# Multiplicative Comparisons

Students will interpret a multiplication equation as a comparison and represent a verbal statement of a multiplicative comparison as a multiplication equation.

## Lesson Objective

The lesson is aligned to the Common Core State Standards for Mathematics – 4.OA.1 Operations and Algebraic Thinking - Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

## Materials Required

Calculator

## Interpreting a Multiplication Equation as a Comparison

**Part A**

Look at the multiplication equation below.

14 = 2 x 7

This multiplication equation compares the numbers 14, 2 and 7.

The symbol “=" means “is" and the symbol “x" means “times as many as."

The equation means 14 is 2 times as many as seven.

The equation can also mean 14 are 7 times as many as two.

**Part B**

Look at the multiplication equations below. Explain in words what each equation means. Write the two statements.

- 36 = 12 x 3
- 56 = 8 x 7
- 81 = 3 x 27
- 117 = 9 x 13
- 344 = 4 x 86

**Answers:**

- 36 is 12 times as many as 3 and 36 is 3 times as many as 12.
- 56 is 8 times as many as 7 and 56 is 7 times as many as 8.
- 81 is 3 times as many as 27 and 81 is 27 times as many as 3.
- 117 is 9 times as many as 13 and 117 is 13 times as many as 9.
- 344 is 4 times as many as 86 and 344 is 86 times as many as 4.

## Representing Verbal Statements of Multiplicative Comparisons as Multiplication Equations

**Part A**

Look at the verbal statement below.

18 is 2 times as many as 9

This verbal statement compares the numbers 18, 2 and 9.

The word “is" means equal. We use the symbol “=" to represent the word “is."

The words “times as many as" means multiply. We use the symbol “x" to represent the words “times as many as."

The verbal statement can be represented by the multiplication equation 18 = 2 x 9.

**Part B**

Look at the word statements below. Write the equation that represents each word statement.

- 48 is 4 times as many as 12
- 72 is 9 times as many as 8
- 90 is 5 times as many as 18
- 136 is 4 times as many as 34
- 520 is 8 times as many as 65

**Answers:**

- 48 = 4 x 12
- 72 = 9 x 8
- 90 = 5 x 18
- 136 = 4 x 34
- 520 = 8 x 65

## Individual or Group Work

**Part A**

Explain in words what each equation means. Write the two statements.

- 16 = 2 x 8
- 24 = 2 x 12
- 30 = 10 x 3
- 92 = 4 x 23
- 144 = 12 x 12

**Part B**

Write the equation that represents each word statement.

- 27 is 3 times as many as 9
- 48 is 6 times as many as 8
- 50 is 5 times as many as 10
- 64 is 8 times as many as 8
- 93 is 3 times as many as 31

**Answers:**

**Part A**

Explain in words what each equation means. Write the two statements.

- 16 is 2 times as many as 8 and 16 is 8 times as many as 2
- 24 is 2 times as many as 12 and 24 is 12 times as many as 2
- 30 is 10 times as many as 3 and 30 is 3 times as many as 10
- 92 is 4 times as many as 23 and 92 is 23 times as many as 4
- 144 is 12 times as many as 12 and 144 is 12 times as many as 12

**Part B**

Write the equation that represents each word statement.

- 27 = 3 x 9
- 48 = 6 x 8
- 50 = 5 x 10
- 64 = 8 x 8
- 93 = 3 x 31