# 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 2

Focus on four basic problems that relate. Discuss the problems. Give students the opportunity to use manipulatives and draw pictures to solve the problems. 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
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2 children are playing. 9 more children come to play. How many children are playing in all?

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Problem 2
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2 children were playing and some more children came. Then there were 11 children all together. How many children came?

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Problem 3
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Some children were playing and 9 more children came to join them. Then there were 11 children all together. How many children were there at the start?

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Problem 4
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11 children are playing. 2 children go home. How many are still playing?

Again, I would discuss Problem 3 with the students. Have you ever seen a problem like this? How is this problem different from the other two problems? Carpenter and authors refer to this problem as “initial unknown.” In the book,
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Children’s
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Mathematics
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, they discuss the fact that children seem to have the most trouble with these types of problems because of the “unknown.” Some children would think ___+ 9=11 while others would subtract to get the answer, 11-9=2. Both strategies, they say come naturally to children. Children do not have to be taught that a particular strategy goes with a particular type of problem. In
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Children’s Mathematics
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, the authors focused on students using manipulatives (counters or blocks) to solve a word problem. Lastly, the authors state that in an environment that encourages children to use procedures that are meaningful to them, they will construct these strategies for themselves.

The teacher should discuss how these problems are the same? Students should see that they are using the same numbers and are the same fact family. This is a great time to compare these problems, how are they different? Students should see that the problems are worded differently. They may also comment on different operations, for some problems addition is used while others use subtraction.

It is important to give students the opportunity to communicate. Students should have the opportunity to lead the discussion. They may want to show students how they solved a particular problem and explain why they did what they did. Students will learn terms and vocabulary from one another. Most importantly, students will learn different strategies from other students. For example, one student may show the class how he or she drew a picture to solve a word problem. So students will see the different methods that can be used to solve word problems.

Posing problems of all types based on the same fact family will help teachers understand how well students grasp when subtraction is called for. It will also help students understand that better, give them practice with calculation, and reinforce the idea of fact families.
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