# 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 4

Now that students have seen the relationship between addition and subtraction using single-digit numbers, move to two-digit numbers. Discuss how these problems differ from the previous lessons. Discuss how the problems relate to each other. Discuss two-digit fact families. Focus 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
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18 apple trees are in a field. 42 peach trees are in the same field. How many trees are there altogether

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Problem 2
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18 apple trees are in the field. 42 peach trees are in the field. How many more peach trees are there than apple trees? ? (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

There are 60 trees in the field. If 18 of them are apple trees, how many are peach trees?

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Problem 4
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Altogether there are 60 trees in a field. If 42 of them are peach trees, how many are apple trees?

These problems are more complex because students are asked to regroup. In Problem 1, students are adding the two numbers. In that problem students must regroup. In Problem 2, the students are subtracting the two numbers. In this problem students do need to regroup. Teacher should ask how these two problems are the same and how are they different? Students should explain that they use the same numbers but in one problem there is addition and in other problem there is subtraction. Most importantly, in Problem 1 and Problem 2 students must regroup.

In Problems 3 and 4, students are subtracting with regrouping. This may be a good time to introduce a sequence of problems that cross the regrouping divide. Some problems involve regrouping and some do not. An example of these problems is as follows: 69-34, 70-34, 71-34, and 72-34. I would also do problems like this for addition, for example, 34+45, 34+46, 34+47, and 34+48. Teachers may wish to discuss these problems as is or discuss them as word problems. If you choose to discuss them as word problems you may wish to extend the lesson period or revisit this at the beginning of the next lesson. It is important to note that the subtraction problem requires regrouping exactly when the associated addition problem does. In giving these problems, students may need to do each one from scratch while others may see how to modify the answer to get another.