# 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 A

A.1. Tony and I were comparing our baseball card collections. I have 5 less than Tony. I have 19. How many cards does Tony have?

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A.2. Tony and I were comparing our baseball card collections. I have 5 less than Tony. Tony has 24. How many cards do I have?

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First Step: Identify the givens and the question
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A.1.

Givens:

Question:

- - I have 5 cards less than Tony
- - I have 19 cards

- - How many cards does Tony have?

A.2.

Givens:

Question:

- - I have 5 cards less than Tony
- - Tony has 24 cards

- - How many cards do I have?

Second Step: Problem Analysis

A.1.

Addition must be done in this problem. It states that I have 5 less than Tony, so Tony must have 5 more than me. Since I have 19 and Tony has 5 more, then addition should be used.

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A.2.

The problem states that I have 5 cards less than Tony and that Tony has 24. If I have 5 less then 5 should be subtracted from 24 to find my total number of cards.

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Third Step: Identify the operation(s) needed to find the answer and then solve
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A.1.

Addition

19 + 5 = 24 cards

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A.2.

Subtraction

24 - 5 = 19 cards
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Fourth Step: Identify the connection between both problems and reasoning.

It first can be seen that the problems are connected because they utilize the same numbers within both equations. The equations use inverse operations to solve, addition and subtraction. It can be seen that when 5 cards are taken from 24 cards there are 19 cards left and when those 5 cards are added back to the 19 cards, then there are 24 cards once again. Simply translated, the problem shows that if I have 5 cards less than Tony, then Tony has 5 cards more than I do, so to find the number of Tony’s cards I would add 5 to my cards. Thus the solution is 5 + 19.

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