Math Gr4 Ch8

Chapter 8Multiply by Two-Digit Numbers

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Lesson 8-1 Multiply by TensLesson 8-2 Estimate ProductsLesson 8-3 Problem-Solving Strategy: Act

It OutLesson 8-4 Multiply Two-Digit NumbersLesson 8-5 Multiply Three-Digit Numbers

by Two-Digit NumbersLesson 8-6 Problem-Solving Investigation:

Choose a StrategyLesson 8-7 Multiply Greater Numbers

8Multiply by Two-Digit Numbers



Five-Minute Check (over Chapter 7)Main IdeaCalifornia StandardsExample 1Example 2

8-1 Multiply by Tens



• 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 × 5035 × (10 × 5)35 × (5 × 10)

(35 × 5) × 10175 × 10

1,750

Write the problem.Think of 50 as 10 × 5.Commutative PropertyAssociative PropertyMultiply. 35 × 5 = 175 Mental Math.



Another Way: Paper and Pencil

3550×

Step 1 Multiply the ones.

0

Step 2 Multiply the tens.

3550×

01,75

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



A. 1,350

B. 1,250

C. 135

D. 125

Find 45 × 30.


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



×$159

200




×$159

200$3,18

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


Check


20 × $159 Write the problem.(2 × 10) × $159 Think of 20 as 2 × 10.(10 × 2) × $159 Commutative Property10 × (2 × $159) Associative Property

10 × $318 Multiply. 2 × $159 = $318.$3,180 Mental Math

So, the answer is correct.

Think of 20 × 159 as 2 × 10 × 159.



A. $6,370

B. $5,530

C. $5,370

D. $4,170

Find $179 × 30.



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

8-2 Estimate Products



• 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.

×1621 ×

2020


Step 2 Multiply.


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

×2020

400



A. 400

B. 425

C. 450

D. 500

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


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.


×90953 ×

90050


Step 2 Multiply.

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


×90050

45,000



A. $45,000

B. $48,000

C. $53,000

D. $56,000

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



Five-Minute Check (over Lesson 8-2)Main IdeaCalifornia StandardsExample 1: Problem-Solving Strategy

8-3 Problem-Solving Strategy: Act It Out



• 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.

So, the answer is correct.

1 quarter + 3 dimes + 2 nickels


= (1 × 25 ) + (3 × 10 ) + (2 × 5 )

= 65= 25 + 30 + 10




8-4 Multiply Two-Digit Numbers



• I will multiply 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 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

5714×28

20070

500+

Multiply 4 × 7.Multiply 4 × 50.Multiply 10 × 7.Multiply 10 × 50.Add partial products.798



One Way: Partial Products




5714×

228

Step 1 Multiply the ones.2





5714×

228

2

570




Step 3 Add the products.

5714×

228

2

570+798

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



A. 368

B. 378

C. 935

D. 945

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


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

36288




×$48

36288

1,440+


Step 3 Add the products.


×$48

36288

1,440+1,728

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


Check for Reasonableness


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

Check

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



A. $3,456

B. $3,157

C. $2,456

D. $2,157

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




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



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



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 the relationships between them to simplify computations and to check results.





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


Step 1 Multiply 194 by 2.

Estimate 12 × 194 10 × 200 = 2,000.

×194

12388


Step 2 Multiply 194 by 1 ten.


×194

12388

1,940

1

Step 3 Add the products. ×

19412

3881,940

1

+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.



A. 3,210

B. 3,814

C. 3,752

D. 3,852

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


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


Step 1 Multiply $308 by 2.

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

×$308

52$616

1



Step 2 Multiply $308 by 50.

×$308

52$616

1

$15,400

4



Step 3 Add the partial products.

×$308

52$616

1

$15,400

4

+$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.



A. $22,088

B. $23,088

C. $21,088

D. $20,088

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



Five-Minute Check (over Lesson 8-5)Main IdeaCalifornia StandardsExample 1: Problem-Solving Investigation

8-6 Problem-Solving Investigation: Choose a Strategy



• 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


240 minutes

60 minutes60 minutes60 minutes

+ 60 minutes30

15× 12

+ 150180 230 minutes

35 minutes45 minutes

+ 180 minutes

time Gregory said he spent at carnival

time spent riding rides

time spent on 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



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




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?

Step 1 Multiply the ones. Regroup if necessary.


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

×4,562

529,124

111




×4,562

529,124

111

228,100

32


Step 3 Add the partial products. Check for reasonableness.


×4,562

529,124

111

228,100

32

+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.



A. 427,700

B. 427,590

C. 426,790

D. 427,800

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



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

Step 1 Multiply the ones. Regroup if necessary.

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

×23,149

15115,745

421




×23,149

15115,745

421

231,490



Step 3 Add the partial products.

+347,235

×23,149

15115,745

421

231,490

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




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



A. 594,975

B. 595,864

C. 595,975

D. 594,323

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




Five-Minute Checks


Lesson 8-1 (over Chapter 7)Lesson 8-2 (over Lesson 8-1)Lesson 8-3 (over Lesson 8-2)Lesson 8-4 (over Lesson 8-3)Lesson 8-5 (over Lesson 8-4)Lesson 8-6 (over Lesson 8-5)Lesson 8-7 (over Lesson 8-6)


(over Chapter 7)

A. 426

B. 405

C. 406

D. 425

Multiply. Check for reasonableness.203

× 2


(over Chapter 7)

A. 1,283

B. 3,502

C. 1,273

D. 3,542

Multiply. Check for reasonableness.506

× 7


(over Chapter 7)

A. 21,105

B. 21,095

C. 10,368

D. 21,405

Multiply. Check for reasonableness.3 × 7,035


(over Chapter 7)

A. $32,743

B. $33,672

C. $13,097

D. $33,752

Multiply. Check for reasonableness.8 × $4,209


(over Chapter 7)

A. 30,042

B. 30,108

C. 30,708

D. 30,048

Multiply. Check for reasonableness.6 × 5,008


(over Lesson 8-1)

A. 807

B. 187

C. 870

D. 957

Multiply. 87

× 10


(over Lesson 8-1)

A. 1,020

B. 912

C. 102

D. 1,054

Multiply. 34

× 30


(over Lesson 8-1)

A. 5,240

B. 520

C. 5,265

D. 5,200

Multiply. 65

× 80


(over Lesson 8-1)

A. $1,173

B. $115

C. $1,150

D. $1,138

Multiply. $23

× 50


(over Lesson 8-1)

A. $6,480

B. $7,110

C. $711

D. $7,189

Multiply. $79

× 90


(over Lesson 8-1)

A. $3,420

B. $3,042

C. $3,477

D. $3,480

Multiply. $57

× 60


(over Lesson 8-2)

A. 1,400; more

B. 1,600; less

C. 1,600; more

D. 1,200; less

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

39× 35


(over Lesson 8-2)

A. 2,700; less

B. 2,400; less

C. 3,000; more

D. 2,700; more


63× 44


(over Lesson 8-2)

A. $4,300; less

B. $4,400; less

C. $4,800; more

D. $4,000; less


$54× 81


(over Lesson 8-2)

A. $5,400; more

B. $3,000; less

C. $6,000; more

D. $4,125; less

Estimate. Tell whether the estimate is more or less than the actual product.$274 × 16


(over Lesson 8-2)

A. 63,000; less

B. 64,800; more

C. 70,000; more

D. 64,800; less

Estimate. Tell whether the estimate is more or less than the actual product.719 × 94


(over Lesson 8-3)

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

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?


(over Lesson 8-4)

A. 308

B. 34

C. 187

D. 200

Multiply. 17

× 11


(over Lesson 8-4)

A. 840

B. 210

C. 720

D. 740

Multiply. 35

× 24


(over Lesson 8-4)

A. 2,708

B. 590

C. 2,995

D. 2,714

Multiply. 59

× 46


(over Lesson 8-4)

A. $2,248

B. $2,368

C. $640

D. $2,512

Multiply. $64

× 37


(over Lesson 8-4)

A. $5,082

B. $4,242

C. $942

D. $4,642

Multiply. $77

× 66


(over Lesson 8-4)

A. 1,936

B. 7,628

C. 1,104

D. 7,728

Multiply. 92

× 84


(over Lesson 8-5)

A. 4,852

B. 1,612

C. 496

D. 1,602

Multiply. 124

× 13


(over Lesson 8-5)

A. 6,482

B. 1,030

C. 5,810

D. 6,592

Multiply. 206

× 32


(over Lesson 8-5)

A. 25,065

B. 24,865

C. 5,013

D. 22,635

Multiply. 557

× 45


(over Lesson 8-5)

A. 47,948

B. 7,128

C. 47,952

D. 45,322

Multiply. 648

× 74


(over Lesson 8-5)

A. 17,534

B. 62,469

C. 11,438

D. 62,909

Multiply. 817

× 77


(over Lesson 8-5)

A. 13,902

B. 85,398

C. 74,398

D. 77,688

Multiply. 993

× 86


(over Lesson 8-6)

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.

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?


(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.


(over Lesson 8-6)


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

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Education

Math Gr4 Ch8