# The Craft of Word Problems

## CONTENTS OF CURRICULUM UNIT 04.05.02

- Purpose of Unit
- Introduction and Rationale
- New Haven Public Schools Mathematics Standards
- Unit Objectives
- Whole Class Interaction
- Discussion
- Guided Practice
- Independent Practice
- Lesson Plan Timeline
- Bibliography for Teachers
- Student Resources
- Materials for Classroom Use
- Appendix A
- Appendix B
- Appendix C
- Appendix D
- Appendix E
- Appendix F
- Appendix G
- Appendix H
- Appendix I
- Notes

### Unit Guide

## Developing Word Problems: A Student’s Task

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## Appendix H

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STEP CHART (example)
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A: Word problem
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Madeline and Pat were comparing their doll collection. Madeline has 3 less than Pat. Madeline has 2 dolls. How many dolls does Pat have?

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B: Inverse Word problem
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Madeline and Pat were comparing their doll collection. Madeline has 3 less than Pat. Pat has 5 dolls. How many dolls does Madeline have?

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First Step: Identify the givens and the question
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A:
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Givens:

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Madeline has 3 less than Pat- -
Madeline has 2 dolls

Question:

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How many dolls does Pat have?

B:

Givens:

- -
Madeline has 3 less than Pat- -
Pat has 5 dolls

Question:

- -
How many dolls does Madeline have

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Second Step: Identify the operation(s) needed to find the answer and then solve
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A:

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Operation identified
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Addition

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Equation written and solved
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2 + 3 = 5 dolls
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Pat has 5 dolls.

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B:
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Operation identified
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Subtraction

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Equation written and solved
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5 - 3 = 2
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Madeline has 2 dolls.

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Third Step: Identify the connection between both problems and reasoning.

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The connection between the problems is explained.
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Addition is the opposite of subtraction. If 2 + 3 = 5, then 5 - 2 must equal 3, and 5 - 3 must equal 2.

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The reasoning behind the method and solution is given.
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A: It is stated that Madeline has 2 dolls but also has 3 less than Pat. If Madeline has 3 less, then Pat then must have 3 more than Madeline. Since Pat has 3 more than Madeline, 3 must be added to the 2 dolls Madeline has to come up with Pat’s total of 5.

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B:
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It is stated that Pat has 5 dolls and that Madeline has 3 less than Pat. Since Madeline has 3 less than the given number of 5 that Pat has, 3 must be subtracted from 5 to total Madeline’s 2 dolls.