Math Gr4 Ch8

Chapter 8
Multiply by Two-Digit Numbers
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8

Lesson 8-1 Multiply by Tens
Lesson 8-2 Estimate Products
Lesson 8-3 Problem-Solving Strategy: Act It Out
Lesson 8-4 Multiply Two-Digit Numbers
Lesson 8-5 Multiply Three-Digit Numbers by
Two-Digit Numbers
Lesson 8-6 Problem-Solving Investigation:
Choose a Strategy
Lesson 8-7 Multiply Greater Numbers

8-1 Multiply by Tens

Five-Minute Check (over Chapter 7)
Main Idea
California Standards
Example 1
Example 2


• I will multiply a whole number by a multiple of ten.


Standard 4NS3.3 Solve problems
involving the multiplication of multidigit
numbers by two-digit numbers.


Standard 4NS3.2 Demonstrate an
understanding of, and the ability to use,
standard algorithms for multiplying a multidigit
number by a two-digit number and for dividing a
multidigit number by a one-digit number; use
relationships between them to simplify computations
and to check results.


There are 35 packs of markers in an art classroom.
Each pack contains 50 markers. How many markers
are there in all?

You need to find 35 50.


One Way: Use Properties

35 × 50 Write the problem.
35 × (10 × 5) Think of 50 as 10 × 5.
35 × (5 × 10) Commutative Property
(35 × 5) × 10 Associative Property
175 × 10 Multiply. 35 × 5 = 175
1,750 Mental Math.


Another Way: Paper and Pencil

Step 1 Multiply the Step 2 Multiply the
ones. tens.

35 35
× 50 × 50
0 1,75 0

Answer: So, there are 1,750 markers in all.


Find 45 30.

A. 1,350

B. 1,250

C. 135

D. 125


A store has 20 children’s bicycles in stock that
cost $159 each. How much do all of the bicycles
cost altogether?

Step 1 Multiply the ones.

$159
20
0


Step 2 Multiply the tens.

$159
20
$3,18 0

Answer: So, all of the bicycles cost $3,180.


Check
Think of 20 × 159 as 2 × 10 × 159.

20 × $159 Write the problem.
(2 × 10) × $159 Think of 20 as 2 × 10.
(10 × 2) × $159 Commutative Property
10 × (2 × $159) Associative Property
10 × $318 Multiply. 2 × $159 = $318.
$3,180 Mental Math

So, the answer is correct.


Find $179 30.

A. $6,370

B. $5,530

C. $5,370

D. $4,170

8-2 Estimate Products

Five-Minute Check (over Lesson 8-1)
Main Idea
Example 1
Example 2


• I will estimate products by rounding.


Standard 4NS3.3 Solve problems involving
multiplication of multidigit numbers by two-digit
numbers.

Standard 4NS1.3 Round whole numbers
through the millions to the nearest
ten, hundred, thousand, ten thousand, or
hundred thousand.


Kaylee is awake for about 16 hours each day.
About how many hours is she awake in 3 weeks?

There are 21 days in 3 weeks. So, estimate 16 21.
Round each factor to its greatest place. Then multiply.

Step 1 Round each factor to the nearest ten.

16 20
21 20


Step 2 Multiply.

20
20
400

Answer: So, Kaylee is awake for about 400 hours
in 3 weeks.


A koala sleeps for about 19 hours a day. About
how many hours does one sleep in 3 weeks?

A. 400

B. 425

C. 450

D. 500


A company bought 53 computers for $909 each.
About how much did they spend in all? You need
to estimate $909 × 53.

Step 1 Round each factor to its greatest place.

909 900
53 50


Step 2 Multiply.

900
50
45,000

Answer: So, the company spent about $45,000.


A school bought 57 laptops for $837 each. About
how much did the school spend in all?

A. $45,000

B. $48,000

C. $53,000

D. $56,000

8-3 Problem-Solving Strategy: Act It Out

Main Idea
Example 1: Problem-Solving Strategy


• I will solve a problem by acting it out.


Standard 4MR2.3 Use a variety of methods,
such as words, numbers, symbols, charts,
graphs, tables, diagrams, and models, to
explain mathematical reasoning.


Standard 4NS3.0 Students solve problems
involving addition, subtraction, multiplication, and
division of whole numbers and understand the
relationships among the operations.


Sonoda has 6 coins in his
bank. The coins equal 65¢.
What combination of coins
does he have in his bank?


Understand
What facts do you know?
• Sonoda has 6 coins.
• The value of the 6 coins is 65¢.

What do you need to find?
• Find the coins Sonoda has in his bank.


Plan
You can use play money to act out different
combinations of 65¢.


Solve
One way to make 65¢ is
with 2 quarters, 1 dime,
and 1 nickel. But, that is
the only 4 coins. You
need two more coins.


Solve
Take 1 quarter and
exchange it for 2
dimes and 1 nickel.
The value stays the
same, and the number
of coins increases to 6.

Answer: So, Sonoda has 1 quarter, 3 dimes, and
2 nickels.


Check
Look back at the problem.

1 quarter + 3 dimes + 2 nickels
= (1 × 25 ) + (3 × 10 ) + (2 × 5 )
= 25 + 30 + 10
= 65

So, the answer is correct.

8-4 Multiply Two-Digit Numbers

Main Idea
Example 1
Example 2


• I will multiply two-digit numbers.


understanding of, and the ability to use, standard
algorithms for multiplying a multidigit number by a
two-digit number and for dividing a multidigit
number by a one-digit number; use the relationships
between them to simplify computations and to
check results.


Preparation for Standard 4NS3.3 Solve
problems involving multiplication of multidigit
numbers by two-digit numbers.


How far can a truck travel in 14 hours if it is
traveling an average of 57 miles per hour?


One Way: Partial Products

57
× 14
28 Multiply 4 × 7.
200 Multiply 4 × 50.
70 Multiply 10 × 7.
+ 500 Multiply 10 × 50.
798 Add partial products.


One Way: Partial Products



2
57
× 14
228



2
57
× 14
228
570



Step 3 Add the 2
products. 57
× 14
228
+ 570
798

Answer: So, the truck can travel 798 miles in
14 hours at 57 miles per hour.


How far can a car travel in 15 hours if it is traveling
an average of 63 miles per hour?

A. 368

B. 378

C. 935

D. 945


The Jones family spends an average of $48 a
month going to the movies. How much does the
family spend in 3 years?

Estimate 50 × 40 = 2,000.


$48
36
288



$48
36
288
+ 1,440


Step 3 Add the products.

$48
36
288
+ 1,440
1,728

Answer: So, the Jones family spends $1,728 in
3 years.


Check

1,200 + 240 + 240 + 48 = 1,728

Check for Reasonableness

Since 1,728 is close to the estimate of 2,000, the
answer is reasonable.


Lauren spends about $72 a month on gas for her
car. How much does she spend on gas in 4 years?

A. $3,456

B. $3,157

C. $2,456

D. $2,157

8-5 Multiply Three-Digit Numbers by Two-Digit Numbers

Main Idea
Example 1
Example 2


• I will multiply a three-digit number by a two-digit
number.


understanding of, and the ability to use,
standard algorithms for multiplying a multidigit
number by a two-digit number and for dividing a
multidigit number by a one-digit number; use the
relationships between them to simplify computations
and to check results.


numbers.


Antonio spends 194 minutes taking piano lesson
each month. How many minutes does he spend
taking piano lesson in a year?

Estimate 12 × 194 10 × 200 = 2,000.

Step 1 Multiply 194 by 2.

194
12
388


1
Step 2 Multiply 194 194
by 1 ten. 12
388
1,940

1
Step 3 Add the 194
products. 12
388
+ 1,940
2,328


Answer: So, Antonio spends 2,328 minutes taking
piano lessons in a year.



Since 2,328 is close to the estimate, 2,000. So,
the answer is correct.


Lui spends about 321 minutes a month writing
to pen pals. How many minutes does he spend
writing letters in a year?

A. 3,210

B. 3,814

C. 3,752

D. 3,852


Rai is paid $308 a week for her part-time job at the
city library. What is Rai’s annual salary?

Estimate $308 × 52 300 × 50 = $15,000.

Step 1 Multiply $308 by 2.
1
$308
52
$616


Step 2 Multiply $308 by 50.
4
1
$308
52
$616
$15,400


Step 3 Add the partial products.
4
1
$308
52
$616
+ $15,400
$16,016

Answer: So, the product of $308 and 52 is $16,016.



Since $16,016 is close to the estimate, the answer
is reasonable.


Monique gets paid $444 a week at her job. How
much does she get paid in a year?

A. $22,088

B. $23,088

C. $21,088

D. $20,088

8-6 Problem-Solving Investigation: Choose a Strategy

Main Idea
Example 1: Problem-Solving Investigation


• I will choose the best strategy to solve a problem.


Standard 4MR1.1 Analyze problems by
identifying relationships, distinguishing relevant
from irrelevant information, sequencing and
prioritizing information, and observing patterns.


Standard 4NS3.0 Students solve problems
involving addition, subtraction, multiplication, and
division of whole numbers and understand the
relationships among the operations.


GREGORY: I spent 4 hours at a
school carnival. I spent 35 minutes
eating and 45 minutes playing
games. I also rode 12 rides, which
took about 15 minutes each because
I had to stand in lines.

YOUR MISSION: Determine if Gregory
is correct in saying that he spent
4 hours at the carnival.


Understand
What facts do you know?
• Gregory spent 35 minutes eating.
• He spent 45 minutes playing games.
• He rode 12 rides, which lasted 15 minutes each.

What do you need to find?
• Find if Gregory is correct in saying he spent
4 hours at the carnival.


Plan
Find the total number of minutes spent on
carnival activities and compare to 4 hours.


Solve
Gregory gave the amount of time spent at the
carnival in hours. The amount of time spent on
each activity was given in minutes. So, change
hours to minutes. Then compare the two
amounts of time.


Solve
60 minutes 15
60 minutes × 12 35 minutes
60 minutes 30 45 minutes
+ 60 minutes + 150 + 180 minutes
240 minutes 180 230 minutes
time Gregory said time spent time spent on
he spent at carnival riding rides carnival activities


Solve
The amount of time Gregory said he spent at
the carnival does not equal the amount of time
he spent of carnival activities.

Answer: So, Gregory was not correct.


Check
Look back at the problem. Use subtraction to
check the amount of time spent on carnival
activities.
133 – 55 – 46 – 32 = 0. So, Gregory was not
correct.

8-7 Multiply Greater Numbers

Main Idea
Example 1
Example 2


• I will multiply four- and five-digit numbers by a
two-digit number.


numbers.

Standard 4MR2.1 Use estimation to verify the
reasonableness of calculated results.


A science museum gets an average of 4,562
visitors every week. How many visitors does
it get in a year?

Estimate 52 4,562 50 × 5,000 = 250,000

Step 1 Multiply the ones. Regroup if necessary.

1 11
4,562
52
9,124


2 3
1 11
4,562
52
9,124
228,100


Step 3 Add the partial products. Check for
reasonableness.
2 3
1 11
4,562
52
9,124
+ 228,100
237,224

Answer: So, the science museum gets 237,224
visitors a year.



Since the answer, 237,224, is close to the estimate,
the answer is reasonable.


An amusement park gets an average of 8,225
visitors every week. How many visitors does
it get in a year?

A. 427,700

B. 427,590

C. 426,790

D. 427,800


A web site gets an average of 23,146 hits each
month. How many hits does it get in 15 months?

Estimate 15 23,149 20 × 20,000 = 400,000

Step 1 Multiply the ones. Regroup if necessary.

1 24
23,149
15
115,745



1 24
23,149
15
115,745
231,490


Step 3 Add the partial products.

1 24
23,149
15
115,745
+ 231,490
347,235

Answer: So, the website gets 347,235 hits in
15 months.



Since 347,235 is close to the estimate, the answer
is reasonable.


Another web site gets an average of 19,225 hits a
day. How many hits does the website get in a 31
day month?

A. 594,975

B. 595,864

C. 595,975

D. 594,323

8

Five-Minute Checks

8

Lesson 8-1 (over Chapter 7)
Lesson 8-2 (over Lesson 8-1)

8
(over Chapter 7)

Multiply. Check for reasonableness.
203
2

A. 426

B. 405

C. 406

D. 425

8
(over Chapter 7)

506
7

A. 1,283

B. 3,502

C. 1,273

D. 3,542

8
(over Chapter 7)

3 7,035

A. 21,105

B. 21,095

C. 10,368

D. 21,405

8
(over Chapter 7)

8 $4,209

A. $32,743

B. $33,672

C. $13,097

D. $33,752

8
(over Chapter 7)

6 5,008

A. 30,042

B. 30,108

C. 30,708

D. 30,048

8
(over Lesson 8-1)

Multiply.
87
10

A. 807

B. 187

C. 870

D. 957

8
(over Lesson 8-1)

Multiply.
34
30

A. 1,020

B. 912

C. 102

D. 1,054

8
(over Lesson 8-1)

Multiply.
65
80

A. 5,240

B. 520

C. 5,265

D. 5,200

8
(over Lesson 8-1)

Multiply.
$23
50

A. $1,173

B. $115

C. $1,150

D. $1,138

8
(over Lesson 8-1)

Multiply.
$79
90

A. $6,480

B. $7,110

C. $711

D. $7,189

8
(over Lesson 8-1)

Multiply.
$57
60

A. $3,420

B. $3,042

C. $3,477

D. $3,480

8
(over Lesson 8-2)

Estimate. Tell whether the estimate is more or less
than the actual product.
39
35

A. 1,400; more
B. 1,600; less
C. 1,600; more
D. 1,200; less

8
(over Lesson 8-2)

63
44

A. 2,700; less
B. 2,400; less
C. 3,000; more
D. 2,700; more

8
(over Lesson 8-2)

$54
81

A. $4,300; less
B. $4,400; less
C. $4,800; more
D. $4,000; less

8
(over Lesson 8-2)

$274 16

A. $5,400; more
B. $3,000; less
C. $6,000; more
D. $4,125; less

8
(over Lesson 8-2)

719 94

A. 63,000; less
B. 64,800; more
C. 70,000; more
D. 64,800; less

8
(over Lesson 8-3)

Solve. Use the Act it Out strategy. Carlos has 8
coins in his pocket. The total value of the coins is
73¢. What coins does Carlos have?

A. 1 quarter, 4 dimes, 1 nickel, 3 pennies

B. 2 quarters, 1 dime, 2 nickels, 3 pennies

C. 3 dimes, 2 nickels, 3 pennies

D. 2 quarters, 2 dimes, 3 pennies

8
(over Lesson 8-4)

Multiply.
17
11

A. 308

B. 34

C. 187

D. 200

8
(over Lesson 8-4)

Multiply.
35
24

A. 840

B. 210

C. 720

D. 740

8
(over Lesson 8-4)

Multiply.
59
46

A. 2,708

B. 590

C. 2,995

D. 2,714

8
(over Lesson 8-4)

Multiply.
$64
37

A. $2,248

B. $2,368

C. $640

D. $2,512

8
(over Lesson 8-4)

Multiply.
$77
66

A. $5,082

B. $4,242

C. $942

D. $4,642

8
(over Lesson 8-4)

Multiply.
92
84

A. 1,936

B. 7,628

C. 1,104

D. 7,728

8
(over Lesson 8-5)

Multiply.
124
13

A. 4,852

B. 1,612

C. 496

D. 1,602

8
(over Lesson 8-5)

Multiply.
206
32

A. 6,482

B. 1,030

C. 5,810

D. 6,592

8
(over Lesson 8-5)

Multiply.
557
45

A. 25,065

B. 24,865

C. 5,013

D. 22,635

8
(over Lesson 8-5)

Multiply.
648
74

A. 47,948

B. 7,128

C. 47,952

D. 45,322

8
(over Lesson 8-5)

Multiply.
817
77

A. 17,534

B. 62,469

C. 11,438

D. 62,909

8
(over Lesson 8-5)

Multiply.
993
86

A. 13,902

B. 85,398

C. 74,398

D. 77,688

8
(over Lesson 8-6)

Use any strategy to solve. Nitin spent 55 minutes
mowing the lawn, 48 minutes cleaning his room, 23
minutes vacuuming, and 32 minutes doing laundry.
Is it reasonable to say that Nitin spent 3 hours on
completing his chores?

A. Yes, it is reasonable because he spent exactly 3
hours completing his chores.

B. No, it is not reasonable because he spent over
3 hours completing his chores.

8
(over Lesson 8-6)


C. No, it is not reasonable because he spent less
than 3 hours completing his chores.

D. Yes, it is reasonable because he spent almost
3 hours completing his chores.

8
(over Lesson 8-6)


C. No, it is not reasonable because he spent less
than 3 hours completing his chores.

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Math Gr4 Ch8

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