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Chapter 8Multiply by Two-Digit Numbers

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Chapter 8Multiply by Two-Digit Numbers

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http://ca.gr4math.com/

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

88Multiply by Two-Digit Numbers



Five-Minute Check (over Chapter 7)

Main Idea

California Standards

Example 1: Multiply by Tens

Example 2: Multiply by Tens

8-18-1 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 the bicycles cost altogether?



×$159

200




0×

$15920

$3,18

Answer: So, the bicycles cost $3,180 altogether.


Check


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.

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 Idea


Example 1: Estimate Products

Example 2: Estimate Products

8-28-2 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 4 weeks?

There are 28 days in 4 weeks. So, estimate 16 × 28. Round each factor to its greatest place. Then multiply.


Step 1 Round each factor to the nearest ten.

×1628 ×

2030


×2030

Step 2 Multiply.


Answer: So, Kaylee is awake for about 600 hours in 4 weeks.

600



A. 400 hours

B. 425 hours

C. 450 hours

D. 500 hours

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?

Step 1 Round each factor to its greatest place.


×90953 ×

90050

You need to estimate $909 × 53.


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?



Main Idea


Example 1: Problem-Solving Strategy

8-38-3 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 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



Main Idea


Example 1: Real-World Example

Example 2: Multiply Money

8-48-4 Multiply Two-Digit Numbers



• I will multiply two-digit numbers.



Preparation for 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

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 miles

B. 378 miles

C. 935 miles

D. 945 miles

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

There are 12 months in one year and 36 months in 3 years.




×$48

36288


$4836

288×

1,440+




1,728

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

$4836

288×

1,440+


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?



Main Idea




8-58-5 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?


Estimate 12 × 194 10 × 200 = 2,000

Step 1 Multiply 194 by 2.

×194

12388



Step 2 Multiply 194 by 1 ten. ×

19412

3881,940

1


1,940

1

×194

12388

+2,328



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




Since 2,328 is close to the estimate, the answer is reasonable.



A. 3,210 minutes

B. 3,814 minutes

C. 3,752 minutes

D. 3,852 minutes

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?


Estimate $308 × 52 300 × 50 = $15,000

Step 1 Multiply $308 by 2.

×$308

52$616

1



Step 2 Multiply $308 by 50.

$15,400

4

$616

$30852

1

×



Step 3 Add the partial products.

$616$15,400

4

$30852

1

×

+$16,016

Answer: So, Rai’s annual salary 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?



Main Idea


Example 1: Problem-Solving Investigation

8-68-6 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 carnival. I spent 45 minutes eating and 55 minutes playing games. I also rode 12 rides, which took about 15 minutes each.

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 45 minutes eating.

• He spent 55 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 minutes60 minutes60 minutes

+ 60 minutes 240 minutes

time Gregory said he spent at carnival

30

15× 12

+ 150180

time spent riding rides

45 minutes55 minutes

+ 180 minutes 280 minutes

time spent on carnival activities


Solve


Answer: Since 240 minutes does not equal 280 minutes, Gregory is not correct.


Check


Look back at the problem. Use subtraction to check the amount of time spent on carnival activities.

280 – 180 – 55 – 45 = 0

So, Gregory was not correct.



Main Idea




8-78-7 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.


9,124

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.

×4,562

52

111




228,100

32

4,56252

9,124

111

×


Step 3 Add the partial products. Check for reasonableness.


+237,224

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

4,56252

9,124

111

228,100

32

×



A. 427,700 visitors

B. 427,590 visitors

C. 426,790 visitors

D. 427,800 visitors

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 23,149 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.



A. 594,975 hits

B. 595,864 hits

C. 595,975 hits

D. 594,323 hits

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

Math Tool Chest

Image Bank


To use the images that are on the following four slides in your own presentation:

1. Exit this presentation.

2. Open a chapter presentation using a full installation of Microsoft® PowerPoint® in editing mode and scroll to the Image Bank slides.

3. Select an image, copy it, and paste it into your presentation.



Lesson 8-1 (over Chapter 7)

Lesson 8-2 (over Lesson 8-1)







(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


$274 × 16


(over Lesson 8-2)

A. 63,000; less

B. 64,800; more

C. 70,000; more

D. 64,800; less


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)

Answer:

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

This slide is intentionally blank.

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