# The Craft of Word Problems

## CONTENTS OF CURRICULUM UNIT 04.05.01

- Narrative
- Place Value
- Addition and Subtraction (within 10)
- Fact Families
- Addition and Subtraction (within 20)
- Addition and Subtraction with and without regrouping
- Strategies for solving problems
- Lesson 1
- Lesson 2
- Lesson 3
- Lesson 4
- Lesson 5
- Lesson 6
- In the Future
- Mathematics Standards
- Bibliography for Teachers and Students

### Unit Guide

## The Relationship between Addition and Subtraction in Problem Solving

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## Lesson 1

Focus on four basic problems that relate. Discuss the problems. Students should be given manipulatives to solve the problems (counters, blocks, etc.). Discuss how these problems are the same and how they are different.

Objectives

To have students use the four basic strategies to solve a set of word problems.

To have students communicate using mathematical terms and vocabulary.

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Problem 1

6 students are reading in the library. 3 more students come along. How many students are reading in the library?

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Problem 2
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9 students were reading in the library. 3 students go home. How many students are still reading?

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Problem 3
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Some students are reading and 6 more students came. Then there were 9 students all together. How many students were reading at the start?

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Problem 4
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3 students were reading, and some more students joined them. Then there were 9 students reading. How many students were in the group that came?

In this set of problems, I arranged them so that the operations alternate, addition then subtraction. Is there a pattern that you notice? Then I would ask the students how these problems are the same? I hope that they would notice that these problems use the same numbers, therefore are the same fact family. Finally, I would ask, “How are these problems different?” It seems that students find it easier to detect the differences. Some of the differences are the operation that is used (addition or subtraction) and the wording of the problems.

I would spend more time discussing Problem 3. This problem seems to give students more trouble than Problems 1, 2, and 4. Carpenter and authors discuss this type of problem in their book,
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Children’s Mathematics
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. They classify subtraction problems into several groups. The groups are as follows:

Take away

Part-part-whole, second part unknown

Part-part-whole, initial unknown

Comparison

Carpenter and authors would classify Problem 3 as part-part-whole, initial unknown. They describe these problems as difficult to children because of that “unknown.” Therefore, I think it is important to discuss this problem with the students. How is this problem different from the others? How would you solve it? Some students may solve this by subtracting, while others may write an addition problem to try to find the “unknown.”