 # Multiplication as Scaling (Grade 5)

Related Topics:
Lesson Plans and Worksheets for Grade 5
Lesson Plans and Worksheets for all Grades

Videos, examples, solutions, and lessons to help Grade 5 students learn to interpret multiplication as scaling (resizing), by:

A. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

B. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

Common Core: 5.NF.5

### Suggested Learning Targets

• I can think of multiplication as the scaling of a number
• I can predict the size of the product based on the size of the factors.
For example: fraction × fraction = smaller fraction, fraction × whole number = smaller number, whole number × mixed number = larger than the original whole number.
When we multiply by a fraction equivalent to 1, the value is unchanged. For example: 4/4 × 5 is equal to 5.
When we multiply by a fraction less than 1, the value becomes smaller. For example: 3/4 × 5 is less than 5.
When we multiply by a fraction greater than 1, the value becomes bigger.
For example: 1 2/3 × 5 is greater than 5.

Activities:
Circle the greater value. DO NOT calculate to find your answer. Choose 1 item and explain how you know which value is greater.
a) 66  or  2/3 × 66
b) 2 1/3 × 23 or 1/3 × 23
c) 2/3  × 3/9  or  3/9
d) 1/6 × 7  or  7
e) 8 1/2 × 2 or  1/2  ×  8

Multiplication as scaling Estimating When Multiplying Fractions
5.NF.5.a and b - How to interpret multiplication as scaling or resizing?

Scaling and Fractions
What happens when you multiply a whole number and an improper fractions?
What happens when you multiply a whole number and a regular fraction? Interpreting Fraction Multiplication as Scaling
In this lesson, you will learn how multiplying by a fraction greater than or less than 1 creates a product that can be compared to the factors in size.

1. The Ling family has 4 boxes of cereal. They ate 3/4 of all the cereal during the week.
a. Write an expression for 3/4 of 4 boxes of cereal.
b. Will the product be equal to, less than or greater than 4?

2. The Carter family has only 1/2 of a box of cereal at the beginning of the week. They ate 3/4 of the 1/2 box of cereal.
a. Write an expression to show 3/4 of 1/2 box of cereal.
b. Will the product be equal to, greater than, or less than 1/2? than 3/4?

3. Lola is making cookies. She plans to multiply the recipe by 3 so that she can make enough cookies for the whole class. If the recipe calls for 2/3 cup of sugar, will she need more than 2/3 or less than 2/3 cup of sugar to make all the cookies?
a. Write a multiplication expression to show this problem.
b. Draw a model to show this problem.

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