5.NF.5 Interpret multiplication as scaling

• Interpret multiplication as scaling (resizing), by:

• 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.

• 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

Without performing multiplication determine whether the product is <, >, or = to 6.

Explain your reasoning.

2 4

x 6 3 6

x 6 3 4

x 624 2

x 6

By comparing the sizes of the products for each circle, what pattern do you observe when you multiply a fraction by ?

5th

¼

¼

⅛⅛

⅛⅛

1 2

x 2 2

2 4

= 2 4

x 2 2

4 8

= 4 8

2 2

5.NF.5 Mathematical Practice(s): 2

Without performing the indicated multiplication, use < , >, or = to make each equation true by comparing the size of the product to the size of one factor on the basis of the size of the other factor.

7 3

461 x

3 3

461 x

2 3

461 x

3 3

461 x

5.NF.5 Mathematical Practice(s): 2

Without performing the indicated multiplication, use < , >, or = to make each equation true.

7 7

643 x

2 2

643 x

1 2

461 x

4 8

643 x

5.NF.5 Mathematical Practice(s): 2

Are the statements below True or False about the product of 372 and ¼ ?

The product is less than 272 x ¼

The product is greater than 272 x ¼

The product is less than 372

The product is greater than 372

5.NF.5 Mathematical Practice(s): 2

Are the statements below True or False about the product of 485 and ?

The product is less than 485 x

The product is greater than 485 x

The product is less than 485

The product is greater than 485

6 3

2 3

8 3

5.NF.5 Mathematical Practice(s): 2

Write Yes or No to indicate whether each fraction can make the equation a true inequality

2 3

10 4

× >2 3

4 4 4

10

5.NF.5 Mathematical Practice(s): 2

Write Yes or No to indicate whether each fraction can make the equation a true inequality

5 6

10 14

× >5 6

8 814

10

5.NF.5 Mathematical Practice(s): 2

Move each equation to the correct box

Less Than ⅗ Equal to ⅗ Greater Than ⅗

3 5

x 1 2

3 5

x 8 3

3 5

x 4 5

3 5

X 5 3 5

x 5 5

3 5

x 1 10