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Solving Word Problems using TAPE DIAGRAMS CMC South October 25 TH, 2014 Presented by Tracey Dunn traceyd@ers.tcoe.org

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GOALS Explore the visual representation of tape diagrams as a tool to solve word problems and support student learning. Rate yourself from 1 to 5 on how familiar you are with tape diagrams and using them with students?

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WHAT IS A TAPE DIAGRAM? CCSS Glossary: Tape Diagram: A drawing that looks like a segment of tape, used to illustrate number relationships. Also known as a strip diagram, bar model, fraction strip, or length model. 15 25

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WORD PROBLEMS Read the problem. Write an answer sentence. What are we trying to find? A total? A part? Are we comparing? Draw a sketch representing the problem. Use your diagram to solve the problem. Check the answer.

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Commoncoretools.me

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2.OA.1 Represent and solve problems involving addition and subtraction Use addition and subtraction within 100 to solve one- and two- step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 6

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http://commoncoretools.files.wordpress.com/2011/05/ccss_progression_cc_oa_k5_2011_05_302.pdf Addition and Subtraction Problem Types K-5 Progression on Counting and Cardinality and Operations and Algebraic Thinking

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ADDITION AND SUBTRACTION PROBLEM TYPES 9 boys and 8 girls were in the class. How many total children were in the class? 17 children were in the class. 9 were boys and the rest were girls. How many girls were in the class ? 17 children were in the class. There were some boys and 8 girls. How many boys were in the class? 98 17 BoysGirls

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COMPARISON: ADDITION/SUBTRACTION Ali had $9. Maria had $5. How many more dollars did Ali have than Maria? Ali had $9. Maria had $5. How many fewer dollars did Maria have than Ali? 9 Al i 5 Maria 4

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A Pencil and a Sticker 2.OA.1 A pencil costs 59 cents, and a sticker costs 20 cents less. How much do a pencil and a sticker cost together? 10 www.illustrativemathematics.org

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Multiplication and Division Problem Types http://www.cde.ca.gov/be/st/ss/documents/ccssmathstandardaug2013.pdf

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3.OA.3 Represent and solve problems involving multiplication and division Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 13

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Gifts from Grandma 3.OA.3 Juanita spent $9 on each of her 6 grandchildren at the fair. How much money did she spend? Nita bought some games for her grandchildren for $8 each. If she spent a total of $48, how many games did Nita buy? Helen spent an equal amount of money on each of her 7 grandchildren at the fair. If she spent a total of $42, how much did each grandchild get? 14 www.illustrativemathematics.org

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Two Interpretations of Division Maria cuts 12 feet of ribbon into 3 equal pieces so she can share it with her two sisters. How long is each piece? Maria has 12 feet of ribbon and wants to wrap some gifts. Each gift needs 3 feet of ribbon. How many gifts can she wrap using the ribbon? 15 www.illustrativemathematics.org

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4.OA.2 Use the four operations with whole numbers to solve problems. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. 16

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Multiplication Carla has 4 packages of silly bands. Each package has 8 silly bands in it. Agustin is supposed to get 15 fewer silly bands than Carla. How many silly bands should Agustin get? 17 http://commoncoretools.files.wordpress.com/2011/05/ccss_progression_cc_oa_k5_2011_05_302.p df

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Comparing Money Raised– 4.OA.2 a. Helen raised $12 for the food bank last year and she raised 6 times as much money this year. How much money did she raise this year? 18 www.illustrativemathematics.org

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Comparing Money Raised– 4.OA.2 Sandra raised $15 for the PTA and Nita raised $45. How many times as much money did Nita raise as compared to Sandra? 19 www.illustrativemathematics.org

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Comparing Money Raised– 4.OA.2 a. Sandra raised $15 for the PTA and Nita raised $45. How many times as much money did Nita raise as compared to Sandra? 20 www.illustrativemathematics.org

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Comparing Money Raised– 4.OA.2 Luis raised $45 for the animal shelter, which was 3 times as much money as Anthony raised. How much money did Anthony raised? 21 www.illustrativemathematics.org

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Comparing Money Raised– 4.OA.2 Luis raised $45 for the animal shelter, which was 3 times as much money as Anthony raised. How much money did Anthony raised? 22 www.illustrativemathematics.org

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Two-Step Problems 23 http://commoncoretools.files.wordpress.com/2011/05/ccss_progression_cc_oa_k5_2011_05_302.p df CC & OA Progression Page 28 CC & OA Progression Page 28

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Multiplicative Comparison A big penguin will eat 3 times as much fish as a small penguin. The big penguin will eat 420 grams of fish. All together, how much will the two penguins eat? 24 http://commoncoretools.files.wordpress.com/2011/05/ccss_progression_cc_oa_k5_2011_05_302.pdf

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Multiplicative Comparison 25 CC & OA Progression Page 29 CC & OA Progression Page 29 http://commoncoretools.files.wordpress.com/2011/05/ccss_progression_cc_oa_k5_2011_05_302.pdf

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http://www.mathplayground.com/t hinkingblocks.html

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Multiplicative Comparison Model There are four groups of students in a hall. There are twice as many boys as girls in each group. a. In Group A, there are 12 girls. How many boys are there in Group A? b. In Group B, there are 12 boys. How many students are there in Group B? c. In Group C, there are 12 students. How many girls are there in Group C? d. In Group D, there are 12 more boys than girls. How many students are there in group D? 28

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PLANS How do you plan to use tape diagrams with your students? What are your next steps with tape diagrams?

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Progressions http://ime.math.arizona.edu/progressions/

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www.illustrativemathematics.org

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Resources Common Core Connect http://commoncore.tcoe.org http://commoncore.tcoe.org Tracey Dunn traceyd@ers.tcoe.org 33

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Questions 45907

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