PACKET - Whole Number Multiplication & Division

Name _______________________________ HR ______

Test Date __________________________

Whole number

multiplication

&

division

UNIT 3

RECALL PRIOR KNOWLEDGE

Find 5 x 3.

Recall how many there are in 5 groups of 3. 5 x 3 = 5 groups of 3

= 3 + 3 + 3 + 3 + 3

= 15

Find 12 ÷ 4

Recall how many groups of 4 are in 12.

12 — 4 = 8 means taking away a group of 4 to leave 8. 8 — 4 = 4 means taking away a group of 4 to leave 4.

4 — 4 = 0 means taking away another group of 4 to leave 0. There are 3 groups of 4 in 12.

So, 12 ÷ 4 = 3.

Find 7 x 6 by skip counting. So, 7 x 6 = 42.

Find 400 x 8 using related multiplication facts. 4 x 8 = 32

40 x 8 = 320 400 x 8 = 3,200

Multiplication is like repeated addition

Division is like repeated subtraction

Find 232 x 3.

Step 1

Multiply the ones by 3. 2 ones x 3 = 6 ones

2 x 3 = 6 Multiplying without regrouping

Step 2

Multiply the tens by 3. 3 tens x 3 = 9 tens

2 x 3 = 6 30 x 3 = 90

Step 3

Multiply the hundreds by 3. 2 hundreds x 3 = 6 hundreds 2 x 3 = 6 30 x 3 = 90 200 x 3 = 600

Find 125 x 7. Step 1

Multiply the ones by 7. 5 ones x 7 = 35 ones

Regroup the ones. 35 ones = 3 tens and 5 ones Step 2

Multiply the tens by 7.

Add the tens. 14 tens + 3 tens = 17 tens Regroup the tens. 17 tens = 1 hundred 7 tens Step 3

Multiply the hundreds by 7. 1 hundred x 7 = 7 hundreds

Add the hundreds. 7 hundreds + 1 hundred = 8 hundreds So, 125 x 7 = 875

Find 43 ÷ 5.

43 ones ÷ 5 = 8 ones with remainder 3 ones = 8 R3

Quotient = 8 ones = 8

Multiplying with regrouping in hundreds, tens, and ones

Dividing with remainders

5 43

- 40 5 x 8 3

Quick check

▶_{Multiply using repeated addition.}

4 x 8 = 4 groups of

= + + + = 6 x 9 = 6 groups of

= + + + + + =

▶_{Divide using repeated subtraction.}

15 ÷ 5 =

15 — — — = 0 32 ÷ 8 =

32 — — — — = 0

▶_Multiply.

6 x 6 = 9 x 4 =

7 x 100 = 320 x 3 =

215 x 3 = 187 x 5 =

▶_Divide.

17 ÷ 3 = 35 ÷ 2 =

86 ÷ 2 = 96 ÷ 4 =

56 ÷ 4 = 72 ÷ 3 =

lesson 3.1 - multiplying by a 1-digit number

Lesson Objective:

• Use different methods to multiply up to 4-digit numbers by 1-digit numbers, with or without regrouping.

☞YOU CAN REPRESENT MULTIPLICATION THE FOLLOWING WAYS☜

Repeated Addition: 213 x 4 = 213 + 213 + 213 + 213

Multiply the Value of the Digits:

Area Model:

200 + 10 + 3

4

800 + 40 + 12 = 852

213 X 4

(1)

(2)

(3)

guided learning

▶_{Multiply using the repeated addition strategy.}

63 x 2 + =

735 x 3 + + =

1,534 x 2 + =

▶_{PROBLEM SOLVE: Use the repeated addition strategy to solve.}

There are 156 science books in Mr. K’s classroom. Mrs. Pompei has 4 times as many books as Mr. K. How many books are in Mrs.Pompei’s classroom?

▶_{Complete the missing values in the rectangular array.}

The rectangular array shows x 3.

x = ones x 3 + tens x +

hundreds x + thousands x (1)

(2)

(3)

multiplication -

_{Standard Algorithm}

Roy’s Market sold 2,476 oranges. Ana’s Market sold 3 times as many oranges as Roy’s Market. How many oranges did Ana’s Market sell?

Step 1: Multiply the ones by 3. 6 ones x 3 = 18 ones = 1 ten 8 ones

Step 2: Multiply the tens by 3. 7 tens x 3 = 21 tens Add the tens.

21 tens + 1 ten = 22 tens = 2 hundreds 2 tens

Step 3: Multiply the hundreds by 3. 4 hundreds x 3 = 12 hundreds Add the hundreds.

12 hundreds + 2 hundreds = 14 hundreds

= 1 thousand 4 hundreds

1 2, 4 7 6

x 3

8

1

2, 4 7 6 x 3

2 8

2 1

2, 4 7 6 x 3

4 2 8

Step 4: Multiply the thousands by 3. 42 thousands x 3 = 6 thousands Add the thousands.

6 thousands + 1 thousand

1 2 1

2, 4 7 6

guided learning

▶_{Find the missing numbers in each step.}

The next month, Roy’s Market sold 6,139 oranges. Ana’s Market sold 9 times as many oranges as Roy’s Market.How many oranges did Ana’s Market sell?

6,139 x 9 = ? Step 1:

9 ones x 9 = 81 ones

= tens ones Step 2:

3 tens x 9 = 27 tens Add the tens.

tens + tens = tens

= hundreds tens

Step 3:

1 hundred x 9 = 9 hundreds Add the hundreds.

hundreds + hundreds = hundreds

= thousand hundreds Step 4:

6 thousands x 9 = 9 thousands Add the thousands.

▶_{Multiply. Use place-value charts to help you.}

☞

Look at Multiplication Another Way

☜

(1) (2) (3)

(5) (4)

4 x 5

70 x 5

600 x 5

multiplication

-

▶_{Multiply using the standard algorithm.}

294

3

436

8

6 x 8

30 x 8

400 x 8

4 x 3

90 x 3

200 x 3

+

+

x

x

283

5

826

7

6 x 7

20 x 7

800 x 7

3 x 5

80 x 5

200 x 5

+

x

+

x

4 8 1

x 9

(5)

3, 9 6 2

x 7

MATH JOURNAL

EXAMPLE:

Look at the steps for multiplying a 3-digit umber.

Multiply the ones by 7. 5 ones x 7 = 35 ones. Regroup the ones.

35 ones = 3 tens 5 ones. Multiply the tens by 7. 1 ten x 7 = 7 tens. Add the tens.

7 tens + 3 tens = 10 tens Regroup the tens.

10 tens = 1 hundred. Multiply the hundreds by 7.

2 hundreds x 7 = 14 hundreds. Add the hundreds.

14 hundreds + 1 hundred = 15 hundreds. Regroup the hundreds.

15 hundreds = 1 thousand 5 hundreds

The product is 1,505.

What are the steps to find the product of 6,875 and 3? READING & WRITING MATH

(1)

(2)

2 1 5

x 7

1, 5 0 5

3 1

let’s explore

Three students completed these multiplication problems. Find the errors.

Discuss with your classmates some common errors that students make in multiplication.

▶_{Multiply and find the missing numbers.}

7 ones x 4 = ones

= tens ones

8 tens x 5 = tens

= hundreds tens

6 hundreds x 3 = hundreds

= thousand hundreds

9 thousands x 2 = thousands

= ten thousands thousands WORKING TOGETHER

(1) (2) (3)

Let’s Practice

(1)

(2)

(3)

▶_Multiply.

8 x 3 = 80 x 3 = 800 x 3 = 8,000 x 3 =

▶_Multiply.

(8) (6) (5)

(7)

(16) (15)

(10) (11)

(14) (13)

lesson 3.2 - Multiplying by a 2-digit number

Lesson Objectives:

• Multiply by 2-digit numbers, with or without regrouping. • Estimate products.

Kevin packs 4 bags of apples. Each bag contains 10 apples. How many apples does Kevin pack altogether?

4 x 10 = ?

Rafael buys 3 packages of crayons. Each package contains 20 crayons. How many crayons does Rafael buy?

VOCABULARY

• round • estimate

• product

Multiply by tens.

4 x 10 = 4 x 1 ten = 4 tens = 40

Kevin packs 40 apples altogether.

guided learning

▶_{Find the missing numbers.}

14 x 10 = x ten = tens =

7 x 30 = x tens = tens = 9 x 40 = 9 x tens = tens =

58 x 60 = x tens = tens = 47 x 80 = x tens = tens =

Find the product of 24 and 300.

Method 1

24 x 300 = 24 x 3 x 100 = 72 x 100 = 7,200

Method 2

24 x 300 = 24 x 100 x 3 = 2,400 x 3 = 7,200

(1)

(2) (3) (4)

(5)

guided learning

▶_{Find the missing numbers.}

43 x 50 = 43 x x 5 = x 5 =

216 x 30 = 216 x x 10 = x 10 = 37 x 200 = 37 x x 100 = x 100 = 75 x 800 = 75 x x 8 = x 8 =

▶_Multiply.

32 x 10 = 93 x 30 = 41 x 500 =

SKILL BUILDER VIDEO: https://www.youtube.com/watch?v=-q-9Zf3cFik&feature=youtu.be

Create an area model and use partial products to find the product. Look at the area model below.

Can you figure out what two factors are being multiplied?

If you said 24 x 6, you are correct.

a. First, expand the multi-digit number.

b. Multiply 6 x 20 and place the partial product in the first box. c. Multiply 6 x 4 and place the partial product in the second box. d. Finally, add up the two partial products.

Therefore, 24 x 6 = 164. (1)

(2) (3) (4)

(5)

Multiply using an area model.

practice -

▶_{Use the area model strategy to find the products.}

8 x 573 = ________

6 x 945 = ________

4 x 273 = ________

+

500

70

+

3

8

+

900

40

+

5

6

(1)

(2)

(3)

+

200

70

+

3

4

+

Add the Partial Products.

+

guided learning -

▶_{Use the area model strategy to find the products.}

Florham Park Gardens has 27 barrels filled with rainwater. Each barrel contains 32 liters of water. What is the total amount of water in the barrels?

☞

Step - By - Step

☜

Use your knowledge of multiplying multiples of 10 & 100 to find each partial product.

Add the 4 partial products.


Therefore, 27 x 32 =

+

20 7

30

2

+

20 x 30 7 x 30

20 x 2 7 x 2

Add all the sub products.

(1) (2)

(3)

▶_{Use the area model strategy to find the products.}

54 x 73 = ________

92 x 64 = ________

50 4

70

3

+

50 x 70 4 x 70

3 x 50 3 x 4

Add all the sub products.

+

90 2

60

4

+

90 x 60 2 x 60

4 x 90 4 x 2

Add all the sub products.

+

+

(1)

(1)

INDEPENDENT PRACTICE -

▶_{Write the multiplication sentence for each area model. Then multiply.}

_____ x _____ = _______

_____ x _____ = _______

Add all the sub products.

+

Add all the sub products.

+

(1)

estimate products

Estimate 23 x 59.

23 is closer to 20 than to 30. 59 is closer to 60 than to 50.

20 x 60 = 1,200

23 x 59 is about 1,200.

▶_{Estimate the product of 38 x 715.}

x =

Use a number line to estimate products.

38 is closer to

practice

▶_{Use the area model method to multiply. Then estimate to check that your answers}

are reasonable. Round each number to its greatest place value.

68 x 94 = Estimate: x =

489 x 27 = Estimate: x = (1)

+

x x

x x

Add all the sub products.

+

+

(2)

+

x

Add all the sub products.

+

+

x x

x x

x

▶_{Use scrap paper to find the product by using the method of multiplying by tens}

and hundreds.

86 x 40 = 60 x 59 =

47 x 500 = 300 x 94 =

▶_{Use the communicator or scrap paper to make an area model when finding the}

product.

25 x 75 = 89 x 46 =

705 x 36 = 915 x 18 =

▶_{Use the number line to estimate the product.}

47 x 53

47 is closer to than to . 53 is closer to than to .

x = .

47 x 53 is about . LET’S PRACTICE

(1)

(4) (3)

(2)

(5)

(8) (7)

(6)

▶_{Estimate the product.}

Round each number to its greatest place value.

76 x 249 is about x 33 x 84 is about x

= =

23 x 415 is about x 33 x 278 is about x

= =

52 x 536 is about x 139 x 75 is about x = =

462 x 53 is about x =

▶_{Multiply. Use the communicator or scrap paper to make an area model when}

finding the product. Then estimate to check that your answers are reasonable. Round each number to its greatest place value.

64 x 92 = 71 x 839 =

Estimate: Estimate:

389 x 64 = 24 x 73 =

Estimate: Estimate:

(10) (11)

(12) (13)

(14) (15)

(16)

(20) (19)

Lesson 3.3 - whole number division

▶_VOCABULARY

dividend: ______________________________________________________ ___________________________________________________________________

divisor: ________________________________________________________ ___________________________________________________________________

quotient: _______________________________________________________ ___________________________________________________________________

remainder: _____________________________________________________ ___________________________________________________________________

☞

What do these terms look like?

☜

dividend ÷ divisor = quotient

←

4

←

divisor

→

3

)

12

(1)

(2)

(3)

(4)

what does division look like?

When dividing, you are breaking a larger group into smaller groups. You can represent division by making arrays with disks. Let’s see how it’s done!

The division equation is:

20 ÷ 4 = 5

Start with 20 disks. Sort them into 4 groups. How many disks are in each group.

This is one way to represent division - create an array.

GUIDED INSTRUCTION:

Visualize With An Array Model

There are 15 T-shirts in a pack. If Annie divides the T-shirts evenly among 3 soccer teams, how many people are there on each team?

USE CHIPS MAKE EQUAL GROUPS

}

20 all together 1 group of 5 ➸

1 group of 5 ➸

division relative to multiplication

▶_{Find the number that completes the multiplication and division equation.}

1.

20 ÷ 4 = ____

32 ÷ 8 = ____

____ x 4 = 20

____ x 8 = 32

2.

48 ÷ 8 =

30 ÷ 6 = ____

____ x 8 = 48

____ x 6 = 30

3.

24 ÷ 3 = ____

35 ÷ 7 = ____

____ x 3 = 24

____ x 7 = 35

4.

72 ÷ 8 =

21 ÷ 3 = ____

____ x 8 = 72

____ x 3 = 21

5.

28 ÷ 4 =

56 ÷ 7 = ____

____ x 4 = 28

____ x 7 = 56

6.

54 ÷ 6 =

27 ÷ 9 = ____

divide multiples of 10, 100, & 1,000

An amusement park has 5 entrances. If 1,500 people entered the amusement park and separated into equal lines, how many people are in each line?

You need to divided 1,500 people into equal groups Find 1,500 ÷ 5.

So there are 300 people in each line.

guided practice

▶_{Complete each set of division patterns.}

Use basic facts to divide

Solve:

150 ÷ 5 = 30 1,500 ÷ 5 = 300

12 ÷ 4 = 120 ÷ 4 = 1,200 ÷ 4 =

36 ÷ 6 = 360 ÷ 6 = 3,600 ÷ 6 =

35 ÷ 5 = 350 ÷ 5 = 3,500 ÷ 5 =

42 ÷ 7 = 420 ÷ 7 = 4,200 ÷ 7 = (1)

(4) (3)

practice

▶_{Use your knowledge of division facts and patterns to name the quotients.}

▶_{Divide. Use mental math patterns and your knowledge of division facts.}

1,600 ÷ 8= 4,200 ÷ 6 =

5,400 ÷ 6 = 1,500 ÷ 3 =

8,100 ÷ 9 = 2,400 ÷ 4 = ▶_{PROBLEM SOLVE.}

6 ÷ 3 = 60 ÷ 3 = 600 ÷ 3 = 6,000 ÷ 3 =

8 ÷ 2 = 80 ÷ 2 = 800 ÷ 2 = 8,000 ÷ 2 =

14 ÷ 7 = 140 ÷ 7 = 1,400 ÷ 7 = 14,000 ÷ 7 =

63 ÷ 9 = 630 ÷ 9 = 6,300 ÷ 9 = 63,000 ÷ 9 = (1)

(4) (3)

(2)

(5)

The Smith family collected 2,400 pennies. The pennies will

be divided evenly among the 4 children. How many pennies

will each child get?

Mr. and Mrs. Pompei have 1,800 party favors. Each guest will receive 3 favors. How many guests are Mr. and Mrs. Pompei

estimate quotients

GET READY to Learn: Circuses have been around for more than 200 years. They sometimes

travel by train. Suppose a circus travels 642 miles in 8 hours. About how many miles per hour did the train travel?

So the circus train is traveling about 80 miles per hour.

Check:

There are different ways to estimate quotients. One way is to use compatible numbers. Compatible numbers are

numbers that are easy to divide mentally.

guided practice

ESTIMATE THE QUOTIENT: Check with multiplication facts. (The first one is done for you.)

715 ÷ 8

1 Ask yourself - Are 71 and 8 compatible?

2 NO

3 So, round 715 to 720 because 8 is a

factor of 72 which makes the compatible.

4 Complete the basic division fact of 72 ÷ 8.

5 Add the zero.

715 ÷ 8 715 ÷ 8 = 90

Therefore, 715 ÷ 8 is ABOUT 90

161 ÷ 4

1 Ask yourself - Are 16 and 4 compatible?

2 YES

3 So, round 161 to 160.

4 Complete the basic division fact of 16 ÷ 4.

5 Add the zero.

161 ÷ 4

160 ÷ 4 = 40

Therefore, 161 ÷ 4 is ABOUT 40

❶ 123 ÷ 3

120 ÷ 3 = 40

40 x 3 = 120

❷ 162 ÷ 2

_____ ÷ _____ = _____

_____ x _____ = _____

❸ 345 ÷ 7

_____ ÷ _____ = _____

_____ x _____ = _____

❹ 415 ÷ 6

_____ ÷ _____ = _____

_____ x _____ = _____

❺ 2,431 ÷ 8

_____ ÷ _____ = _____

_____ x _____ = _____

❻ 7,160 ÷ 9

_____ ÷ _____ = _____

_____ x _____ = _____

❼ 4,187 ÷ 7

_____ ÷ _____ = _____

_____ x _____ = _____

❽ 8,052 ÷ 9

GET READY -

prepare for long division

▶

Example:

8 times 4 is as close to 33 as you can get, without going over. 8 x 4 = 32

1. 9 times ____ is as close to 58 as you can get, without going over. 9

2. 5 times ____ is as close to 54 as you can get, without going over. 5

3. 4 times ____ is as close to 38 as you can get, without going over. 4

4. 8 times ____ is as close to 65 as you can get, without going over. 8

5. 4 times ____ is as close to 15 as you can get, without going over. 4

6. 2 times ____ is as close to 17 as you can get, without going over. 2

7. 6 times ____ is as close to 38 as you can get, without going over. 6

8. 10 times ___ is as close to 104 as you can get, without going over.

9. 4 times ____ is as close to 14 as you can get, without going over. 4

10. 7 times ____ is as close to 17 as you can get, without going over. 7

11. 10 times ____ is as close to 32 as you can get, without going over.

12. 7 times ____ is as close to 36 as you can get, without going over.

13. 5 times ____ is as close to 53 as you can get, without going over. 7

14. 4 times ____ is as close to 18 as you can get, without going over.

divide naming partial quotients

VIDEO INTRODUCTION: http://everydaymath.uchicago.edu/teaching-topics/computation/div part-quot/

Make a list of multiplication facts for the divisor.

Subtract an easy multiple of the divisor from the dividend (for example 100x, 10x, 5x, 2x). Write the partial quotient in a column to the right of the problem.

Repeat step 2 until the dividend has been reduced to 0 or there is a remainder (a number left over that is less than the dividend).

Add up the partial quotients to find the answer.

☞

EXAMPLE: 81 ÷ 3

☜

REMEMBER: When using the long division symbol, the divisor

comes first. Multiplication Facts for 3

1 x 3 = 3 2 x 3 = 6 3 x 3 = 9 4 x 3 = 12 5 x 3 = 15 6 x 3 = 18 7 x 3 = 21 8 x 3 = 24 9 x 3 = 27 10 x 3 = 30 11 x 3 = 33 12 x 3 = 36 20 x 3 = 60 30 x 3 = 90 40 x 3 = 120 50 x 3 = 150 100 x 3 = 300

27

3)81

- 60

21

- 21

0

= 3 x

20

=

3 x

7

20

+

7

= 27

(1) (2)

(3)

2-digit dividends: no remainders

▶

quotients strategy.

5 9 5

8 9 6

7 8 4

3 7 5

(1) (2)

3-digit dividends: no remainders

▶

quotients strategy.

4 5 3 2

3 6 2 4

5 3 3 5

6 7 3 2

(1) (2)

4-digit dividends: no remainders

▶

quotients strategy.

6 1, 5 3 6 4 7, 2 1 6

divide naming partial quotients with remainders

Not all division problems end with a whole number. When there is anything left over, we call it a remainder.

Solve the problem the same way you did in the previous lessons, but now there will be a remainder added to the answer.

☞

EXAMPLE: 77 ÷ 3

☜

(2)

REMEMBER: When using the long division symbol, the divisor

comes first. Multiplication Facts for 3

1 x 3 = 3 2 x 3 = 6 3 x 3 = 9 4 x 3 = 12 5 x 3 = 15 6 x 3 = 18 7 x 3 = 21 8 x 3 = 24 9 x 3 = 27 10 x 3 = 30 11 x 3 = 33 12 x 3 = 36 20 x 3 = 60 30 x 3 = 90 40 x 3 = 120 50 x 3 = 150 100 x 3 = 300

25 r1

3)77

- 60

16

- 15

1

= 3 x

20

= 3 x

5

20

+

5

= 25

2-digit dividends: with remainders

▶

quotients strategy.

4 9 1

2 5 7

6 8 7

3 8 9

3-digit dividends: with remainders

▶

quotients strategy.

4 4 6 1

3 7 8 7

4-digit dividends: with remainders

▶

quotients strategy.

Find 438 ÷ 5.

Related multiplication facts: 5 x 8 = 40 & 5 x 9 = 45 438 ÷ 5 is about 450 ÷ 5. The estimated quotient is 90.

7 2, 1 1 6 3 4, 1 3 5

(1) (2)

guided learning

▶

83 ÷ 2 is about ÷ 2 96 ÷ 5 is about ÷ 5 = =

865 ÷ 3 is about ÷ 3 586 ÷ 6 is about ÷ 6

= =

269 ÷ 6 is about ÷ 6 2,079 ÷ 7 is about ÷ 7

= =

764 ÷ 8 is about ÷ 8 7,175 ÷ 9 is about ÷ 9

= =

47 ÷ 5 is about ÷ 5 383 ÷ 4 is about ÷ 4

= =

617 ÷ 6 is about ÷ 6 3,555 ÷ 9 is about ÷ 9

= =

▶

communicator and use the partial quotients method.)

7,146 ÷ 7 = 6,351 ÷ 8 =

Estimate: Estimate:

÷ 7 = ÷ 8 =

7,146 ÷ 7 is about 6,351 ÷ 5 is about (1)

(5)

(7)

(9)

(11) (12)

(10) (8) (6) (4) (2)

(5)

let’s explore!

WORKING TOGETHER

Four students, Allen, Ben, Carol, and Dawn, solved this problem.

Estimate the quotient 468 ÷ 5. These are the answers they got.

Allen: 2,500 Ben: 450 Carol: 90 Dawn: 9 Discuss with your classmates how they got their answers. Explain which of the answer are unreasonable.

let’s practice

▶

8,000 ÷ 4 = thousands ÷ 4 = thousands =

9,000 ÷ 3 = thousands ÷ 3 = thousands =

1,200 ÷ 6 = thousands ÷ 6 = thousands =

1,500 ÷ 5 = thousands ÷ 5 = thousands = (1)

(2)

(3)

▶

9,968 ÷ 8 = 6,850 ÷ 5 =

▶

9 tens ÷ 4 24 ones ÷ 5

Quotient = Quotient =

Remainder = Remainder =

15 hundreds ÷ 6 12 thousands ÷ 7

Quotient = Quotient =

Remainder = Remainder =

▶

5,235 ÷ 5 3,581 ÷ 8

Q = R = Q = R =

▶

4 713 9 1,708

▶

92 ÷ 5 is about ÷ 5 791 ÷ 4 is about ÷ 4

= =

▶

2,826 ÷ 9 = 9,528 ÷ 8 =

(1) (2)

(3) (4)

(6) (5)

(7) (8)

(10) (9)

(11) (12)

real-world problems: multiplication & division

▶

• Solve real-world problems.

• Solve multi-step word problems using the four operations.

• Represent the problems with a letter standing for the unknown quantity.

Mr. Benson and Mr. McKenzie have $4,686 altogether. Mr. Benson’s share is twice as much as Mr. McKenzie’s.

How much is Mr. McKenzie’s share?

Mr. Benson’s money

Mr. McKenzie’s money

3 units 4,686

1 unit $4,686 ÷ 3 = $1,562

Mr. McKenzie’s share is $1,562.

How much is Mr. Benson’s share? $1,562 x 2 = $3,124.

Mr. Benson’s share is $3,124.

If Mr. Benson spends $500 on books, how much money does he have left?

$3,124 — $500 = $2,624

Mr. Benson has $2,624 left.

Solve 3-step problems using models.

(a)

(b)

▶

Mrs. Romero has $3,756 to spend on equipment for the school media room. She saves $650 for later purchases. She spends the rest on 12 monitors and some software. The monitors cost $205 each. How much does she spend on software?

$3,756 — $650 = $

She spends $3,106 altogether.

1

2 x $205 = $

The 12 monitors cost $

$3,106 — $ = $

She spends $ on software. (a)

(c) (b)

Lisa had 1,750 stamps. Minah had 480 fewer stamps than Lisa. Lisa gave some stamps to Minah.

Now, Minah has 3 times as many stamps as Lisa.

How many stamps did Minah have at first?

1,750 — 480 =

Minah had stamps.

How many stamps does Lisa have now? 1,750 + 1,279 =

4 units

1 unit ÷ 4 = Lisa has stamps now.

Solve 3-step problems using models.

(a)

guided learning

▶

Ms. Spinelli had $1,240 in her savings account. Her dad had $4,730 in his savings account. Ms. Spinelli’s dad transferred some money from his account to her account. Now, Ms. Spinelli has twice as much money in her account as her dad does.

How much money does Ms. Spinelli’s dad have now?

$ + $ = $

Ms. Spinelli and her dad had $ altogether.

$ ÷ 3 = $

Ms. Spinelli’s dad has $ .

How much money did Ms. Spinelli’s dad give her? $4,730 — $ = $

Ms. Spinelli’s dad gave her $ . (a)

$

Tim and Ali had 96 marbles altogether. Tim loses 24 marbles to Ali during a game. Now, Ali has twice as many marbles as Tim.

How many marbles did Ali have before the game?

After the game:

3 units

1 unit ÷ 3 = 2 units 2 x = Ali has marbles after the game.

Before the game: — 24 =

Sally is making party bags of finger puppets for a birthday party. Sally has 45 troll puppets and twice as many animal puppets. If she puts 8 finger puppets in each bag, how many bags can she make? How many puppets will be left over?

How many puppets does she have in all?

1 unit = 45

3 units = 3 x 45 =

In all, she has puppets.

How many party bags with 8 puppets in each can she make?

Number of party bags = 135 ÷ 8 =

She can make party bags and finger puppets will be left over. Solve division problems and interpret the remainder.

(a)

guided learning

Rico collected $78 and Susan collected 3 times as much. With their money, they bought T-shirts costing $7 each to give to charity.

How much money did they collect altogether?

1 unit =

4 units = x =

Together they collected $

How many T-shirts did they buy? How much money did they have left?

Number of T-shirts = ÷

= R

They bought T-shirts and had $ left. (a)

(b)

Carlo’s bakery sold 3,840 packs of granola bars.

Carlos bakery sold twice as many packs of granola bars as Sam’s bakery. There were 4 bars in each pack.

How many granola bars did Carlo’s bakery sell?

Let the letter “c” represent the number of granola bars Carlo’s bakery sold. c = 3,840 x 4

c =

Carlo’s bakery sold 15,360 granola bars. How many granola bars did the two bakeries sell altogether?

Let the letter “s” represent the number of granola bars Sam’s bakery sold. s = 15,360 ÷ 2

s =

Sam’s bakery sold granola bars.

Let “a” represent the number of granola bars Carlo’s and Sam’s bakeries sold altogether.

a = 15,360 + 7 a =

Carlo’s and Sam’s bakeries sold granola bars altogether.

▶

In a school, there are 254 girls. There are three times as many boys in the school. How many boys are there in the school? Let the number of boys be “a”.

a = 254 x =

There are boys in the school.

Use a letter to represent the unknown number in a word problem.

(a)

(b)

How many students are there in the school? Let the number of students be “b”.

b = + =

MATH JOURNAL

Write real-world multiplication problems using the words and numbers given. Then solve the problems.

(b)

READING & WRITING MATH

(1)

(2)

5 times

manager

$860

Mr. Smith

Ms. Jackson

total weight

127 pounds

weight

bag

each

let’s explore

Mrs. Soong and Mrs. Nathan often meet each other in a local market. Mrs. Soong goes to the market every 2 days and Mrs. Nathan goes to the market every 3 days. Both of them meet at the market on January 1 of the calendar year. List the next four dates on which they will meet again at the market.

Look at the dates on which they meet at the market. Find the pattern. Use the pattern to find four other dates on which they will meet.

▶_{Solve. Show your work.} (Show all work in your journal.)

A store owner buys 1,257 cans of paint. Each can holds 4 quarts of paint. If he sells 620 cans, how many quarts of paint will he have left?

A grower packs 4,568 peaches. He packs the most peaches possible, dividing them equal into 9 boxes, and then gives away the remaining peaches.

How many peaches are in each box? How many peaches does he give away?

If he sells 7 boxes, how many peaches does he have left?

Alan, Bob, and Many sold tickets to raise money for charity. Alan sold 125 tickets. Bob sold 14 times as many tickets as Alan. Candy sold half as many tickets as Bob. How many tickets did they sell altogether?

(1)

(2)

Let’s Practice

(1)

(2)

(a) (b) (c)

Sam runs laps around a rectangular field 4 times a week. The field is 320 meters long and 240 meters wide. He runs 6 laps each time. What distance does he run in a week?

Maya and Emily were playing a board game. Mays had $2,740 in play money and Emily had $3,560. Maya had to give some play money to Emily. After that, Emily had 4 times the amount of play money as Maya.

How much money did Maya have in the end? How much money did Emily have in the end?

Mr. Rossi has two accounts. Account A and account B. He had $2,370 in Account B and a total of $7,480 in both accounts. He transferred some money from Account B to

Account A. In the end, the amount of money in Account A is 3 times the amount of money in Account B.

How much money is there in Account A in the end?

How much money did Mr. Rossi transfer from Account B to Account A?

▶_{Use different letters to represent the unknown numbers. Then solve.}

Michelle picked 480 strawberries. Sasha picked 240 fewer strawberries than Michelle. Rita picked 3 times as many strawberries as Sasha. Rita then bake fruit tarts, with 7 strawberries in each tart.

How many strawberries did Rita pick? How many tarts did Rita make?

How many strawberries were left over?

In her shop, Poppa has 655 roses and 450 sunflowers.

PUT ON YOUR THINKING CAP

▶_{PROBLEM SOLVING: Which two numbers below give each product?}

540 5,640

38,925 21,150

▶_Solve.

At a stadium, the number of men is 3 times the number of women. The number of women is 5 times the number of children at the stadium.

How many times the number of children is the number of men? If there are 730 children, how many men are there?

Kartik places 4 posts along the width of a rectangular garden as shown. The space between two posts is 125 centimeters. He places 10 posts in a similar pattern along the length of the garden. What is the perimeter of the garden?

CRITICAL THINKING SKILLS

45

470

865

12

(1) (2)

(3) (4)

(5)

UNIT WRAP UP

▶_{You have learned….}

unit review/test

▶_{VOCABULARY - Choose the correct word.}

The number left over when a number cannot be divided evenly is the .

When a number is expressed to the nearest ten or hundred, it

is .

The answer to a division problem is called a .

A number close to the exact amount is an .

The answer to a multiplication problem is the .

▶_{CONCEPT & SKILLS: Multiply} (Use the area model strategy for multi-digit multiplication.)

2,755 x 4 =

48 x 19 =

485 x 54 =

▶_{CONCEPT & SKILLS: Divide} (Use the partial quotients strategy for multi-digit division.)

723 ÷ 3 =

1,800 ÷ 6 =

▶_{Multiply. Then estimate to check that your answers are reasonable.}

6,694 x 7 = 809 x 90 =

Estimate: Estimate:

▶_{Divide. Then estimate to check that your answers are reasonable.}

623 ÷ 7 = 3,627 ÷ 9 = Estimate: Estimate:

▶_{PROBLEM SOLVING: Solve. Show your work!}

A factory produces 9,236 computers. It sells 5,630 computers. The remaining computers are either damaged or donated to charity. The number of donated computers is twice the number of damaged computers.

How many computers are DONATED to charity?

A bookshop has three tines as many magazines as books. There are 2,244 magazines. What equation can you use to find how many books there are? (Use the letter “b” to represent the number of books.)

How many books AND magazines are there altogether? What equation can you use to find the answer? Use the letter “t” to represent the total.

(12) (13)

(14) (15)

(16)

(17) (a)