# 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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## Lesson Plan Timeline

Since the focal point of the unit is the student generation of word problems, there is an expectation that the students will have a somewhat firm grasp of basic facts and operations. Multiplication and division are not introduced until the second half of the year, so the unit should fall after those operations have been taught. It is also to be hoped that before the unit is started, that the students have some exposure to the idea of inverse relationships in mathematical operations. To allow enough time for students to achieve mastery of the inverse concept, it should be introduced in the beginning of the year and practiced (or discussed) until the unit begins.

Lesson #1

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Exploration of word problems and modeling of discussion
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The word problems are read together (teacher and students) but not with the intention to solve. They are read with the intention to explore and discuss the methods and strategies that could be used to solve. The teacher and the students can share their ideas about how to go about identifying which operations are necessary to arrive at the answer and any other issues that may arise.

Lesson #2

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Introduction of the Step Chart and identifying the givens
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The teacher introduces and models the use of the Step Chart in Appendix I to the students. Students are also encouraged to engage in conversations about how to identify the given information in the word problems, as well as comparing and contrasting the two inverse problems.

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Lesson #3

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Guided practice solving problems and discussion
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Students are taken step by step through the solving of the word problems (several problems of each type or set should be considered before going on to the next step). Discussions about how problems are solved and the relationship between inverse operations are encouraged, especially those led by students.

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Lesson #4

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Composition of equations and inverse equations
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After students are comfortable with the language of word problems and the steps in which to solve them, they will then take the step of writing the equations (and inverse equations). The equations that they compose will be used in their word problems. They must write them starting with a one-step equation with the basic operation of addition or subtraction. After that the equations must get progressively more difficult, utilizing multiplication and division, as well as multiple steps.

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Lesson #5

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Composition of word problems
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Students will now integrate their original equations into carefully worded problems. Since they are the creators and in essence, the teachers of their own problems, they must write their problems in the Step Chart. The Step Chart will allow the students to think about their choice of words and digits, making sure the problems they compose are coherent and can be solved.

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Lesson #6

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Solving problems of peers
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When the students are finished composing their own problems, they will be able to trade with their peers. Having another person look at and attempt to solve the problems will make the student authors accountable for what they compose. It is a good assessment tool for the students to discover if they have written a quality word problem that is challenging but also clear and concise.