Comparison Situations and Tape Diagrams

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013

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.


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.– .


Addition Comparison Problem Situations


1.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


Four kindergarten problem subtypes

Skilled by the end of Grade 1

Experience at Grade 1 and skilled by the end of Grade 2


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.


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)


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


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.


A General Comparison Model for Addition and Subtraction

larger quantity

smaller quantity difference


Multiplicative Comparison Problem Situations


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.


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.


Multiplicative Comparison ProblemsRead the handout aboutMultiplicative Comparison Problems.

•Highlight as you read, noting ideas that you understand and those that still confuse you.


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.


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.


Sense Making….

Share with your shoulder partner a few ideas that struck you as critical to developing a sound understanding of multiplicative comparison problems.


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


Your Turn …

Connie ran 50 meters.Melissa ran 200 meters.

On your slate, write three problems using this information:

Larger quantity unknownSmaller quantity unknownCompare quantity unknown


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.


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.


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?


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


Reflecting on the Practices


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.– .

Documents

Comparison Situations and Tape Diagrams