Lesson 22Objective: Compare the size of the product to the size of the

factors

By the end of the lesson, I will be able to…

5th Grade Module 4– Lesson 22K. Clauson

Find the Unit Conversion

3 ¼ gal = _____ qt 3 ¼ gal = 3 ¼ x 1 gallon

How many quarts are in one gallon?

Write an equivalent multiplication sentence using an improper fraction and quarts.

Solve and show.

Find the Unit Conversion

More Practice!

2 2/3 yd = _____ ft 5 ½ pt = _____ c

2 5/6 ft = _____ yd ½ c = _____pt

??

??

??

??

Multiply Fractions by Whole Numbers

½ x 10 =

1/3 x 12 =

12 x 1/3 =

15 x 1/5 =

1/5 x 15 =

½ x 6 =

2/2 x 6 =

3/2 x 6 =

8 x 1/4 =

8 x 4/4 =

8 x 5/5 =

5

4

4

3

3

3

6

9

2

8

8

Group Count by Multiples of 100

Count by tens to 100

How many tens are in 100?

Count by twenties to 100

How many twenties are in 100?

20 x 5 = 100

5 x ____ = 100 How many fives are in 100?

Application ProblemTo 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 it is, as well as the money amount in decimal form. What should Isabella tell her father?

Show your calculations.

Problem 1 Find the products of these

expressions 4/4 x 12 inches =

3/4 x 12 inches =

5/4 x 12 inches =

Concept Development

Let’s compare the size of the products you found to the size of this factor. (12 inches)

Did multiplying 12 inches by 4 fourths change the length of this string? Why or why not?

12 inches

The product is equal to 12 inches. We multiplied and got 48 fourths, but that’s just another name for 12 using a different unit. It’s 4 fourths of the string, all of it.

Problem 1b 3/4 x 12 inches = 9 inches

Did multiplying by 3 fourths change the size of our other factor, 12 inches? If so, how?

¾ x 12 < 12

I hear you saying that 12 inches was shortened, resized to 9 inches. How can it be that multiplying made 12 smaller when I thought multiplication always made numbers get bigger?

The string became shorter because we only took 3 of 4 parts of it. We got almost all of 12 inches, but not quite. We wanted 3 fourths of it rather than 4 fourths, so the factor became smaller after we multiplied. We got 9 inches this time instead of 12 inches.

Problem 1c 5/4 x 12 inches = 15 inches

How did multiplying by 5 fourths change or not change the size of the other factor, 12? How would it change the length of the string?

5/4 x 12 > 12

15 is 5 fourths as much as 12. True or False?

15 is 1 and ¼ times as much as 12. True or False?

The answer to this one was greater than 12 inches because it’s more than 4 fourths of it.

The product was greater than 12 inches. 5 fourths of the string would be 1 fourth longer than the string is now.

Scaling Factor We compared our products to one factor, 12

inches, in each of the expressions.

We explained the changes we saw by thinking about the other factor.

A scaling factor can change the size of the other factor.

Problem 2Find the products of these

expressions 4/4 x 1/3 =

3/4 x 1/3 =

5/4 x 1/3 =

Let’s compare the size of the products you found to this factor. (1/3)

What is the product of the first one? Did the size of 1/3 change when we multiplied it by a scaling factor equal to 1?

1/3

3/12 = 1/4

5/12

Let’s compare the size of the products you found to this factor. (1/3)

What is the product of the second one? Is the scaling factor more or less than 1? What happened to the size of 1/3 when we multiplied it by a scaling factor less than 1?

Let’s compare the size of the products you found to this factor. (1/3)

What is the product of the third one? Is the scaling factor more or less than 1? Is 5/12 more than, less than, or equal to 1/3?

Problem 3 I am going to show you some multiplication

expressions where we start with ½. The expressions will have different scaling factors.

Think about what will happen to the size of 1 half when it is multiplied by the scaling factor. Tell whether the product will be equal to ½, more than ½, or less than ½.

Problem 3

1 x 52 51 x 32 5

1 x 92 5

1 x 22 3

1 x 12 2

1 x 42 31 x 82 8

Problem 4At 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 most? The least?

Get Ready to Finish theProblem Set on Your Own!

We will complete the A problems together.

Complete Problem Set for Lesson 22.

You will have 10 minutes to work!

------------------------------------------------------------------------------------

Fast finishers:

- Math Center Activities- choice boards, extra Sprint challenge

- CML packets/ worksheets

- Problem Solving pages

5th Grade Module 4– Lesson 22

K. Clauson

5th Grade Module 4- Lesson 22K. Clauson

LET’S DEBRIEF

• Take 2 minutes to check your answers with your partner.

• Let’s share any insights you had while solving these problems.

5th Grade Module 4– Lesson 22

K. Clauson

EXITTICKETLESSON 22