding numbers will be taught in Activity 12. Activity 11: Order Those Numbers! (GLE: 5) Material List: number line, hundreds chart, 3 x 5 cards Use a number line and a hundreds chart to review how to use the location of two numbers on a number line or on a hundreds chart to tell which number is greater than or less than. When shown three or four 1-digit numbers, have students order the numbers from least to greatest, using the hundreds chart as a reference. To practice putting numbers in order, instruct each student to write a number from 0 through 40 on a 3” x 5” card. Ask two or three students to bring their cards and line up in order from least to greatest. Next, choose three or four students to stand with their cards and put themselves in the correct designated order (greatest to least or least to greatest). Keep index cards for Activity 12. Activity 12: Rounding to Nearest 10 (GLE: 10) Materials List: 0, 10, 20, 30, 40 written on colored index cards, 3 x 5 cards made in Activity 11, clothesline, clothespins, math learning logs Prior to class write the numbers 0, 10, 20, 30, and 40 on colored index cards. Hang the multiples of 10 on a clothesline. Pass out index cards used in Activity 11. Have each student determine which two tens his/her number is between and then determine which 10 the number is closer to. As each student discovers which ten the number rounds to have him/her pin the number to the bottom of the appropriate colored index card. Repeat until all students have had a chance. Ask if students can determine why numbers are rounded a certain way. Students should be able to reason that 32 is rounded to 30 because on a number line 32 is closer to 30 than to 40. In the same way, 36 is rounded to 40 because it is closer to 40 than to 30. Explain the rule for a number ending in 5. At the completion of this activity, ask students to list the numbers that would round to 50 (45, 46, 47, 48, 49, 50, 51, 52, 53, 54). It is very important when teaching rounding to always ask which two tens the number is between or which ten the number is closer to. Have students explain to a younger sibling the rules for rounding with examples in their math learning logs (view literacy strategy descriptions). Have them give an example of when you round up, round down or when a number ends in 5 what rule applies. Teacher Note: For students that have trouble with this activity, have them use a hundreds chart to help them determine the closest ten. Grade 2 MathematicsUnit 1Numbers, Numerals, and Data 9 Louisiana Comprehensive Curriculum, Revised 2008 Activity 13: Round About! (GLE: 10) Materials List: number line, newspaper advertisement or school supply list with items priced less than $1, paper, pencil Explain that a rounded number tells about how many instead of exactly how many. Use a number line to round 14, 12, and 16 to the nearest 10. Allow the students to brainstorm (view literacy strategy descriptions) ideas about when to round numbers in real-life situations. Explain how to round money amounts to the nearest 10 cents. Have small groups (2–4 students) use a newspaper advertisement or a list of school supplies to list prices of items and round the cost to the nearest 10 cents. Example: Eraser 87¢ rounds to 90¢ Sticker 13¢ rounds to 10¢ Activity 14: Place Value Word Grid (GLEs: 1, 5, 6, 10) Material List: Number Sense BLM, pencil After students have learned how to round numbers and skip count by 5‟s and 10‟s have them fill out the Number Sense BLM that utilizes a word grid (view literacy strategy descriptions) that demonstrates their mastery of place value, rounding, counting forward and backwards. After the word grid is filled in, allow time for students to quiz each other on the information in preparation for class activities and quizzes. Word Grid Numeral Tens Ones Number Number Nearest Multiple Multiple Before After Ten of 10 of 5 yes or no yes or no 21 2 1 20 22 20 no no 47 70 57 35 62 Activity 15: Professor Know-It-All (GLEs: 1, 5, 6, 10) Materials List: cards with 2-digit numbers, Place Value Certificate BLM Ask for a volunteer to be professor know-it-all (view literacy strategy descriptions). The student is given a two-digit number. He/she is expected to model the number with manipulatives, write the number in words, write it in expanded form, state a number that Grade 2 MathematicsUnit 1Numbers, Numerals, and Data 10 Louisiana Comprehensive Curriculum, Revised 2008 comes directly before it and after it, and round it to the nearest ten. When the task is complete, give the student a certificate that states he/she has earned the status of being a Professor of Place Value. Activity 16: The Guessing Jar (GLEs: 3, 26) Materials List: 2 glass jars that are the same size, some sort of filler for jars, Post-it® notes, poster, pencil Introduce the terms estimate and exact. Show students a jar (the same size as the Guessing Jar) with only 10 or 20 jellybeans or other small yummy treats. This will give the students a point of reference for making estimates. Ask the students to guess how many items are in the Guessing Jar. Have each student write a guess on a sticky note and place it on a poster. Arrange their guesses into a line plot. Discuss how students decided on their guesses and how they might determine how close their estimates might be. Count the items to find the exact number. Talk about which were good estimates. Do not emphasize or reward the student that got the closest to the exact number. This goes against the reason we estimate. Using the line plot, discuss how many students overestimated vs. how many underestimated the number of items in the jar. Teacher Note: There is an example of a line plot in the assessment section of this unit. Activity 17: Estimate (GLEs: 3, 5, 10, 26) Materials List: Popscicle® sticks, Post-it® notes, poster, pencil, marker Count out 62 Popsicle® sticks before class. Have students estimate how many sticks they think there are. Count out 10 sticks and ask students if they would like to adjust their estimates. Have students record their estimates on a sticky note. Ask students to round their estimate to the nearest ten. Construct a line plot after determining the range of the estimates. Use multiples of ten on the line plot. Have students place their sticky notes above the multiple of ten that corresponds to their rounded estimate. Ask questions relating to the line plot. Finally, count out sticks in bundles of ten. Website of an interactive estimation game with place value blocks http://www.learningbox.com/base10/Estimation.html Grade 2 MathematicsUnit 1Numbers, Numerals, and Data 11 Louisiana Comprehensive Curriculum, Revised 2008 Activity 18: Exactly! (GLE: 3) Materials List: T-chart, chalk Discuss the difference between exact and estimated numbers using items in the classroom and vocabulary such as more than, almost, nearly, and about to describe and compare numbers of items. For example, “There are about fifty books on the bookshelf” is an estimate. “We have fifteen boys and nine girls in our classroom” is an exact number. Provide students with opportunities throughout the year to practice and give examples of estimated and exact numbers. Lead discussions about situations that would require exact numbers and those in which only estimates are required. Record situations on a T-chart labeled estimate – exact. estimate exact Activity 19: Responding to a Venn Diagram (GLEs: 25, 26, 28, 29) Materials List: Venn diagram poster, overhead pen, tally chart, linking cubes, pencil Make a graphic organizer (view literacy strategy descriptions) of a single Venn diagram poster and laminate it. Post a statement each day and have students sign their names in the location of the poster that represents their responses. Point out that everyone has a place on the Venn diagram. Students who do not agree with the statement place their signatures outside the box containing the statement. Suggested statements: I like chocolate ice cream. I have a sister. I have a sister. I have a brother. Teacher Note: It is important for students to realize that if a signature is placed outside of the statement box, it could mean that the student has only brothers or he/she is an only child. Transfer results to a tally chart. Review how to record tally marks. Represent the data using linking cubes. Have students write two questions that could be answered using the data. Grade 2 MathematicsUnit 1Numbers, Numerals, and Data 12 Louisiana Comprehensive Curriculum, Revised 2008 Have a sister Don‟t have a sister Activity 20: Playing Around with Vennie! (GLEs: 25, 29) Materials List: colored chalk, paper, pencil Draw a large graphic organizer (view literacy strategy descriptions) of a Venn diagram that has two overlapping circles on the playground. Choose students to act out various combinations to demonstrate the correct use of the two-circle Venn diagram. For example, label the circles “I like to read.” and “I like to play video games.” Call up students that like to read and have them stand in the first circle. Then call up those that like to play video games and have them stand in the other circle. Ask if there are any students that like to both read and play video games. Those students should stand in the overlapping part. Have those who don‟t like reading or playing video games stand outside the circles. Dramatize other comparison situations using the large Venn diagram. Have students brainstorm (view literacy strategy descriptions) to identify animals that live on land and animals that live in water. Have students draw or cut out two pictures to represent animals that live on land and those that live on water. Next, show the students an example of an empty two-circle Venn diagram which has been drawn on a large chart or bulletin board. Label the circles “land animals” and “water animals.” Ask students which type of animals would go in the overlapping part of the circles; discuss and conclude that it would be those that live on both land and water. Have the students glue their animal pictures in the correct position in the two-circle Venn diagram, explaining why they should be placed there. Ask questions to show student understanding of the data posted on the Venn. Use and, or, and is/is not statements to describe the information represented in the diagram. Activity 21: Graphs (GLEs: 25, 26, 28) Materials List: My Predictions Worksheet BLM, Bar Graph BLM, overhead of Bar Graph BLM, red marker, blue marker, pencil, paper Students will use an anticipation guide (view literacy strategy descriptions) during class. The purpose of the guide is to have students anticipate answers -use their estimation skills in mathematics. After estimating, they will find the actual numbers and compare them to Grade 2 MathematicsUnit 1Numbers, Numerals, and Data 13 Louisiana Comprehensive Curriculum, Revised 2008 their estimates. The emphasis is on students‟ ability to estimate and not the “exactness” of their estimates. 1. Give each student the anticipation guide entitled My Predictions Worksheet BLM. Count how many students are present in class today, and record that number on the My Predictions Worksheet BLM. Instruct students to predict how many of their classmates were born in each month. The sum of their predictions should equal the number of students in attendance. 2. Give each student a Bar Graph BLM. Have them use the red marker to color in the number of squares above each month that represents their predictions. 3. Next, have students come up and color a square blue on the overhead transparency to show the month that they were born. Ask the students to help title the graph. A possible title is Birthday Months. 4. Have students use their blue marker to fill in the second bar next to each month to show the actual number of birthdays in each month. 5. Have students count the number of blue squares above each month. Record this information on their My Predictions Worksheet BLM. 6. Have students fill in the last column of the My Predictions Worksheet BLM. They can compare the number, or they can look at the bars on their graph to determine if their predictions were over, under, or exact in relation to the actual number of birthdays each month. Have students share information about how close they were on their predictions. Also ask which method they used to compare their prediction to the actual number - the chart or the bar graph. Finally, talk about the information they can learn from the graph. Ask questions that can be answered by looking at the graph, such as, “Which month has the most/least birthdays?” and “How many more birthdays does March have than April?” Remind students to look at the blue bars when asking the questions. Activity 22: Favorite Type of Cookie (GLEs: 25, 26, 27) Materials List: pictograph poster, cut out circles, table with cookies listed, graph paper, pencil Before class begins, make a pictograph outline and cut out circles to represent 4 types of cookies. Make a table with the types of cookies listed. Have each student vote for his/her favorite type of cookie by placing a tally mark next to the name of the cookie. After students have voted, count the votes for each type of cookie. Tell students they are going to construct a pictograph to display their data. Have students group themselves Grade 2 MathematicsUnit 1Numbers, Numerals, and Data 14 Louisiana Comprehensive Curriculum, Revised 2008 according to their favorite type of cookie. Tell students that you have paper cookies and that each paper cookie represents two votes. Have students line up in pairs and give each pair of students one paper cookie to place on the pre-made pictograph outline. If there is an odd number of students, have students decide how to represent that student‟s vote on the graph (i.e., place a half cookie to represent one vote). Ask students to make up questions that could be answered using the data on the graph. Have students transfer data to a bar graph. Challenge them to set up the vertical scale, horizontal axis, and title. Activity 23: Using technology to Create a Class Graph (GLEs: 25, 28) Materials List: computer, graphing program Graph Club® or Excel®, paper, pencil, list of survey questions Have students respond to a question. Collect the data and show them how to create a graph using a program like Graph Club® or Excel®. Show students how the same data can be used in different types of graphs. Have students work in pairs to create a survey question. Each pair should ask 20 students to respond to their survey. Have students use a computer program to input their data and create a graph. Have students write 2 questions that could be answered using their graph. Activity 24: Daily Graph (GLEs: 6, 25, 26, 27, 28) Materials List: students pictures pasted on a magnet, laminated sentence strip, laminated index cards with magnets, graph paper, paper, pencil Each day, write a question that students must respond to on a sentence strip. Use a magnetic board or your filing cabinet to set up the graph. Use index cards attached to magnets to be the horizontal axis. Have students place their picture above the index cards that indicates their response to the question. Have students transfer the data to a chart or create a pictograph with each picture representing 2 responses. Also challenge them to write questions that could be answered using the data. Throughout the year have students use a key of 2 when transferring the data to a pictograph. Which of the days listed do you like to watch TV the most? Monday Wednesday Friday Grade 2 MathematicsUnit 1Numbers, Numerals, and Data 15 Louisiana Comprehensive Curriculum, Revised 2008 Sample Assessments Performance and other types of assessments can be used to ascertain student achievement. Observation and performance based assessments will be used whenever possible. Following are some examples: General Assessments Maintain portfolios which contain copies of individual and group projects completed successfully during this unit: one- and two-circle Venn diagrams, a student-made game using the hundreds chart, tables, charts, graphs, or pictures made by the student, and teacher-made tests on specific topics studied. Using data from the class, the student will create a two-circle Venn diagrams showing statements such as I have a bike, I have a Playstation 2®, Game Cube®, or X-box®. The teacher will observe the finished product and ask questions to check for understanding. Given a bar graph, pictograph, or line plot, the student will interpret and write/answer questions pertaining to the data. Activity-Specific Assessments Activities 1-4: Given several models, students write the numeral, number word, and expanded form of the number. Activities 5, 7: Students fill in ten missing numbers in a hundreds chart. Activities 1, 2, 3, 4, 9, 10, 11,: Students draw models of 30, 67, 42, 59, 29, and 15, write them in word form and expanded form and then arrange them in order from least to greatest. They will also complete statements such as these: 29 is more than__________ 59 is less than___________ _______is the greatest number listed What number would be on the left of 42 on a number line? __________ What number would be on right of 29 on a number line?_________ Activities 12 and 13: Students solve problems such as this: Paul said he had about $20. What amounts could he have that would round to $20? Do you know exactly how much money he has? Grade 2 MathematicsUnit 1Numbers, Numerals, and Data 16 Louisiana Comprehensive Curriculum, Revised 2008 Activities 17: Given a line plot, students transfer information to a table using tally marks and answer questions related to the information given. x x x x x x x x x x x x x x x x grapes strawberries cherries apples Activities 19 and 20: Students place numbers in their proper places on a Venn. Example: 21, 27, 29, 26, 23, 25, 40, 15, 35 Numbers that Round to 30 Activities 16, 17, 18: Students complete this Performance Assessment. Label four identical jars as A, B, C, and D. Fill jars A and B with the same number of Cheerios®. Fill a third jar with the least amount of cereal. Fill the fourth jar with the greatest amount of cereal. The student will come to the table and estimate the number of Cheerios® in the jars. The teacher will tell the class how many Cheerios® are in Jar A and then each student will compare the contents of jars B, C and D to that of Jar A, estimating the number of Cheerios® in each jar. Use a checklist to evaluate the student‟s estimation skills. _____Student determined which jars were filled with the same amount. _____Student identified the jar with the least amount. _____Student identified the jar with the greatest amount. _____Estimates were reasonable when compared to Jar A Activities 16, 17, and 18: Students complete the following self-assessment. Each student will bring a personal collection of objects (e.g., stamps, pins, marbles) numbering fewer than 100 in a plastic zip-lock bag or appropriate see-through container. Students will place all the collections on a long table and number the collections and number a piece of paper with the correct Grade 2 MathematicsUnit 1Numbers, Numerals, and Data 17 Louisiana Comprehensive Curriculum, Revised 2008 number of collections. The student will guess/estimate the number of objects in each collection and record the estimates by the correct numbers on his/her paper. (Give the students only a few seconds at each collection by ringing a bell to signal that they should move to another collection.) The students will check his/her estimates as owners of the collections give the correct numbers. Activity 21-24: Pairs of students will survey their classmates on assigned topics (favorite color or snack, lunchbox or lunch tray, how they get to school, and so on). Each pair will create a bar graph to show the data collected and correctly title and label the graph. Students will use a computer program to graph the data if one is available. Grade 2 MathematicsUnit 1Numbers, Numerals, and Data 18 Louisiana Comprehensive Curriculum, Revised 2008 Grade 2 Mathematics Unit 2: Extending Facts and Operations Time Frame: Approximately five weeks Unit Description This unit focuses on basic addition and subtraction facts. Student Understandings Students use basic addition and subtraction facts to help them solve real-life problems. They recognize when a situation calls for addition or subtraction and use facts and related fact families to solve such settings. Students will write number sentences using the correct symbols. Guiding Questions 1. Can students give all addition and subtraction facts through 9 + 9 with ease and apply related family facts? 2. Can students apply facts to solve real-life problems and complete 1- and 2- digit addition and subtraction problems without regrouping? 3. Can students locate sums and differences on the number line? 4. Can students use appropriate symbolism for operations and number sentences? 5. Can students use number sentences to model problems and find missing values in fact-related equations? Unit 2 Grade-Level Expectations (GLEs) GLE # GLE Text and Benchmarks Number and Number Relations 1. Model, read, and write place values for numbers through 999 in word, standard, and expanded form (N-1-E) 5. Read, write, compare, and order whole numbers through 999 using words, number lines, and models (N-3-E) (N-1-E) 6. From a given number, count forward and backward and count to 100 by 2s (N-3-E) (N-1-E) (N-4-E) 7. Know all basic facts for addition and subtraction and use them to solve real-life problems (N-5-E) (N-6-E) (N-7-E) (N-8-E) (N-9-E) Grade 2 MathematicsUnit 2Extending Facts and Operations 19 Louisiana Comprehensive Curriculum, Revised 2008 GLE # GLE Text and Benchmarks 8. Recognize, select, connect, and use operations, operational words and symbols (+, ) for addition (join, part/part/whole) or subtraction (take away, comparison, missing addend, and set/subset) situations (N-6-E) (N-5-E) 9. Add and subtract 1- and 2-digit numbers (N-6-E) (N-7-E) Algebra 12. Use number sentences to represent real-life problems involving addition and subtraction (A-1-E) (A-2-E) 13. Find the missing number in an equation involving addition or subtraction (e.g., # + 4 = 7, 8 - # = 3) (A-2-E) (N-4-E) Data Analysis, Probability, and Discrete Math 25. Collect and organize data using observations, surveys, and experiments (D-1-E) Patterns, Relations, and Functions 30. Recognize, extend, create, and explain patterns of addition and subtraction as represented in charts and tables and in varied forms of skip-counting (P-1-E) (P-2-E) 32. Recognize and apply patterns in problem-solving in other content areas and real- life situations (P-3-E) (N-9-E) Sample Activities Activity 1: Addition Strategies (GLE: 7) Materials List: paper, pencil, fact practice sheets, addition fact flashcards Write the following problems on the board. 5 boys + 0 boys =____boys 6 girls + 1 girls = ____girls 6 cats + 6 cats = _____cats 7 rings + 6 rings + _____rings 9 candies + 4 candies = ________candies Ask students to share how they solved each problem. Listed below are strategies that might help a student who has yet to learn the facts. +0 Adding Zero – When 0 is added to a number, the number doesn't change. 5 boys plus 0 boys is 5 boys because the amount doesn't change when I add zero boys. +1 or +2 Counting On – To add 1 or 2 to a number, start with the larger number and count forward. 6 girls plus 1 more girl is 6 and 1 more = 7. Grade 2 MathematicsUnit 2Extending Facts and Operations 20 Louisiana Comprehensive Curriculum, Revised 2008 6 + 6 is a Double – When students are learning facts for the first time, teaching them all the doubles is a strategy that can be used. 7 + 6 is a Double + 1 – Have students use what they know about doubles to help them find sums that are a double plus one more. It helps to think 7 + 6 = 6 + 6 +1 which is 12 and 1 more = 13. 9 + 4 Compensation – To add these numbers, have students make a 10 by taking 1 from the 4 and put it with the 9 to make 10 so 10 + 3 = 13. Facts they must memorize: 3 + 5, 3 + 6, 3 + 7, 3 + 8, 4 + 6, 4 + 7, 4 + 8, 5 + 7, 5 + 8, 6+8 Target a strategy each week, and practice facts the first 5-10 minutes of your lesson. Use fact practice sheets. Have students write the facts, and use flashcards to practice facts. Activity 2: Digit Run (GLE: 7) Materials List: 2 sets of enlarged digit cards (0-9) each digit written on a 8 x 11 sheet of paper, addition flashcards Divide the class into two teams. Give each student a digit from 0-9 that has been enlarged to fit on an 8 1 x 11 piece of paper. Have the students on each team line up in order 2 according to the digit they are holding. The teacher uses the flashcards to call out an addition fact. Ask the student (s) holding the digit(s) on each team that represents the sum to walk quickly to the front and turn toward their team. Example: 6 + 7 = ? The student that has the 1 digit card and the student that has the 3 digit card must walk quickly and position themselves so that the 1 is on the left and the 3 is on the right. The first team to represent the answer is awarded a point. Students return to their team. Then another problem is called out. After students learn their subtraction facts, play the game using subtraction facts. Activity 3: Addition Sentences (GLEs: 7, 8, 12) Materials List: 10 books, paper, pencil, vocabulary cards, 10 counters per pair of students, math learning log Gather ten books. Place two books in the first pile and three books in the second pile. Ask students how many books there are in all. Write the number sentence, 2 books + 3 books = 5 books, on the board. Ask the students to make a generalization about addition. Grade 2 MathematicsUnit 2Extending Facts and Operations 21 Louisiana Comprehensive Curriculum, Revised 2008 part + part = total Rearrange the book piles so that there are three books in the first pile and two books in the second pile. Write the number sentence, 3 books + 2 books = 5 books, on the board. Ask the students if the total number of books has changed. Make vocabulary cards (view literacy strategy descriptions) for: addend, sum, addition sign and equal sign. Each card should resemble and include the information on the following sample card: Definition: Characteristics: The numbers Found in addition being added in problems. an addition problem. addends Term/Concept Examples: Illustration: 3+4=7 3 and 4 are the addends. When students create vocabulary cards, they see connections between words, examples of the word, and the critical attributes associated with the word. This vocabulary strategy also helps students with their understanding of word meanings and key concepts by relating what they do not know with familiar concepts. Vocabulary cards require students pay attention to words over time, thus improving their memory of the words. In addition, vocabulary cards can become an easily accessible reference for students as they prepare for tests, quizzes, and other activities with the words. Repeat the process using a different number of books. Guide students to the conclusion that the order in which the numbers (addends) are added does not affect the total number of books (sum). So it doesn‟t matter which part you start with – when you put the two parts together, they equal the total. Have students work in pairs. Give each pair of students 10 counters. Have them write a number sentence and its commutative number sentence (turn around fact) for 8 counters, 4 counters, and 10 counters. Allow students to share their sentences. Ask students to write 7 + 1 = 8 in the math learning logs (view literacy strategy descriptions). Have them identify the addends, addition sign, and sum. Grade 2 MathematicsUnit 2Extending Facts and Operations 22 Louisiana Comprehensive Curriculum, Revised 2008 Activity 4: Addition Battle (GLE: 7) Materials List: deck of cards with face cards and 10s removed for each pair of students Give each pair of students a deck of cards. Have them remove all the face cards and the 10s from the deck. The ace will represent 1. Have one student in each pair deal all the cards. Play begins as both students flip over one card at the same time. The student who says the sum of the two cards faster gets both cards. Play continues until all cards have been played. Have students count their cards to see who won the game. A variation of this game is to play with three students with students adding three numbers to find the sum. Teacher Note: Four sets of digit cards may be used for each pair instead of using playing cards. Activity 5: Modeling Number Sentences (GLEs: 7, 8, 12 ) Materials List: paper bags, marker, two different colors of cubes or tiles, paper, pencil Prior to class use marker to number paper bags 1-15. Start with bag #1 and put some (1- 9) cubes of the same color in each bag. Repeat the process using a different color of cubes. Do not put more than 18 cubes in a bag. Use two different color linking cubes to model addition and subtraction sentences. Make sure students use correct terminology (addends, sum, difference), the operation symbols for addition (+) and subtraction (–), and the equal (=) sign. The objective is to demonstrate the relationship between addition and subtraction. Model the four related addition and subtraction sentences using 8 of one color and 4 of the other color cube. While modeling, have a student write the math sentences on the board. Also, have students use a modified version of split page notetaking (view literacy strategy descriptions) to record the related sentences as in the example below. This is done by drawing a line down the page. The page should be split into one-thirds/two thirds format. Students will list the total number of cubes on the left and write all the related number sentences on the right. The strategy has been modified by using numbers instead of words. Example: 8 cubes + 4 cubes = 12 cubes Bag #12 Related Sentences 4 cubes + 8 cubes = 12 cubes 12 cubes – 8 cubes = 4 cubes 12 cubes 12 cubes – 4 cubes = 8 cubes 8 + 4 = 12 4 + 8 = 12 12 – 4 = 8 12 – 8 = 4 Grade 2 MathematicsUnit 2Extending Facts and Operations 23 Louisiana Comprehensive Curriculum, Revised 2008 Ask students if it makes a difference which number (addend) they write first in an addition statement. Then ask if it makes a difference which number they write first in a subtraction statement. Put students into pairs. Give each pair a bag with 2 different color cubes. Have them record the number of cubes on the bag. Then have them model and write the addition and the related subtraction sentences using their cubes using the modified version of split- page notetaking. Then have students share their related facts on the board. Have students exchange bags and repeat the activity. Demonstrate for students how they can study their split-page notes by covering information in one column and recalling information in the other. Allow them time to quiz each other on the information in their notes in preparation for tests and other class activities. Activity 6: Single Out (GLEs: 7, 9, 30) Materials List: calculator, Single Out 3 x 3 Grid BLM, transparency of Single Out 3 x 3 Grid BLM, pen, paper, pencil, die per pair of students, math learning log, calculator (optional) Play Single Out. Single Out The object of the game is to get as many equal sums as possible. Handout Single Out 3 x 3 Grid BLM. Model a game using the overhead transparency. Have students record the numbers on their BLM as you record them on the transparency. Roll a die and call out a number. Have a student go to the overhead and place the number on the grid. Repeat the process until all the squares are filled. Have a student find the sums of the three numbers on each row and each column, writing each sum on the blank outside the grid. Examine all the sums. Have a student cross out the sums that appear only once and add up the remaining sums to find the score. (Students could use a calculator to check the sums.) Students will soon learn that there is a strategy to the game and then they will carefully place the numbers on the grid so that they can get multiple representations of the same sum. Put students into pairs. Repeat the game this time letting students play against one another on the extra boards on their recording sheets. Grade 2 MathematicsUnit 2Extending Facts and Operations 24 Louisiana Comprehensive Curriculum, Revised 2008 Have students describe what they think the strategy is for Single Out in their math learning log (view literacy strategy descriptions). Teacher Note: After the students have played this game with the teacher, provide pairs of students with grids and die and have them play against each other. Activity 7: Subtraction Number Sentences (GLEs: 7, 8, 12) Materials List: 10 counters, connecting cubes, Subtraction Sentences BLM, paper, pencil Place 10 counters on the overhead. Remove 2 counters. Ask students to identify the operation being modeled when they have a total amount and then take something away. Review with the students how to write a subtraction number sentence. total - part = part 10 counters – 2 counters = 8 counters Use connecting cubes to make a tower that has 7 cubes and one that has 3 cubes. Ask students how many more cubes does the 7-cube tower have than the 3-cube tower? Remind students that when we compare two things, we take away the amount that the things have in common, and the amount that is left is how they are different. When comparing 7 to 3, first take away what they have in common (3 cubes) then what is left is how they are different – 4 cubes. Ask students to identify the operation that is being modeled when we compare two things to find their difference. Write the subtraction number sentence. 7 cubes – 3 cubes = 4 cubes Model several problems for them using the total and removing a part model and the comparison type problem that requires subtraction. Give each student a Subtraction Sentences BLM. Have him/her model the subtraction problem to find the solution. If the situation is a comparison problem, have him/her model both numbers and remove what the numbers have in common. If the problem is a total with a part removed, have him/her start with an amount and remove the necessary counters to solve the problem. Add difference, subtrahend, subtraction sign and minuend to vocabulary cards (view literacy strategy descriptions). Grade 2 MathematicsUnit 2Extending Facts and Operations 25 Louisiana Comprehensive Curriculum, Revised 2008 Activity 8: Number Line Subtraction (GLEs: 7, 8, 12) Materials List: masking tape, chalk, paper, pencil, Number Line Sentences BLM, two counters per student Make a large number line on the floor with masking tape and chalk. Number the line 0 through 12. Have one student start at 0 and walk 7 spaces forward and then hop back three spaces. Ask, Where are you are now? (4) Write the number sentence to show what happened. (7 spaces– 3 spaces =4 spaces) Have a student walk to 9 and another student walk to 2. Ask what did the students that are standing on 9 and 2 do alike? (They both walked to 2.) Then ask what did the students standing on 9 and 2 do differently? (9 is 7 spaces ahead of 2 on the number line.) (9 – 2 = 7) Allow students to return to their desks and make up story problems that can be modeled on the Number Line Sentences BLM using a counter(s). When students are finished, have them return to the number line and chose other students to dramatize their story on the number line. Record the number sentence on the board that matches the story problem. Assign students a RAFT (view literacy strategy descriptions) writing assignment. Once students have acquired new content information and concepts, they need opportunities to rework, apply, and extend their understandings. RAFT writing is uniquely suited to do just that (Santa & Havens, 1995). This form of writing gives students the freedom to project themselves into unique roles and look at content from unique perspectives. From these roles and perspectives, RAFT writing has been used to explain processes, describe a point of view, envision a potential job or assignment, or solve a problem (Fisher & Frey, 2003). It‟s the kind of writing that when crafted appropriately should be creative and informative. RAFT is an acronym that stands for: R – Role (role of the writer) A – Audience (to whom or what the RAFT is being written) F – Form (the form the writing will take, as in letter, song, etc.) T – Topic (the subject focus of the writing) Next tell students to pretend that they are a number line and some one is walking on them. Have them write a story problem from the view point of the number line using the following guide: R- Number Line A- Students in the class R- Word problem T – Number sentence Grade 2 MathematicsUnit 2Extending Facts and Operations 26 Louisiana Comprehensive Curriculum, Revised 2008 Example: Someone was standing on me and walked 4 steps forward from 0. Then he hopped back two spaces. What number of mine is he standing on? 4 steps forward - 2 steps backwards = standing on 2 Allow time for students to share their RAFT writing with a classmate or the whole class. Ask students to listen for accuracy and logic. Activity 9: Which Operation is Needed? (GLEs: 7, 8, 9, 12) Materials List: paper, pencil, calculators After solving two or three addition or subtraction story problems, discuss with the students how they will decide if they should add or subtract (add when joining sets and subtract when separating sets or comparing numbers). Have students brainstorm (view literacy strategy descriptions) examples of times when they might need to add or subtract. Make a T-chart with columns labeled "Times I would Add” and “Times I would Subtract" to display students' examples. List key words in the problem that help identify whether students need to add or subtract. Example: I am playing a game with 3 friends and 2 more friends come to play. What is the total number of people playing the game? Have students write story problems. Have students read their problems. The class must determine whether they would add or subtract to find the solution. List words in their problems on the T-chart that help identify whether to add or subtract. Have a student write the number sentence for each problem on the board, and then have students use a calculator to check the solution to the problem. Activity 10: Color Counter Problems (GLEs: 7, 12) Materials List: counters – 4 different colors (9 of each color), Spinner 0-8 BLM, paper, pencil, calculators, large paper clip Model the following activity for students. Then put students into groups and have them make sets and write problems. In small groups, give students red, yellow, blue, and green counters and a Spinner 0 – 8 BLM. Have each group spin four different numbers and make sets showing each number with the different color counters. Have students make up addition or subtraction sentences using the piles of counters. Example: 6 yellow counters plus 7 green counters is 13 counters. All students in the group record the sentence. Grade 2 MathematicsUnit 2Extending Facts and Operations 27 Louisiana Comprehensive Curriculum, Revised 2008 Ask the next student to make up a sentence that hasn‟t been used by their group members. Continue playing until all addition/subtraction sentences have been listed. Have students check their problems using a calculator. Activity 11: Picture Problems (GLEs: 8, 9, 12) Materials List: addition and subtraction flashcards, digital cameras, construction paper, glue, paper, pencil Put students into groups and give them a flashcard with a basic addition or subtraction fact on it. Have them make a model of the fact and take a picture(s) of the model with a digital camera. Print the pictures and glue them on construction paper and laminate them. Number the pictures, circulate them among groups, and have each group write the number sentence that it sees depicted in the picture. If a camera is not available, use magazine photographs or illustrations showing sets of objects that can be described in an addition or subtraction story. Hang the “posters” on a bulletin board for all to evaluate. Example: 3 children + 2 children = 5 children Activity 12: Number Sentences on the Computer (GLEs: 7, 12) Materials List: computers for students, Kidpix®, printer Have students illustrate addition and subtraction sentences using a computer drawing program. For example, if the program has an autoshape feature, have students select a shape and copy and paste the shape to illustrate the number sentence. If the students have access to a program like Kidpix® have them select a stamp and use it to illustrate their number sentence. Print students‟ illustrations and assemble them to make a number sentence book. Activity 13: Adding Tens (GLEs: 1, 8, 9, 12) Materials List: digit cards, paper, pencil Flip over 2 cards from a set of digit cards and form a 2-digit number using the digits selected. Each card will represent a number of tens. Example: Teacher turns over a 2 and 7 She says and writes: 2 tens and 7 tens = 9 tens Then she writes: 20 + 70 = 90 Grade 2 MathematicsUnit 2Extending Facts and Operations 28 Louisiana Comprehensive Curriculum, Revised 2008 Repeat the process two more times modeling for students how to say and write their number sentences. If students get numbers that add to more than 9 tens, allow them to leave it as tens. 9 tens + 4 tens = 13 tens When students share their number sentences with the class, ask them, “What do you know about 13 tens?” 13 tens = 10 tens and 3 more tens 10 tens = 100 and 3 tens = 30 100 and 30 = 130 Put students into pairs. Have students repeat the activity as many times as time will allow, writing their number sentences as they go along. Have students share their number sentences. Activity 14: Number Puzzles (GLEs: 7, 9, 13) Materials List: transparency of Number Puzzles BLM, paper, pencil, Blank Number Puzzles BLM, calculator Make a transparency of Number Puzzles BLM. Use the transparency to guide students through how to find the missing digit in the problem. Have students complete the Number Puzzles BLM. They may use a calculator to check their answers. 1 8 3 9 + 7 + 3 + 2 + 3 4 8 9 5 5 4 5 9 Then, have students create their own puzzles on Blank Number Puzzles BLM. Next, have students exchange puzzles with classmates and solve. Finally, have students check their solutions using a calculator. Activity 15: Missing Addends (GLE: 13) Materials List: paper cup, cubes, paper, pencil Place three cubes in a paper cup. Show students the cup and seven cubes which have been aligned in a row. Tell them that there are ten cubes in all. Ask how many cubes they see (7) and how many are in the cup (3). Why? (3 + 7 is 10) Have students write the addition sentence that was described (i.e., _______cubes + 7 cubes = 10 cubes). Explain that this is a missing-addend problem: one addend is 7 and one is 3, making a sum of 10. Continue with other examples, including some with 10 and 0 as addends. Grade 2 MathematicsUnit 2Extending Facts and Operations 29 Louisiana Comprehensive Curriculum, Revised 2008 Have a student come to the front of the room, place some cubes in the cup, and make a row of cubes. He/she must tell the class the total number of cubes that have been used. Have a volunteer write the addition sentence on the board as each is done. Ask students to solve the missing addend problem. Ask students how they could use subtraction to find the missing addend. (Subtract the known addend from the sum) Put students into groups of 4. Have students then write story chain problems (view literacy strategy descriptions) that have a missing addend. Example: Student 1: I have 6 counters in my left hand. Student 2: I have some counters in my right hand that I will add to my left hand. Student 3: I now have 13 counters Student 4: How many counters did I add? (I added 6 + ? = 13. 13 – 6 = 7 So, I must have added 7 counters.) After students have had time to create their story chains, have them read the stories to the class. Make sure the problem has been solved accurately, and make sure students share how they solved the problem. Teacher Note: This is a great bell-ringer activity. Put counters in each of your hands. Open one hand and show students how many counters are in that hand. Then tell them the total number you are holding. Have students write the number sentence, and solve for the missing counters. Activity 16: What’s Missing? (GLEs: 12, 13) Materials List: paper, pencil, math learning logs Have students solve real-life problems with missing addends. Have them write the number sentences to represent the story using labels. Examples are as follows: Patrick saved $8. He needs $15 to buy a CD. How much more does he need to buy the CD? $8 that Patrick saved + _____money he needs = $15 to buy the CD. Make the connections between addition and subtraction by showing that the student can subtract $8 from $15 to find out what the missing addend will be. $15 to buy CD - $8 Patrick saved = ______money he needs There were 9 people at the beginning of the birthday party. At the end of the party there were 16 people. How many more people came to the party? 9 people at the beginning + _________more people = 16 people at the end 16 people at the end – 9 people at the beginning = ________additional people. Grade 2 MathematicsUnit 2Extending Facts and Operations 30 Louisiana Comprehensive Curriculum, Revised 2008 Jacob and Steven ate some cookies. Jacob ate 5 cookies. Together they ate 12 cookies. How many cookies did Steven eat? 5 cookies Jacob ate + _____cookies Steven ate = 12 cookies together 12 cookies together - 5 cookies Jacob ate = ______cookies Steven ate. Have students write missing addend problems in their math learning logs (view literacy strategy descriptions). Activity 17: Candy Store (GLEs: 5, 9, 12, 13) Materials List: paper, pencil Use prices of candy to have students practice adding 2-digit numbers without regrouping. Write the candy prices on the board (21¢, 35¢, 53¢, 14¢, and 42¢). Make sure students understand the term "expensive" before beginning. Write the following questions on the board. Have students write a number sentence for each problem. What is the cost of the two most expensive pieces of candy? What is the cost of the two least expensive pieces of candy? Which two items have a total cost of 49¢? Which two items have a total cost of 56¢? If you had 75¢, how many different items could you buy? How much did the second item cost if you bought an item for 14¢ and you spent 56¢? Tell students that the candy store is interviewing for the head cashier position. It is looking for a professor know-it-all (view literacy strategy descriptions) that can add prices correctly. Ask students to submit their papers if they would like to be considered for a head cashier position. Students that get all the problems right get a sticker (button) that says “Head Cashier.” This is a modified version of professor know-it-all. Students normally are questioned by the teacher or fellow classmates to check for understanding of a concept. Once they have demonstrated that they “know it all,” another group is called to the front of the class for questioning. Activity 18: Magic Squares (GLEs: 13, 30) Materials List: Magic Squares BLM, paper, pencil, calculator, math learning log The objective of this activity is to fill a square with the digits 1 – 9 so that all the rows, columns, and diagonals have the same sum. Give each student a copy of Magic Squares BLM. Grade 2 MathematicsUnit 2Extending Facts and Operations 31 Louisiana Comprehensive Curriculum, Revised 2008 Tell students that they are to use the digits 1 – 9 only once to fill in the puzzle so that all the rows, columns, and diagonals have the same sum. Have students find the digits that are missing in the puzzle and write them above the puzzle. (1, 3, 6, and 8). Add the numbers in the first row with a calculator. (2 + 9 + 4 = 15) 15 is the target number. Now add 7 + 5 = 12. 12 + ? = 15. (3) Add three to the second row. Continue to find the missing addends. 2 9 4 solution 2 9 4 7 5 7 5 3 6 1 8 Continue to guide students through each square. They should first list the digits that are missing from the square. If a row/column/diagonal has two numbers recorded, students should add those two numbers and subtract that sum from 15 to find the missing addend. By process of elimination, students will be able to fill in the square. Discuss students‟ answers. Ask students to draw a 3 x 3 grid in their math learning logs (view literacy strategy descriptions). Tell students to place the digits 6, 5, and 7 in the diagonal. Make sure students place 5 in the center. Have students determine the magic number. (18) Then ask them to place the digits from 2, 3, 4, 6, 7, and 10 in the empty squares to find the solution to the puzzle. Remind students that all the digits must add to the same number in every row, diagonal, and column. Give students hints if needed. Have students share their solutions. 6 4 8 example of 1 solution 10 5 3 2 9 7 Activity 19: Write the Questions (GLEs: 12, 25) Materials List: paper, pencil Give students situations and have them write an addition and a subtraction question for each situation. Examples: Mica has 9 dolls. Joy has 8 dolls. How many dolls do they have altogether? How many more dolls does Mica have? Mark has 20¢. Jonathan has 50¢. How much money do they have together? How much more money does Jonathan have then Mark? Grade 2 MathematicsUnit 2Extending Facts and Operations 32 Louisiana Comprehensive Curriculum, Revised 2008 A variation of this activity would be to use grocery ads. Be selective in the combination of items since students have not been introduced to regrouping. Activity 20: Problem Solving with Patterns (GLE: 30) Materials List: Hundreds Chart BLM, 20 nickels, 10 dimes, counter, paper, pencil Put students into pairs. Ask students how they might find the value of 12 nickels. Students may suggest counting by 5s to find the value. Remind students this is called skip counting. Give each pair of students a Hundreds Chart and 12 nickels. Ask students to count out loud by 5s and place a nickel covering the multiples of 5 on the chart as they count. Have students check each other‟s charts and describe the pattern. Ask students how many nickels it will take to have 95¢. Next, give 7 dimes to each pair and have students find the value of 7 dimes by placing dimes on multiples of 10 on the 100s chart. Finally, tell students you saw 17 animals in the woods. Ask, “How many eyes did I see?” This time give students counters to figure out the pattern that will allow them to answer the question. Activity 21: Function Machines (GLEs: 7, 30) Materials List: function machine, index cards with answers, rule card, number cards 0-9 Use a function machine to demonstrate basic facts in addition and subtraction. Choose a student to be the output coordinator (he/she will send the correct answer card out of the function machine). Write a rule on a card, and place it in a pocket or tape it to the front of the machine. Choose a volunteer to enter a number card 0 through 9 into the input slot of the machine. If the rule card says +2, then the output coordinator must send out the correct sum through the output slot on the machine. Directions for making a function machine are as follows: Use a box turned on its side and covered with paper or painted to look like a machine with dials, buttons, windows, and so on. Cut a slot on the top and side for input and output, and glue a pocket to the front for the rule card. Make a set of cards to match the numbers you want to practice. Variation: Mentally determine a rule. Put a card with a number in the function machine, and mentally apply the rule. Show a card that represents the original number and the Grade 2 MathematicsUnit 2Extending Facts and Operations 33 Louisiana Comprehensive Curriculum, Revised 2008 output. Put several cards through the machine with the same rule being applied to them, and then ask students to try to determine the rule. Activity 22: Using a T-chart (GLE: 30) Materials List: paper, pencil Draw a T-chart graphic organizer (view literacy strategy descriptions) on the board. Have students use a T-chart to organize information when skip counting. Example: How many wheels are on 5 tricycles? Tricycles Wheels 1 3 wheels 2 6 wheels 3 9 wheels 4 12 wheels 5 15 wheels Additional examples: Number of legs on _____dogs Number of eyes on _____cats Number of days in ____weeks Activity 23: Number Patterns (GLES: 6, 32) Materials List: paper, pencil Write the following problems on the board. Have students solve each problem and explain the pattern. Customers were standing outside of Best Deal. The manager gave the second person in line 1 coupon, the fourth person in line 2 coupons, the sixth person in line 3 coupons. How many coupons did the manager give the 12th person in line? Yolanda was putting stickers on the corners of each pentagon on her page. How many stickers did she need if there were 6 pentagons on the page? Alison looked into the woods and saw 14 eyes. How many animals did she see? Grade 2 MathematicsUnit 2Extending Facts and Operations 34 Louisiana Comprehensive Curriculum, Revised 2008 Paul bought a soda for 65¢. He used only nickels. How many nickels did Paul put in the machine? Activity 24: Missing Numbers in Patterns (GLE: 32) Materials List: paper, pencil Write the following problems on the board and have students find the missing numbers. 1, 3, 5, _____, ______, _______ 10, 20, 30, ______, _______, _______ 17, 15, 13, ______, _______, _______ 50, 45, 40, ______, _______, ________ Sample Assessments Performance and other types of assessments can be used to ascertain student achievement. Following are some examples: General Assessments Use portfolio assessment to evaluate the unit. Included in the portfolio will be samples of Magic Squares, stories and pictures, work samples, and teacher- made tests. Write a journal entry -The student will make up a story problem that goes with the number sentence, 9 + 5 = 14. Give an illustration of addition or subtraction problem on a number line. Students will write the related number sentence. Activity-Specific Assessments Fact test should be given weekly throughout this unit after teaching students a strategy. Activity 5: Students write 2 addition sentences and the 2 related subtraction sentences using the numbers in the example. The following colors of crayons were counted in the art center: 5 red 7 blue 11 brown 3 white 4 orange 2 yellow 9 black 6 pink 1 purple 10 green Grade 2 MathematicsUnit 2Extending Facts and Operations 35 Louisiana Comprehensive Curriculum, Revised 2008 Example: 4 orange crayons + 9 black crayons = 13 crayons 9 black crayons + 4 orange crayons = 13 crayons 13 orange and black crayons - 9 black crayons = 4 orange crayons 13 orange and black crayons – 4 orange crayons = 9 black crayons Activity 8: Give the student a number line from 1 through 20. Direct each student to start at a given number, and indicate that he/she is to model hopping so many spaces forward or backwards and state what number he/she landed on. The student will write the number sentence to show which operation was used. Example: Start on 7, and hop 3 spaces forward. Where are you?_______ 7 + 3 = 10 Start on 12, and hop 5 spaces backwards. Where are you?________ 12 – 5 = 7 Activities 8, 9, 12: Given different real-life situations, the student will identify which operation is needed to solve the problem, write a number sentence with labels, and solve it. Activity 20: Students use the 100s chart to: find and record the value of 10 nickels find and record the value of 9 dimes find the value of 27 pennies Activity 21: Have each student bring a box (any size) and design his/her own Function Machine. The student will turn in the box and a card stating the rules to be used. Use a rubric to grade the project. Sample rubric: _____All addends written and coded to sums - 5 points _____ Rule card - 2 points _____ Sum cards are correct - 5 points _____Design of machine - 3 points Teacher Note: These may be used to practice facts at home, or they may be shared with other classrooms in a peer-tutoring activity to practice basic facts. Save them to use for multiplication, too. Grade 2 MathematicsUnit 2Extending Facts and Operations 36 Louisiana Comprehensive Curriculum, Revised 2008 Grade 2 Mathematics Unit 3: Money and Time Time Frame: Approximately four weeks Unit Description This unit extends number and operation skills to include money (skip counting by 5s) and time (telling time to the nearest 5 minutes). Student Understandings Students should be able to recognize and deal with money situations. They tell time to the nearest 5 minutes and indicate their understanding of elapsed time by stating time one hour before and after a given time. Guiding Questions 1. Can students find and write the value of coins and $1 bills? 2. Can students use one-to-several correspondence to trade single items for a greater quantity of items with equal value? 3. Can students tell time to the nearest 5 minutes and relate 5s on a clock to skip counting by 5s? 4. Can students solve problems using elapsed time? Unit 3 Grade-Level Expectations (GLEs) GLE # GLE Text and Benchmarks Number and Number Relations 2. Model the concepts of thirds, fourths, fifths and sixths using regions, sets, and fraction words (e.g. one-third, three-fourths, five-sixths) (N-1-3) 4. Count and write the value of amounts of money up to $1.00 using ¢ and $ (N-2-E) (N-6-E) (M-1-E) (M-5-E) 6. From a given number, count forward and backward and count to 100 by 2s (N-3-E) (N-1-E) (N-4-E) 11. Use the concept of one-to-several correspondence to trade single items for a greater quantity of items with unequal value (1 nickel for 5 pennies, 1 dime for 2 nickels) (N-9-E) Measurement 16. Tell time to the nearest 5 minutes, and identify the time one hour before or after a given time (M-1-E) (M-3-E) Grade 2 MathematicsUnit 3Money and Time 37 Louisiana Comprehensive Curriculum, Revised 2008 25. Collect and organize data using observations, surveys, and experiments (D-1-E) 26. Construct and read line plots and tables (D-2-E) 29. Solve logic problems involving two sets by using elementary set logic (i.e., and , or, and is/is not statements) (D-3-E) 30. Recognize, extend, create, and explain patterns of addition and subtraction as represented in charts and tables and in varied forms of skip-counting (P-1-E) (P-2-E) Sample Activities Activity 1: Everything you wanted to Know about Coins (GLE: 4) Materials List: examples of each type of coin, Word Grid BLM, pencil, transparency of Word Grid BLM As a prerequisite to this unit on money, give each student a modified word grid (view literacy strategy descriptions). Using the Word Grid BLM, have students examine each coin and fill in as much of the grid as possible. Then go through each coin giving students the necessary information. Once the grid is complete, quiz the students as to how the coins are alike and different. Students can also quiz each other in preparation for tests and other class activities. Review how to count the value of coins by skip counting. Have students count out the value of pennies, nickels, and dimes. coin color value front of coin back of coin penny nickel dime quarter half-dollar dollar Finally, have students do a rubbing of the front and back of each coin. Have students use the rubbings to indicate differences in the coins. Using this modified word grid, the review of information students learned in previous grades and puts the information in a concise format so that students may reference it later. Grade 2 MathematicsUnit 3Money and Time 38 Louisiana Comprehensive Curriculum, Revised 2008 Activity 2: Counting Coins (GLEs: 4, 6) Materials List: Hundreds Chart BLM, 10 nickels, 10 pennies, transparency of Hundreds Chart BLM, overhead nickels, pennies Give each student a Hundreds Chart BLM, 10 nickels, and 10 pennies. Tell students to take out 2 nickels and 3 pennies (13¢). Have a student demonstrate how he/she would find the value of these coins. Then question students why it would be appropriate to start the counting with the nickels. Next, invite students to discuss how they might use a hundreds chart to help them find the value of coins. Inquire about where their coins should be placed on the hundreds chart. Use the transparent 100s chart and coins, and model for students how to place their coins on the chart (2 nickels and 3 pennies) Encourage students to start with the coin that has the greatest value. Start with one of the nickels. Ask students, “What is the value of a nickel?” (5 cents). Count five spaces on the 100s chart, and place the nickel on the 5. Using the second nickel count 1, 2, 3, 4, 5 from the 5 on the 100s chart, and place the second nickel on the 10. Ask students, “What is the value of a penny?” (1 cent). Start with the 10 on the 100s chart count 1, place the penny on the 11. With the next penny count 1, and place it on 12. With the last penny count 1, and place it on 13. Then say, “Let‟s see if the value of our coins matches the placement of our coins.” Count 5, 10, 11, 12, 13. Is the value of our coins 13 cents? (yes) Have students clear their charts. Give them a different combination of nickels and pennies. Students should make the connection between using nickels and skip counting by 5s on the 100s chart. Then they should just add on 1 for each penny that they have. After students have practiced several combinations, give them an amount and have them find the total number of nickels and pennies it would take to model that amount. This activity should be practiced throughout the week. Vary the coins that students use each day. Suggested order: nickels and pennies, dimes and pennies, dimes and nickels, then dimes, nickels and pennies. Finally, introduce quarters. Teacher Note: Students entering 2nd grade have counted coins using 1 denomination. Before they can be expected to make change, they should have many experiences counting different denominations of coins. Grade 2 MathematicsUnit 3Money and Time 39 Louisiana Comprehensive Curriculum, Revised 2008 Activity 3: Which Coins am I Holding? (GLEs: 4, 29) Materials List: empty film canister, coins, chalkboard, chalk Place coins in a film canister. Write the number of coins and their value on the board. Students have 10 tries to guess the combination of coins in the canister. Record each student‟s guess and record your response. You may only reply “yes” or “no” to the questions. It is important that you record each student‟s guess so that students may use deduction in determining the coins in the canister. Example: Tell students, “I have 4 coins that have a value of 17¢.” Students might ask, “Do you have a dime?” You would respond, “Yes.” “Do you have a quarter?” (no) This question should be discussed at the end of the activity. Students should realize that they “wasted” a question because a quarter has a value greater than 17¢. This is a great informal assessment of what students know about the value of coins. Questioning continues until they ask 10 questions or they guess the coin combination in the canister. Teacher Note: This is a great activity to keep handy. It can be used as a bellringer or as a filler when you have an extra 5 minutes during the day. Activity 4: Coin Patterns (GLEs: 4, 6, 30) Materials List: overhead coins, coins, paper, pencil, math learning log Create a pattern with coins such as penny, nickel, nickel, penny, nickel, nickel. Have students identify the elements in the cycle and fill in the next three elements. Then have students find the value of the coins (33 cents). Repeat the process using different patterns. Give students coins and have them create patterns and find the value of the pattern. Finally, give students an amount and have them create a pattern that demonstrates that amount in their math learning logs (view literacy strategy descriptions). Activity 5: Rolling in the Money (GLEs: 4, 6, 11) Materials List: per pair – 2 number cubes, a bag of play coins with nickels and dimes, play one-dollar bills, Rolling in the Money Recording Sheet BLM Put students into pairs. Give each group a pair of number cubes, a bag of coins, one- dollar bills, and a Rolling in the Money Recording Sheet BLM. Tell students, “Today we are going to play nickels and dimes. The object of the game is to get the most money.” One person in each pair will roll a pair of number cubes and record the numbers rolled on Grade 2 MathematicsUnit 3Money and Time 40 Louisiana Comprehensive Curriculum, Revised 2008 a recording sheet. Have the students take the number of coins rolled from the bag of coins and find their value, and then record the value on the Rolling in the Money Recording Sheet BLM. Instruct their partner to count the coins to verify the partner‟s work. The person who rolled the dice will keep the coins if he/she provides the correct value. If incorrect, the coins are returned to the bag. The next student rolls the number cubes. Play continues until all students have had three turns. When everyone has finished his/her rolls, have students trade their coins in for $1 bills and find their total amount. The person with the highest amount wins the game. Play two games if time permits. Dimes Nickels Value Total amount Roll 1 4 3 55¢ is Roll 2 ___dollar(s) and ___cents Roll 3 After you introduce the quarter, make a recording sheet that shows quarters, dimes, and nickels. When you adjust the game to using 3 coins, have students toss three number cubes. Activity 6: In How Many Different Ways Can You Make Fifteen Cents? (GLEs: 4, 11, 25) Materials List: Money Table BLM, bag of coins-quarters, dimes, and nickels, Money Table BLM transparency Put students into groups. Give each student a bag of coins and use Money Table BLM. The Money Table BLM is to be used as a graphic organizer (view literacy strategy descriptions) to help students make an organized list of their coin combinations. Ask students to find all the different ways they could model 20 cents without using pennies. As they model an example of 20 cents, have them record their findings in the Money Table. After students think they have found all of the different ways to model 20 cents, guide them through recording their combinations using an organized list starting with the largest coin and trading coins as they go. Have students use the second table on their sheet to find all the different coin combinations of 25 (without using pennies). Continue to give students different amounts each day to model. Activity 7: School Supply Shopping (GLEs: 4 , 6) Materials List: each pair – 2 quarters, 4 dimes, 5 nickels, and 10 pennies, items for school supply store priced less than $1, chalk, chalkboard, paper, pencil Put students into pairs. Give each pair 2 quarters, 4 dimes, 5 nickels, and 10 pennies. Set up a school supply store with items priced less than a dollar. Back to school sale papers may be substituted for real items. Have students take turns buying items and counting out the exact amount needed to buy the item from their partner. The partner then returns Grade 2 MathematicsUnit 3Money and Time 41 Louisiana Comprehensive Curriculum, Revised 2008 the item to the table and selects something he/she would like to buy. They repeat the process of using the exact amount needed to buy the item. Students continue to shop as long as time permits. Back to school sale papers may be substituted for real items. Use SQPL-Student Questions for Purposeful Learning (view literacy strategy descriptions) to discuss the role that the penny plays in our currency system. Write the statement “The U.S. Mint is going to stop producing pennies.” on the board. Put students into groups and have them write one question that relates to the statement. Call on each group and record their question. Add your own questions if you see the need. Use all the questions to talk about what role the penny plays in our current monetary system. Make sure to include in your discussion what would happen to items that are priced 21¢ and 37¢. Stop periodically to have students check which questions have been answered. Activity 8: Toy Pictures (GLEs: 4, 6) Materials List: per group – 20 pennies, 10 dimes, 20 nickels, 4 quarters, and a-dollar bill, pictures of toys from catalogs, index cards Give each group a set of coins (20 pennies, 10 dimes, 20 nickels, 4 quarters, and $1 bill of play money). Have students cut pictures from a toy catalog and put the picture with the cost on a index card. As cards are displayed, have students show different ways to make the correct amount. Model how students should start counting with the coin of greatest value. Later the picture cards can be used as a Toy Store Center with the cashier making change as needed, as students “buy” from the store. After subtraction with regrouping is taught, have students check their change by setting up a subtraction problem. Activity 9: Grocery Store (GLEs: 4, 6) Materials List: coins, items marked with price less than 25¢ Making change is an extremely difficult skill for 2nd graders. They need to practice this all year long. First, have students buy items priced under a quarter. Have them pay with a quarter while another student counts the change. When counting change, have the student put the item in the customer‟s hand and then count up. Students are not expected to do mental math subtraction at this time of the year. Gradually increase the price of items several times, and have students buy items and pay with a dollar bill. Have students continue to put the item in the buyer‟s hand and count up to 100 when making change. The end-of- the year goal is to have students make change for a dollar with the fewest coins possible. Students enjoy playing “store.” Set up a center and leave it up throughout the year, varying the cost of items and the coins available. After subtraction with regrouping is taught, have students check their change by setting up a subtraction problem. Grade 2 MathematicsUnit 3Money and Time 42 Louisiana Comprehensive Curriculum, Revised 2008 Activity 10: Do I have enough Money? (GLEs: 4, 6, 11) Materials List: pictures with prices less than $1, coins, snack menu Show pictures and costs of two snacks from a refreshment stand to two- or three-member teams who have a set of coins equaling less than $1.00. Have students decide which of the 2 items they can afford to buy. Ask if the listed price is more or less than the amount they have. Ask students what would happen if a child gave the salesperson more money than the price of the snack. Display a snack menu listing five or six snack items with price tags of less than $1.00. Give each team coins totaling less than $1.00. Ask, “How much does the item cost? Do you have enough money? Should you get change back?” Have each team model how much change it should get back. Activity 11: Pocket Full of Money (GLEs: 4, 6) Materials List: Pocket Full of Money Recording Sheet BLM, bags with coins and bills Before class begins, make bags of money containing coins less than a dollar and one- dollar bills. Label the bags to match the names on the recording sheet. Show students how to count and record the value of money if they have bills ($1) and change. Make a big deal about the decimal point separating the whole number of bills and the change. Set up this scenario: Each time I do the wash, I find a wad of bills and change in someone‟s pocket. Tell students that they are going to count how much they find in a pocket full of money. Put students into groups. Give each group a Pocket Full of Money Recording Sheet BLM. Have students determine the value of the money in the bag, record the value, and then pass the bag to the next group. After all bags have circulated throughout the groups, have students report their findings. Finally, tell students that they found $1.53 in a pocket. Have them record the amount in their math learning log (view literacy strategy descriptions). Have students list three different bill and coin combinations that could be in that pocket. Activity 12: How do they make Money? (GLE: 4) Materials List: The Go-around Dollar by Barbara Johnston Adams, computer, paper, pencil Read a book like The Go-around Dollar by Barbara Johnston Adams and discuss with students how money is made. Visit the website http://www.ustreas.gov/. Have students draw several $1 bills and coins. Have students exchange papers and find the value of the money that is depicted. Grade 2 MathematicsUnit 3Money and Time 43 Louisiana Comprehensive Curriculum, Revised 2008 Conclude the activity with a RAFT (view literacy strategy descriptions) writing assignment. R – a dollar bill A – fellow classmates F – postcard T – A dollar bill started in their home town and traveled across the United States. Example: I am a dollar bill sitting in a drawer in a Baton Rouge, Louisiana. Yesterday I was in Houston, Texas, in a gas station. The day before that I was sunning myself in the pocket of someone in Los Angeles, California. You would think I would be tired. I am looking forward to seeing where I end up tomorrow. Allow students to share their RAFTs with a partner or the class. Students should listen for accuracy and logic in their classmates‟ RAFTs. Activity 13: That’s a Long Time! (GLE: 16) Materials List: How Many Can I Do? BLM, Blank Clock BLM, analog clock with second hand, crayons Cut apart the How Many Can I DO? BLM and give a chart to each student. Time the students as they close their eyes for 1 minute. Ask students to raise their hands when they think 1 minute is up. Signal the end of the minute. Show students how to time 1 minute on a clock with a second hand. Explain that there are 60 seconds in 1 minute. Have students fill out the modified anticipation guide (view literacy strategy descriptions) How Many Can I Do? BLM. They are to estimate how many they think they can do of each listed activity in 1 minute. Then have students take turns doing a physical activity (hop, clap, close their eyes, and so on) for 1 minute while timing the minute. Have them record the actual number after each activity. Finally, give students the Blank Clock BLM, which has a large blank clock face. Have them color between the “hash” marks of the clock, alternating colors for each minute. Activity 14: Counting the minutes! (GLE: 16) Materials List: student clocks, demonstration clock Distribute student clocks. Go over the parts of a clock (i.e., face, hour hand, minute hand). Use a demonstration clock to show students how the hour hand moves between the hours as the minute hand approaches 30 minutes. Set a clock to the hour/half-hour without showing students, and then call out the time. Have students set their clocks and then check their clocks with the clock you set. Next, have students count out the minutes Grade 2 MathematicsUnit 3Money and Time 44 Louisiana Comprehensive Curriculum, Revised 2008 in an hour going around the clock face. Ask students if they noticed anything special when they got to a numeral on the clock face (i.e., these are the numbers they say when they skip count by 5s). Have students move the minute hand on their clocks skip counting by 5s. Call out different times using multiples of 5 minutes (e.g., 2:20, 3:45), and have students set their clocks. Make the connection between a digital clock and an analog clock. Show students how a digital clock is set by first setting the hour and then holding down the minute button to watch the minutes change from 01-59 minutes. Ask students why they can‟t set a digital clock to 5:60. Set times to the 5 minutes on the digital clock, and have students model them on their analog clock. Activity 15: Time Flashes By! (GLE: 16) Materials List: time flash cards with clocks showing time to 5 minutes, set of cards from 1-12, chalk, yardstick, ruler Make a set of time flash cards with minutes written from :00 to :55 in 5 minutes increments. Also make a set of hour cards numbered from 1-12. (If you label the back of the cards with minutes or hours, it will be easy to keep them separated.) Put the cards in two different stacks. Create a clock face on the floor, and have students “walk” the numbers counting by 5s. Then use a yard stick and a ruler as the hands of the clock. Call out a time, and have a student model the time. Next, put students into pairs, and have them select a card from each of the piles. Have pairs work together to model the time using the large clock hands. Have class members state the time represented on the clock. Instruct students to make adjustments of the hands on the clock if needed. Continue until all pairs have had a turn. Activity 16: Quarters of an Hour (GLEs: 2, 16) Materials List: Blank Clock BLM (used in activity 13), colors, 4 quarters, Popsicle® stick, large paper clip, transparency of Blank Clock BLM On individually designed analog clock faces, have students divide the face into fourths (quarters), coloring each quarter part a different color. Ask students how many different parts they have divided their clocks into (4). Lead students to understand that the correct wording to use is “the clock is divided into fourths” instead of into 4. Have students mimic you as you travel along the edge of the clock saying 1 fourth, 2 fourths, 3 fourths, and 4 fourths. Then take out 4 quarters and ask them how quarters are like the parts that they colored on the clock. (It takes four quarters to make a dollar, and it takes 4 fourths of an hour to make an hour.) Tell students that people say one-quarter of the hour has passed instead of saying one-fourth of an hour has passed. Grade 2 MathematicsUnit 3Money and Time 45 Louisiana Comprehensive Curriculum, Revised 2008 Use the overhead transparency of Blank Clock BLM to guide students through the following task. Have students put their fingers on the outer edge and travel along the clock saying 5, 10, 15, a quarter of an hour has passed; 20, 25, 30, two quarters or 1 of an 2 hour has passed; 35, 40, 45, three quarters of an hour have passed; and then 50, 55, 60 four quarters or a whole hour has passed. Give each student a Popscicle® stick and a large paper clip to use as hands on their clocks. Have students model 3:15, 3:30, 3:45 and 4:00. Ask students what they notice about those times. Have students model 3:15 again. Ask, “Why do some people say „a quarter after three’ when reading this time?” (Because a quarter of an hour has passed.) Have students model 6:30 on the clock. Ask students if they have ever heard someone say two quarters past 6. (No, they usually hear people say half-past the hour.) Emphasize that two quarters of an hour and half-past the hour are the same thing. Have students model 7:45 on their clocks. Ask them how they would read this clock using quarters of an hour. Ask students if they have ever heard anyone say 3 quarters of an hour past 7. Ask students if they have ever heard someone say a quarter till 8. How are a quarter till 8 and 7:45 alike? Have students model different quarters of an hour reading their clock faces two different ways. Activity 17: Found it! (GLE: 16) Materials List: 10 index cards that have been stamped with a clock face, baggie, pencil Give each pair of students 10 index cards that have been stamped with a clock face. If a stamp is not available, copy a page of blank clock faces and have students cut and paste them on the index cards. Also give each pair a baggie. Have students draw the hands on 10 clock faces to represent time to 5 minutes. Have them write the time shown on each face on the back of their card. Instruct students to make 1-2 cards that are incorrect. Check each groups cards before exchanging them. Ask students to exchange cards with another group to check the information on the cards. If pairs disagree with a time, they “challenge” the card and you check the card for correctness. Students who correctly identify the card or cards with errors receive one point per card. Have students finish checking the cards, bag them, and then pass them on to another group. Activity 18: How Long is an Hour? (GLE: 16) Materials List: student clocks, timer Have students set their clocks to the current time to the nearest five minutes. Set a timer for 60 minutes. When the timer goes off, have students move their minute hand around the clock counting by 5s as they go. Then have students adjust their hour hand. Continue Grade 2 MathematicsUnit 3Money and Time 46 Louisiana Comprehensive Curriculum, Revised 2008 the activity throughout the day to give students a sense of an hour. Next, ask students questions that pertain to elapsed time. Example: John got home from school at 3:45. He ate a snack and watched TV for an hour and then started his homework. What time did he start his homework? Activity 19: School Routine (GLEs: 16, 25, 26) Materials List: math learning log, pencil Have students log their school routine to the nearest 5 minutes in their math learning log (view literacy strategy descriptions). Have them answer questions according to their findings. Example: What time is lunch? What will the class be doing an hour later? Repeat the activity the next day. Have students compare their findings. Ask students to log their activities until they go to bed one night to the nearest 5 minutes. The next day have students come up with categories to represent what they do after school (e.g., playtime, watch TV, play video games, eat, do homework). Have each student determine which activity he/she did the longest. Lead the class as it organizes the information into a table, and then create a bar graph or line plot. Ask students to write two questions that could be answered by looking at the graph/plot. Activity 20: Activity Time (GLE: 16) Materials List: paper, pencil, pictures or drawings, class clock label with time units Have students brainstorm activities that take 1 minute, 1 hour, or 1 day, and collect or draw pictures of the activities to include on a class chart or bulletin board. Use a class clock to demonstrate time passed by counting on to find the elapsed time. Have students model with their clocks. Ask students to show time in hours (5:00) on their clocks, then reset the clock to 1 hour later (6:00) or 1 hour before (4:00). Play a time game with the whole group. Label a die to represent the following: 1 hour later 1 hour before 5 minutes later 5 minutes before 30 minutes later 30 minutes before Call on a student to call out a time, have students show that time on their clocks, and then roll the die and set their clocks to the new time. Continue practicing counting up or counting back on the clocks. Grade 2 MathematicsUnit 3Money and Time 47 Louisiana Comprehensive Curriculum, Revised 2008 Activity 21: What Time is it Now? (GLE: 16) Materials List: demonstration clock, student clocks, elapsed time cards Prior to class make a set of elapsed time cards using index cards. Make a dozen or more cards labeled with elapsed time statements such as these: 1 hour later or 1 hour before. Set a time on your demonstration clock and have students set their clocks. Have a student select an elapsed time card. The student reads the card and everyone sets his/her clocks according to the description on the card. The teacher then shows her clock, and students check their clocks for accuracy. Then another student chooses a card and the class sets its clocks. This process continues until are cards have been selected. Sample Assessments General Assessments Math Learning Log: If I found a dollar, I could buy____________that costs _____________. Explain if you would or would not get change back. Counting Money: Use a checklist to note students that are having difficulty counting money. Using a large demonstration clock, set time to 5 minute intervals and assess whether the student can identify the correct time displayed. Activity-Specific Assessments Activity 1 – Give students a double Venn diagram and have them compare and contrast a penny and a nickel by filling in characteristics of the coins. penny nickel penny nickel 1¢ round 5¢ copper silver coin color color Activity 4: Give students patterns using coins. Have them complete the pattern and determine the value of the pattern. Grade 2 MathematicsUnit 3Money and Time 48 Louisiana Comprehensive Curriculum, Revised 2008 Activity 6: Provide a money table labeled quarter(s), dime(s), nickel(s) and pennies. The student will then represent 37 cents as many ways as possible always using only 2 pennies. Activity 10: Set up stations with coins and $1 bills, number the stations, and give each student a recording sheet that corresponds to the numbers on the stations. The student will circulate throughout the stations counting how much money is at each station and recording that amount next to the station‟s number on his/her recording sheet. Activities 13 through 21: Provide the student with a clock and the student will: _____ Identify the parts of a clock (minute hand, hour hand, face) _____ Set the clock to the hour _____ Set the clock to the nearest half-hour adjusting the hour hand _____ Count by 5s around the clock _____ Model 6:45 _____ Model a written time, such as 2:20 _____ Model a quarter past 5 _____ Represent 9:10 and tell what time it would be an hour later Activity 16: Students make up 5 time riddles for others to solve and to be made into a class book. (For example: My hour hand points to 3. My minute hand points to 5. What time is it?) As each student shares his or her riddle, the student will show the time on his/her individual clock face and count by 5s from twelve to find the correct answer. Observe students for mastery of this skill as students create and solve the riddles. Activities 17 and 21: Give students a test made up of clock faces. On some of the clocks, have students identify the time to 5 minutes. On the other clock faces, have students draw in the hands when given the time. Also, give students problems where they must determine the time that has elapsed when given a starting or finishing time. Grade 2 MathematicsUnit 3Money and Time 49 Louisiana Comprehensive Curriculum, Revised 2008 Grade 2 Mathematics Unit 4: Place Value and 2-Digit Addition Time Frame: Approximately four weeks Unit Description This unit extends place-value concepts through 999 and includes writing those numbers in expanded, standard, and word forms. This knowledge is then used to enhance understanding of 2-digit addition problems by regrouping. Student Understandings Students can represent numbers through 999 in expanded, standard, and written/verbal forms and can use this information to add 2-digit numbers with regrouping. Students develop capabilities to estimate the number of objects in collections of less than 100 objects. Guiding Questions 1. Can students represent numbers to 999 with objects and in standard, expanded, and written/verbal forms? 2. Can students make appropriate order comparisons of numbers through 999 in all representations? 3. Can students complete 2-digit addition problems with and without regrouping, including notational work? 4. Can students estimate the number of objects in collections of less than 100 objects? Unit 4 Grade-Level Expectations (GLEs) GLE # GLE Text and Benchmarks Number and Number Relations 1. Model, read, and write place values for numbers through 999 in word, standard, and expanded form (N-1-E) 3. Make reasonable estimates of the number of objects in a collection with fewer than 100 objects (N-2-E) 5. Read, write, compare, and order whole numbers through 999 using words, number lines, and models (N-3-E) (N-1-E) Grade 2 MathematicsUnit 4Place Value and 2-Digit Addition 50 Louisiana Comprehensive Curriculum, Revised 2008 GLE # GLE Text and Benchmarks 8. Recognize, select, connect, and use operations, operational words and symbols (+, ) for addition (join, part/part/whole) or subtraction (take away, comparison, missing addend, and set/subset) situations (N-6-E) (N-5-E) 9. Add and subtract 1- and 2-digit numbers (N-6-E) (N-7-E) 10. Round numbers to the nearest 10 or 100 and identify situations in which rounding is appropriate (N-7-E) (N-9-E) 30. Recognize, extend, create, and explain patterns of addition and subtraction as represented in charts and tables and in varied forms of skip-counting (P-1-E) (P- 2-E) Sample Activities Activity 1: What is 100? (GLE: 1) Materials List: Base 10® blocks Show students ten rods (tens) and ask them how many blocks there are. (100) Ask students what group could be exchanged for the ten rods. (A flat of 100) Ask students how to write one hundred in standard form. Guide them to understand that this means 0 ones, 0 tens, and 1 hundred. (100) Ask students what the model of 345 looks like. Have a student model the number. Continue calling on students to model 3-digit numbers using flats, rods, and unit Base 10® blocks. Activity 2: Spinning for Numbers (GLEs: 1, 5) Materials List: Base 10® blocks, 0-9 Spinner BLM, Spinning for Numbers Recording Sheet BLM, paper clip, pencil Use the Spinner BLM. 1. Place the point of a pencil through a large paper clip. 2. Place the point of the pencil on the center of the spinner. 3. Adjust the paper clip so that the end of the paper clip is on the center of the spinner. 4. “Flick” the paper clip to spin it. Put students into groups and provide each group with Base 10® blocks, 0-9 Spinner BLM and 2 copies of Spinning for Numbers Recording Sheet BLM. Have one student in each group spin the 0-9 spinner three times to make a 3-digit number. Record the number created. Ask another student to model the number using Base 10® blocks and draw the model in the Base 10® column on the Spinning for Numbers Recording Sheet BLM. . Have another student fill in another part of the chart (e.g., the digit in the hundreds place, the expanded form of the number). Continue passing the chart until all the parts of the chart are filled in. Grade 2 MathematicsUnit 4Place Value and 2-Digit Addition 51 Louisiana Comprehensive Curriculum, Revised 2008 Number Created 213 Place Value Chart Expanded Form Standard Form Word Form Base 10 H T O 200 + 10 + 3 213 Two Model 2 1 3 hundred thirteen Call on each group to share how it recorded one of their numbers. Have students repeat the process five more times. Collect the recording sheets if you are doing Activity 3 on another day. Observe students and make note of those students who need more practice with each part of the chart. Activity 3: Comparing Numbers (GLEs: 1, 5) Materials List: paper, glue, Spinning for Numbers Recording Sheet from Activity 2, scissors Put students into the same groups used in Activity 2 and return their Spinning for Numbers Recording Sheets BLM. Have students cut apart their sheets and put the 6 charts in order from least to greatest using the numbers that were created. Have students glue the charts down after they are sure they have them in the correct order. Ask groups to explain what part of their charts they used to compare their numbers (i.e., they looked at the values of the digits in the hundreds place, then the tens place, and so on). Activity 4: I Have….Who Has? (GLE: 1) Materials List: I Have..Who Has? Cards BLM Prior to class, run off cards on cardstock, laminate them and then cut them out. Play a round of I have…Who has? Provide one clue card for each student. Make sure to hand out all of the cards. It does matter who starts reading the first clue since the cards will circulate back to first person from the last clue. Direct the student holding the “I have 140” card to start first. First clue I have 50. I have 406. I have 30. I have 550. reads – Who Who has 4 Who has 3 Who has 5 Who has 5 Last clue leads back to has ? hundreds tens ? hundreds tens and 0 first card. and 6 ones? and 5 tens? ones? Grade 2 MathematicsUnit 4Place Value and 2-Digit Addition 52 Louisiana Comprehensive Curriculum, Revised 2008 Activity 5: Ordering Numbers in the Hundreds (GLEs: 5, 10) Materials List: index cards, electronic equipment pictures with prices, paper, pencil Prior to class, glue pictures of electronic equipment with their prices on index cards. Select items whose prices are in the hundreds. A set of 5 cards per group is needed. Count out 5 cards and label them Set A. Count out another 5 cards and label them Set B. Continue until all cards are labeled. Put students into groups. Give each group a set of cards. Have students order the cards from least expensive to most expensive. Ask students to record their results by writing the letter of the set of cards they are using, and then write the prices in order. Have students exchange cards with a different group. Continue until all sets of cards have circulated among groups. Teacher Note: After rounding to the nearest hundred has been taught, use these cards in a rounding activity. Have students round each price to the nearest hundred. Give students a limited amount of money to shop with, and have them find how many items they can buy. Activity 6: Rounding to the Nearest Hundred (GLEs: 1, 5, 10) Materials List: Rounding to the Nearest Hundred BLM, marker, tape, pencil, postcard Prior to class, take 11 BLM patterns houses and number them from 0, 100, 200, ….1,000. Hand out blank Rounding to the Nearest Hundred BLM house patterns. Have each student use a marker to write a three-digit number in the large rectangle on the BLM pattern. Ask students to come to the front of the class in pairs to compare their numbers. Then have students come up three at a time and compare their numbers. Have the whole class organize themselves into a number line using their house numbers. Finally, post a set of house patterns that you have numbered from 0,100, 200,… to 1000 on the bulletin board/chalkboard. Ask students to determine where their houses would be placed. Have them indicate which two hundreds their house is between and which “hundreds” house it would be closer to. Have students post their house patterns in numerical order around the room. Conclude the activity with a RAFT (view literacy strategy descriptions) writing assignment. R – Role (role of the writer) A – Audience (to whom or what the RAFT is being written) F – Form (the form the writing will take, as in letter, song, etc.) T – Topic (the subject focus of the writing) Grade 2 MathematicsUnit 4Place Value and 2-Digit Addition 53 Louisiana Comprehensive Curriculum, Revised 2008 R – a number that has been rounded to 100 A – fellow classmates F – postcard T – provide clues on the postcard as to what number they represent that has been rounded to 100. Allow time for students to share their RAFT writing with a classmate or the whole class. Ask students to listen for accuracy and logic. Activity 7: The Guessing Jar (GLE: 3) Materials List: 3 jars of the same size, 3 different fillers for jars, baby food jar with objects, Post-it notes, poster Bring the students into a math circle and show them three jars that are the same size but contain 20 each of three different objects. For example, one jar would contain 20 cubes, one would contain 20 peanuts, and the third would contain 20 paper clips. Lead a discussion about the fact that there are the same number of objects in each jar, but one jar may look like it has more. Ask why. Explain that a point of reference for the collection of objects is a tool that can be used to help them estimate. Before initiating an estimation activity, provide students with a numerical benchmark (a collection of 10, 20, or 50 of the object that will be placed in the guessing jar). The Guessing Jar Place a number of small objects into a baby food jar. (Always begin the year by using small jars, and gradually increase the size of the jars and the number of objects that the students will be estimating.) Have students guess the number of objects, write their names and estimates on small sticky notes, and place them on a poster shaped like a big jar. When all have guessed, have the student with the closest estimate fill the jar for the next guessing game. After each estimation activity, ask students to bring their estimate to a whole group discussion area and discuss whether they overestimated or underestimated. Ask them if they can determine why they guessed too many or too few. Make the activity fun and yummy by using small food items such as peanuts, M&Ms®, Sweet Tarts®, or raisins. After guessing, divide the food items among the students, and allow students to eat them. Grade 2 MathematicsUnit 4Place Value and 2-Digit Addition 54 Louisiana Comprehensive Curriculum, Revised 2008 Activity 8: How many dots do you see? (GLES: 3, 30) Materials List: transparency of How Many Dots Do You See? BLM, overhead projector Five dots are in the rectangle below. Tell students they will use this as their benchmark to help them estimate how many dots are in the large rectangle. Show students how to section off the large rectangle into smaller rectangles that are the same size as the benchmark to help them estimate how many dots are in the large rectangle. Have students count off the dots in the large rectangle: 5, 10, 15, 20, 25, 30 dots After the activity, emphasize that counting each grid section by “5” is only an estimate because some of the grid sections have more than “5” dots in them. Apply this gridding technique to any situation that asks students to estimate how many are in a picture. Activity 9: Ordinal Numbers (GLE: 5) Materials List: number cards from 1-8, Ordinal Numbers BLM, pencil, number cards (1- 31), ordinal cards (first – thirty-first) Have eight students stand in line and count off in order using the correct ordinal numbers. Have these students select the cardinal number card (1-8) that corresponds to their order. Next, using the Ordinal Numbers BLM, have all students create a chart showing cardinal numbers for 2-31 and ordinal numbers and ordinal number words (1st-first-1). If ordinal number words are not posted, give students a word list. Model writing ordinal numbers and words 21st–31st. Play the following ordinal memory game: Make as many sets of cards as there are groups. 1. Write numbers and the corresponding ordinal number words on cards. (1-31) and (first – thirty-first) 2. Shuffle the cards and turn face down in rows and columns. 3. Have students take turns flipping cards to find a match. 4. The student who finds a match takes the cards. 5. When all cards are matched, the student with the most cards wins the game. Grade 2 MathematicsUnit 4Place Value and 2-Digit Addition 55 Louisiana Comprehensive Curriculum, Revised 2008 Activity 10: The Way We Were Game (GLE: 5) Materials List: student baby pictures, list of student names alphabetized Have students bring in baby pictures of themselves; line the pictures along the chalk tray. Give each student an alphabetical list of student names. Have students guess who they think is first to last, writing the ordinal number two ways (i.e., 1st and first) by the name they think is first, second, third, and so on. When all students have made their guesses, reveal the correct names with pictures. Have students label a page in their math learning logs (view literacy strategy descriptions) Being First. Have them divide their page into two sections. On one side, have students write about situations when it is good to be first. On the other side, have students write about situations where they might not want to be first. Discuss some examples before requiring the students to generate their own. Let students share their writings. Activity 11: Standing in Line (GLE: 5) Materials List: Standing in Line BLM, pencil Hand out Standing in Line BLM. Discuss about where students think the “1st circle” is and why. Have students label the circles using ordinals. Have them follow directions given by the teacher such as these: draw a triangle around the 15th person in line; Mark is 9th in line. Put a M on the circle that represents where Mark is standing. Ticket Booth Activity 12: More than 9 (GLE: 1) Materials List: per group of students – More than 9 BLM, large paper clip, 2 number cubes, Base 10® flats, rods, and unit cubes Ask students, “What digit is used to represent a number when there is one more than 9?” They should say, “There is no single digit that represents ten.” Ask, “What digits are used to represent ten?” Then remind students that the digits have a meaning according to where they are placed. Tell students that our number system teaches that when we have more than 9, we make a group of 10. The number 10 means 1 group of ten and no extra. When we have 10 tens, we create a group; we call that group a hundred (100). Grade 2 MathematicsUnit 4Place Value and 2-Digit Addition 56 Louisiana Comprehensive Curriculum, Revised 2008 Play More than Nine Put students into groups. Give each group a More than 9 BLM, two number cubes, Base 10® flats, rods, and unit cubes. Player 1 rolls both number cubes and spins the spinner. The spinner will determine which base 10 block they are to use. The sum of the dice tells them how many Base 10® blocks to take. Example: The first person spins and lands on tens, and the sum of the roll is 6. He/she counts out six rods. He/she says, “6 tens is sixty.” There is no need to regroup. He/she returns the Base 10® blocks to the center of the group. The next player spins, and the spinner lands on ones and he/she rolls a 5 and 6. He/she counts out 11 unit cubes. Then he/she says, “Eleven is more than 9, so I need to regroup. I need to group 10 unit cubes and trade for a rod. Eleven is 1 ten and 1 one.” Play continues until all players have had four turns. Points many be awarded each time a member needs to regroup. The next player rolls 5 and 6, and the spinner lands on tens. The student must say, “5 tens and 6 tens is 11 tens. 11 tens is more than 9, so I have to regroup 10 tens for a flat.” Have students respond to “It‟s Good to be a 10” in their math learning logs (view literacy strategy descriptions). Example: 10 is an important number in our number system. Any time you have a group of 10, a trade for 1 of the next place value can be made. If you have 10 of something, you can change the way that you look and still have the same value. 10 units can change to a rod. 10 tens can change to a hundred, and10 dimes can change to a dollar. After students have had sufficient time to respond, have them share the reasons why they think it would be good to be a 10. Activity 13: Regrouping (GLEs: 1, 9) Materials List: bills (ones, tens, hundreds) per group of students, Base 10® blocks or Popscicle® sticks, pencil, chalk, chalkboard, paper Model this problem using one-dollar and ten-dollar bills. Patrick had $15 in his wallet. His sister, Natalie, gave him $6 for washing her car. How much money does he have now? Display a ten-dollar bill and 5 one-dollar bills. Ask students what operation is needed to solve this problem. Then add 6 one-dollar bills to the display. Ask students how much Patrick has now. Model putting like amounts together (5 ones + 6 ones is 11 ones). Ask students what happens when there are more than 9 ones? (We need to create a group of 10.) Trade 10 ones for a 10-dollar bill. Add the new 10-dollar bill to the existing 10- dollar bill. That gives Patrick 2 ten-dollar bills and 1 one-dollar bill. Patrick has $21 after washing Natalie‟s car. Grade 2 MathematicsUnit 4Place Value and 2-Digit Addition 57 Louisiana Comprehensive Curriculum, Revised 2008 Model several examples with students and then have them work problems using either money or Base 10® blocks to help them when they need to regroup. Give students many examples of this type of problem throughout the year. Have students record the number sentences as they solve problems. Have the students perform the operations on paper after each modeling. This will make the connection for them. Have students pay close attention to how they are lining up their digits. Show students how to record the actions they went through as they were putting their amounts together. 1 5 + 6 = 11 $ 15 11 is more than 9 so I + 6 need to create a group of 10. That leaves 1. Put my new group of $ 21 10 in the tens group. Develop a process guide (view literacy strategy descriptions) to help students with the steps involved in adding numbers. Process guides scaffold students‟ comprehension within unique formats. They‟re designed to stimulate students‟ thinking during or after their reading, listening, or involvement in any content area instruction. Guides also help students focus on important information and ideas, making their reading or listening more efficient. Example: Step 1 – Record numbers by lining up digits Step 2 – Look at the digits in the one‟s place value. Is their sum over 9? Do I need to regroup? Step 3 – Add and record the sum of the digits in one‟s place. If you need to regroup, record a 1 in the ten‟s place to represent 1 ten. Step 4 – Add and record the sum of all the digits in ten‟s place. Have students copy the process guide. They should refer to the steps each time they solve an addition problem until the steps become a natural thought process. Activity 14: Do I Need to Regroup? (GLE: 9) Materials List: worksheet with examples of addition problems that require regrouping, calculator, chalk, chalkboard Give students examples of 2-digits plus 1-digit problems, and have them circle the problems that require regrouping. Call on different students and have them explain why they circled the problem. Then have students solve the problems they circled. Examples: 2 7 boys 5 8 fish 6 4 students + 8 girls + 4 fish + 3 students 3 5 students 6 2 fish Grade 2 MathematicsUnit 4Place Value and 2-Digit Addition 58 Louisiana Comprehensive Curriculum, Revised 2008 Use an opinionnaire (view literacy strategy descriptions) to poll students about the following statement: This is the 21st century. Students should be able to use a calculator to solve all math problems. Opinionniares are highly beneficial in promoting deep and meaningful understandings of content area topics by activating and building on relevant prior knowledge and building interest in and motivation to learn more about particular topics. Opinionnaires also promote self-examination, value youths‟ points of view, and provide a vehicle for influencing others with their ideas. Form 2 groups according to if they agree or disagree with the statement. Provide time for students to come up with examples as to why calculators should or should not be used. Record all of the students‟ responses. Choose one person from each group to debate the groups‟ statements. Finally, have students come up with a general statement that either supports or doesn‟t support the statement after hearing all the reasons. Make sure to make the point that if calculators were used all the time students would not learn their facts and would be unable able to do mental math. Also you want to make the connection to regrouping. That a calculator automatically regroups. If students use a calculator they wouldn‟t learn how to regroup. Activity 15: Rods to Flats (Tens to Hundreds) (GLE: 1) Materials List: number cube, rods, flats Set up a “bank” of rods and flats. Divide the class into two teams. Have students form two lines. Have the first member of each team roll a number cube to indicate how many rods he/she collects from the “bank.” Have the first person hand the rods to the second person who must roll and collect more rods. The second person passes the rods to the third person who either rolls or regroups the rods for a hundreds flat. Inform students that they may not roll if they need to regroup but must go to the bank, trade 10 rods for a flat, and then pass the blocks to the next person. Example: The first player rolls a 6 and collects 6 rods, then passes them to the second person in line. The second person must roll because he/she can‟t regroup. He/she rolls a 5 and collects 5 rods from the “bank” and passes all 11 rods to the third person in line. The third person in line must go to the bank and trade 10 rods for a flat, then pass the flat and the rods to the fourth person in line who must roll. Play continues until the last person in line has a chance to roll or trade. If the last Grade 2 MathematicsUnit 4Place Value and 2-Digit Addition 59 Louisiana Comprehensive Curriculum, Revised 2008 person collects more than 10, base10 blocks, he/she must regroup before returning to their line. Each line must announce how much the line collected. Activity 16: Adding Two-digit Numbers + Two-digit Numbers (GLE: 9) Materials List: Base 10® blocks, practice problems, pencil Give students a real-life problem involving regrouping in the ones place only. Jacob ate two servings of chips. Each serving has 18 grams of carbohydrates. How many carbohydrates did he eat in all? Model the problem. Put like items together and make a new package if possible. After using place value blocks, show students how to do the problem numerically adding ones to ones and tens to tens, and making a new group if necessary. Make sure students understand how to line up digits before adding. Model several problems for students. After modeling problems, put students into pairs and have them work problems. Materials should be available for modeling problems as long as students need them. Have students practice problems throughout the year. Activity 17: Ten Tens (GLE: 1) Materials List: 17 ten-dollar bills, hundred-dollar bills, per group of students, 2 number cubes per group, 10 and 100-dollar bills, Ten Tens BLM per student, pencil Ask students: What is 10 tens? Have them model what happens when they have one more than 9 tens. Count out 10, ten-dollar bills. Have students count with you saying 10, 20, 30,…100. Ask students what happens if they have 13 tens. Count out 13 ten-dollar bills and then count the money saying 10, 20, 30, …100, 110, 120, 130. Point out to students that 10 tens is 100 and 13 tens is 130. Ask students what the value would be of 17 ten-dollar bills. Play Trading for 100 Put students into groups. Give each group 2 number cubes, 10 and 100-dollar bills, and a Ten Tens Recording Sheet BLM for each member of the group. Have students roll the two number cubes, count out that many 10-dollar bills, then trade them for 100-dollar bills when they can, recording their amounts after each roll. Have students continue trading money after each roll if they can. Play four rounds and have students find who has the largest amount of money in their group. Play addition games if time will permit or leave materials in a center for rainy day activity. The recording sheet has a place for three games. Grade 2 MathematicsUnit 4Place Value and 2-Digit Addition 60 Louisiana Comprehensive Curriculum, Revised 2008 Roll #1 ____tens = _________ Roll #2 ____tens = _________ ________ total so far Roll #3 ____tens = _________ _________ total so far Roll #4 ____tens = _________ _________ final total Activity 18: Regrouping in the Tens (GLEs: 1, 8, 9) Materials List: Base 10® blocks, problem set that requires regrouping into the hundred‟s place Ask a student to model solving the problem below. Anne earned 63 points while playing the video game. Jerry earned 45 points while playing the game. How many points did they earn altogether? After the student has modeled the problem with Base 10® blocks, review the procedure for recording the problem numerically. Make sure that students know that 6 tens plus 4 tens is 10 tens or 100. Have students record this example. Give students more problems to practice. After a student has modeled a problem ask him (or another student) to demonstrate the problem numerically. Give assistance as needed using questioning to lead the student to the correct answer. Activity 19: Flip 4 (GLEs: 5, 9) Materials List: Flip 4 BLM, 2 sets of digit cards per pair of students, paper, pencil Prior to playing the game have students fill out an anticipation guide (view literacy strategy descriptions) -Flip 4 BLM. Before playing the game, students fill in the “top” half of the BLM. After playing five rounds, have students return to the guide and fill in the “bottom” half. Discuss students‟ answers. Put students into pairs. Give each pair 2 sets of digit cards, paper and pencil. Each player turns over 4 digit cards. Have each student create two, 2-digit numbers and find his/her sum. The object of the game is to create the largest sum possible. Instruct students to record their numbers and their sum. The student that has the largest sum for that round is awarded a point. Play continues until one player earns 5 points. Grade 2 MathematicsUnit 4Place Value and 2-Digit Addition 61 Louisiana Comprehensive Curriculum, Revised 2008 Activity 20: Estimate or Exact Answer (GLEs: 8, 10, 9) Materials List: chalkboard, chalk, Estimate or Exact Answer BLM Model the use of mental math to solve addition problems by using 10s or 100s, and then use basic facts to solve the problems (for example, 2 4 ; 20 40 ; 200 400 ). When an estimate is all that is needed, estimate the answer by rounding (for example, 53 68 to 50 70 ). Discuss when estimates might be used instead of exact numbers (when you need to know about how many or how much). Demonstrate estimating money (rounding to the nearest dollar) to determine about how much is needed to buy something (for example, 77¢ rounds to $1.00; $2.35 rounds to $2.00). Have students fill out the anticipation guide (view literacy strategy descriptions) – Estimate or Exact Answer BLM. . They are to record how many times a day they estimate and how many times a day they get exact answers doing the activities listed in the chart. After they fill out the chart, they are to use the sheet the following next few days to record the number of times they actually found estimates or exact answers for the activities listed. Once students have had time to fill out their forms, have students share their findings. Students need to realize the importance of rounding and mental math. Sample Assessments Performance and other types of assessments can be used to ascertain student achievement. Following are some examples: General Assessments Provide a word problem, then the student will use Base 10® blocks to model the problem. Observe if the student knows when to regroup. Write ten addition problems in context using 2-digit numbers for the student to solve correctly using concepts learned. (Notice that the student is lining up the digits according to the correct place value.) Students use ordinal number words to describe his/her schedule for the school day and will share the list with the class (list at least ten activities). Students write story problems using addition of numbers that are to be rounded to find an estimated answer. He/she will share the work with a classmate after explaining the answers to the teacher. Grade 2 MathematicsUnit 4Place Value and 2-Digit Addition 62 Louisiana Comprehensive Curriculum, Revised 2008 Activity-Specific Assessments Activity 2: Provide each student with a chart with column titles, Base10, place value chart, standard, words, and expanded form. Fill in one representation of a number in each row and the student will fill in the rest. Activities: 3, 5, and 6: Provide each student with a list of 5 prices in the hundreds. The student will list prices in order and round prices to the nearest hundred. The students will provide list of items that could be purchased when provided a limit on spending. Activity 8: Given a benchmark, the student will estimate using the “sectioning off” method to determine how many items are in a diagram and show the sections used to get the estimate. Activity 11: Given a line of items, the student will identify each item‟s position. Grade 2 MathematicsUnit 4Place Value and 2-Digit Addition 63 Louisiana Comprehensive Curriculum, Revised 2008 Grade 2 Mathematics Unit 5: Place Value and 2-Digit Subtraction Time Frame: Approximately three weeks Unit Description This unit parallels the previous unit with a focus on place value but with the operational focus on subtraction of 2-digit numbers. Student Understandings Students can subtract 2-digit numbers with and without regrouping during activities. They exhibit their understanding of the subtraction algorithm by recording what happens during these activities. Students will recognize when to add and when to subtract in problem-solving situations. Guiding Questions 1. Can students complete 2-digit subtraction problems with and without regrouping, including notational work? 2. Can students distinguish between addition and subtraction situations and work accordingly? Unit 5 Grade-Level Expectations (GLEs) GLE GLE Text and Benchmarks # Number and Number Relations 1. Model, read, and write place values for numbers through 999 in word, standard, and expanded form (N-1-E) 6. From a given number, count forward and backward and count to 100 by 2s (N-3-E) (N-1-E) (N-4-E) 8. Recognize, select, connect, and use operations, operational words and symbols (+, ) for addition (join, part/part/whole) or subtraction (take away, comparison, missing addend, and set/subset) situations (N-6-E) (N-5-E) 9. Add and subtract 1- and 2-digit numbers (N-6-E) (N-7-E) Grade 2 MathematicsUnit 5Place Value and 2-Digit Subtraction 64 Louisiana Comprehensive Curriculum, Revised 2008 Sample Activities Activity 1: Subtraction with Regrouping (GLEs: 1, 8, 9) Materials List: Base 10 ® blocks, overhead Base 10 ® blocks, overhead projector Write this problem on the board or on a transparency: Marcus has 23 trading cards. He gives Alonzo 17 cards. How many cards does he have left? Guide students through the problem. Ask, “Which operation is needed to solve this problem?” Instruct students to model the number 23 with their Base 10® blocks and then to remove 17 blocks. Remind students that seventeen indicates that 7 ones and 1 ten are to be removed. Ask, “Is that going to be a problem? What must be done in order to remove 7 ones? Are there enough blocks left to remove 1 ten? How many cards does Marcus have left?” Repeat this activity many times using different problems. Give students at least one day of practice in which they go through the actions without recording their actions. Allow students access to manipulatives for this entire unit. Activity 2: Recording what Happens in a Subtraction Problem (GLEs: 1, 8, 9) Materials List: Subtraction BLM, Base 10 ® blocks, overhead Base 10 ® blocks, overhead projector Write the problem on the board or on a transparency: Paul has 32 cookies in his pack. He and his friends ate 27 cookies. How many cookies does he have left? Guide students through the problem. Model the problem first, and make the necessary regrouping in order to subtract the 7 ones. Then show students how to record their actions. Write the problem on the board/transparency, and talk through each action relating it to what just happened when you were modeling. Grade 2 MathematicsUnit 5Place Value and 2-Digit Subtraction 65 Louisiana Comprehensive Curriculum, Revised 2008 Example: I need to remove 7 ones from 2 ones. Do I have enough ones? No, so I need to regroup. I take a 10 from 3 tens and that leaves 2 tens. The ten that I took I break apart into 10 ones and put with my other 2 ones. Now I can remove 7 ones from 12 ones. That leaves 5 ones. Next, I remove 2 tens from 2 tens which leaves 0 tens. Paul has 5 cookies left. 2 12 3 2 cookies - 2 7 cookies 5 cookies Put students into pairs. Handout Subtraction BLM. Have students first model the problem, then have them solve the problem and record their actions. Observe students and make note of places where students are making mistakes in the problem modeling process. When everyone has finished, allow students to share their answers. Activity 3: Regrouping in Subtraction (GLEs: 1, 8, 9) Materials List: Place Value Mat BLM, Base 10 ® blocks, overhead Base 10 ® blocks, overhead projector Discuss how to decide whether or not to regroup in subtraction. Write 23 – 2 on the board and ask for a solution. Ask, “Is regrouping needed to solve this subtraction problem?” (No). Ask, “Why?” Hand out Base 10 blocks and Place Value Mat BLM. Then, write 23 – 4 and have students model the subtraction by using Base 10® blocks (rods and ones) and their Place Value Mat BLM, as you model on the overhead projector. Point out that they need to regroup when the 1s they are subtracting (taking away) are more than the 1s they are subtracting from. Write several 2-digit subtractions on the board (vertical and horizontal form) and practice solving them together using the Base 10® blocks, deciding first whether regrouping is needed. Model using the overhead while the students follow your verbal modeling at their seats. Finally, go over how to record subtracting with regrouping. Conclude the activity with a RAFT writing (view literacy strategy descriptions) assignment. Role – the digit 9 Audience – fellow classmates Form – paragraph Grade 2 MathematicsUnit 5Place Value and 2-Digit Subtraction 66 Louisiana Comprehensive Curriculum, Revised 2008 Topic – Why it‟s good to be the digit 9 in the one‟s place value of a 2-digit number. Allow students to share their RAFT writing assignment with a partner or the class. Students should listen for accuracy and logic in their classmates‟ RAFTs. Activity 4: Flip Three (GLEs: 1, 8, 9) Materials List: digit cards, math learning logs, Base 10 ® blocks This is a whole group activity. Divide the class into two teams. Flip over 3 digit cards and challenge students to make a 2-digit minus a 1-digit problem that requires regrouping using the digits on the cards. Have a student from one of the teams come to the front of the room and model the problem he/she has created with the digits. First, have him/her model with manipulatives and then write and solve the problem on the board. Reward the team with one point if the member from their team was able to write a problem that requires regrouping. Next, ask the other team if it was able to create a different problem that requires regrouping. Have a student share the problem and work it out on the board. If they were unable to create a different problem, flip over 3 more cards. Repeat as many times as time will permit. Have students write and answer the following in their math learning logs (view literacy strategy descriptions): Compare and contrast what happens to the number 4 in the problem 34 – 27 and the number 4 in the problem 34 – 22. How are the problems alike? How are they different? Allow students time to share their answers. Activity 5: Can you buy it? (GLEs: 1, 8, 9) Materials List: play money -10s and 1s, 1-8 Spinner BLM, paper clip, chart with prices Present the following problem to students: Molly has $20. She wants to buy a CD that costs $18. Does she have enough money to buy the CD? Model $20 with 2 ten-dollar bills. Ask a student to come up and remove $18. When there are no ones to remove, have student trade a 10-dollar bill for 10 ones. Then have the student remove 8 ones and 1 ten. Molly has enough money to buy the CD because 20 is greater than 18. The students will learn how much greater when they see how much Molly has left. Grade 2 MathematicsUnit 5Place Value and 2-Digit Subtraction 67 Louisiana Comprehensive Curriculum, Revised 2008 Put up a chart that shows toy prices to the nearest dollar. Create a spinner using the Spinner 1-8 BLM. Have students take turns spinning a spinner. The number they land on determines how many tens they are able to spend. Ask students to select an item off the toy chart. Student then models the problem using the play money. Then they write their problem on the board talking out the steps of subtraction. Example: Student spins a 6. Student gets $60 to spend at toy store. Student selects a video game off toy list that cost $57. Student must pay with exact amount. Student trades a 10 for 10 ones. Then the student counts and pays with 7 ones and 5 tens. Student has 3 ones left over. Student then records problem on the board. 5 10 $6 0 - 5 7 3 Continue the activity until all students have had a turn. Have students record problems as students work them on the board. Activity 6: Subtracting with Regrouping using a 100s Chart (GLEs: 8, 9) Materials List: 100s Chart BLM, counters Use a 100s chart and point out that each row has 10 numbers, and the numbers in each column increase by 10. Provide a subtraction sentence orally, such as 44 – 20. Have the students find 44 on their 100s Chart BLM, place a counter there, and then subtract 20 by moving the counter up 2 10s (2 rows), ending on 24. Write and solve other subtraction sentences that involve subtracting 2-digit numbers using a 100s chart. Have students place a counter on the first number given in the subtraction sentence. Have students start with the ones and count backwards the number of spaces that represent the number of ones being subtracted. Then count up rows of 10s to indicate how many tens need to be removed. See if students notice a pattern on the 100s chart when they are required to regroup. Put students into groups of five. Have each group create a math story chain (view literacy strategy descriptions) that begins with a 2-digit number that involves addition or subtraction. Example: Student 1: Start at 72 on your hundreds chart. Student 2: Count back 7 spaces. Student 3: Count up 3 tens. Grade 2 MathematicsUnit 5Place Value and 2-Digit Subtraction 68 Louisiana Comprehensive Curriculum, Revised 2008 Student 4: What space are you on? Student 5: (reviews logic in the story problem and provides correct answer) Have each group ensure logic in its story and accurately solve the problem first, then read the problem and have the class work the problem out using a 100s chart. Activity 7: Counting Back (GLEs: 6, 8, 9) Materials List: Play coins – dimes and pennies, Place Value Mat BLM (see Activity 3 BLM) Ask students to count by 10s, starting at 10 and stopping at 90 and then ask them to count back by 10s, starting at other numbers such as 83, 77, 92, and so on. Use dimes and pennies to demonstrate counting back by dimes. Give a volunteer 9 dimes and 5 pennies (have students count together to find the total amount [95¢]). Then tell the student, “You spent 20¢.” Ask: “How much do you have left?” Have the class count back by 10s to find the answer (75¢). Distribute dimes and pennies to pairs of students and have them practice counting back by 10s. Ask, “How are dimes and pennies like 10s and 1s?” (1 10 equals 10 1s and 1 dime equals 10 pennies.) Using the Place Value Mat BLM, have students use pennies and dimes to show 23¢. Ask, “How would you subtract 7¢ (pennies)?” Explain that to subtract 7 pennies (1s), 1 dime will have to be exchanged for 10 pennies. Show that now there are 1 10 (dime) and 13 1s (pennies). Now, 7 1s (pennies) can be subtracted (taken away) from the 13 1s (pennies) with 1 dime and 6 pennies left. Thus 16¢ is the difference. Have small groups work together to solve other problems with or without regrouping. Activity 8: Do I Have Enough Money? (GLEs: 6, 8, 9) Materials List: Order Please! BLM, calculators, menu Give students an amount such as $5 to spend on lunch. Have students use the menu of a local restaurant to “order” a drink, sandwich, and a dessert. Have them find the total cost of their order using a calculator. Ask students to determine if they have enough money to pay for the lunch that they ordered and what their change will be. Hand out Order Please! BLM. Remind students that a ticket is the bill that the waiter wrote down for the items ordered from the restaurant. Have students list their selections, costs, and total on the BLM and show that they paid with $5.00 and got ______back in change. Torrie‟s Ticket Paid with 75¢ Spent - 62¢ Change 13¢ Grade 2 MathematicsUnit 5Place Value and 2-Digit Subtraction 69 Louisiana Comprehensive Curriculum, Revised 2008 Activity 9: Grocery Store (GLEs: 6, 8, 9) Materials List: Receipt BLM, grocery store items with a sticker priced less than $1, coins If store items are not available use pictures cut from newspaper grocery ads and glue to poster boards. A large poster can be cut into 4 pieces and the “grocery store” can have fruits/vegetables, canned goods, cereals, and snacks. Set up a mock grocery store with items costing less than a dollar. Have students play cashier and consumer. This time have students create a receipt using the Receipt BLM before they can count back change. Have students show the amount paid, minus the cost of the item, to determine how much change they should get back. Activity 10: Add or Subtract? (GLEs: 8, 9) Materials List: index cards Using an index card, have each student create an addition or subtraction story problem where one of the numbers is a 2-digit number. Ask students to read their problems to the class, and let classmates share how they would solve the problem. Have the author of the problem select a student to set up the problem and solve it. If the student is correct, have that student read his problem. Activity 11: Subtraction Story Problems (GLEs: 8, 9) Materials List: sports page, poster, computer Show students the sports page from a newspaper and how to find scores. Have small groups find football or basketball scores (home teams or popular area teams) less than 100 points. Instruct the groups to work together to discover the difference between the two scores and how many points the winning team won by. Have students write a subtraction story problem about their findings to share on a poster titled, Sports Math. If computers are available, have students write their story problems using the computer. Activity 12: Choosing the Correct Operation (GLEs: 8, 9) Materials List: math learning log, 10 index cards, 4 strips of paper Ask students to brainstorm (view literacy strategy descriptions) clues that can be used to decide whether to add or subtract, and make a list to add to the math center and their math learning logs (view literacy strategy descriptions). Addition clues include: How many altogether? How many in all? Subtraction clues include: How many are left? How many more? How many less? Grade 2 MathematicsUnit 5Place Value and 2-Digit Subtraction 70 Louisiana Comprehensive Curriculum, Revised 2008 To play a math game, prepare 10 index cards with a 2-digit number on each and on 4 separate strips of paper, write questions such as: How many in all? How many now? How many are left? How many more? Have small groups or individuals choose two number cards and a question strip and work together to create a story problem using the numbers and questions. Have students record their problem in their math learning log, and then share their problems with the class. Activity 13: Subtract From 99 (GLEs: 8, 9) Materials List: 1-4 Spinner with Recording Sheet BLM, large paper clips, calculators Provide each pair of students with the 1 – 4 Spinner with Recording Sheet BLM and large paper clip. Have them spin the spinner twice to make the smallest 2-digit number possible; then subtract that number from 99. Next, ask them to spin again and subtract the new 2-digit number from the first difference. Have them continue spinning and subtracting from the previous difference until they come to a number they cannot subtract. Challenge them to get as close to 0 as possible. Allow students to use a calculator to check their subtraction, if needed. Sample Assessments Performance and other types of assessments can be used to ascertain student achievement. Following are some examples: General Assessments Problem Solving Book: Have students make a class problem solving book. Each student will write a problem in which he/she finds the difference between a 2- digit and 1-digit number that requires regrouping and write the answer on the back of the page. Make a booklet and place it in a center for students to solve each other‟s problems. Journal Writing: Have students explain how addition and subtraction are alike and how they are different. Students will explain how they know when to regroup in a subtraction problem. Grade 2 MathematicsUnit 5Place Value and 2-Digit Subtraction 71 Louisiana Comprehensive Curriculum, Revised 2008 Students will determine if they would use addition or subtraction to solve problems as story problems are read to them. Activity-Specific Assessments Activity 4: Students write a problem using the digits 2, 7, and 9 that would require regrouping. Activity 5: Students match the amounts below so that they can buy each item listed. Video game $37 $30 Camera $41 $40 CD $21 $50 Activity 6: Students model the subtraction problem 57 – 29 using a 100s chart. They will fill in the blanks as the work is done. I started at ________. I moved back _____spaces. Then I moved up ______rows. I ended up on the numeral _________. Activity 8: Students calculate how much change is due when provided information for a restaurant ticket by the teacher. Activity 12: Students decide which operation to use and then set up and solve real-life problems provided by the teacher. Grade 2 MathematicsUnit 5Place Value and 2-Digit Subtraction 72 Louisiana Comprehensive Curriculum, Revised 2008 Grade 2 Mathematics Unit 6: Shapes and Fractions Time Frame: Approximately four weeks Unit Description This unit focuses on geometric and fractional number understandings. In geometry, students extend their work to compare and contrast figures, and to identify congruent and similar figures. They also examine the role of fractions in geometric and set contexts. Student Understandings Students identify congruent shapes and deal with orientations of 3-dimensional objects. In the plane, they recognize and use vertical and horizontal references. Students also model fractional parts of a whole and a set. Guiding Questions 1. Can students compare and contrast 2- and 3-dimensional shapes and recognize congruent shapes in space? 2. Can students recognize and draw horizontal and vertical lines? 3. Can students identify a reduction or an enlargement of a figure? 4. Can students identify and discuss thirds, fourths, fifths, and sixths? Unit 6 Grade-Level Expectations (GLEs) GLE # GLE Text and Benchmarks Number and Number Relations 2. Model the concepts of thirds, fourths, fifths and sixths using regions, sets, and fraction words (e.g., one-third, three-fourths, five-sixths) (N-1-E) Geometry 21. Compare and contrast 3-dimensional shapes (i.e., sphere, cube, cylinder, cone, prism, pyramid) according to their attributes (e.g., number of faces, shape of faces) (G-2-E) 22. Identify a reduction or enlargement of a given shape (G-2-E) 23. Identify congruent 3-dimensional solids in a variety of positions and orientations (G-3-E) (G-4-E) (G-2-E) 24. Identify and draw horizontal and vertical line segments (G-5-E) Grade 2 MathematicsUnit 6Shapes and Fractions 73 Louisiana Comprehensive Curriculum, Revised 2008 Patterns, Relations, and Functions 31. Recognize, extend, create, and explain patterns that involve simple rotations or size changes with geometric objects (P-1-E) (P-2-E) 32. Recognize and apply patterns in problem-solving in other content areas and real-life situations (P-3-E) (N-9-E) Sample Activities Introduction Activity (GLE: 21) Materials List: 3-D Vocabulary Self-Awareness Chart BLM, pencil Prior to beginning Unit 6 hand out the 3-D Vocabulary Self-Awareness Chart BLM. Use the BLM (view literacy strategy descriptions) to gauge students‟ knowledge of the vocabulary used in Unit 6. Give each student 3-D Vocabulary Self-Awareness Chart BLM, and direct them to rate their understanding of each word/symbol with either a “+” (understands well), “√ “(limited understanding), or a “ – “ (don‟t know). Over the course of the unit, students are to return to their chart and add new information. The objective is that students will replace all the check and minus marks with plus signs. At the end of the unit, students can utilize the chart to compare and contrast 3-D shapes. Activity 1: Three Dimensional Shapes (GLE: 21) Materials List: a set of Geoblocks® or a collection of objects of different shapes: eraser, crayon box, soup can, ball, alphabet block, tissue boxes, a pointed party hat, chalkboard or chart paper, pictures of 3-D shapes, glue, scissors Display a set of Geoblocks® or a collection of objects of different shapes: eraser, crayon box, soup can, ball, alphabet block, tissue boxes, a pointed party hat. Hold up a cube and ask if anyone knows the name of the shape (cube). Place it so that everyone can see it. Ask the students to describe it as you write their descriptions on the board or on chart paper. When students have completed their descriptions, hold the cube and point to a corner. Tell them that the corner is called a vertex and that the word vertices is used when talking about more than one vertex. Have a student point to and count the number of vertices. Point to a face and say the word face. Ask someone to name the shape of the face of a cube (square). Count the faces and ask if all of the faces have the same shape. Now, point to an edge and tell the students that this part of the cube is called an edge. Count the edges with the students. Using chart paper create a large modified word grid (view literacy strategy descriptions) that has 5 columns and 7 rows. This is a modified word grid in that instead of putting checks, pluses, or minuses in each cell, students must write figure names and numbers. Label the chart “Characteristics of 3-Dimensional Figures.” Label the columns: Picture Grade 2 MathematicsUnit 6Shapes and Fractions 74 Louisiana Comprehensive Curriculum, Revised 2008 of Figure, Name of Figure, Number of Vertices, Number of Faces, and Number of Edges. Draw or glue a paper cutout of a cube or picture of an object that is shaped like a cube (cubic tissue box), and ask the students to help you fill in the columns. Repeat this activity with at least one other object, and add the information to the chart. Have students begin making comparisons between the 3-dimensional objects. Continue to introduce another shape each day until the chart is filled with the shapes (don‟t forget pyramids) and their descriptions. Characteristics of 3-Dimensional Figures Picture of Name of Figure Number of Number of Number of Figure Vertices Faces Edges rectangular 8 6 12 prism Have students return to their Vocabulary Self-Awareness Chart BLM and make adjustments to the marks that indicate their understanding of the vocabulary words, faces, vertices, and edges. Return to the chart throughout the unit to compare and contrast 3-D shapes as students acquire more knowledge. Allow time for students to review the information on the grid with a partner in preparation for quizzes and other class activity. Activity 2: Grab Box (GLE: 21) Materials List: 3-D shapes, box with hole in the top, math learning logs Place 3-D shapes in a box which has a hole in the top. Have students grab an object in the box (but don‟t remove it from the box). Have them describe the attributes that they can feel. After they have described the item, ask them to guess the name of the 3-D shape that they are holding. After guessing, have them pull the object from the box to see if they were correct. Repeat the activity several more times. Have students record the following statements in their math learning logs (view literacy strategy descriptions). Today I picked a _______________in the grab box. I knew it was a _________________because I could feel ____________________. Grade 2 MathematicsUnit 6Shapes and Fractions 75 Louisiana Comprehensive Curriculum, Revised 2008 Activity 3: Digital Scavenger Hunt (GLE: 21) Materials List: index cards, cameras, computer, PowerPoint® program or paper to make shape booklet, magazines, scissors, glue Write the name of 3-D shapes on index cards. Put students into groups. Have a student from each group draw a card. Go on a walk through the school having each group record examples of their shape on the back of their card. If cameras are available, students could take pictures of the examples as they walk. Give each group a camera (digital, disposable, or instant) and have students in each group alternate taking pictures of their shape. When students get back to class, have them create a tally chart of the 3-D shapes they saw. Make a presentation with students' pictures. Create a class PowerPoint® presentation, or put together a shape book. Note: If cameras are not available, do the activity using pictures from magazines. These pictures could be used to assess students‟ ability to identify 3-D shapes at a later date. Activity 4: Top, Front, Bottom Views (GLE: 21) Materials List: Top, Front and Bottom Views BLM, 3-D shapes, pencil Hand out the Top, Front and Bottom Views BLM. Give each student a cube. Have them stand over the shape and look down. Ask, “What shape do you see?” (square) Have students record their answer under Top View on their recording sheet. Without moving the cube, have them look at the cube from the front. Ask, “What shape do you see?” (square) Students record their answer under the proper heading. Finally, have them lift the cube and look at the bottom of the cube. Ask, “What shape do you see?” (square). Students record their answer under the proper heading. Repeat this activity with a cone, pyramid, rectangular prism and sphere. Have students stop after each view and record their answer. Have students group 3-D shapes according to common faces. Collect and check students‟ BLM for understanding. Activity 5: Is it Horizontal or Vertical? (GLE: 24) Materials List: chalkboard, chalk, toothpicks or short straws of congruent length, construction paper, overhead Draw a square on the board. Demonstrate that each side is made of a line segment. Using toothpicks on the overhead, have volunteers model other plane figures studied. Explain that the place where the toothpicks meet is the corner of the plane figure. Ask, “What are the sides called?” (line segments) Model on the board the difference between lines and line segments. Grade 2 MathematicsUnit 6Shapes and Fractions 76 Louisiana Comprehensive Curriculum, Revised 2008 Draw some shapes slowly on the overhead, and ask students to identify the number of line segments used in each. Ask students to find line segments that run straight up and down (square, rectangle) and introduce the term vertical. Have students find line segments that are lying down straight (rectangle, parallelogram, square, trapezoid), and introduce the term horizontal. Ask, “Why are these line segments instead of lines?” In a math circle, give each student about 10 toothpicks and a piece of construction paper to serve as a work mat. Tell them that the toothpicks will be their line segments. Give directions for students to place toothpicks horizontally or vertically on their mat. After a few minutes of having them randomly place their toothpicks, ask them to clear their mats. Now, tell them that they will have to make the shape that you describe. Ask if they know how many vertical and how many horizontal line segments are needed to make a square. After discussion, give directions for laying toothpicks horizontally and vertically with tips touching to make a square. Repeat with other shapes. Revisit the Vocabulary Awareness Chart BLM. Check students‟ vocabulary self- awareness (view literacy strategy descriptions) of the terms vertical and horizontal. Activity 6: Creating a Design (GLE: 24) Materials List: ruler, paper, pencil, red and blue crayons Have students use a straight edge to draw a picture made up only of line segments. After they create the design, have them use a red crayon to trace over all the line segments that are horizontal and use a blue crayon to trace over all the vertical line segments. If their picture has symmetry, have them draw a dotted line through the shape(s) to show symmetry. Have students complete a RAFT (view literacy strategy descriptions) writing assignment to assess their understanding of horizontal, vertical, and lines of symmetry. RAFT Role- Museum director Audience- guest of the Museum Form – Museum brochure T- Draw examples of art that do and do not have lines of symmetry as well as vertical and horizontal lines that are featured in the museum with a description of the art piece. Once RAFTs are completed, allow students to share them with a partner or the whole class. Students should listen for accuracy and logic in the RAFTs. Grade 2 MathematicsUnit 6Shapes and Fractions 77 Louisiana Comprehensive Curriculum, Revised 2008 Activity 7: Congruent and Similar Shapes (GLEs: 22, 31) Materials List: computer, Kidpix® Use a draw program like Kidpix® to show students how to copy and paste a figure. When a figure is copied and pasted, it creates two congruent figures. Explain to students that congruent figures are figures that are exactly alike. Next, have them enlarge the second figure by holding down the shift key as they “stretch” the figure. Lead students to notice that the figures look the same except one is larger than the other. Tell them this is called an enlargement. Repeat the process, this time „shrinking” or reducing the figure – reduction. When teaching about enlargements and reductions, make sure students understand that the original figure has been stretched or shrunk vertically and horizontally by the same factor. Show students how to stretch figures on the computer without holding the shift key. The shape becomes distorted. Show students examples of what is and is not an enlargement. Example: only stretched wide original figure only stretched long stretched long and wide – looks same but bigger Have students create enlargements on the computer. Next have students create a pattern using a figure that follows the pattern: congruent, congruent, enlargement Example: Activity 8: Similar Shapes (GLEs: 22, 31) Materials List: piece of red construction paper, scissors, Geoboards®, rubber bands, Demonstrate cutting out a symmetrical red heart by folding a piece of paper and cutting half of a heart shape and then unfolding the paper to make the heart. Ask a volunteer to point out the line of symmetry and the matching parts. Ask, “How can you be sure the parts are exactly the same size?” (Cut them apart and place them on top of each other to match size and shape.) Define congruent figures as those having the same shape and size. Use a Geoboard® to model making a simple shape. For example, make a square whose sides are 3 units long Grade 2 MathematicsUnit 6Shapes and Fractions 78 Louisiana Comprehensive Curriculum, Revised 2008 as students make an identical shape on their Geoboards®. Ask students if their shapes are congruent to yours. (Yes) Have volunteers make a shape to be copied. Each time ask, “Are these all congruent shapes?” (Yes) Now ask, “Are all shapes congruent to each other?” (No) Have students create triangles that have a base 3 units long and are 3 units tall. Students should note that all triangles are not congruent. Next, create a rectangle that is 4 units long and 1 unit wide. Have 9 students come to the front of the room with their geoboards. Challenge students to create and ABB pattern using the rectangles on their geoboards. Activity 9: Twin Day (GLE: 22) Materials List: Shapes BLM-3 pages, glue, Popsicle® sticks, cardstock Prior to class, run off Shapes BLM on cardstock, cut out each shape, and then glue them on Popsicle® sticks. Position the shapes in different orientations when gluing them on the sticks. Give each student a shape. Have students group themselves. Discuss what attribute they used to group themselves. Next, have students find their family of shapes. The family should all be the same shape. Next, have students find identical twins in the family (congruent figures) and other family members that show an example of an enlargement and reduction. Talk about what makes a shape a reduction or an enlargement. Ask students to look in the real world and bring in examples of enlargements and reductions. Revisit the Vocabulary Awareness Chart BLM. Check students‟ vocabulary self- awareness (view literacy strategy descriptions) of the terms congruent, similar, and enlargement. Activity 10: Tangram (GLEs: 22, 32) Materials List: Grandfather Tang’s Story, Tangrams BLM or a set of plastic tangrams per student, overhead projector, transparency of Tangrams BLM or overhead tangrams, paper, scissors, glue Introduce tangram shapes with the book Grandfather Tang’s Story by Ann Tompert or tell the following story: According to Chinese legend, a man named Tan had a square tile. The tile fell and broke into 7 pieces (show overhead tangram pieces) that looked like this. The pieces are called tans. Identify each piece (triangle, parallelogram, square). Ask students to find an example of an enlargement or reduction. Ask, “Are there any pieces that are congruent?” Grade 2 MathematicsUnit 6Shapes and Fractions 79 Louisiana Comprehensive Curriculum, Revised 2008 Read the story to the students, and model each figure in the book using the overhead tangrams. If the book is not available, tell students, “The tans can be used to represent many different pictures (demonstrate bunny, cat, fish, etc.). Today, you will be able to make a set of paper tangrams. Cut apart the Tangrams BLM or trace plastic tangrams and cut them out.” Have students use the pieces to create a figure. Next, have students glue down the pieces and name their figure. Display students‟ figures on a bulletin board. Website for tangram puzzles: http://pbskids.org/cyberchase/games/area/tangram.html Activity 11: Repeating Pattern Block Designs (GLEs: 31, 32) Materials List: pattern blocks, paper, crayons, examples of tessellations, class chart Have students work in pairs with pattern blocks to create designs on a piece of paper (8 1 2 x 11 inches) with no space or gaps between the pieces. Everything has to fit together (like a puzzle). As they create their designs, have them observe whether or not they have to turn or rotate the shape in any way to make it fit. When completed, instruct students to trace each shape. When the designs are finished, display the designs along the chalkboard and allow each pair to explain how they made their design. (Did they have to rotate any blocks?) Have students identify patterns they used in their designs. Explain that a design or pattern that fits together exactly is called a “tessellation.” Bring in some quilts to demonstrate a pattern that tessellates. Bring in as many real examples as possible (e.g., brick walls, tile floors, stained glass windows, etc.). Use examples of artwork by M. C. Escher to illustrate tessellating shapes. Take a walk around the school to look at patterns in the bricks, floors, or windows. Tell the students to watch for these special patterns in and around their homes and neighborhoods and while they are riding in the car. Create a class chart with the patterns they observe in their environment. Activity 12: Young Architects (GLE: 23) Materials List: wooden building blocks, class chart from Activity 1, paper, pencils Borrow a set of wooden building blocks of different shapes from the kindergarten teacher. Have the students name each shape in the set (e.g., rectangular prism, triangular prism, cube). Allow them to find the shape that it matches on the class chart created in Activity 1, and compare number of faces, edges, and vertices. Divide the class into four or five small groups, giving each group a set of wooden blocks and have them make a building using 6 blocks. Direct them to change the positions of their shapes in as many ways as possible and to just not stack the blocks. Grade 2 MathematicsUnit 6Shapes and Fractions 80 Louisiana Comprehensive Curriculum, Revised 2008 Allow students to inspect the structures made by all groups. As they look at a structure, have students record how many of each block shape they see in the structure. When groups have looked at all structures, lead a discussion in which the class compares answers. Activity 13: Vocabulary Connection (GLEs: 21, 22, 24) Materials List: Vocabulary Self Awareness Chart BLM from Introduction Activity, index cards, pencil Students use their Vocabulary Self Awareness Chart BLM to create vocabulary cards (view literacy strategy descriptions). This activity is done as a culminating activity on terms used to describe geometric figures. The cards can be collected and used as an assessment of students‟ understanding. Before testing their understanding of the key vocabulary, allow time for independent and paired review of the cards. ___________ picture Horizontal real example word A rectangle has two horizontal lines. sentence Activity 14: Letter Rotation (GLE: 31) Materials List: Patterns for Rotations BLM, Capital F BLM, tape, Finish the Pattern BLM, paper, pencil Cut out the arrow from the Patterns for Rotations BLM. Use the arrows and demonstrate a rotation. Tape each arrow to the board as you rotate it. Next, show students how to record the rotation. the figure is turning down left up right Grade 2 MathematicsUnit 6Shapes and Fractions 81 Louisiana Comprehensive Curriculum, Revised 2008 Give each student a capital F. Have the students draw the F in its original position and then turn the F and draw it as it rotates. Hand out and have students complete the Finish the Pattern BLM. Activity 15: Fractions (GLE: 2) Materials List: Fractional Squares BLM, ruler, crayons, math learning logs Draw five large congruent squares on the chalkboard; have a volunteer draw a line to divide one square into two equal parts and color in one of the parts. Write 1 on the 2 board, and explain that the 2 on the bottom (denominator) tells how many parts in all, and the 1 on top (numerator) tells how many parts are colored. One of two parts is colored. 1. Hand out the Fraction Squares BLM. Color in 1 , and write 1 on the side that is not 2 2 colored. 2. Continue to divide the squares on the board into equal parts, and label them to explain 1 , 1 , 1 , and 1 . Have students to continue to color and label squares on 3 4 5 6 their Fraction Squares BLM and label accordingly. Have students explain why 1 is greater than 2 1 4 of the same object in their math learning logs (view literacy strategy descriptions). Activity 16: Circular Fractions (GLE: 2) Materials List: Assorted Fractions BLM, paper plates, scissors, marker, bag Demonstrate to students how to cut paper plates into halves, thirds, fourths, fifths, and sixths. Point out that each of the fraction pieces must be the same size as the others. Demonstrate this by stacking the matching pieces together and/or cutting one plate into two unequal parts. Ask, “Is this plate divided into halves? Why?” (No, the parts are not exactly the same size.) Make another cut for three pieces and then four pieces. Write the appropriate fraction on each plate piece, and choose one student to put them back together, correctly telling the number of pieces to make the whole plate. Give Assorted Fractions BLM that have been divided into equal parts. Have students cut the circles apart, and label each part of the circle. ( 1 , 1 , 1 , 1 , and 1 ). Put all the pieces in a grocery bag, shake them up, and pour 2 3 4 5 6 Grade 2 MathematicsUnit 6Shapes and Fractions 82 Louisiana Comprehensive Curriculum, Revised 2008 them out on the floor. Choose two students to work for one minute to put together as many circles as possible. Continue choosing pairs of students to work for one minute until all circles are complete. Note: If the fraction circles are too small for students to manipulate, use the paper plate pieces instead. Activity 17: Edible Fractions: (GLE: 2) Materials List: raisins, shelled peanuts, M&Ms®, dry cereal (Rice Chex® or Fruit Loops®), 1-cup measuring cups, bowls, small cups, large spoon Divide the class into four groups, and have each group measure 1 cup of each ingredient into a bowl and mix carefully. Draw the illustration on the board. 1 cup of cereal Ask students, “How many cups did we use for the recipe? 1 cup of M&Ms What fraction of the recipe is raisins? What fraction of the 1 cup of peanuts recipe is cereal?” 1 cup of raisins Divide the mix equally among the students in the group, and then discuss what share of the whole they got. (1 part to the total number of students in the group) Activity 18: Set Models (GLE: 2) Materials List: paper, pencil, magnetic shapes, magnetic board, connecting blocks of two colors Have each student draw a picture of his/her family and write a sentence telling what fractional part of the family he/she represents (e.g., I am 1 of my family). Share the 4 pictures with the class and save for a class book. Have six students stand at the front of the class. Have two students raise their hands. Ask, “What fraction of the group has its 2 hands raised? ( 6 ). What fraction of the group is boys? Girls?” Ask, “How many days in the school week? (5) How many days do you have art?” (1) Have students write the fraction that tells the number of art days in the week. Continue using other activities, such as P.E., music, and lunch. Use magnetic shapes to make groups on the board; ask students what fraction of the whole group each shape is (e.g., 2 3 the apples are 5 of the group, and the hearts are 5 of the group). Give volunteers a chance to create a set, and choose someone to make a correct fraction statement about it, writing the fractions on the board. Play a game: Have one of a pair of students use 4 connecting blocks of two colors to show fractions (e.g., one child says 5 of the cubes are blue) while the other student models the fraction and writes it on the board. Grade 2 MathematicsUnit 6Shapes and Fractions 83 Louisiana Comprehensive Curriculum, Revised 2008 Activity 19: Fraction Towers (GLE: 2) Materials List: per pair of students 5 red, blue, yellow, and green cubes, index cards Put students into pairs. Give each pair 5 red, blue, yellow, and green cubes. Have students build towers according to directions. Example: Build a tower that has six cubes. Two- sixths of the tower must be red. Three-sixths of the tower must be green. The rest of the tower is yellow. How many yellow cubes do I need?_________________ Put students into groups of 4. Have each group make a fraction tower with 8 cubes using 4 colors . Then have each group write a math story chain (view literacy strategy descriptions) describing their tower on an index card. The first student should say. Our tower is ___eighths _____. The next student says our tower is ____ eighths _____. The third student says our tower is _____ eighths _______. The fourth student says our tower is _____ eighths ______. Display all the towers. Then read the math story chains and have students identify which tower is being described. Sample Assessments Performance and other types of assessments can be used to ascertain student achievement. Following are some examples. General Assessments: Show the student 3-D shapes, and the student will identify them using the correct terminology. Students make a Shape Book by pasting pictures of 3-D objects into a booklet. Students will put puzzles together that involve fractional pieces. (Pizza that has been cut into fourths.) Activity-Specific Assessments: Activity 1: The student will create a list or chart of real-life objects of each solid shape studied. Give students a word bank, and then hold up a 3-D shape. The student will write down the shape's name. The student will make up solid- shape riddles for others to guess. Example: I have 6 faces that are the same size, 8 vertices, and 12 edges. Activity 5: Give students a drawing where they must identify horizontal and vertical lines within the figure(s). Grade 2 MathematicsUnit 6Shapes and Fractions 84 Louisiana Comprehensive Curriculum, Revised 2008 Activities 7 through 10: Design a worksheet with pairs of shapes, some similar and some congruent. The student will identify the correct category for each pair of figures. Given a grid sheet with a figure drawn, the student will model a congruent and a similar figure on the blank grid sheet. Activity 14: Give students a worksheet where they will complete a pattern that involves a rotation of a figure. Activities 15 through 17: Give each student five minutes to do a Fraction Scavenger Hunt around the room, looking for at least five examples of 2 fractions (for example, 3 of the balls are red; 1 of the windows are open, and 3 so on). Set up three examples without the students knowing it. Grade 2 MathematicsUnit 6Shapes and Fractions 85 Louisiana Comprehensive Curriculum, Revised 2008 Grade 2 Mathematics Unit 7: Measurement in Our World Time Frame: Approximately five weeks Unit Description Measurement tasks are extended to more precise measures, and standard measures for capacity and mass are introduced and used. The focus at this grade level is on gaining a strong feeling for selecting tools and using them to measure length, mass, and capacity. Some conversions are made within the same system. Area of rectangular regions is introduced. Celsius/Fahrenheit temperatures and their estimation are also added. Student Understandings Students select appropriate tools and units for measuring length, perimeter, capacity, mass, and temperature. Students use the appropriate tool and measure to the nearest inch, centimeter, foot, cup quart, liter, pound, and kilogram. They can make simple conversions within the same system. They differentiate between area and perimeter of rectangular regions by using the appropriate tools. Guiding Questions 1. Can students select units and tools for measuring length, perimeter, capacity, mass, and temperature? 2. Can students measure to the nearest unit to find length, perimeter, capacity, and weight/mass (i.e., inch, centimeter, foot, cup, quart, liter, pound, kilogram)? 3. Can students differentiate between and measure perimeter and areas of rectangular regions? 4. Can students read a thermometer in degrees Celsius/Fahrenheit and interpret temperature? 5. Can students compare units within the same system (i.e. inch shorter than a foot, day shorter than a week, cup holds less than a quart)? Grade 2 MathematicsUnit 7 Measurement in Our World 86 Louisiana Comprehensive Curriculum, Revised 2008 Unit 7 Grade-Level Expectations (GLEs) GLE # GLE Text and Benchmarks Measurement 14. Measure and appropriately label measures of length and perimeter (i.e., inch, centimeter, foot), capacity (i.e., cup, quart, liter), and weight/mass (i.e., pound, kilogram) (M-1-E) 15. Read a thermometer in degrees Fahrenheit and Celsius and interpret the temperature (M-1-E) 17. Select and use appropriate tools and units to measure length, time, capacity, and weight (e.g., scales for pounds and kilograms; rulers for inches and centimeters; measuring containers for cup, quarts, and liters) (M-2-E) 18. Use non-standard units to cover a given region (M-2-E) 19. Estimate length in standard units (inch, foot, and centimeter) (M-3-E) 20. Compare units within the same system (inch is shorter than a foot, minute is shorter than an hour, day is shorter than a month, cup holds less than a quart) (M-3-E) Data Analysis, Probability, & Discrete Math 28. Generate questions that can be answered by collecting and analyzing data (D-3-E) Sample Activities Introduction Activity (GLE: 17) Materials List: Measuring Tools Self-Awareness Chart BLM, pencil Prior to beginning Unit 7, hand out the Measuring Vocabulary Self-Awareness Chart BLM. The vocabulary self-awareness chart (view literacy strategy descriptions) will be used to gauge students‟ knowledge of tools used for measurement in Unit 7. Give each student a Measuring Tools Self-Awareness Chart BLM and direct him/her to rate his/her understanding of each word/symbol with either a “+” (have used it before), “√ “(haven‟t used it but know what it is), or a “ – “ (never used it and don‟t know what it is). Over the course of the unit, students are to return to their chart and add new information. The objective is that students will replace all the check and minus marks with plus signs. At the end of the unit students can utilize the chart to review tools used in measuring objects. Activity 1: Measuring to the Nearest Inch (GLEs: 14, 17) Materials List: bag of items to measure per group, transparent ruler, rulers, overhead projector, Measuring to the Nearest Inch BLM, math learning log Use the overhead projector to review with students how to measure to the nearest inch. Model how to correctly place the object on “zero” of the ruler. Make sure students know not to start on 1 of the ruler. Put students into groups. Give each group a bag with several Grade 2 MathematicsUnit 7 Measurement in Our World 87 Louisiana Comprehensive Curriculum, Revised 2008 items to measure to the nearest inch. Give each member in the group an inch ruler and BLM. Have students measure each item to the nearest inch and record their findings. Go over the BLM with students. Have students respond in their math learning logs (view literacy strategy descriptions) to the question: How do you measure an object with a ruler? Students can compare their responses with a partner to reinforce their understanding of measuring with a ruler. Activity 2: How Long is that Road? (GLEs: 14, 17, 19) Materials List: duct tape, scissors, marker, rulers, How Long is that Road? BLM Use duct tape to represent roads. Place tape on the floor and label the tape with street names around the classroom. Put students into groups and have them estimate the length of the road in feet. Have students write down the name of the street and their estimates on their BLM. Then have students measure the road‟s length to the nearest foot by having students lay 1-foot rulers end-to-end. Have students record their findings. Activity 3: Choosing the Best Unit (GLEs: 14, 17) Materials List: bag of objects, ruler, blank word grid on poster or chart Model how to use a ruler to measure objects. Prepare a “grab bag” of objects (e.g., ribbon, a straw, belt) to measure using a ruler. Discuss with students what would be the best unit of measure to use to find the length of each item (inches or feet). Create a word grid (view literacy strategy descriptions) on a poster or chart to be displayed throughout the unit. As tools are introduced in the unit, list the tool and then check off the attribute the tool is used to measure. Tool Attribute measured Length Perimeter Capacity Weight Temperature ruler X After perimeter is taught place an X under perimeter for ruler. Once the grid is completed, allow time for students to quiz each other over the content in preparation for tests and other class activity. Grade 2 MathematicsUnit 7 Measurement in Our World 88 Louisiana Comprehensive Curriculum, Revised 2008 Activity 4: Giant Step (GLEs: 14, 17) Materials List: None Outside, have students play the game Giant Steps as follows: Line players up shoulder to shoulder on one side of the playground; the leader stands on the other. Show students how to take inch (baby) steps, foot (heel of one shoe to toe of the other shoe) steps, or yard (giant) steps. When the leader gives an instruction, “Take 3 giant steps forward,” the student must say, “May I?” or lose a turn. The leader says, “Yes, you may.” And the game continues until someone reaches the teacher. Play several rounds. Activity 5: The Metric System (GLEs: 14, 17, 19) Materials List: cm rulers, objects to measure, examples of polygons Ask, “What units have been used to measure length so far?” Discuss other ways to measure length (e.g., using metrics) and show a centimeter ruler. Give each student a centimeter ruler and write centimeter (cm) on the board. Show students that 1 centimeter is about the size of the width of their index fingers. Have students find 1 cm and 10 cm on their rulers. Model how to measure using the centimeter rulers. Give pairs of students small objects to measure (e.g., spoon, marker, sponge, comb), and have them try to find something in the room that is about the same length. Limit metric measurement to centimeters. Give students examples of polygons. Model how to find the perimeter of a polygon. Have students find the perimeter of each shape in centimeters. Activity 6: Equal Weights (GLEs: 14, 17) Materials List: balance scale, chalkboard eraser, connecting cubes, objects to weigh Model the use of the balance scale to make equal weights. Put a chalkboard eraser into one pan and put connecting blocks into the other pan until the scale is balanced. Have students in small groups estimate and discover the number of connecting cubes needed to balance with other classroom objects. Grade 2 MathematicsUnit 7 Measurement in Our World 89 Louisiana Comprehensive Curriculum, Revised 2008 Activity 7: Weighing In! (GLEs: 14, 17, 28) Materials List: balance scale, 40 beans, 2 markers, boxes marked “Weighs More” and “Weighs Less,” objects to weigh Model how to use the balance scale by placing 20 beans on each side of the scale to show how the scale “balances” when both sides are equal. Next place 20 beans in one pan of the scale and 2 markers in the other. Discuss how to compare the weight of the beans to the weight of the markers. Label one box with “Weighs More” (than 20 beans) and label a second box with “Weighs Less” (than 20 beans). Have students place objects found around the room on one side of the scale pan to see which weighs more (their object or the 20 beans), and put the objects in the correctly labeled box. Continue with each student making predictions (estimating) and then measuring. Activity 8: What is a Pound? (GLE: 14) Materials List: Examples of 1-pound objects, balance scale, objects to weigh Collect several examples of objects weighing one pound (coffee, baking soda, beans, pasta, and powdered sugar). Allow students to handle the objects and determine what a pound feels like in their hands. Put students into groups. Give each group several objects, a pound item, and a balance scale. Have students estimate the weight of each object as weighing a pound, more than a pound, or less than a pound. Have students check their estimates using a balance scale. Activity 9: In Order (GLEs: 14, 17, 28) Materials List: brown paper bags, objects to weigh, balance scale, math learning logs, large bowl, small bowls, knife Place objects of different weight (mass) into numbered brown paper bags (one per bag); use at least five bags; have students pick up and compare the bags, determining which are heaviest and lightest, arranging them in that order. Have several students try this and write down their guesses. Then have a volunteer take the objects out of the bags and put them into the estimated correct order from heaviest to lightest. Use a balance scale to determine if the objects are placed in the correct order. For homework, have students bring in their favorite fruits to weigh. Have students take turns holding their fruit in one hand and the 1-pound bag of beans in the other, guessing and recording whether the fruit weighs about a pound. Have them weigh each fruit to check their estimates. Make a class chart showing results as more than a pound, a pound, or less than a pound. Have students generate questions that could be answered while looking at the data collected in the chart. When weighing is complete, chop the fruits to make a fruit salad. Grade 2 MathematicsUnit 7 Measurement in Our World 90 Louisiana Comprehensive Curriculum, Revised 2008 Students use their math learning logs (view literacy strategy descriptions) to respond to the following question: How is a see-saw like a balance scale? Allow students to compare their responses with a partner. Activity 10: By the Pound (GLEs: 14, 17, 28) Materials List: 2 booksacks, bathroom scale, newspaper/supermarket flyers, scissors, glue, chart paper Show students two different booksacks about the same size. Ask which weighs more or has more mass. How can they find out? Weigh each booksack using a bathroom scale. Determine which booksack weighs more. Have students select items around the room, and weigh them on the scale. Have students bring in ads cut from newspapers/supermarket flyers showing foods that are sold by the pound. Paste their ads on a chart labeled “Be A Consumer.” Then ask questions such as these: Which costs more, one pound of apples or one pound of bananas? How much will you pay for one pound of potatoes and one pound of carrots? Have students generate questions that could be answered while looking at the data collected on the chart. Activity 11: Kilograms (GLEs: 14, 17) Materials list: objects to weigh, 1-kilogram objects, balance scale, 1-pound items, bag of beans Display six objects on the table, and have a student arrange them in order from heaviest to lightest. Write the word kilogram on the board. Tell students a kilogram is used to weigh heavy things in the Metric System. Put an object that weighs 1 kilogram on the balance scale. Add pound items to the balance. Students should conclude that a kilogram is between 2 and 3 pounds. Put two pounds on one side of the balance, and then open a bag of beans and pour about half of the bag into the balance. This should come close to balancing the kilogram. Tell students that a kilogram is about 2 1 pounds. Give students a 2 list of objects and their weights in kilograms. Have students determine if the weight listed for the object is reasonable (i.e., an orange weighs 10 kilograms, a book weighs 1 kilogram). Grade 2 MathematicsUnit 7 Measurement in Our World 91 Louisiana Comprehensive Curriculum, Revised 2008 Activity 12: Finding Capacity (GLEs: 14, 17, 20, 28) Materials List: index cards, markers, a set of several containers (all groups should have identical sets), fillers such as rice, beans, or bird seed, scoop, measuring cups, catch basin (paper box top), Finding Capacity BLM Explain that capacity is the amount a container will hold when it is full. Have students brainstorm (view literacy strategy descriptions) objects that hold liquid (e.g., teapot, mug, watering can, barrel). Write the words on index cards and have students illustrate the words. As they finish illustrating, they should line the cards up on the chalkboard tray in order of smallest capacity to largest capacity. Display several containers of different sizes (e.g., tablespoon, cup, jar, bowl) and ask which will hold more. Scoop beans, seeds, or rice into each of the containers, counting scoops as you fill the container. Tell students a standard scoop is called a cup. Show students a measuring cup. Put students into groups. Give each group several containers, a cup, a catch basin, and filler. Give each student in the group a BLM with the items listed. Have students determine how many cups each container will hold. Have students record their findings. Allow students to share their results. Activity 13: From Cups to Quarts (GLEs: 14, 17, 20) Materials List: cup, quart, and liter containers, scoop, filler, 1-cup measure Show cup, quart, and liter containers. Ask students to arrange the containers according to size. Review the definition of capacity. Ask which holds the most and least. Use water or beans to check predictions. Next, label the containers with the correct word and abbreviation. Explain that the cup and quart are U.S. units of measure and that the liter is a metric unit. Have a volunteer use a 1-cup measure to find out how many cups will fill each container. Measure liquid (water) or dry (beans) capacity. In second grade, students are only expected to compare units within the same system, but this activity will give them a foundation for making comparisons between systems. Students should understand that a liter and a quart are about the same. Have students bring in containers that are labeled cups, quarts, or liters. Activity 14: Comparing a Quart to a Liter (GLEs 14, 17, 28) Materials List: quart of a sport drink, liter of water, 2 clear containers that are the same size, food coloring Show students a quart of a sport‟s drink and a liter of water. Ask students which container has more liquid in it. Add food coloring to the water. Find two clear containers that are exactly alike. Pour the sport‟s drink in a container. Then pour the water into the other container. Ask students if they can tell now which one has more liquid in it. They should be able to see that a liter is a little more than a quart. Grade 2 MathematicsUnit 7 Measurement in Our World 92 Louisiana Comprehensive Curriculum, Revised 2008 Use a Venn diagram - graphic organizer (view literacy strategy descriptions) to have students compare and contrast a quart and a liter. Draw the Venn diagram on the board, and have students copy and complete the diagram using the following terms: Metric System, Customary System, is the same as 4 cups, and measures liquids. Once completed, allow students to quiz each other over the information in the graphic organizer in preparation for quizzes and other class activity. Example: Which liquid measure is used in the metric quart system, a liter or a quart? liter Activity 15: Temperature (GLE: 15) Materials List: Celsius/Fahrenheit thermometers, glasses, water, ice cubes Discuss why it is important to know the temperature. Explain how to read a thermometer by reading the number where the mercury stops. Display a Celsius/Fahrenheit thermometer. Point out to students where the Fahrenheit scale is. Indicate that it is a system for measuring temperature in the standard or customary measurement system, and relate this to the fact that it is the same system as the system that uses feet and inches for length. Fill glasses of water at different temperatures. Have students place the thermometer in different glasses, reading the temperatures. Explain that temperature is measured in units called degrees and show the symbol. Ask: What do you notice about the numbers on the thermometers? Guide students on how to use the scale on the thermometer, if needed. What happens when the temperature is higher? Lower? Be sure to use hot water and ice water in this discovery activity. Put a thermometer outside the window to record changes in daily temperature for a week. Check and record the temperature outside at 8:00 A.M., 12:00 P.M., and 2:30 P.M. Help the students graph the results. Activity 16: Introduction to the Celsius Thermometer (GLEs: 15, 20, 28) Materials List: Celsius/Fahrenheit thermometer Explain to students that the metric system also has a thermometer. Remind students that the metric system uses centimeters instead of inches and liters instead of quarts. The metric thermometer is called a Celsius thermometer. Show students a Celsius thermometer, and tell them that 0 degrees is freezing and 100 degrees is the temperature at which water boils when using this type of thermometer. After demonstrations, show a large theremometer and highlight various points. Example: Point to 35° Celsius and ask Grade 2 MathematicsUnit 7 Measurement in Our World 93 Louisiana Comprehensive Curriculum, Revised 2008 the students if they think the temperature would be cold or warm; would 65° C be hotter or colder than 45° C? Activity 17: Calendars (GLEs: 17, 20) Materials List: calendar, Blank Calendar BLM, markers Ask, “What day is today? yesterday? tomorrow? What month is it? Last month? Next month?” Have each student stand as his/her birthday month is called, and record it on a chart or calendar for the school year. Point out that a calendar shows months, weeks, and days and that numbers on the calendar tell how many days in a month and the date of each day. Ask students questions to have them compare units to time. Example: Which is a longer time period: a day or a week? a month or a week? a month or a day? Look at the class calendar and find today‟s date. Ask: “What is the difference in the date and the day? How many Wednesdays this month? What is the date of the second Thursday? What was the first day of this month?” Distribute Blank Calendar BLM, and have students fill in the month, year, and dates, being sure they begin on the correct day of the week. Also, mark special dates (holidays, birthdays, coming events) on the calendar with words/pictures. They may decorate their calendars in any way they wish to depict the month or season. Play a riddle game as follows: One student gives a clue and the others guess the day or date (e.g., I am the last Friday of the month. What is my date?) Flip through a year-long calendar, naming and repeating the months in order. Learn the rhyme: 30 days hath September, April, June, and November; all the rest have 31, except February, which has 28 unless it is leap year and it has 29. Alternative: Make a fist with both hands with backs of hands facing you; then, with knuckles being mountains (31 days) and “between knuckles” being valleys (30 days); start naming months from your left hand to your right hand. (January is the first mountain, February is the first valley [only 28 days], March is the second mountain, and so on). Have students draw pictures for each month, attach a calendar, and use as gifts for Mother‟s Day, Christmas, or another holiday Activity 18: Perimeter (GLES: 14, 17) Materials List: rulers, objects to measure, paper, pencil, calculator, Perimeter BLM with items filled in prior to running off for students Discuss and explain that perimeter is the distance around the outside edge of a shape. Tell them to look for the word “rim” inside the word “perimeter” as a reminder that rim means edge, and perimeter is the measure of the outside edge of a shape. Ask students to name things in the classroom that would have a perimeter (e.g., windows, chalkboard, Grade 2 MathematicsUnit 7 Measurement in Our World 94 Louisiana Comprehensive Curriculum, Revised 2008 bookcases, doors). Challenge students to think of a way to measure the perimeter of the chalkboard, and have them try some of the ways suggested; discuss which units of measure work best. Have students come up and lay their rulers end-to end to find the length of the board. Assist students in finding the width of the board. Ask students if they need to measure all four sides. (No, because the chalkboard is a rectangle opposite sides must be the same length.) Label the chalkboard with the measurements, and have students find the perimeter. Set up stations with objects for which the students can find the perimeter (e.g., poster board, book, computer disc, index card, piece of construction paper). Put students into groups. Give each student a BLM with the items listed. Have them use a 12-inch ruler to find the perimeter of each object. Students should circulate among stations recording their findings. They may check their sums using a calculator. Discuss students‟ findings after all groups have circulated among all the stations. Activity 19: Cover Up (GLEs: 18, 28) Materials List: plain paper, pencil, popped popcorn, 1-inch grid paper, circular counter, color tiles, Cover Up BLM Use the Cover Up BLM to guide students through a DR-TA (view literacy strategy descriptions) to help them evaluate their predictions and estimations. DR-TA is an instructional approach that invites students to make predictions, and then check their predictions during and after the assignment. DR-TA (Directed Reading – Teaching Activity) provides a frame for self-monitoring because students should pause throughout the assignment to ask students questions. Allow students to adjust their estimations or predictions as they go through the activity. Hand out the Cover Up BLM. Have students answer questions 1 and 2. Next, have each student draw the outline of his/her hand on a piece of plain paper, and then cover the inside of the outline with popped popcorn. Ask: “How many pieces did you use?” Compare results. Have students record the actual number on their BLM. Students might conclude that they used different amounts due to the different sizes of the drawings. Now, have students draw a 4”x 6” rectangle on 1- inch grid paper. Have students answer questions 3 and 4. Next cover the rectangle with popcorn. Ask: Did everyone use the same number of pieces of popcorn? (No) Did you cover the rectangle completely? (No) Make the connection that this time the drawings were the same, but the amount of popcorn was still not the same. Have students answer questions 5 and 6. Next, try covering the rectangle with circular counters and ask the same questions. Have students answer questions 7 and 8. Last, cover the rectangle with square tiles. First, guess (estimate) the number of tiles you will need. Ask, “How many tiles did you use?” (24) How many tiles did the other students use? (24) Which unit covered the rectangle best? Explain: The number of square units needed to cover a shape is its area. The area is measured in square units. Have students answer question number 9 and discuss their answers. Grade 2 MathematicsUnit 7 Measurement in Our World 95 Louisiana Comprehensive Curriculum, Revised 2008 Activity 20: Cover This (GLEs: 14, 18) Materials List: index cards, construction paper, color tiles Have students estimate how many square inch tiles it will take to cover an index card and a sheet of construction paper. Record their estimates. Next, put students into groups and have them cover the index card with square tiles. Have students label the length and the width of the card (3 inches x 5 inches). Discuss students´ results. Ask if anyone would like to adjust his/her estimate for the piece of construction paper. Ask students to share different ways they could find the number of tiles it would take to cover the construction paper (i.e., cover the entire piece with tiles, divide the paper in half, cover 1 , and then 2 double the number of tiles; use the index card and trace it on the paper since we know it takes 15 tiles per index card). Have students find the area of the piece of construction paper. Discuss their results. Activity 21: Can you create this? (GLE: 14) Materials List: computer Using a computer program, create a template of a one-inch square. Teach students how to copy, paste, paint, and move the square. Have students create designs according to your specifications. Example: Create a design that has an area of 5 square units and a perimeter of 12 units. If a computer is not available, give students inch grid paper to complete the activity. Activity 22: Professors Know-it-All (GLEs: 14, 17) Materials List: measuring tools, objects to measure Put students into groups of 4. Each group will be called to the front of the room to see if the group can be labeled professors know-it-all (view literacy strategy descriptions). A member from another group chooses an object. One member of the group must describe what attribute of the object could be measured then another member chooses the tool that should be used to measure it. Another member of the group demonstrates how to measure it. Repeat the process until each group has had a turn. Use simple props such as ties, mortar boards, and clipboards to give the know-it-alls the look of “experts.” Grade 2 MathematicsUnit 7 Measurement in Our World 96 Louisiana Comprehensive Curriculum, Revised 2008 Sample Assessments Performance and other types of assessments can be used to ascertain student achievement. Following are some examples. General Assessments Portfolio: As the student encounters different units of measure, have him/her cut out pictures and glue them to index cards listing the different attributes that can be measured. For a picture of a truck, the student could list the length of the truck, the height of the truck, or the number of scoops of dirt the bed of the truck could hold. Journal Entry: The student will explain the difference between the perimeter and area of an object. Calendar: Have students make a calendar and put holiday stickers on the appropriate dates. The student will draw an outfit that he/she could wear during that month and answer a series of questions pertaining to the calendar. Activity-Specific Assessments Activity 2: Prepare a list of classroom objects for the student to measure. There should be two blanks following the name of each object. First, the student will estimate the length of the object in inches, centimeters, or feet, and then measure the objects and record the true measurement. Allow the student to explain his/her estimates and measurements. Activity 7: Observe each student‟s accuracy as he/she chooses an object which has the same weight as another object and tests the weights using a balance scale. Activity 8: Using a food scale, the student will select items he/she thinks weigh about 1 pound and measure to check. The student will sort the items into groups of “about the same as,” “more than,” and “less than” a pound. Activity 9: Observe each student weighing and recording the weight of a chosen fruit on the chart. The student will write 3 sentences comparing his/her fruit‟s weight with that of others. Example: My apple is heavier than the banana. My apple is lighter than the orange. Activity 18: Provide students with several outlined shapes. The student will measure the perimeter of each shape in inches and centimeters. Grade 2 MathematicsUnit 7 Measurement in Our World 97 Louisiana Comprehensive Curriculum, Revised 2008 Activity 20: The student will use 12 square tiles to form at least 6 different shapes. The student will trace the shapes and create a “Square Units Zoo” by elaborating on the shapes, and adding details and color. Save the pictures for a class mural or book. Grade 2 MathematicsUnit 7 Measurement in Our World 98 Louisiana Comprehensive Curriculum, Revised 2008 Grade 2 Mathematics Unit 8: Extending Number Patterns through 100s and 3-Digit Operations Time Frame: Approximately three weeks Unit Description This unit deals with extending the number system through 999, focusing on developing a deep understanding of 100s, 10s, and 1s in all of their representations. Extensions also include patterns and 3-digit problems without regrouping. Student Understandings Students demonstrate a command of place value and numeration concepts by providing representations of expanded, standard, written, and verbal forms of numbers. Students model numbers with concrete materials. Guiding Questions 1. Can students handle all representations of numbers through 999, including with objects? 2. Can students make reasonable estimates and perform rounding tasks? 3. Can students perform addition and subtraction with 3-digit numbers without regrouping? 4. Can students use number sentences to represent real-life problems involving addition and subtraction? Unit 8 Grade-Level Expectations (GLEs) GLE # GLE Text and Benchmarks Number and Number Relations 1. Model, read, and write place values for numbers through 999 in word, standard, and expanded form (N-1-E) 3. Make reasonable estimates of the number of objects in a collection with fewer than 100 objects (N-2-E) 5. Read, write, compare, and order whole numbers through 999 using words, number lines, and models (N-3-E) (N-1-E) 8. Recognize, select, connect, and use operations, operational words and symbols (+, ) for addition (join, part/part/whole) or subtraction (take away, comparison, missing addend, and set/subset) situations (N-6-E) (N-5-E) Grade 2 MathematicsUnit 8Extending Number Patterns/3-Digit Operations 99 Louisiana Comprehensive Curriculum, Revised 2008 9. Add and subtract 1- and 2-digit numbers (N-6-E) (N-7-E) 10. Round numbers to the nearest 10 or 100 and identify situations in which rounding is appropriate (N-7-E) (N-9-E) Algebra 12. Use number sentences to represent real-life problems involving addition and subtraction (A-1-E) (A-2-E) 13. Find the missing number in an equation involving addition or subtraction (e.g., # + 4 = 7, 8 - # = 3) (A-2-E) (N-4-E) Patterns, Relations, and Functions 30. Recognize, extend, create, and explain patterns of addition and subtraction as represented in charts and tables and in varied forms of skip-counting (P-1-E) (P-2-E) 32. Recognize and apply patterns in problem-solving in other content areas and real-life situations (P-3-E) (N-9-E) Sample Activities Activity 1: Body Math (GLEs: 1, 5) Materials List: sheets of paper labeled 1s, 10s, 100s, Base 10® blocks, Place Value Mat BLM, poster paper, 3 bean bags Have students brainstorm and make a list of 3-digit numbers used in school, at home, and in the neighborhood (house number, oven temperature, or page number in a book). Divide the class into two teams. Put three labels (1s, 10s, 100s) about a foot apart on the floor in front of the room. Write a 3-digit number on the board. Have students on the first team select Base 10® blocks that represent the number. If the number is 324, three students stand behind the 100s label holding flats, two stand behind the 10s label holding rods, and four stand behind the 1s label holding unit cubes. The second team checks their answer and then takes a turn modeling a different 3-digit number. Continue playing several more rounds. Put students in pairs. Use the Place Value Mat BLM and Base 10® blocks to model for the students forming 2- and 3-digit numbers. Write several numbers on the board, and have student partners model them on their BLM. Write 3 digits on the board, and have students use the blocks and place value mats to make as many 3-digit numbers as they can using those 3 digits. Record results and compare with other partners. Play a game such as the following: Put students into groups of 3 or 4 Divide a large piece of poster paper into 10 sections (squares) numbered 0–9. Label 3 different colored bean bags 1s, 10s, and 100s. Grade 2 MathematicsUnit 8Extending Number Patterns/3-Digit Operations 100 Louisiana Comprehensive Curriculum, Revised 2008 Have a volunteer toss each beanbag onto a number on the board. Have partners write the number and make a model with Base 10® blocks as quickly as possible. The first group to build and write their number in word, standard, and expanded form correctly wins. Activity 2: Build It! (GLEs: 1, 5) Materials List: Base 10® blocks, Place Value Mat BLM, paper, pencil Have students practice using the Base 10® blocks to build numbers according to specific instructions such as these: Use your mat and blocks to build a number that has more 100s blocks than 10s blocks. Build a number that has more 1 blocks than 100 blocks. Build a number that has the same number blocks in the 1s and 100s. Write some of the 3-digit numbers on the board and point out that the value of the number depends on its place. For example: a 3 in the 10s place has a value of 30 (3 10s) and a 3 in the 100s place has a value of 300 (3 100s). Continue building 3-digit numbers with Base 10® blocks and place value mat, writing the number on their paper and telling the value of each digit of the number. Then write the number in word and expanded form. Activity 3: Math Chains (GLEs: 1, 5, 8, 12) Materials List: Hundreds Chart BLM, transparency of BLM, calculators, paper and pencil Use the transparency to review how to move on a hundreds chart. Have students use the Hundreds Chart BLM to practice Mental Math Chains of addition by listening as a series of instructions are read. They may use a scrap piece of paper to write the final answer. For example: Start with 36, add 10, subtract 1, and add 20. What is the number? Start with 73, subtract 20, add 7, take away 50. What is the number? Put students into groups of 4. Have students compose their own Mental Math story chains (view literacy strategy descriptions) for others to solve using a hundreds chart. Each person in the group uses the hundreds chart to follow the clues as each person gives his/her clue. The first person in the group writes, Start with the number _________. The second person writes, add/subtract _________. The third person writes, add/subtract ___from the number. The fourth person writes, add/subtract ______ from the number. The first person writes, What number did you end up on? The group discusses the answer and writes the answer on a separate sheet of paper. The group then uses a calculator to check the answer. Groups exchange their math story chains with other groups and solve. Grade 2 MathematicsUnit 8Extending Number Patterns/3-Digit Operations 101 Louisiana Comprehensive Curriculum, Revised 2008 Activity 4: Play a Game: Make 100 (GLEs: 1, 5, 8, 9, 12) Materials List: paper, pencil, math learning log . Draw a large circle on the board, and place 2-digit numbers randomly inside it so that when 2 are added, they will equal 100. Be sure to include some pairs of numbers that will NOT equal 100 and also include three numbers inside the circle so students can discover using 3 numbers to add up to 100 (Example 30, 20, and 50). Students should work fast and can use numbers more than once. After two minutes, call time and compare answers. Play again to increase speed. Give students 5 minutes to write down as many 2-digit plus 2-digit numbers that have a sum of 100 in their math learning logs (view literacy strategy descriptions). Have students share their findings. Activity 5: Rounding to the Nearest Hundred (GLEs: 5, 10) Materials List: Place Value Spinner BLM, colored index cards, clothesline, clothespins, white index cards, markers, spinner, pencil, paper clip, 3-digit number cards with a digit underlined Write the numbers 0-1000 counting by 100s on colored index cards. Hang the numbers in order on a clothesline. Give each student an index card and have them write a 3-digit number on their card. Call on each student to come up and determine which hundred his/her number is closest to. Have them pin their number under the hundred it would round to. Continue until all students have had a turn. Put students into groups. Hand out the Place Value Spinner BLM. Have a member from the group choose a 3-digit number card. Another member from the group spins the spinner. The group must do whatever the spinner indicates. Example: Student 1 selects the number card with 453 written on the card. The second student spins expanded form on the spinner. The group gets together and writes out 400 + 50 + 3. The group has 30 seconds to agree, and then someone writes the answer on the board. If they are correct, they earn the title professor know-it-alls (view literacy strategy descriptions). Then another group is chosen. Play continues until all groups have had a turn. Use simple props such as ties, mortar boards, and clipboards to give the know-it-alls the look of “experts.” If time permits allow groups to challenge one another. Have each group write 4 challenging questions or statements, one for each of the 4 categories on the spinner (rounding, word form, expanded form, and place value). Grade 2 MathematicsUnit 8Extending Number Patterns/3-Digit Operations 102 Louisiana Comprehensive Curriculum, Revised 2008 Examples of challenge statements that students could write: Round it – Find a number that will round to 500. A member from the know-it-alls group says, “472.” Word Form – A member from the challenge group writes the word form of a number on the board. A member from the know-it-alls group must write the standard form. Place Value is spun – A member from the challenge group says, “Write a 3-digit number where the hundreds place value is 200.” A member from the know-it-alls group writes 269 on the board as an example. Expanded Form – A member from the challenge group writes a 3-digit number in expanded form on the board. A member from the know-it-alls group has to write the standard form of the number. Note: If place value is spun on the spinner, the group must identify the value of the underlined digit. Select two groups to come to the front of the room. Flip a coin to determine if a group wants to challenge a group or answer the questions of the other group. If the group answers all 4 challenges correctly then it gets to stay up in front of the room and another group may challenge it to see if it is really a group of professor know-it-alls. Play as long as time will permit. Do not use the spinner for this part of the activity. Groups challenge each other with their 4 questions. Activity 6: Round to the Nearest Dollar (GLEs: 5, 8, 10) Materials List: list of prices Before doing the activity, discuss with the students situations in which rounding is appropriate. Rounding may be used in situations such as deciding if they have enough money to buy something. For example: I am at the grocery store and I pick up three items priced as follows: $2.22, $.78, and $1.68. If I wanted to know about how much these items will cost, I could add all the prices with a paper and pencil; try to add them in my head; or I could estimate by rounding to the nearest dollar, like this: $2.00, $1.00, and $2.00. Now, I can easily figure that I will need about $5.00 to pay for my items. This is a good estimate of the exact amount of $4.68. Give students a list of prices and have them round to the nearest dollar. Then have students find the sum of the list mentally. Grade 2 MathematicsUnit 8Extending Number Patterns/3-Digit Operations 103 Louisiana Comprehensive Curriculum, Revised 2008 Activity 7: Finding Sums and Differences (GLEs: 5, 8, 10) Materials List: Base 10® blocks, 60 index cards Using Base 10® blocks, have a student model 10 + 20 and 100 + 200, as another student writes the appropriate addition sentences on the board. Repeat the process using subtraction problems such as 30–20 and 300–200. Explain that rounding makes addition and subtraction of 3-digit numbers easier. Example: Patrick has 236 baseball cards and 113 Pokemon cards. About how many cards does Patrick have in both of his collections? Tell students to add 236 and 113 by rounding each number to the nearest 100 and then add the numbers. Demonstrate: Round 236 to 200 and 113 to 100. Now, it‟s easy to add 200 and 100 mentally to get 300. So, Patrick has about 300 cards in his collections. Use a number line to move forward or back when rounding 10s and 100s. Play The Estimation Game as follows: Have two or three students write 2-digit numbers on 20 index cards each. Shuffle all the cards and place them face down in a deck. Turn the top card over next to the deck. Have the students take turns flipping over a card and estimating the sum of some or all the face-up cards, trying to find a combined estimated sum of 100. If correct, the student keeps the cards. If not correct, leave the card face up with other unused cards. The winner is the student with the most cards after all the cards are turned over. As students progress in skill, rewrite the cards with 3-digit numbers to find a combined estimated sum of 900. Activity 8: Money Problems (GLEs: 1, 8, 10, 12) Materials List: play money, Place Value Mat BLM, school supplies with prices marked (If students do not have access to grocery store circulars, ask other teachers/neighbors to save their papers.) Model adding/subtracting money (dollars and cents) to practice 3-digit problem solving. Use play money and Place Value BLM as well as the standard form with $ and the decimal to show addition and/or subtraction. Follow the same steps as with other 3-digit numbers (1s, 10s, 100s). For homework, assign students 5 grocery items, and have them find the prices from different stores‟ advertisements or by looking at prices at home. Have them bring their lists to school and compare prices with other students. If the prices are different, subtract to find how much difference, and decide which is the best deal. Review estimation of Grade 2 MathematicsUnit 8Extending Number Patterns/3-Digit Operations 104 Louisiana Comprehensive Curriculum, Revised 2008 sums and differences through rounding to the nearest 100 or dollar. Give extra attention to students who look at the 1s instead of 10s when rounding to the 100s place. Give small groups of students a list of school supplies with prices noted. For example: crayons–$1.98 ruler–$.49 glue–$.98 notebook–$3.95 pencils–$2.98 scissors–$2.00 Have students estimate the costs, and then list all the combinations of items that can be bought for $10.00 or less. Compare their answers with other groups. Activity 9: All Mixed Up! (GLEs: 8, 13) Materials List: 2 sets of digit cards per pair Use two sets of digit cards in small groups to solve a brainteaser like the following example. Write 423 650 479 on the board. Explain that the digits of the addends are mixed-up. Ask students to see if they can rearrange the cards to make the addition correct. Activity 10: Twenty-one (GLEs: 8, 13) Materials List: paper, pencil Let students play the game, Twenty-one. Using the digits 6, 7, 8, or 9, try to find all the ways to get 21 by subtracting 2-digit numbers. You may use each digit more than once in a problem (e.g., 99–78=21). See if you can find 6 different ways to find the difference of 21. Activity 11: Place Value Charts (GLEs: 30, 32) Materials List: Place Value Mat BLM, chart paper, marker Write three 3-digit numbers on the board, and have partners work together to model the numbers on the Place Value Mat BLM (e.g., 350, 322, 416). Ask: Which of these numbers is the greatest? (416). How do you know? (It has 4 in the 100s place and the others have 3 in the 100s place.) Ask: Which of these numbers is the least? (322). How Grade 2 MathematicsUnit 8Extending Number Patterns/3-Digit Operations 105 Louisiana Comprehensive Curriculum, Revised 2008 do you know? 350 and 322 both have three hundreds so I go to the next place value. 350 has more tens than 322, so 322 is the smaller number. Draw a table on a poster with 3-digit numbers listed in the center column (e.g., 158, 256, 783, 809, 540, 428) and a column to the left labeled 100 less and a column to the right labeled 100 more. Have volunteers fill in the table, writing the correct standard numbers. Have students look for patterns in the table. 100 less 3-digit number 100 more Activity 12: Estimate! (GLE: 3) Material List: poster, marker or stickers Show students a poster with 100 or fewer circles on it for about 30 seconds (just don‟t let them count the circles). Have students discuss how they could estimate how many circles are on the poster. Section off one part of the poster by drawing square or rectangle around a set of circles. Count how many circles are in that section. Use that section as a benchmark. Give students another brief look at the circles and allow them to adjust their estimates. Section off the rest of the poster with other squares or rectangles the same size as the benchmark and estimate the number of circles on the poster. Activity 13: Solve It! (GLE: 12) Materials List: paper, pencil, computer Put students into pairs. Have each student do a RAFT (view literacy strategy descriptions) writing assignment. Instruct students that they are to write a story problem that involves adding a 2-digit plus 2-digit number or 3-digit plus 3-digit number. R- pretend they are the author of a math textbook A – the audience for the textbook is second grade students F – write a word problem T – adding a 2- digit to a 2-digit number or a 3-digit to a 3-digit number should be task After students share their RAFTs with the class and their problem is checked for accuracy and logic, have students type their problem on the computer. They may insert graphics if they are available and then print their problems. After all problems are printed, copy them and make a textbook for all. Grade 2 MathematicsUnit 8Extending Number Patterns/3-Digit Operations 106 Louisiana Comprehensive Curriculum, Revised 2008 Sample Assessments Performance and other types of assessments can be used to ascertain student achievement. Following are some examples: General Assessments Give the student one representation of a number, and the student will give at least two other ways to represent the number. Example: Model a number, then the student will give the standard form, expanded form, or word form of that number. Observe as the student uses different problem-solving strategies such as guess and check, draw a picture, make a chart, or phone a friend to find the answers to math story problems. Provide the student with a chart or table with some patterns that use addition and subtraction of a constant (i.e., skip counting forwards and backwards) and have him/her “find” the patterns. Activity-Specific Assessments Activity 4: Place several 2-digit numbers that have a sum of 100 randomly inside of a rectangle. The student will find as many number pairs with a sum of 100 as he/she can. Activities 4 and 5: Give the student a list of items with their prices. The student will round each price to the nearest dollar. Next, the student will find how many items he/she could buy for $10.00. Activity 7: When given 10 addition/subtraction problems with 3-digit numbers by the teacher, the student will estimate by rounding to find the answer. The student should round to the nearest hundred. Activity 11: Observe as the student builds and identifies 3-digit numbers using Base 10® blocks. The students will write the number in word form and expanded form. When given a 3-digit number with values underlined, the student will identify the value of each underlined digit. Grade 2 MathematicsUnit 8Extending Number Patterns/3-Digit Operations 107