**Lesson Objective:** The lesson is aligned to the Common Core State Standards for Mathematics –

**3.OA.4 Operations and Algebraic Thinking:** Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

**Materials Required:** arrays, blocks, books, triangles

## Lesson Procedure

Begin the lesson by working through some examples and walking students through the logical process they would use to solve the problems.

**Example 1:** Solve for the unknown in the equation **3 x ? = 12.**

Have students think of the three numbers that relate. Encourage them to recognize that 3, 4, and 12 relate because 3 x 4 = 12. Discuss the 4 number sentences that relate to 3, 4, and 12:

- 3 x 4 = 12
- 4 x 3 = 12
- 12 / 3 = 4
- 12 / 4 = 3

**Example 2:** Solve for the unknown in the equation **? x 5 = 15.**

Have students think of the three numbers that relate. Encourage them to recognize that 3, 5, and 15 relate because 3 x 5 = 15. Discuss the 4 number sentences that relate to 3, 5, and 15:

- 3 x 5 = 15
- 5 x 3 = 15
- 15 / 5 = 3
- 15 / 3 = 5

**Example 3:** Solve for the unknown in the equation **8 / ? = 4.**

Have students think of the three numbers that relate. Encourage them to recognize that 2, 4, and 8 relate because 2 x 4 = 8. Discuss the 4 number sentences that relate to 2, 4, and 8:

- 2 x 4 = 8
- 4 x 2 = 8
- 8 / 2 = 4
- 8 / 4 = 2

**Example 4:** Solve for the unknown in the equation **35 / ? = 5.**

Have students think of the three numbers that relate. Encourage them to recognize that 5, 7, and 35 relate because 5 x 7 = 35. Discuss the 4 number sentences that relate to 5, 7, and 35:

- 5 x 7 = 35
- 7 x 5 = 35
- 35 / 5 = 7
- 35 / 7 = 5

## Individual or Group Work

Find the unknown number that makes the equation true in each of the following equations.

1. 7 x 8 = ?

2. 4 x ? = 24

3. 32 / ? = 4

4. ? / 10 = 7

5. ? x 3 = 33

6. 2 x 5 = ?

7. 3 x ? = 18

8. ? x 4 = 28

9. ? / 3 = 3

10. 20 / 5 = ?

**Answers:**

1. 56

2. 6

3. 8

4. 70

5. 11

6. 10

7. 6

8. 7

9. 9

10. 4

**Goal:** Students should be able to demonstrate the ability to solve for an unknown in multiplication and division equations by recognizing the three related numbers.

## This post is part of the series: Introducing Multiplication and Division in 3rd Grade Math

- Teaching the Basic Facts of Multiplication
- Basic Facts of Division: 3rd Grade Math Lesson
- Solving Multiplication and Division Word Problems
- Solving for Unknown Quantities: 3rd Grade Math Lesson
- 3rd Grade Math Assessment on Multiplication and Division