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Multiplication as Scaling (Grade 5)

Videos 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.
Related Topics:
Common Core for Grade 5, More Lessons for Grade 5

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.

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&b [interpret multiplication as scaling (resizing)].

Scaling and Fractions
What happens when you multiply a whole number times an improper fractions? 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.


Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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