Lesson for Middle School
Multiplication
as Scaling
Scaling Superpower!
Multiplying Fractions and Whole
Numbers
Lesson Outline
Multiplication for Scaling
Introduction
Multiplication can make the number bigger or smaller.
Let's explore together how it works!
Multiplying Numbers
When we multiply a number by a whole number, the value of the number gets larger.
When we multiply a number by a fraction,
the value of the number gets smaller.
After multiplying the apples by 2,
the number of apples becomes 4.
After getting one-half of the apple,
the number of apples becomes 1.
2
2 x 2
2
2 x
1
2
7
4
4
7
A fraction less than 1
has a numerator less
than the denominator.
Let’s Review
A fraction greater than 1
has a numerator greater
than the denominator.
3
2
4 x
= 6
Multiplying 4 by means having 3 groups of 4. Then, getting half of it.
3
2
Multiplying by a Fraction greater than 1
4
Multiplying by a Fraction greater than 1
4
We can see that from 4, it increases to 6.
6
When we multiply a number by a fraction greater than 1, the number increases.
Multiplying by a Fraction less than 1
Multiplying 4 by means having 3 groups of 4. Then, getting the fourth of it.
3
4
3
4
4 x
= 3
4
Multiplying by a Fraction less than 1
4
We can see that from 4, it decreases to 3.
When we multiply a number by a number less than 1, the number decreases.
3
5
4
3
8
9
10
2
5
Which fractions, when multiplied from 10, will result in a higher number?
Which one will result
in a lower number?
Summary
In multiplying a number by a fraction,
if the fraction is greater than 1, the value
will increase.
if the fraction is less
than 1, the value
will decrease.
Aside from visual models, what are
other ways to show the change
in values when a number is multiplied
by a fraction greater than or less than 1?
Assignment
Mathspace. “8.02 Multiplication as scaling | Grade 5 Math | Common Core 5 - 2022 Edition.” Accessed 10 June 2023,https://mathspace.co/textbooks/syllabuses/Syllabus-
1091/topics/Topic-21216/subtopics/Subtopic-274739/?searchString=
Mathspace. “8.03 Fractions of a quantity | Grade 5 Math | Common Core 5 - 2022 Edition.” Accessed 10 June 2023, https://mathspace.co/textbooks/syllabuses/Syllabus-
1091/topics/Topic-21216/subtopics/Subtopic-274740/?searchString=
Mathspace. “8.04 Multiples of unit fractions| Grade 5 Math | Common Core 5 - 2022 Edition.” Accessed 10 June 2023, https://mathspace.co/textbooks/syllabuses/Syllabus-
1091/topics/Topic-21216/subtopics/Subtopic-274741/?searchString=
Mathspace. “8.05 Multiply fractions by whole numbers | Grade 5 Math | Common Core 5 - 2022 Edition.” Accessed 10 June 2023, https://mathspace.co/textbooks/syllabuses/Syllabus-
1091/topics/Topic-21216/subtopics/Subtopic-274742/?searchString=
References
Scaling Superpower!
Poster Making Activity
Design a poster illustrating how multiplying
a number by a fraction greater than 1 or
less than 1 affects the product's value.
Instructions:
Introduce scaling through multiplication.
Multiplying Fraction and Whole Numbers
Whiteboard Activity
What happens when we multiply a number by a fraction greater than 1?
Place equations here.
Write a short explanation related to the illustration.
Include a footer for references, legends, and other footnotes.
What happens when we multiply a number by a fraction less than 1?
Place equations here.
Write a short explanation related to the illustration.
Include a footer for references, legends, and other footnotes.
Step 1
Locate on the number line.
2
3
2
3
4 x
MARK THE
WHOLE NUMBERS
0
1
How many equal parts should 1 unit be divided into?
Let's explore the multiplication of fractions and whole numbers.
Find the product of the given values using the number line.
Step 2
Locate 4 x on the number line.
2
3
USE THE ARROWS TO EMPHASIZE THE NUMBER OF JUMPS
0
1
2
3
4 x
=
?
?
Let’s Recap:
Elaborate on what you want to discuss
Thank You!
Elaborate on what you want to discuss
Elaborate on what you want to discuss
Resource Page
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