# 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 5

Students have seen the relationship between addition and subtraction using single-digit numbers and have worked on two-digit numbers. This lesson is to reinforce the previous lesson. My hope is that students will make a connection as if to say, “Didn’t we do this same problem yesterday.” But my feeling is that practice makes perfect, the more students are exposed to word problems, the better their understanding will be. Students will also feel more confident and comfortable because they are familiar with the problems.

Discuss how these problems differ from the previous lessons. Discuss how the problems relate to each other. Discuss two-digit fact families. This lesson focuses on regrouping in addition and subtraction.

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

14 brown baskets are on the truck. 26 red baskets are on the same truck. How many baskets are there?
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Problem 2
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14 brown baskets and 26 red baskets are on the truck. How many more red baskets are there than brown baskets? (Technically, the answer to this question is not in the same fact-family as the other problems in this lesson.)

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Problem 3
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There are 40 red and brown baskets. If 26 are red baskets, how many are brown baskets?

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Problem 4
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A total of 40 red and brown baskets are on the truck. If there are 14 brown baskets, how many red baskets are there?

In discussing these problems, I would begin by asking how the problems are alike and how they are different. Now that we have been working on word problems, I expect students to use mathematical terms. When comparing and contrasting these problems, I hope students would say that there is only one addition problem (Problem 1). Problem 2, 3, and 4 are subtraction problems with regrouping. Most importantly, this is a fact family because all of the problems use the numbers 14, 26, and 40.

In the previous lesson, we discussed a sequence of problems that cross the regrouping divide. During this lesson, teachers may want to revisit that set of problems or a similar set of problems. By working on and examining these sets of problems, students will see where they do not need to regroup and where they do need to regroup. Students may even be able to follow the pattern to find the solutions.

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