Lesson 5 Introduction Multiply Whole Numbers...Lesson 5 Multiplying Whole Numbers Lesson 5 M ultipl hol umbers Solve the problems. 1rs. Cady constructs a cube with 512 magnetic blocks.

Introduction

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Use What You Know

Lesson 5 Multiply Whole Numbers

Lesson 5Multiply Whole Numbers

The area model above shows the length and width of each space.

a. What is the total length of the outdoor space?

What is the total width?

b. How is the area of each space found?

c. How can you find the total area?

d. The product of 127 and 46 is the total area of the outdoor area. How can you find the

area for grass?

How can you find the area for the sidewalk?

e. What is the total area?

A mall is designing an outdoor space. The available space is 127 feet by 46 feet. The plan is for a grassy section with a width of 40 feet. Next to the grass will be a cement sidewalk with a width of 6 feet. What is the area of the available space in square feet?

100 feet

40 feet

6 feet

46 feet

20 feet 7 feet

127 feet

? ? ?

??4,000 square feet

In grade 4, you multiplied two-digit numbers by two-digit numbers. Now you’ll multiply three-digit numbers by two-digit numbers. Take a look at this problem.

not to scale

5.NBT.B.5

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One way to multiply multi-digit numbers is to find partial products. Break apart one of the factors into parts. Then multiply each of the parts by the other factor to get parts of the product, or partial products. Then, add the partial products to find the total product.

• One way to show using partial products to find 127 3 46:

Break apart 46 into (40 + 6): 127 3 46 5 127 3 (40 1 6)

Find each partial product.

127 3 40

5,080

127 3 6

762

partial products

Then find the sum of the two partial products.

5,080 1 762 5 5,842

• Another way to show using partial products to find 127 3 46:

127 3 46

762 1 5,080

5,842

area for sidewalk area for grass

total area

Reflect1 How is multiplying by a three-digit number similar to multiplying by a

two-digit number?

Modeled and Guided Instruction

Learn About


Lesson 5

Multiplying Three-Digit Numbers


Read the problem below. Then explore different ways to multiply a three-digit number by a two-digit number.

There are 128 pens in a full box. How many pens are in 35 full boxes?

Model It Use an area model to show partial products.

Sketch a rectangle with dimensions 128 by 35.

128 3 35

128 is 100 1 20 1 8.

35 is 30 1 5.

30 3 100 5 3,000 30 3 20 5 600 30 3 8 5 240

100 20 8

5 3 100 5 500

30

1

1 1

5 5 3 20 5 100 5 3 8 5 40

First row: 3,000 1 600 1 240 5 3,840

Second row: 500 1 100 1 40 5 640

So, 128 3 35 5 3,840 1 640 5 4,480.

Model It Use the distributive property to find partial products and add them.

128 3 35 5 128 3 (30 1 5)

128 3 (30 1 5) 5 (128 3 30) 1 (128 3 5)

128 3 30

240 600

1 3,000

3,840

(30 3 8) (30 3 20) (30 3 100)

128 3 5

40 100

1 500

640

(5 3 8) (5 3 20) (5 3 100)

3,840 1 640 5 4,480

©Curriculum Associates, LLC Copying is not permitted. 37Lesson 5 Multiply Whole Numbers

Connect It Now you will compare the two ways to multiply using partial products.

2 Why is the area model divided into six sections?

3 How do the three partial products in each multiplication equation in the second

Model It relate to the three sections in each row of the area model?

4 Would the product change if 30 and 5 on the left side of the area model were

changed to 20, 10, and 5? Explain.

5 List two different ways you could break up the factors in 239 3 64 to find the

product. Explain why both ways would have the same product.

Try It Use what you just learned about multiplying numbers to solve this problem. Show your work on a separate sheet of paper.

6 A bookshelf at a library holds 156 books. There are 15 bookshelves in the children’s section. How many children’s books can the library place on the bookshelves?

Guided Practice

Practice


Lesson 5

Multiplying Whole Numbers

Example


Pair/ShareHow are the regrouped ones and tens used to find the partial products?

Pair/ShareShow and explain howto solve this problemusing a differentmethod.

7 A certain dishwasher uses 29 kilowatts of energy per hour. If the dishwasher was used 156 hours last year, how many kilowatts of energy did the dishwasher use last year?

Show your work.

Solution

There are 366 days in a leap year and 24 hours in a day. How many hours are in a leap year?

Look at how you could show your work.

366 3 241,464

1 7,3208,784

21

21

Solution

Study the example below. Then solve problems 7–9.

8,784 hours

Why does the product of 366 and 2 tens have a 0 in the ones place?

What is the role of place value when multiplying two numbers?


Pair/ShareDoes Jared’s answer make sense?

Pair/ShareWhy is multiplication used to solve this problem? What other operation is used?

8 If 1 stamp costs 45 cents, what does a roll of 125 stamps cost in cents? What is this amount in dollars and cents?

Show your work.

Solution

9 Raquel can type 63 words every minute. Rick can type 73 words every minute. How many more words can Rick type than Raquel in 135 minutes? Circle the letter of the correct answer.

A 1,350

B 4,599

C 8,505

D 9,855

Jared chose B as the correct answer. How did he get that answer?

How could I first estimate the answer to this problem?

How can I use the difference in the number of words typed by Rick and Raquel every minute to solve this problem?

Independent Practice

Practice


Lesson 5

Multiplying Whole Numbers


Solve the problems.

1 Mrs. Cady constructs a cube with 512 magnetic blocks. Students in her two classes will each make an identical cube. There are 28 students in one class and 25 students in the other class. How many blocks does she need for all her students?

A 5,120

B 12,800

C 14,336

D 27,136

2 What are the values of the regrouped amounts in the multiplication below?

435 3 173,045

1 4,3507,395

2 3

A 2 and 3

B 20 and 3

C 200 and 30

D 2,000 and 300

3 Choose Yes or No to tell whether the expression is equivalent to 179 3 44.

a. 179 3 (4 1 4) Yes No

b. (179 3 40) 1 (179 3 4) Yes No

c. (100 3 4) 1 (70 3 4) 1 (9 3 4) Yes No

d. 4,000 1 2,800 1 360 1 400 1 280 1 36 Yes No

e. (100 3 44) 1 (70 3 44) 1 (9 3 44) Yes No

Self Check


Go back and see what you can check off on the Self Check on page 1.

4 Show two different ways to complete the multiplication problem.

3 1 4

3 5

1 6

3 1 4

3 5

1 6

5 At the start of the day there are 78 boxes of DVDs in a warehouse. Each box has 116 DVDs. Then 19 of the boxes are shipped. Now how many DVDs are left in the warehouse?

Show your work.

Answer DVDs

6 Use the distributive property two different ways to find the product of 127 and 32.

Show your work.

Lesson 5 Introduction Multiply Whole Numbers...Lesson 5 Multiplying Whole Numbers Lesson 5 M ultipl hol umbers Solve the problems. 1rs. Cady constructs a cube with 512 magnetic blocks.

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