 # Scaling Factor

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Common Core For Grade 5

Videos, examples, solutions, and lessons to help Grade 5 students learn how to compare the size of the product to the size of the factors.

New York State Common Core Math Module 4, Grade 5, Lesson 22, Lesson 23

Common Core Standards: 5.NF.5, 5.NF.6

Lesson 22 Application Problem

In order to test her math skills, Isabella’s father told her he would give her 6/8 of a dollar if she could tell him how much money that is and what that amount is in decimal form.

What should Isabella tell her father? Show your calculations.

Lesson 22 Concept Development

Problem 1
a. 4/4 × 12 inches
b. 3/4 × 12 inches
c. 5/4 × 12 inches

Problem 2
a. 4/4 × 1/3
b. 3/4 × 1/3
c. 5/4 × 1/3

Problem 3
a. 1/2 × 5/5
b. 1/2 × 3/5
c. 1/2 × 9/5
d. 1/2 × 2/3
e. 1/2 × 1/2
f. 1/2 × 4/3
g. 1/2 × 8/8

Problem 4
At the book fair, Vlad spends all of his money on new books. Pamela spends 2/3 as much as Vlad. Eli spends 4/3 as much as Vlad. Who spent the most? The least?

Lesson 22 Problem Set

1. Solve for the unknown. Rewrite each phrase as a multiplication sentence. Circle the scaling factor and put a box around the number of meters.
a. 1/2 as long as 8 meters = ______ meters
b. 8 times as long as 1/2 meter = _______ meters

2. Draw a tape diagram to model each situation in Problem 1, and describe what happened to the number of meters when it was multiplied by the scaling factor.

3. Fill in the blank with a numerator or denominator to make the number sentence true.

4. Look at the inequalities in each box. Choose a single fraction to write in all three blanks that would make all three number sentences true. Explain how you know.

5. Johnny says multiplication always makes numbers bigger. Explain to Johnny why this isnӴ true. Give more than one example to help him understand.

6. A company uses a sketch to plan an advertisement on the side of a building. The lettering on the sketch is 3/4 in tall. In the actual advertisement, the letters must be 34 times as tall. How tall will the letters be on the building?

7. Jason is drawing the floor plan of his bedroom. He is drawing everything with dimensions that are 1/12 of the actual size. His bed measures 6 ft by 3 ft, and the room measures 14 ft by 16 ft. What are the dimensions of his bed and room in his drawing? Lesson 22 Homework

This video shows how to judge products when multiplying by values greater than, less than, and equal to one whole.

1. Solve for the unknown. Rewrite each phrase as a multiplication sentence. Circle the scaling factor and put a box around the number of meters.
a. 1/3 as long as 6 meters = ______ meters

4. Look at the inequalities in each box. Choose a single fraction to write in all three blanks that would make all three number sentences true. Explain how you know.
a. 2/3 × _____ > 2/3
4 × _____ > 4
5/2 × ____ > 5/2

b. a. 2/3 × _____ < 2/3
4 × _____ < 4
5/2 × ____ < 5/2 Lesson 22 Homework

7. In blueprints, an architectӳ firm drew everything 1/24 of the actual size. The windows will actually measure 4 ft by 6 ft and doors measure 12 ft by 8 ft. What are the dimensions of the windows and the doors in the drawing?

Lesson 22 Concept Development

Problem 1
Find the products of these expressions.

a. 4/4 × 12 inches
b. 3/4 × 12 inches
c. 5/4 × 12 inches

Lesson 22 Homework

1. Solve for the unknown. Rewrite each phrase as a multiplication sentence. Circle the scaling factor and put a box around the number of meters.

1/3 as long as 6 meters = ______ meters

Lesson 23 Concept Development

19.4 × 0.96
19.4 × 1.04
19.4 × 1.00

Lesson 23 Homework

1. Sort the following expressions by rewriting them in the table.
The product is less than the boxed number:
The product is greater than the boxed number:

Lesson 23 Problem Set

1. Fill in the blank using one of the following scaling factors to make each number sentence true.
a. 3.4 × _______ = 3.4
b. _______ × 0.21 > 0.21
c. 8.04 × _______ < 8.04

2. a. Sort the following expressions by rewriting them in the table.
b. Explain your sorting by writing a sentence that tells what the expressions in each column of the table have in common.

3. Write a statement using one of the following phrases to compare the value of the expressions.
Then explain how you know.
a. 4 × 0.988 _____________ 4
b. 1.05 × 0.8 ______________0.8
c. 1,725 × 0.013 ____________ 1,725
d. 989.001 × 1.003 ___________ 1.003
e. 0.002 × 0.911 ____________ 0.002

4. During science class, Teo, Carson, and Dhakir measure the length of their bean sprouts. Carsonӳ sprout is 0.9 times the length of Teo's, and Dhakir's is 1.08 times the length of Teo's. Whose bean sprout is the longest? The shortest? Explain your reasoning.

5. Complete the following statements, then use decimals to give an example of each.
a × b > a will always be true when b is...
a × b < a will always be true when b is... Lesson 23 Homework

This video shows how to compare products and its factors using scaling factors in relation to one whole.

1. Sort the following expressions by rewriting them in the table.
The product is less than the boxed number:
The product is greater than the boxed number:

2. Write a statement using one of the following phrases to compare the value of the expressions. Then explain how you know.

is slightly more than, is a lot more than, is slightly less than, is a lot less than

a. 14 × 0.999 _______________________________ 14
b. 1.01 × 2.06 _______________________________ 2.06

3. Rachel is 1.5 times as heavy as her cousin, Kayla. Another cousin, Jonathan, weighs 1.25 times as much as Kayla. List the cousins, from lightest to heaviest, and explain your thinking. Lesson 23 Homework

4. Circle your choice.
a. a × b > a
For this statement to be true, b must be greater than 1 or less than 1 Write two expressions that support your answer. Be sure to include one decimal example.
b. a × b < a
For this statement to be true, b must be greater than 1 or less than 1 Write two expressions that support your answer. Be sure to include one decimal example.

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