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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Comparison Situations and Tape Diagrams Tuesday September 11, 2012 Common Core Leadership in Mathematics (CCLM ^2) This material was developed for use by participants in the Common Core Leadership in Mathematics (CCLM^2) project through the University of Wisconsin-Milwaukee. Use by school district personnel to support learning of its teachers and staff is permitted provided appropriate acknowledgement of its source. Use by others is prohibited except by prior written permission.

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Learning Intentions & Success Criteria We are learning to… –Understand how to solve comparison problems and use tape (strip) diagrams to illustrate the solutions. We will be successful when…. –Clearly explain the difference between additive and multiplicative comparison situations. –Understand CCSSM expectations for compare situations in grades 1 & 2 and grades 3 &4. –.

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Addition Comparison Problem Situations

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. Revisiting 1.OA.1

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Four kindergarten problem subtypes Skilled by the end of Grade 1 Experience at Grade 1 and skilled by the end of Grade 2

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, A Comparison Word Problem Blakely has 9 plates and 5 cookies. If a whole cookie is put on each plate, how many more plates are there than cookies? Model this problem with cubes. Then draw a tape diagram to illustrate the solution.

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, As children move to Level 2 strategies, “they no longer need representations that show each quantity as a group of objects.” (OA Progressions, p. 16)

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Blakely has 9 plates and 5 cookies. If a whole cookie is put on each plate, how many plates won’t get a cookie? Concrete Use concrete objects to form two groups to compare quantities. Representational 5 cookies ? 9 plates 5 cookies ? 9 plates

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, The Packers played the Bears for the NFL Championship. The Packers scored 52 points. The Bears had 39 points. How many more points did the Packers score than the Bears? Use tape diagrams to show the relationship among the quantities in this compare situation.

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, A General Comparison Model for Addition and Subtraction larger quantity smaller quantity difference

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Multiplicative Comparison Problem Situations

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Standard 4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 equals 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Standard 4.OA.1 Read standard 4.OA.1 Divide your slate in half. On one side, rephrase this standard and on the other side, provide an example. Share with your partner.

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Multiplicative Comparison Problems Read the handout about Multiplicative Comparison Problems. Highlight as you read, noting ideas that you understand and those that still confuse you.

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Standard 4.OA.2 Cluster: Use the four operations with whole numbers to solve problem. 4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Standard 4.OA.2 Read standard 4.OA.2 Divide your slate in half. On one side, rephrase this standard and on the other side, provide an example. Share with your partner.

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Sense Making…. Share with your shoulder partner a few ideas that struck you as critical to developing a sound understanding of multiplicative comparison problems.

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Tape Diagram A drawing that looks like a segment of tape, used to illustrate number relationships. Also known as strip diagrams, bar model, fraction strip or length model. CCSSM Glossary p. 87

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Your Turn … Connie ran 50 meters. Melissa ran 200 meters. On your slate, write three problems using this information: Larger quantity unknown Smaller quantity unknown Compare quantity unknown

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, A Parking Lot Problem A fourth grade class counted the number of vehicles that went by the front entrance of the school between 9 o'clock and 10 o'clock. The total number of vehicles counted was156. There were 3 times as many passenger cars as trucks. How many passenger cars and how many trucks were counted? Use a tape diagram to illustrate and solve this problem.

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Farmer problem A farmer has 7 ducks. He has 5 times as many chickens as ducks. How many more chickens than ducks does he have? On your slate, draw a diagram to help you solve this problem. Record your thinking.

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Let’s Look at Some Student Problems Solve the problems (from Singapore Mathematics 3A) with your partner. How did the tape diagram help you think multiplicatively?

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, The Power of Strip Diagrams With the aid of simple strip diagrams, children can use straightforward reasoning to solve many challenging story problems conceptually. Beckmann 2004

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Reflecting on the Practices

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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Learning Intentions & Success Criteria We are learning to… –Understand how to solve comparison problems and use tape (strip) diagrams to illustrate the solutions. We will be successful when…. –Clearly explain the difference between additive and multiplicative comparison situations. –Understand CCSSM expectations for compare situations in grades 1 & 2 and grades 3 &4. –.

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