Math Worksheets

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Explore How Big Is a Million?

Print This 1–1 Page

P

PRACTICE

Solve. 1. How many 10-by-10 grids would

2.

you need to make a thousand cube?

How many thousand cubes would you need to make a million?

3. How many hundreds are in 1,000? 4. How many hundreds are in 10,000? 5. How many thousands are in 1,000? 6. How many thousands are in 10,000? 7. How many thousands are in 100,000?

© McGraw-Hill School Division

8. How many thousands are in 1,000,000? 9. How many ten thousands are in 10,000? 10. How many ten thousands are in 100,000? 11. How many ten thousands are in 1,000,000? 12. How many hundred thousands are in 100,000? 13. How many hundred thousands are in 1,000,000?

Use with Grade 4, Chapter 1, Lesson 1, pages 2–3. (1)

NS 1.1




R

RETEACH

You can show numbers in different ways. You can think of 1,000 in the following ways: 1 thousand 10 hundreds 100 tens 1,000 ones 1 thousand

10 hundreds

1. What number is shown below?

Complete. Name each number in different ways.


2. 10,000

3. 100,000

4. 1,000,000

ten thousand

hundred thousand

million

thousands

ten thousands

hundred thousands

hundreds

thousands

ten thousands

tens

hundreds

thousands

ones

tens

hundreds

ones

tens ones


NS 1.1




E

ENRICH

A Million Pizzas Skye just opened Skye’s Pizzas. Her dream is to sell one million pizzas. She wants to see how long it will take. Answer these questions to help her find out. 1. Skye says, “If I sell 100 pizzas every day, I can sell 1,000,000 pizzas

in

days!” She frowns. “That’s a long time.”

2. Suddenly Skye snaps her fingers. “I know! I’ll open more stores!

If I have 10 stores and each store sells 100 pizzas every day, it will only take

days to sell 1,000,000 pizzas!”

3. “Wait a minute!” she exclaims. “What if I have 100 stores and

each store sells 1,000 pizzas every day? How long will it take to sell 1,000,000 pizzas?” “Why don’t you try to sell 1,000,000 pizzas in just 1 day?” Skye’s friend Emma asks. “Hmmm,” Skye murmurs. “How many stores would I need? How many pizzas would each store need to sell?” 4. Decide how many stores Skye would need and how many pizzas


each store would need to sell in 1 day.

5. What if you were Skye? What would be your plan? Tell about your plan.


NS 1.1



Place Value Through Millions

P

PRACTICE

Write the word name and the expanded form for each number. 1. 1,420,316

2. 2,672,400

3. 12,060,072

4. 785,004,012

Write the value of each underlined digit. 5. 842,753

6. 6,782,141

7. 153,428,090

8. 715,124,068

Write each number in standard form. 9. one million, two hundred thousand, five 10. thirty-eight million, four hundred thousand, eight


11. five hundred eighty million, sixty-two thousand, seventeen 12. two hundred fifty-four million, seven thousand, five

Algebra & Functions Write the missing number. 13. 42,865 40,000

800 60 5

14. 168,943 100,000 60,000 8,000 15. 888,888 800,000


40 3

8,000 800 80 8 NS 1.1




R

RETEACH

Numbers in the millions have three periods. Each period is separated by a comma.

Millions

Thousands

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

7

0

1

2

2

1

3

5

4

Expanded form:

700,000,000 1,000,000 200,000 20,000 1,000 300 50 4

Standard form:

701,221,354

Word name:

seven hundred one million, two hundred twenty-one thousand, three hundred fifty-four

Complete. 1. 824,124 =

+ 20,000 + 4,000 +

2. 7,624,139 = 7,000,000 + 3. 42,521,012 =


Standard Form

+ 20,000 + + 2,000,000 + 500,000 + Expanded Form

4.

3,000,000 200,000 500 20

5.

2,000,000 400,000 50,000 7,000 800 20 1

6.

30,000,000 7,000,000 800,000 50,000 2,000 4

7.

40,000,000 9,000,000 300,000 50,000 2,000 6


+

+ +

+ +

+ + 10 +

Word Name

NS 1.1




E

ENRICH

And the Number Is . . . Use the digits below only once in each exercise. 1

2

3

4

5

6

7

8

9

1. What is the greatest number with 4 in the hundred millions place?

,

,

2. What is the greatest number with 5 in the hundred thousands place?

,

,

3. What is the least number with 6 in the millions place?

,

,

4. What is the least number with 3 in the ten thousands place?

,

,

5. What is the greatest number with 8 in the thousands place?

,

,

6. What is the greatest number with 1 in the ten millions place?

,

,

7. What is the least number with 9 in the millions place and 2 in

the ten thousands place? ,

,


8. What is the greatest number with 7 in the hundred thousands

place and 1 in the thousands place? ,

,

9. How did you use place value to help you make the greatest

possible number? the least possible number?


NS 1.1



Compare and Order Numbers and Money

P

PRACTICE

Compare. Write >, <, or =. 1. 3,874 4. 14,624 7. $101.42

3,862 1,462 $126.41

2. 5,741

5,862

3. $78.24

$77.24

5. 42,542

41,617

6. 32,145

32,264

8. 25,632

25,632

9. 89,000

87,999

10. 150,420

100,042 11. 434,121

432,154 12. 187,654

197,541

13. 782,421

782,342 14. 642,134

642,134 15. 874,158

972,421

Order from greatest to least. 16. 3,421; 3,641; 3,481; 3,562 17. $216.49; $218.42; $206.49 18. 72,642; 71,848; 70,621 19. 748,629; 747,832; 748,532

Order from least to greatest. 20. $64.21; $68.78; $87.68; $65.43 21. 25,421; 24,462; 24,416


22. 324,621; 324,742; 325,697 23. 524,607; 525,712; 524,872

Problem Solving 24. Sean has 1,575 bird stamps and Li has 25. Sean’s stamp album cost $12.75 and 2,075 bird stamps. Cindy has a Li’s album cost $18.50. Cindy’s album number of stamps between Sean’s and cost the most. Is it $18.75 or $11.75? Li’s numbers. Is it 1,075 or 1,755? Explain. Explain.


NS 1.2




R

RETEACH

You can use a place-value chart to compare numbers. Start at the left. Look for the first place where the digits are different. Compare 4,872 and 4,892. Thousands

Hundreds

Tens

Ones

4

8

7

2

4

8

9

2

same number of thousands

same number of hundreds

4,892 has more tens than 4,872.

So, 4,892

4,872.

Compare $306.97 and $319.23. Hundred Dollars

Ten Dollars

One Dollars

Cents

3

0

6

97

3

1

9

23

same number of hundred dollars

$319.23 has more ten dollars than $306.97.

So, $319.23

$306.97.

Use the place-value chart to compare the numbers. Write , , or . 1. Compare 3,234 and 3,216.


Thousands

Hundreds

3,234 Tens

3,216 Ones

Compare. Write , , or . 2. 8,504

8,515

3. $25.16

4. 5,558

5,585

5. 6,117

6. $324.89 8. 56,619 10. 502,300

$314.89 56,916 510,239


7. 50,281

$21.12 6,117 51,002

9. $285.45

$293.45

11. 832,077

822,077 NS 1.2




E

ENRICH

Greater Numbers Look at the value that each letter represents. Then order the letters from least to greatest values in the boxes below.

A. There are 9,123 public libraries in the United States. B. There were 54,773 poodles registered by the American Kennel Club, Inc. C. There were 54,470 beagles registered by the American Kennel Club, Inc. D. The area of Mexico is 761,604 square miles. E. In the year ending December 31, 1997, there were 4,819 Maine coon cats

registered in the United States. F. The area of the United States is 3,618,770 square miles. G. In the 1864 United States Presidential election, Abraham Lincoln received

2,216,067 votes.


H. In the 1868 United States Presidential election, Ulysses S. Grant received

3,015,071 votes. I. The area of Japan is 145,856 square miles.


NS 1.2



Problem Solving: Reading for Math

P

PRACTICE

Reading Skill

Using the Four-Step Process Read the problem. Then read each step in the problem-solving process. Write a number next to each step to show the order in which the steps are done. Write a 1 for the first step, and so on. 1. A male elk weighs 600 pounds. A male moose weighs

1,000 pounds. A male caribou weighs 300 pounds. What is the order of the three animals from greatest to least weight? Check your answer. Identify what you need to find. You need to find the order of the male elk, the male moose, and the male caribou from greatest to least weight. Read the problem. Identify what you know: A male elk weighs 600 pounds. A male moose weighs 1,000 pounds. A male caribou weighs 300 pounds. Make a plan for solving the problem. Order the animals by comparing their weights two at a time. List the animals from greatest to least weight. Follow your plan to solve the problem. What is the order of the three animals from greatest to least weight?

2. A mink can be 20 inches long. A wolverine can be 36 inches long.

A black-footed ferret can be 18 inches long. Which animal can grow to the greatest length?


Identify what you know. A mink can be 20 inches long. A wolverine can be 36 inches long. A black-footed ferret can be 18 inches long. Check your answer. Make a plan for solving the problem. Order the animals by comparing their lengths two at a time. List the animals from least to greatest length. Identify what you need to find: Which animal can grow to the greatest length? Follow your plan to solve the problem. Read the problem. Which animal can grow to the greatest length? Use with Grade 4, Chapter 1, Lesson 4, pages 12–13. (10)

MR 1.1, 1.2, 2.3, 2.4, 3.2




P

Using the Four-Step Process

PRACTICE

Math Skills Test Prep

Choose the correct answer. A bottle-nosed dolphin can weigh up to 440 pounds. A common dolphin can weigh up to 165 pounds. Which kind of dolphin can be heavier? 1. Which of these statements is true?

A A bottle-nosed dolphin cannot be as heavy as a common dolphin. B A common dolphin can weigh 615 pounds. C A bottle-nosed dolphin can weigh 440 pounds.

2. Which plan will help you solve the

problem? F Add 440 and 165. G Compare 440 and 165. H Subtract 165 from 440.

On Friday, 660 people went to Ocean World Animal Park. On Saturday, 1,096 people went to Ocean World. On Sunday, 998 people went to Ocean World. On which day did the most people go to Ocean World? 3. Which plan can you use to solve this

4. On which day did the most people

problem?

go to Ocean World?

A Compare 660; 1,096; and 998. B Add 660 and 1,096. C Add 1,096 and 998.

F Friday G Saturday H Sunday


Lassie’s Dog Walking Service walks 68 dogs per week. Doggie Express walks 57 dogs per week. Top Dog Company walks 101 dogs per week. List the dog walking services in order from least dogs walked per week to most dogs walked per week. 5. Which statement is true?

A Lassie’s Dog Walking Service walks the most dogs per week. B Doggie Express walks 57 dogs per week. C Top Dog Company walks 68 dogs per week


6. Which plan can you use to solve the

problem? F Compare the numbers of dogs walked two at a time. G Find the difference between the number of dogs walked by Top Dog Company and the number walked by Lassie’s. H Find the total number of dogs walked by the three services. MR 1.1, 1.2, 2.3, 2.4, 3.2


Problem Solving: Reading for Math Using the Four-Step Process


P

PRACTICE


Choose the correct answer. Ocean World Animal Park needs 750 customers each day to make money. On Monday, Ocean World had 803 customers. On Tuesday, Ocean World had 691 customers. On Wednesday, Ocean World had 911 customers. On which day or days did Ocean World make money? 7. Which plan will help you solve the

problem? A Compare the daily customer totals two at a time. B Compare each daily customer total to 750. C Order the daily customer totals from greatest to least. Solve. 9. A marlin can move at a speed of 50 miles per hour. A striped dolphin can move 19 miles per hour. A killer whale can move 55 miles per hour. List the animals in order from slowest to fastest.


11. A poll shows that 311 students have

dogs, 424 students have cats, 96 students have birds, and 38 students have a different pet. Which kind of pet is owned by the most students?

13. Dylan spots 48 birds. Nicole spots 51

birds. Who spots fewer birds?


8. On which day or days did Ocean

World make money? F Tuesday only G Wednesday only H Monday and Wednesday only

10. Brandon, Timothy, and Norah have

pet care services. Last year, Brandon earned $712, Timothy earned $1,110, and Norah earned $650. List the people in order from greatest amount earned to least amount earned.

12. The pet shelter has 324 dogs in

April, 411 dogs in May, and 399 dogs in June. List the months in order from least number of dogs to greatest number of dogs.

14. In 1997, about 36,000,000 people went

to aquariums and about 86,000,000 people went to zoos. Did more people go to aquariums or to zoos?

MR 1.1, 1.2, 2.3, 2.4, 3.2



Round Numbers and Money

P

PRACTICE

Round to the given place. 1. 923 to the nearest

2. $0.93 to the nearest

ten


ten cents


dollar

dollar

5. 862 to the nearest


hundred

7. 4,357 to the nearest

dollar


thousand

9. 8,553 to the nearest

ten cents

hundred

10. 380,256 to the nearest 11. 61,479 to the nearest 12. 1,555 to the nearest

hundred thousand

ten thousand


ten cents

hundred

14. 7,502,475 to the

15. 2,653,789 to the

nearest million

nearest hundred thousand

Algebra & Functions Find the rule. Complete the table. 16.


Rule: Input

57,124

Output

60,000

64,142

91,722

234,162

478,234

Problem Solving 17.The radio announcer said that there

were 1,532 bluebird sightings on the island. To the nearest hundred, how many sightings were there?


18.Joe’s class bought a bird feeder for

$38.75. To the nearest dollar, what was the cost?

NS 1.3




R

RETEACH

You can use a number line to help you round.

40,000 41,000 42,000 43,000 44,000 45,000 46,000 47,000 48,000 49,000 50,000

Round 46,208 to the nearest ten thousand. Think: 46,000 is closer to 50,000 than 40,000. So, 46,208 rounds up to 50,000.

$6.00

$6.10 $6.20

$6.50 $6.60

$6.30 $6.40

$6.70

$6.80

$6.90 $7.00

Round $6.38 to the nearest dollar. Think: $6.30 is closer to $6.00 than $7.00. So, $6.38 rounds down to $6.00. Round to the nearest ten thousand. 1. 42,496

2. 49,009

3. 43,875

4. 45,800

5. 42,900

6. 47,250

7. 44,987

8. 41,875

9. 45,203


Round to the nearest million. 10. 7,450,000

11. 7,550,000

12. 7,832,010

13. 7,289,999

14. 7,362,800

15. 7,512,300

Round to the nearest dollar. 16. $12.60

17. $12.45

18. $12.13

19. $12.93

20. $12.53

21. $12.39

22. $12.25

23. $12.62

24. $12.59


NS 1.3




E

ENRICH

Mystery Numbers 1. If you round me to the nearest hundred, you get 400.

If you round me to the nearest ten, you get 430. The sum of my digits is 8. What number am I? 2. If you round me to the nearest thousand, you get 3,000.

If you round me to the nearest hundred, you get 2,600. Three of my digits are the same. The sum of my digits is 17. What number am I? 3. If you round me to the nearest thousand, you get 4,000.

The sum of my digits is 10. If you read me forward or backward, I am the same. What number am I? 4. If you round me to the nearest ten thousand, you get 50,000.

My first two digits add up to 10. The digit in my hundreds place is one more than 2. My last three digits add up to 8, and round (to the nearest hundred) to 400.


What number am I? 5. The sum of my seven digits is 60. Six of the digits are the same.

Rounding me to the nearest ten, hundred, thousand, ten thousand, or million will give you the same number. What number am I? 6. If you round me to the nearest 100,000, you get 600,000.

Each of my six digits is the same. What number am I? Use with Grade 4, Chapter 1, Lesson 5, pages 14–17. (15)

NS 1.3



Problem Solving: Strategy

P

PRACTICE

Make a Table Make a table. Use data from the table to solve problems 1 and 2. Elliot—dog Marion—cat Tina—hamster Paula—fish Sam—cat

What is your favorite kind of pet? Howard—dog Jane—bird Noriko—bird Teri—cat Yolanda—dog Sarah—cat Barry—cat Bruce—dog Juan—dog Mike—cat

Rebecca—bird Melanie—cat Traci—dog Noreen—fish Sylvia—cat

1. Which pet had the most votes?

2. Which pet had the least votes?

3. Mark cuts out letters to make a sign.

4. Which letter does Mark need to

The sign says, "Get Pet Kittens for Free." How many different kinds of letters does Mark need to make?

Mixed Strategy Review Solve. Use any strategy. 5. A pet store sold 137 bags of dog food called The Vet’s Choice. It sold 249 bags of a dog food called Fido’s Friend. How many more bags of Fido’s Friend than The Vet’s Choice were sold?

make the most of? How many of these letters does Mark have to make?

6. In 1999, The Pet Palace made about

$100,000. In 2000, The Pet Palace increased this amount by $10,000. How much did The Pet Palace make in 2000?


Strategy: Strategy: 7. Science Adult sun bears usually

weigh from 60 to 100 pounds. Adult grizzly bears weigh from 350 to 500 pounds. Adult Asiatic black bears weigh about 250 pounds. Which bear weighs the least?

8. Create a problem you would make

a table to solve. Share it with others.

Strategy: Use with Grade 4, Chapter 1, Lesson 6, pages 20–21. (16)

NS 1.2; SDP 1.3; MR 1.1, 2.3, 3.2




R

RETEACH

Make a Table Page 21, Problem 2

Which type of fish has the greatest number of varieties? Different Varieties of Tetras, Goldfish, and Angelfish tetras—black neon tetra goldfish—black moor angelfish—gold angel tetras—lemon tetra

goldfish—fan tail goldfish tetras—white skirt tetras—silver dollar angelfish—marble angel

goldfish—lionhead tetras—black neon tetras angelfish—silver angel

Step 1

Read

Be sure you understand the problem. Read carefully. What do you know? • There are different varieties of , and

, .

What do you need to find? • You need to know how many different varieties of ,

, and

there are. Step 2

Plan ■


■

■

■

■

■

■

■

■

■

Make a Table or List Write a Number Sentence Work Backward Act it Out Find a Pattern Make a Graph Guess and Check Logical Reasoning Solve a Simpler Problem Draw a Picture

Make a plan. Choose a strategy. A table can help you organize what you know. Make a table to solve the problem.


NS 1.2; SDP 1.3; MR 1.1, 2.3, 3.2



R


RETEACH

Make a Table Step 3

Solve

Carry out your plan. Make a table to solve. Tally the number of for each fish. Write a number for each set of tallies. Compare the numbers. Complete the table. Type of Fish

Tally of Different Varieties

Number

Tetras Goldfish

3

Angelfish There are

different kinds of tetras.

There are

different kinds of goldfish.

There are

different kinds of angelfish.

There are more varieties of two kinds of fish. Step 4


Look Back

than either of the other

Is the solution reasonable? Reread the problem. Does your answer match the data given in the problem?

Practice 1. Jack lists the fish in his aquarium. He has a fan tail goldfish, a lionhead goldfish, a gold angel angelfish, a lemon tetra, and a black neon tetra. Of which type of fish does Jack have the least?


2. Alex, Brian, and Yumi each like one kind

of dog. The dog is either a terrier, a retriever, or a poodle. Alex does not like retrievers. Brian does not like poodles or retrievers. Who likes poodles?

NS 1.2; SDP 1.3; MR 1.1, 2.3, 3.2



Count Money and Make Change

P

PRACTICE

Write the amount of money shown. 1.

2.

3.

8 8

SCHOOL MONEY

8

8

8

8

SCHOOL MONEY

8 8

Tell which coins and bills make the amount.

4. $0.89

5. $3.62

6. $7.67

8. Price: $2.45

9. Price: $7.81

Find the amount of change. 7. Price: $0.59

Amount given: $1.00

10. Price: $0.86 © McGraw-Hill School Division

Amount given: $5.00

Amount given: $5.00

11. Price: $3.09

Amount given: $10.00

12. Price: $9.25



Problem Solving 13. Andy gives the cashier $5.00 to pay

for a $3.75 calendar. How much change does he receive?


14. Lowanda receives 1 quarter, 2 dimes,

and 1 nickel in change. How much money is that?

NS 1.0; MR 2.4




R

RETEACH

To make change, start with the cost. Then count up to the amount given to you. Use the fewest number of bills and coins possible. You sell a pen for $2.49. Someone gives you $5.00 for the pen.

$2.49 Cost

$2.50

$2.75

$3.00

$4.00

$5.00

Count the bills and coins to find the change: $2.51. Count up. Find the amount of change. 1. Amount given: $6.00

$5.34 Cost Amount of change:


2. Amount given: $10.00 8 8

SCHOOL MONEY

8 8

$3.79 Cost Amount of change:


NS 1.0; MR 2.4




E

ENRICH

Money Detective Use the clues to find which coins and bills are inside each bank. 1.

2.

$0.47

$0.58

Clue: 6 coins

3.

Clue: 13 coins

4.

$0.73

$0.81

Clue: 10 coins

5.

Clue: 8 coins

6.

$1.00

$7.45


Clue: 19 coins, but only two kinds

7.

Clue: 3 bills, 3 coins

8.

$15.55



$23.00


NS 1.0; MR 2.4



Negative Numbers

P

PRACTICE

Write a positive or negative number to represent each situation. 1. Lose $4

2. Deposit $50

3. 300 feet above sea level

4. 12F below zero

5. Gain 3 pounds

6. Go 3 floors down

7. Take 8 steps back

8. Earn $25

9. 52F

10. Lose 10 pounds

Compare. Write or . You may use a number line to help. 11. 0 15.

4

19. 1 23. 27.

5

4


31. 11 35.

6

9

12. 2

3

7

16. 0

12

20. 6

2

8

24.

8

12

24 13

11 32. 0

8

1

36.

2

17.

10

28. 17

13.

10

2

14.

0

18.

22. 7

4 3

21. 12 25. 29. 33. 37.

12

5 3

0

26.

30. 0

11

15

9

15

9

34. 13

4

38.

4

3

6

6

10

12

9

11 3

7

Problem Solving 39. Manuel deposited a check for $25 in

his savings account. Then he withdrew $30. Write a number to represent each situation.


40. An airplane descended 1,000 feet. Ten

minutes later, it climbed 9,500 feet. Write a number to represent each situation.

NS 1.8



Negative Numbers

R

RETEACH

You can use a number line to understand and compare positive and negative numbers.

6

5

4

negative numbers

positive numbers

less than zero

greater than zero

3

1

2

1

0

2

3

4

5

6

Numbers to the right are greater than numbers to the left.

2 is to the right of 2, so 2 2.



Complete. 1. 2. 3. 4.


5. 6.

5 is to the right of 3, so 5

3.

of 1, so 1

of 6, so 5

of 1, so 4

of 6, so 6

of 4, so 2

1 is to the 5 is to the 4 is to the 6 is to the 2 is to the

1. 6.

1. 6.

4.

Compare. Write or . You may use a number line to help. 7. 11. 15. 19.

14

14

12

21

6 7

8. 12.

15

16.

7

20.

13

31

25

5

10

8

12

2


9. 13. 17. 21.

9 8 2 9

15 2 12 8

10. 14.

20

18

20

20

22. 0

18.

4

4

10 NS 1.8



Negative Numbers

E

ENRICH

Are You Positive or Negative? Play with a partner. You will need 10 blank cards for each player. • Each player writes five different negative and five different positive integers, one on each card. They should use the integers from 10 to 10. Each player mixes up their cards and spreads them out face down. • To play, each player touches one of these cards. One player announces “Mine is greater than (or ‘less than’ or ‘equal to’) yours.” Both players turn over their card. If the statement was correct, that player gets both cards. If not, they go to the original player.

9

• Repeat touching cards and taking turns making the statements. When all cards are collected, the player with the most cards wins.

7

8


2

0

1

6

3

5


4 NS 1.8


Problem Solving: Application

Print This Page

1–9 Part A WORKSHEET Decision Making

Applying Place Value Record your data. Answers may vary. Store

Cost of 20 Pounds of Dog Food

Cost of Gas for Trip to Store

Pet Supply

Animal World

Pet’s Place


Discount Pet Food

Your Decision What is your recommendation for Stacia? Explain.


NS 1.2; MR 1.1, 2.3


Print This Page

1–9 Part B WORKSHEET


Math & Science

How do you compare with your partner? Record your data. Data for Student 1

Data for Student 2

Are the two sets of data the same or close to being the same?

1. Your favorite number

2. Number of hours you sleep

each night 3. Number of push-ups you can do

in 30 seconds 4. Number of objects in your desk

right now 5. Number of cups of water you

drank yesterday 6. Number of cats and dogs you know


7. Length of your arm from shoulder

to wrist 8. How long you can stand on one foot

9. Number of times you breathe in

one minute 10. Your age


NS 1.2; MR 1.1, 2.3, 3.3


Problem Solving: Application How do you compare with your partner?

Print This Page

1–9 Part B WORKSHEET Math & Science

1. How many times were you and your partner the same? different?

2. Explain how you decided whether you and your partner were the

same. Did the numbers have to be exactly alike? Why or why not?

3. In which areas did you vary the most from your partner?


4. In which areas did you vary the least from your partner?

5. Why is it good to have variation in nature?


NS 1.2; MR 1.1, 2.3, 3.3



Use Properties of Addition

P

PRACTICE

Complete the set of related number sentences. 1. 5 , 3, 8

2. 6, 8, 14

5n8

68n

n38 85n 8n5

8 n 14

4. 3, 7, 10

3. 6, 9, 15

n 6 15 6 n 15 15 n 6 15 6 n

14 6 n 14 n 8 5. 22, 5, 27

6. 34, 4, 38

3 n 10

22 n 27

34 n 38

37n

5 22 n

4 n 38

n37 10 n 3

n 22 5 27 5 n

38 n 34 n 4 34

Find the sum or difference. Write the related number sentences. 7. 2 9

8. 35 4

9.

54 0

Write the related number sentences for the set of numbers.


10. 4, 5, 9

11. 11, 24, 35

Problem Solving 13. Ken has 6 coins in his collection.

Barb has 5 more coins than Ken. How many coins does Barb have?


12. 0, 46, 46

14. Meg has 13 coins in her collection.

Then she gives 7 coins to her cousin. How many coins does Meg have now?

NS 3.1; AF 1.1




R

RETEACH

Every number sentence in a set of related number sentences uses the same numbers. The model below shows a set of related number sentences. 538 358

}

Commutative Property: 5 3 8 is the same as 3 5 8.

835 853 You can also use the properties and the idea of related sentences with greater numbers. Look at each model. Write the related number sentences. 1.

2.

Find the sum. Write the related number sentences.


3. 8 3

n

4. 2 7

n

5. 18 0

n

Write the related number sentences for the set of numbers. 6. 26, 17, 43

7. 0, 56, 56


8. 9, 45, 54

NS 3.1; AF 1.1




E

ENRICH

Properties and Rules Complete each number sentence. Then write the property or rule you used. 1.

MNM N

2. A

3.

CDC D

4.

HH

5.

6.


BB

JJ

Z0

7.

QQP

8.

0W

Write the related number sentences. 9.

ANB


10.

DEF

NS 3.1; AF 1.1



Addition Patterns

P

PRACTICE

Complete the pattern. 1. 8 8

n

2. 7 6

n

80 80 n

70 60 n

800 800 n

700 600 n

8,000 8,000 n

7,000 6,000 n

80,000 80,000 n

70,000 60,000 n

800,000 800,000 n

700,000 600,000 n

3. 5 9

n

4. 8 9

n

50 90 n

80 90 n

500 900 n

800 900 n

5,000 9,000 n

8,000 9,000 n

50,000 90,000 n

80,000 90,000 n

500,000 900,000 n

800,000 900,000 n

Add mentally. 5. 500 400

6. 3,000 9,000

7. 30,000 80,000

8. 700 800

9. 600 500


11. 100,000 900,000

10. 70,000 30,000 12. 800,000 500,000

Problem Solving 13. A music store made $50,000 selling

CDs and tapes in December. In January, the store made $30,000. How much did the store make in all?


14. The Green Hornets sold 800,000

copies of their first CD. They sold 500,000 copies of their second CD. How many CDs did the Green Hornets sell in all?

NS 3.1; MR 1.1



Addition Patterns

R

RETEACH

You can use addition facts and patterns to add multiples of ten mentally. Add the front digits. Then write a zero to match each place value. 5 7 12

5 7 12

5,000 7,000 12,000

5,000 7,000 12,000

50 70 120

50 70 120

50,000 70,000 120,000

50,000 70,000 120,000

500 700 1,200

500 700 1,200

500,000 700,000 1,200,000

500,000 700,000 1,200,000

Complete the pattern.


1. 3 8

n

2. 5 9

n

30 80 n

50 90 n

300 800 n

500 900 n

3,000 8,000 n

5,000 9,000 n

30,000 80,000 n

50,000 90,000 n

300,000 800,000 n

500,000 900,000 n


4. 9,000 7,000

5. 80,000 80,000

6. 5,000 4,000

7. 900 500

8. 700,000 600,000

9. 800,000 700,000 11. 300 700 Use with Grade 4, Chapter 2, Lesson 2, pages 46–47. (32)

10. 60,000 50,000 12. 80,000 90,000 NS 3.1; MR 1.1



Addition Patterns

E

ENRICH

Pascal’s Triangle The triangle below is called Pascal’s Triangle. Each row begins and ends with the number 1. Every other number is the sum of the two numbers above it. Complete this Pascal’s Triangle. Row 1

1

Row 2

1

Row 3

1

Row 4

1

Row 5

Row 7

2 3

1

Row 6

1 1 3

1

6

1

1

1

1

1

Now complete this Pascal’s Triangle. Each row begins and ends with 200. Row 1

200

Row 2

200


Row 3

200

Row 4

200

Row 5

200

Row 6 Row 7

200 200


200 400

600

200 600

1,200

200 200 200 200

NS 3.1; MR 1.1



Add Whole Numbers and Money

P

PRACTICE


Find each sum. 1.

688 207

2.

574 434

3.

757 529

4.

$8.72 1.38

5.

$2.98 0.59

6.

989 624

7.

8,489 2,467

8.

$3,824 962

9.

5,174 327

10.

$12.57 7.43

11.

6,672 878

12.

$78.29 45.32

13.

12,345 67,890

14.

43,802 7,526

15.

24,316 893

16.

183,462 570,184

17.

$3,421.78 1,657.18

18.

204,177 678,687

19.

741,243 85,278

20.

$427,535 6,280

21. $7.77 $6.66

22. 5,872 754

23. 3,489 87 741

24. $256.82 $357.47 $83.95

25. 42,608 7,709 3,047

26. 782,070 879,162 115,603

Problem Solving 27. At the Lakeside School, 522 students

ride the bus and 714 students walk or are driven to school. How many students attend Lakeside School?


28. Last week, $325 worth of play tickets

and $729 worth of carnival tickets were sold. How much money was collected altogether?

NS 3.1



Add Whole Numbers and Money Add 587 269. Step 1 Add the ones. Regroup if necessary. H

T

Step 2 Add the tens. Regroup if necessary. O

H

T

1

1

5 2

8 6 5

1

5 2

8 6

7 9 6

R

RETEACH

Step 3 Add the hundreds. Regroup if necessary. O

H

T

O

1

1

7 9

5 2

8 6

7 9

6

8

5

6

7 ones 9 ones 16 ones 1 ten 8 tens 6 tens 1 hundred 5 hundreds 15 tens 2 hundreds 8 hundreds 16 ones 1 ten 6 ones 15 tens 1 hundred 5 tens


Find each sum. 1.

413 228

2.

336 574

3.

$4.80 2.57

4.

327 425

5.

$828 16

6.

187 219

7.

534 394

8.

$9.34 3.68

9.

692 810

10.

$7.99 7.99

11.

1,245 3,717

12.

$31.15 85.29

13.

6,289 764

14.

8,147 3,988

15.

5,326 383

16.

71,128 3,511

17.

87,421 2,032 5,857

18.

25,784 4,408 64,726

19.

399,625 99,990 437,487

20.

$62.41 7.38 1.21


NS 3.1



Add Whole Numbers and Money

E

ENRICH

Hindu Addition The Hindu people of ancient India added numbers from the left and moved to the right. Here is an example of Hindu addition. Add the hundreds.

589 782 12

Next add the tens. 8 8 16. Regroup to the hundreds place.

Last, add the ones. Regroup to the tens place. The sum is 1,371.

589 782 126 3

589 782 1261 37


Use the Hindu method of addition to find the sum. Show your work. 1.

56 35

2.

96 87

3.

538 247

4.

322 489

5.

289 556

6.

$9.63 8.75

7.

238 849

8.

766 984

9.

$1.87 7.58

10.

11.

385 496

12.

874 496

$6.11 9.97

Compare the Hindu method of addition to the method of addition you use. Which method do you like best? Explain.


NS 3.1



Use Mental Math to Add

P

PRACTICE


2. 21 64

3. 35 13

4. $39 $24

5. 48 31

6. 298 311

7. 595 409

8. 255 344

9. 238 495

10. 730 214

11. 891 108

12. $256 $222

13. 4,524 3,173

14. 8,999 1,333

15. 2,295 2,124

16. 1,487 1,511

Algebra & Functions Find each missing number. 17. 36

a 86

19. $498 21.

c $698

e 657 957

23. $725

k $1,125


25. 1,650

n 3,300

18.

b 61 81

20.

d 298 598

22. $63

h $243

24.

m 837 1,137

26.

r $750 $1,500

Problem Solving 27. There are 38 dogs and 24 cats at the

pet show. How many cats and dogs are there in all?


28. The pet show committee spends

$316 on dog treats and $299 on cat treats. How much does the committee spend on treats?

NS 3.1; AF 1.1




R

RETEACH

You can use these two strategies to add mentally. Compensation Use compensation when a number is close to a ten or a hundred. 197 → 200 254 → 251 451

Add 3 to make 200: 197 3 200. Subtract 3 from the other number: 254 3 251.

Zig-zag Use the zig-zag method to add 356 627. Take apart 627. 627 600 20 7 Then add each place separately. 356 627

356 600 956

956 20 976

976 7 983



2. 54 17

3. 202 248

4. $316 $455

5. $625 $330

6. 437 128

7. 499 252

8. 697 140

9. $29 $56

10. $62 $78

11. $268 $441

12. 298 465

13. 752 247

14. 365 113

15. 599 109

16. 232 657

17. 253 35

18. 849 52

19. 425 222

20. 723 245

21. 3,398 1,343

22. 2,377 196

23. $6,512 $950

24. 1,783 5,097


NS 3.1; AF 1.1




E

ENRICH

Countdown! Move from left to right. Add each pair of numbers mentally. Shade any box that is the sum of the previous two boxes. Example: In row 1, add 19 and 53. The sum is 72. Shade the box with 72 in it. Add 53 and 72. If the sum is 125, then shade the box with 125 in it. 19

53

72

125

197

232

429

661 1,090 1,000 3,090 4,090

195

302

402

67

469

12

480

115

595

110

805

915

17

21

37

58

95

22

127

149

270

199

39

238

34

51

99

154

253

307

560

857 1,317

174

399

573

79

15

94

109

203

311

514

825 1,339 2,064 2,213 4,277

1. Look at the shaded boxes. What number do the boxes form? 2. Which method did you use to add pairs of numbers mentally when:

the sum of the digits was less than 9? one number was close to 10, 100, or 1,000?


the sum of the digits was greater than 9? How is mental math different from estimation?


NS 3.1; AF 1.1



Estimate Sums

P

PRACTICE

Estimate each sum. Show your work 1. 478 597 2. $8.65 $7.15 3. $0.32 $0.65 4. 4,990 405 5. 2,188 5,621 6. 47,522 3,721 7. 863,122 254,087

Add. Estimate to check that each answer is reasonable. 8. 621 308

9. 2,188 5,621

10. $4.20 $8.12

11. 601,128 328,125

Compare. Write or to make a true sentence. 12. 176 335 14. 500

251 127

16. 1,348 2,489


18. 9,000

13. 243 50

400

15. 900

5,000

4,487 5,672

20. 22,152 28,174

60,000

300 895 68

17. 4,725 321 19. 8,000

3,923 289

6,081 950

21. 49,912 2,839

5,000

Problem Solving 22. Julio wants to buy drawing paper

for $8.50 and brushes for $19.95. About how much will he spend?


23. The fourth-grade students make

268 posters about bicycle safety. The fifth-grade students make 229. About how many posters do the students make altogether?

NS 2.1; 3.1; MR 2.1, 2.5



Estimate Sums

R

RETEACH

To estimate a sum, you can round each number. Then add the rounded numbers. Estimate 252 49. Round each number to the nearest ten. Add.

Estimate $5.95 $7.25. 252 49 250 50

Round each $5.95 $7.25 ↓ ↓ number to the nearest dollar. $6.00 $7.00

250 50 300

Add.

↓

↓

So, 252 49 is about 300.

$6.00 $7.00 $13.00

So, $5.95 $7.25 is about $13.00.

To which place will you round each number? Circle the digits in that place. Then estimate each sum. Show how you rounded. 1. $7.89 $5.29

2. $0.32 $0.48

3. 6,714 8,217

4. 27,822 2,321

5. 5,214 642

6. 38,629 5,927

Estimate each sum.


7. 469 563

8. $9.08 $12.75

9. 143 431

10. 5,723 3,501

11. 1,827 764

12. 2,357 8,605

13. $38,956 $7,653

14. $46.90 $327.54

15. 896,455 11,321

16. 477,995 865,311


NS 2.1, 3.1; MR 2.1, 2.5



Estimate Sums

E

ENRICH

Star Estimates There are five paths. Each path has six numbers. Round each number to the nearest hundred. Then estimate the sum of the rounded numbers on each path of the star. Write your estimate in the box at the end of each path.

3.

30,800 23,724

5,627

3,846

1.

Start 225 5.

45,672

152

172

429

47,600 874

44,100 810

126,582

714


381

825

524

418,670 174

41,321

432 2.

129,600


645 4.

447,700

NS 2.1, 3.1; MR 2.1, 2.5




P

PRACTICE

Reading Skill

Estimate or Exact Answer Solve. Explain why you gave an estimate or an exact answer. 1. James, Max, and Melba collect baseball cards. James has 870 cards,

Max has 569 cards, and Melba has 812 cards. Do the three friends have more than 2,000 baseball cards?

2. Nicki has a collection of 79 shells and 64 rocks. How many items are

in her collection?

3. Kelly has a coin collection. Her quarters are worth $104.50. Her

dimes are worth $75.10. Her nickels are worth $27.75. What is the total value of Kelly’s coin collection?

4. The Comic Book Show sells 474 tickets on Friday and 396 tickets on

Saturday. About how many tickets does the Comic Book Show sell?


5. Eldon has 98 rock CDs, 121 classical CDs, and 25 folk music CDs.

How many CDs does Eldon have?

6. Molly has 221 stamps from the United States and 395 stamps from

other countries. About how many stamps does Molly have?


MR 1.1, 2.1, 2.3, 2.4, 2.5, 3.1, 3.2




P

Estimate or Exact Answer

PRACTICE


Choose the correct answer. Jenny has a collection of 249 football cards. Ken has a collection of 329 football cards. Are there more than 500 cards in these two collections altogether? 1. Which of the following statements is

2. Which number sentence will help

true?

you solve the problem?

A Jenny has more cards than Ken.

F 249 329 500

B Ken has more than 500 cards.

G 329 249 500

C Jenny has 249 cards.

H 500 249 500

Paco has 129 toy cars. His brother has 167 toy cars. How many toy cars do they have in all? 3. Which plan can you use to solve the

4. How many toy cars do they have

problem?

in all?

A Estimate the sum of 129 and 167.

F 300

B Add 129 and 167.

G 296

C Compare 129 and 167.

H 200


Hiroshi has 429 football cards, 278 baseball cards, and 97 hockey cards. Does Hiroshi have more than 1,000 cards in all? 5. Which of the following statements is

true? A Hiroshi has 278 baseball cards. B Hiroshi has 429 cards in all. C Hiroshi has 97 football cards.

6. What do you have to do to solve this

problem? F Find the exact sum for 429 278 97. G Estimate to tell if 429 278 is greater than 1,000. H Estimate to tell if 429 278 97 is greater than 1,000.


MR 1.1, 2.1, 2.3, 2.4, 2.5, 3.1, 3.2




P

Estimate or Exact Answer

PRACTICE


Choose the correct answer. On Friday, 529 people see the museum’s collection of antique dolls. On Saturday, 994 people see the collection. On Sunday, 812 people see the collection. How many people came to see the antique doll show during the three days? 7. Which plan can you use to solve the

problem? A Estimate the sum of 529, 994, and 812.

8. How many people came to see

the antique doll show during the three days? F 2,335

B Add 529, 994, and 812.

G 2,300

C Order 529, 994 and 812 from least to greatest.

H 1,523

Solve. 9. Chelsea has 635 postcards from the

United States, 291 postcards from Canada, and 456 postcards from Europe and Asia. Does she have more than 2,000 postcards?


11. Miles has 75 old movie posters,

63 concert posters, and 54 posters from plays. How many posters does Miles have?

13. Nina has 379 stamps from the

United States and 458 stamps from other countries. How many stamps does she have?


10. Gus has 65 autographs from sports

players, 97 autographs from actors and actresses, and 27 autographs from singers. About how many autographs does he have?

12. Evan has 4,212 cards. His sister has

5,349 cards. If they put their cards together, will they have more than 9,000 cards?

14. Morris has a collection of

44 quarters, 92 dimes, and 89 pennies. About how many coins does he have?

MR 1.1, 2.1, 2.3, 2.4, 2.5, 3.1, 3.2



Subtraction Patterns

P

PRACTICE


n

2. 16 7

n

120 80 n

160 70 n

1,200 800 n

1,600 700 n

12,000 8,000 n

16,000 7,000 n

120,000 80,000 n

160,000 70,000 n

1,200,000 800,000 n

1,600,000 700,000 n

3. 11 5

n

4. 15 8

n

110 50 n

150 80 n

1,100 500 n

1,500 800 n

11,000 5,000 n

15,000 8,000 n

110,000 50,000 n

150,000 80,000 n

1,100,000 500,000 n

1,500,000 800,000 n

Subtract mentally. 5. 1,200 600

6. $8,000 $3,000

7. 600,000 500,000

8. 70,000 50,000

9. $13,000 $9,000 © McGraw-Hill School Division

11. 140,000 50,000

10. 160,000 80,000 12. 1,200,000 600,000

Problem Solving 13. A video store rented 900,000 videos

last year. This year the store rented 1,500,000 videos. How many more videos did it rent this year?


14. The price for a house is $120,000.

Ms. Smith decides to make an offer that is $30,000 less than the price. How much does Ms. Smith offer for the house?

NS 3.1; MR 1.1




R

RETEACH

You can use subtraction facts and patterns to subtract multiples of ten mentally. Subtract the front digits. Then write a zero to match each place value. 12 7 5

12 7 5

12,000 7,000 5,000

12,000 7,000 5,000

120 70 50

120 70 50

120,000 70,000 50,000

120,000 70,000 50,000

1,200 700 500

1,200 700 500

1,200,000 700,000 500,000

1,200,000 700,000 500,000

Complete the pattern.


1. 11 8

n

2. 14 5

n

110 80 n

140 50 n

1,100 800 n

1,400 500 n

11,000 – 80,000 = n

14,000 5,000 n

110,000 800,000 n

140,000 50,000 n

1,100,000 8,000,000 n

1,400,000 500,000 n

Subtract mentally. 3. 1,400 600

4. $16,000 $7,000

5. 160,000 80,000

6. 1,200 500

7. $1,500 $700

8. 110,000 50,000

9. 14,000 8,000 11. 1,800,000 900,000


10. $1,700,000 $900,000 12. 120,000 40,000

NS 3.1; MR 1.1




E

ENRICH

Subtraction Squares (Diffy) Each subtraction square is made up of eight numbers. To find the missing numbers, subtract the two corner numbers in each square and write the difference in between the numbers. Find the missing numbers. Subtract until you reach the center of the square.

70

150

10

30 20

60

10

80

20

40 0

0 0 0 20 0 0 20

30

30

0 0 0 0


20

90

20 10

20 10

40

50

2. What happens in the center of the squares?

3. What do you think will happen if you choose four other corner

numbers for the largest square? Try it and check your prediction!


NS 3.1; MR 1.1



Explore Subtracting Whole Numbers

P

PRACTICE

Subtract. 1. Use models to subtract 525 272.

Subtract the ones.

5 2

2 7

5 2

Subtract the tens. Regroup 1 hundred as 10 tens.

5 2

2 7

5 2

Subtract the hundreds.

5 2

2 7

5 2


Subtract. 2.

187 95

3.

612 74

4.

356 127

5.

923 707

6.

319 79

7.

711 380

8.

425 258

9.

857 79

10.

562 348

11.

227 138

12. 684 327

13. 573 495

14. 813 75

15. 263 88


NS 3.1




R

RETEACH

Use models to subtract 322 145. Step 1 Model the greater number.

You need to subtract 145, or 1 hundred 4 tens 5 ones.

322 145

1 12

Step 2 Subtract the ones. Regroup a ten for 10 ones, if necessary.

Subtract 5 ones.

Step 3 Subtract the tens. Regroup a hundred for 10 tens, if necessary.

3 2/ 2/ 145 7 2 11 12

3/ 2/ 2/ 145 77 Subtract 4 tens.

Step 4 Subtract the hundreds.

2 11 12

3/ 2/ 2/ 145 177

Subtract 1 hundred.


Subtract. Use or draw models to help you subtract. 1.

724 318

2.

916 108

3.

568 59

4.

428 247

5.

353 182

6.

964 281

7.

735 586

8.

327 299

9.

863 575

10.

651 93

11. 274 126


12. 745 67

NS 3.1




E

ENRICH

Crack the Code Find each difference. Match the code number beside each problem with the correct code letter. Problems

Code Numbers

1. $3.63 $1.77

6

761 S

2. $4.25 $2.86

4

88 A

3. 181 92

9

$1.39 U

4. 573 397

13

176 T

5. 426 326

14

304 C

6. 880 119

5

$1.59 N

7. 625 317

2

89 V

12

$1.86 E

8. 682 594 9. 170 98

308 M

7

10. 590 399

15

11. 731 427

11

77 N

3

191 O

16

47 A

14. 464 387

8

138 A

15. 222 175

1

72 O

16. 832 694

10

$1.16 O

12. $9.05 $7.89 13. $6.52 $4.93


Code Letters

100 I

Use this code to solve the riddle. Write the correct letter above each number. Riddle: What animal is gray and has a trunk? 1

2

3

4

5

6

7


8

9

10

11

12

13

14

15

16

NS 3.1



Subtract Whole Numbers and Money

P

PRACTICE


Subtract. Check by adding. 1.

757 28

2.

$582 492

3.

693 516

4.

851 569

5.

$2.48 1.95

6.

2,345 1,658

7.

$67.89 18.95

8.

$11,321 979

9.

4,672 873

10.

3,523 2,846

11.

$33,572 13,689

12.

74,125 65,239

13.

49,785 8,998

14.

98,142 617

15.

$224.39 15.87

16.

$4,561.71 291.68

17.

389,243 136,354

18.

$672,145 98,276

19.

914,617 117,814

20.

$7,211.53 5,926.84

21. 827 468

22. $9.12 $7.58

23. 42,625 9,846

24. 65,932 46,464

25. $311.42 $4.65

26. $578,423 $89,743

27. 982,561 678,984

28. $2,176.53 $1,993.76

Problem Solving 29. A toy factory made 32,154 board

30. A store earned $12,415 selling

games on Monday. On Tuesday it made 31,687 board games. How many more board games did the factory make on Monday?

puzzles this week. Last week it earned $9,326 selling puzzles. How much more did the store earn this week?


NS 3.1




R

RETEACH

Subtract 7,617 5,789. Step 1 Subtract the ones. Regroup if necessary. TH

7 5

H

6 7

T

O

0

17

1/ 8

7 / 9

Step 2 Subtract the tens. Regroup if necessary. TH

7 5

H

T

O

5

10 0/

17

6/ 7

1/ 8

7 / 9

2

8

8

Step 4 Subtract the thousands.

Step 3 Subtract the hundreds. Regroup if necessary.

TH

H

T

O

15 5/

10 0/

17

6

7 / 9

7/ 5

6/ 7

1/ 8

7 / 9

8

1

8

2

8

TH

H

T

O

15 5/

10 0/

17

6

7/ 5

6/ 7

1/ 8

8

2

Use the same steps to subtract money.



577 385

2.

872 465

3.

$6.21 4.43

4.

3,457 965

6.

4,872 3,785

7.

7,501 6,874

8.

8,142 6,527

9.

12,435 8,679

11.

24,652 9,788

12.

$56,716 39,897

13.

347,072 59,687


14.

5.

10.

$2.49 0.98

$6,423 2,496

743,219 $6,192.48 15. 1,671.39 19,733

NS 3.1




E

ENRICH

Sumerian Numbers The Sumerians were an ancient civilization. Sumerians were one of the first people to develop a written number system and compute with it. They had five number symbols. The chart shows the value of each symbol.

1

10

60

600

3,600

The symbols were combined to represent numbers. Example:

3,600 600 60 10 10 4,280 Solve the Sumerian subtraction problems. Translate the Sumerian symbols to the numbers in our system and subtract. Then write the difference using Sumerian symbols. 1.

133

125

2.

1,263


1,821 1,205

7,280

626

637

8

4.

3.

5.

3,750

616


3,650

100

4,861

2,419

6.

1,242 922

320

NS 3.1



Regroup Across Zeros

P

PRACTICE



804 565

2.

701 387

3.

$500 244

4.

600 58

5.

300 108

6.

3,000 2,987

7.

9,000 5,431

8.

4,050 2,542

9.

2,000 784

10.

8,000 2,450

11.

$15,000 7,641

12.

70,700 8,633

13.

50,000 25,625

14.

80,000 35,189

15.

30,000 7,984

16.

600,003 25,178

17.

$900,000 321,229

18.

400,707 39,698

19.

210,303 101,506

20.

575,000 89,342

21. 602 423

22. 800 68

23. 3,400 1,762

24. 6,000 672

25. $20,800 $13,972

26. 70,000 52,087

27. 160,000 149,999

28. 307,000 198,621

Problem Solving 29. Crystal Lake School held a dance

30. At the festival, 39,251 people

festival. There were 3,000 dancers at the festival. Of those dancers, 2,682 did not win prizes. How many dancers did win prizes?

watched the dancers. Another 700,000 people watched the festival on television. How many more people watched the festival on television?


NS 3.1




R

RETEACH

Subtract 500 185. Step 1 No ones. No tens. Regroup the hundreds. H

T

4 5/

10 0 /

5 / 1

0/ 8

O

0 5

5 hundreds 4 hundreds 10 tens There are not enough ones to subtract 9 ones.

Step 3 Subtract the ones, the tens, and then the hundreds.

Step 2 Regroup the tens.

H

T

O

H

T

O

4

9 10 /

10

4

9 10 /

10

5 / 1

0/ 8

0/ 5

5 / 1

0/ 8

0/ 5

3

1

5

10 tens 9 tens 10 ones

10 ones 5 ones 5 ones 9 tens 8 tens 1 ten 4 hundreds 1 hundred 3 hundreds


Subtract. Check by adding. 304 150

1.

602 314

2.

700 203

3.

$900 306

4.

800 523

6.

$4,000 1,527

7.

2,005 1,083

8.

3,000 2,225

9.

5,000 259

10.

6,000 1,326

$40,050 32,037

15.

45,000 2,374

11.

68,000 11,770

12.

80,000 13. 74,800 5,287 27,862

14.

5.

16. 300,077 124,364

17. $200,008 $187,053

18. 107,006 84,119

19. 906,004 205,457

20. 60,000 29,730

21. $500,600 $50,250


NS 3.1




E

ENRICH

Missing Digits Find the missing digits. 1.

8

0

7

1

3

4.

0

1

7.

10.

6, 3,

7 2


13.

7

16.

2.

8 9

5.

4

, 2

0

7

, 7

3

9

0 8

6

8.

2 2

9

8 9

3

0 8

6

1

6

6,

7

3 1

17.

5

2

0

0

2 3

3


3

6

1

4,

12.

3

5,

6.

1

5 2

8 7

9.

7

9 2

3.

3

,

7 0

2 7

6

3

14.

7

5

8

2, 1,

11.

4

5 2

0 3

2

4 7

0 6

5, 2,

9

0 8

3 6

5 7

7 9

15.

6

5, 3,

5

2,

2

7, 3,

3

0 5

8

4

5

0 8 8

3

3 0

8

0 5

, 2

1

5

, 0 4, 8

7 8

, 1

18.

7 , , 2 5,

7

1 4

1 3

4 6

NS 3.1




P

PRACTICE

Write a Number Sentence Write a number sentence to solve. 1. Meg buys candle-making supplies for

$37. She has $25 left. How much money did Meg have before she bought the supplies?

3. Eric sells a painting for $125. He sells

a sculpture for $390. How much money does Eric earn in all?

2. Sally has finished 86 squares in her

quilt. The quilt will have 100 squares. How many squares does Sally still have to make?

4. Noah has saved $42. How much

more money does he need to buy a rare coin for $90?

Mixed Strategy Review Solve. Use any strategy. 5. Howard has 75 shells. On a trip, he

collects another 16 shells. How many shells does he have now?

6. Tom makes letters for a sign that

says “Arts and Crafts Fair.” Which letter does Mark need to make the most of?

Strategy: Strategy:


7. Social Studies During the 1800s,

sailors made carvings called scrimshaw on whale teeth, whalebone, and tortoise shells. Suppose a sailor made a carving in 1805. A collector buys the carving in 2000. How many years old is the carving?

8. Create a problem which you could

write a number sentence to solve. Share it with others.

Strategy:


NS 3.1; AF 1.1, 2.1; MR 1.1




R

RETEACH

Write a Number Sentence Page 69, Problem 2

Ms. Green had 29 buttons to sew on dolls. She has 14 buttons left. How many buttons has she already sewn on? Step 1

Read

Be sure you understand the problem. Read carefully. What do you know? • Ms. Green had • She has

buttons to sew on dolls. buttons left.

What do you need to find? • You need to find how many . Step 2

Plan ■

■

■

■

■


■

■

■

■

■

Make a Table or List Write a Number Sentence Work Backward Act It Out Find a Pattern Make a Graph Guess and Check Logical Reasoning Solve a Simpler Problem Draw a Picture

Make a plan. Choose a strategy.

You can write a number sentence to solve the problem. Since you know the original total and the number left, you can write a subtraction sentence.


NS 3.1; AF 1.1, 2.1; MR 1.1




R

RETEACH

Write a Number Sentence Step 3

Solve

Carry out your plan. • You know Ms. Green had • You know she has

buttons to sew on dolls. buttons left.

Write a subtration sentence to represent the situation. 29 n 14 number of buttons buttons left buttons she had already sewn on Then use a related sentence to solve.

number of buttons she had

buttons left

She has already sewn on Step 4

Look Back

buttons already sewn on

buttons.

Is the solution reasonable? Reread the problem. Does your answer make sense? Did you answer the question?

Yes Yes

No No

How can you check your answer?


What other stategies could you use to solve the problem?

Practice 1. Keshawn spends $45 on glass and copper molding. He pays with a hundred-dollar bill. How much change does Keshawn get back?


2. Melanie sells a model sailing ship and

a model airplane for a total of $40.95. She receives $23.49 for the ship. How much money does Melanie receive for the airplane?

NS 3.1; AF 1.1, 2.1; MR 1.1



Subtract Using Mental Math

P

PRACTICE

Subtract mentally. 1. 46 7

2. 81 36

3. 53 19

4. 99 19

5. $78 $49

6. 92 28

7. 74 38

8. 95 37

9. 64 37

10. 687 48

11. $273 $58

12. 394 86

13. $704 $589

14. 745 597

15. 782 203

16. 613 309

17. 555 299

18. 998 145

19. 578 465

Algebra & Functions Find each missing number. 20. 648 22.

a 548

21.

b 60 340

c 412 388

23.

d 235 665

24. 950


26.

e 400

25. 823

h 123

k 599 301

27. 450

m 100

28. 775

n 200

29.

r 300 1,456

Problem Solving 30. Josh buys a wooden horse for $4.89.

He gives the cashier $5.00. How much change should Josh receive?


31. A bicycle shop has 309 water-bottle

holders in stock. Ashley buys 259 water-bottle holders from the shop. How many water-bottle holders does the store have left?

NS 3.1; AF 2.1




R

RETEACH

You can use these two strategies to subtract mentally. Compensation Use compensation when one number is close to a ten or a hundred. Add or subtract the same number from both numbers. 95 28

97 → → 30

Add 2 to 28 to make 30: 28 2 30. Add 2 to the other number: 95 2 97.

67 103 45

→ 100 → 42

Subtract 3 from 103 to make 100: 103 3 100. Subtract 3 from 45: 45 3 42.

58 Zig-zag Use the zig-zag method to subtract 95 28. Take apart 28. 28 20 8 Then subtract each place separately. 95 28

95 20 75

75 8 67


Subtract mentally. 1. 26 7

2. 84 32

3. 79 31

4. $58 $17

5. 94 38

6. 86 24

7. 196 49 9. 395 91

8. $253 $42 10. 888 277

11. 245 197

12. $428 $117

13. 482 204

14. 613 307

15. 354 99

16. $755 $402

17. 519 404

18. 505 301

19. $535 $122

20. 350 198

21. 657 312

22. 648 305


NS 3.1; AF 2.1




E

ENRICH

Crossnumber Puzzle Subtract mentally to complete the crossnumber puzzle. A

4

8

E

2 G

9

B

2


9

5 2

4

F

5

8

6

5

L

2

4

6

I M

8 3

J

4 2

7

5 O

4

1 3

H

5 8

D

3

1

7 K

N

C

3

7

Across

Down

A. 596 111

A. 626 197

C. 879 65

B. 360 308

E. 281 28

D. 237 105

G. 192 95

F. 591 76

H. 383 99

I. 950 113

K. 1,253599

J. 765 723

M. 194 162

K. 686 28

N. 448 203

L. 635 179

O. 662 25

N. 228 199

Look at N. Down. What method did you use to subtract mentally?


NS 3.1; AF 2.1



Estimate Differences

P

PRACTICE

Estimate each difference. Show your work. 1. 467 215 2. 2,835 1,487 3. $13.95 $7.25 4. 65,074 15,472 5. 174,921 18,421

Subtract. Estimate to check that each answer is reasonable. 6.

835 487

$81.79 31.55

7.

8.

6,984 322

11. $0.88 $0.35

9.

242,003 49,887

10.

654,026 529,620

12. 787,008 117,584

Compare. Write or to make a true sentence. 13. 4,173 2,589 15. $300.00

2,000 $367.20 $59.45

17. 15,425 3,535


19. 42,345 16,174

10,000 20,000

14. 8,329 957 16. 600

7,000

938 452

18. 8,053 7,645 20. 48,592 961

1,000 4,000

Problem Solving 21. There were 787,897 copies of the

Science Monthly sold last year. This year, 914,632 copies were sold. About how many more were sold this year?


22. The Hoop Store spends $129.99 for

an ad in the Science Monthly. The store spends $19.29 for an ad in the Allentown News. About how much more does the store spend on advertising in the Science Monthly than in the Allentown News?

NS 2.1, 3.1; MR 2.1, 2.5




R

RETEACH

To estimate a difference, you can round each number. Then subtract the rounded numbers. Estimate $6.98 $4.59.

Estimate 486 27. Round each number to the nearest ten. Subtract.

490 30

Round each number $6.98 $4.59 ↓ ↓ to the nearest dollar $7.00 $5.00

490 30 460

Subtract.

486 27

↓

↓

So, 486 27 is about 460.

$7.00 $5.00 $2.00

So, $6.98 $4.59 is about $2.00.

To which place will you round each number? Circle the digits in that place. Then estimate each difference. Show how you rounded. 1. $14.95 $8.35

2. $0.78 $0.29

3. 7,842 799

4. $589.10 $85.25

5. 53,425 20,741

6. 425,697 289,721


Estimate each difference. 7. 529 158

8. $683 $475

9. 947 349

10. 5,522 1,378

11. $12.48 $3.98

12. 3,241 678

13. 52,745 47,523

14. 72,393 8,088

15. 232,500 83,900

16. 809,765 528,750


NS 2.1, 3.1; MR 2.1, 2.5




E

ENRICH

A-Mazing Differences Estimate each difference. Circle the correct answer. Use your answers to find the path through the maze. 1. 961 472

2. 874 215

3. 4,971 2,364

4. 729 346

A. 400

A. 500

A. 3,000

A. 300

B. 500

B. 600

B. 2,000

B. 400

C. 600

C. 700

C. 1,000

C. 500

5. 526 481

6. $8.16 $1.92

7. $72.59 $24.71

8. 9,742 6,381

A. 0

A. $5.00

A. $30.00

A. 2,000

B. 100

B. $6.00

B. $40.00

B. 3,000

C. 200

C. $7.00

C. $50.00

C. 4,000

9. 5,692 3,766

10. 42,874 16,422

11. 69,124 31,346

12. 892,617 85,600

A. 40,000

A. 700,000

B. 2,000

B. 30,000

B. 30,000

B. 800,000

C. 3,000

C. 40,000

C. 20,000

C. 900,000

7C

6B 6A

6C

7B

4C

B sh

12

C

11 A 11 C

Fi

12

B

ni

12

3B

A

11 B

8B

3A

3C

2C 2A

10

10

A

1B 2B


1C

4A

10

C

8C

4B

1A

5C

9B

5A

7A 8A

5B

t ar St

7A

A. 20,000

9C

A. 1,000


NS 2.1, 3.1; MR 2.1, 2.5


Problem Solving: Application Applying Addition and Subtraction

Print This Page


Record your data.


Burgers-to-Go

Ruby’s Healthy Diner

Carnival Lunch Menu

Your Decision Where do you think The Outdoor Club should eat? Explain.


MR 1.1; NS 3.1


Problem Solving: Application Which materials block a magnet?

Print This Page


Record your data. Material used as blocker

Number of paper clips Find the difference. that the magnet can hold (Number of paper clips a when this material is magnet can hold with used as a blocker no blocker) minus (Number of paper clips a magnet can hold when this material is used as a blocker)

Magnet only


Magnet with paper

Magnet with foil

Magnet with tape


NS 1.2, 3.1; MR 1.1, 3.1


Print This Page



Math & Science

Which materials block a magnet? 1. What is the difference between the number of paper clips a magnet

can hold with no blocker and the number of paper clips a magnet can hold with each of the different blockers you used?

2. Put the three materials in order from best blocker to worst.

3. Explain the results of your activity in terms of shielding.

4. What are some other materials that you think would be good


blockers? Explain.

5. What are some other materials that you think would be bad

blockers? Explain.


NS 1.2, 3.1; MR 1.1, 3.1



Tell Time

P

PRACTICE

Write the time in two ways. 1.

2.

3.

9 48

Choose the most reasonable units of time. Write seconds, minutes, or hours. 4. Debbie spends 20

at the dentist.

5. You are in school for about 6

.

6. Jerry walks to the store in 15

.

7. Ben swims underwater for 30

.

Tell how much time. 8. 120 minutes = 1 10. 2 hour =


12.

hours

9.

minutes

seconds = 3 minutes

11. 15 minutes =

minutes = 2 12 hours

13.

hour

minutes = 1 41 hours

Algebra & Functions Describe and complete the conversion patterns. 14.

15.

Minutes

60

120

Hours

1

2

Minutes

1

2

Seconds

60

120


180

240

300

3

4

5

MR 1.1, 2.3



Tell Time

R

RETEACH

You can read time in different ways.

5 40 Read: five-forty

Read: forty minutes after five

Read: twenty minutes before six or twenty minutes to six

Write: 5:40 Write the time in as many different ways as you can. 1.

2.

3.

4.

5.

6.


4 15

7.

3 20

8.


2 50

9.

MR 1.1, 2.3



Tell Time

E

ENRICH

Patterns in Time The times shown on the clocks are in a pattern. What time would the next clock show? What is the pattern? 1.

11 12 1 2 10 3 9 4 8 7 6 5

Time: 2.

5 :45 Time:

3.

11 12 1 2 10 3 9 4 8 7 6 5

Time:


4.

3 :10 Time:

5.

11 12 1 2 10 3 9 4 8 7 6 5

Time:

11 12 1 2 10 3 9 4 8 7 6 5

11 12 1 2 10 3 9 4 8 7 6 5

Pattern: Increase by

5 :30

hour.

5 :15

Pattern: Decrease by 11 12 1 2 10 3 9 4 8 7 6 5


3 :00 Pattern: Decrease by 11 12 1 2 10 3 9 4 8 7 6 5



hour. 11 12 1 2 10 3 9 4 8 7 6 5

hour.

2 :50 hour. 11 12 1 2 10 3 9 4 8 7 6 5

hour.

MR 1.1, 2.3



Elapsed Time

P

PRACTICE

How much time has passed? 1. Begin: 12:00 P.M.

2. Begin: 1:15 A.M.

3. Begin: 11:05 P.M.

End: 2:20 P.M.

End: 1:50 A.M.

End: 1:00 A.M.

4. Begin: 2:25 A.M.

5. Begin: 3:40 P.M.

End: 5:40 A.M.

7. Begin: 8:10 P.M.

6. Begin: 5:45 A.M.

End: 12:00 A.M.

End: 12:15 P.M.

8. Begin: 9:30 A.M.

9. Begin: 10:35 P.M.

End: 2:10 P.M.

End: 8:00 A.M.

End: 1:55 A.M.

What time will it be in 1 hour 20 minutes? 10.

11.

12.

8 50


Algebra & Functions Write the missing numbers. 13. 5:16 A.M. is

minutes after 5:00 A.M.

14. 2:45 P.M. is

minutes before 3:00 P.M.

15. 7:22 P.M. is

hours

16. 9:58 A.M. is

minutes before

minutes after 7:00 P.M. A.M.

Problem Solving 17. Lisa leaves her house at 8:45 A.M.

She gets to karate class 35 minutes later. At what time does Lisa get to karate class?


18. The Big Beach bus leaves the city at

6:40 P.M. The bus arrives at the beach at 8:25 P.M. How long is the trip to the beach?

MR 1.1, 2.3



Elapsed Time

R

RETEACH

Elapsed time is the amount of time that passes from the start to the end of an action. Follow these steps to find how much time has elapsed from 8:20 A.M. to 11:35 A.M. First count the number of hours.

Then count the number of minutes.

From 8:20 to 11:20 is 3 hours.

From 11:20 to 11:35 is 15 minutes.

So, 3 hours 15 minutes have passed. How much time has passed? 1. Begin End

3. Begin

End

2. Begin

End

4. Begin

End


12 15

5. Begin

End

6 00

6. Begin

10 30


3 15

End

2 15

2 35

MR 1.1, 2.3



Elapsed Time

E

ENRICH

Flying Time Use the time zone map to answer each question. Show your answer in local time. Remember to include the time zone; for example, 7:00 A.M. Central Time. Pacific Time

Mountain Time

Central Time

Eastern Time

11 12 1 2 10 3 9 4 8 7 6 5

11 12 1 2 10 3 9 4 8 7 6 5

11 12 1 2 10 3 9 4 8 7 6 5

11 12 1 2 10 3 9 4 8 7 6 5

Seattle

New York City

Los Angeles

Phoenix

Atlanta Dallas

Miami

1. It takes about 5 hours to fly from Los Angeles to New York City.

If a plane leaves Los Angeles at 8:00 A.M., at what time will it arrive in New York City? 2. It takes 4 hours 30 minutes for a plane to fly from Atlanta to

Phoenix. If a plane departs from Atlanta at 10:00 A.M., at what time will it arrive in Phoenix? 3. A plane flew from Seattle to Atlanta. It arrived in Atlanta at

1:05 A.M. The flight lasted for 5 hours 40 minutes. At what time did it depart from Seattle? 4. The flight between Dallas and Miami takes 2 hours 41 minutes. © McGraw-Hill School Division

Complete the flight schedule below. Depart Dallas

Arrive Miami

Depart Miami

7:00 A.M. CT

2:30 P.M. ET

9:10 A.M. CT

4:45 P.M. ET

11:20 A.M. CT

6:57 P.M. ET

Arrive Dallas

5. How did you adjust for the time zones in your answers?


MR 1.1, 2.3



Calendar

P

PRACTICE

Use the calendars for July and August for exercises 1–8.

July 2000 S

M

T

W

August 2000

T

F

S

S

M

1

T 1

W

T

F

S

2

3

4

5

Nick arrives!

2

3

4

5

6

7

8

6

7

8

9

10

11

12

15

16

17

18

19

25

26

Independence Day!

9

10

11

12

13

14

15

13

14

16

17

18

19

20

21

22

20

21

22

23

24

23

24

25

26

27

28

29

27

28

29

30

31

30

31

1. What is the date of the fourth

Thursday in July?

3. Cindy will return from vacation on


the Monday after Nick arrives. On which date will Cindy return?

5. Justin is moving to a new town on

August 1. The movers are coming 4 days before that. On which date will the movers arrive?

Football practice begins!

2. On which day of the week is

Independence Day?

4. If soccer camp runs from July 7

through the following Saturday, how long is soccer camp?

6. Jason has a violin lesson every

Wednesday. How many lessons will he have in July and August?

8. Pat saw the dentist on July 25. He has 7. Nick will leave on August 30.

For how many weeks will he visit?


another appointment 10 days later. On which date is Pat’s appointment?

MR 1.1, 2.3



Calendar

R

RETEACH

You can use a calendar to find elapsed time. Suppose today is May 8. How many days is it until Mother’s Day? Count on from May 8 to May 14. It is 6 days from May 8 to May 14.

May 2000 S

June 2000

M

T

W

T

F

S

S

M

T

1

2

3

4

5

6

7

8

9

10

11

12

13

4

5

6

14

15

16

17

18

19

20

11

12

13

Mother’s Day

21

W

T

F

S

1

2

3

7

8

9

10

14

15

16

17

Flag Day

22

23

24

25

26

27

18

19

20

21

22

23

24

26

27

28

29

30

31

Father’s Day

28

29

30

31

25

Use the calendars above for exercises 1–8. 1. How long is it from Flag Day to

Father’s Day?

3. Sports camp runs from June 19 through © McGraw-Hill School Division

June 30. How long is camp?

5. On which day of the week is Flag Day?

2. How long is it from Mother’s Day

to the following Sunday?

4. How many weeks are there from May

1 to June 5?

6. Memorial Day is celebrated on the last

Monday in May. Which date is that?

7. Dave will return from vacation on the

Monday after Flag Day. On which date will he return?


8. The last day of school is June 7. Tom’s

birthday is 5 days before that. When is Tom’s birthday?

MR 1.1, 2.3



Calendar

E

ENRICH

Calendar Calculations Use the calendar to solve the problems. January

February

March

April

May

June

S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S 1 1 1 2 3 4 5 1 2 3 4 1 2 3 4 5 6 1 2 3 2 3 4 5 6 7 8 6 7 8 9 10 11 12 5 6 7 8 9 10 11 2 3 4 5 6 7 8 7 8 9 10 11 12 13 4 5 6 7 8 9 10 9 10 11 12 13 14 15 13 14 15 16 17 18 19 12 13 14 15 16 17 18 9 10 11 12 13 14 15 14 15 16 17 18 19 20 11 12 13 14 15 16 17 16 17 18 19 20 21 22 20 21 22 23 24 25 26 19 20 21 22 23 24 25 16 17 18 19 20 21 22 21 22 23 24 25 26 27 18 19 20 21 22 23 24 23 24 25 26 27 28 29 27 28 29 23 24 25 26 27 28 29 28 29 30 31 26 27 28 29 30 31 25 26 27 28 29 30 30 31 30

July

August

September

October

November

S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S 1 1 2 3 4 5 1 2 1 2 3 4 5 6 7 1 2 3 4 2 3 4 5 6 7 8 6 7 8 9 10 11 12 3 4 5 6 7 8 9 8 9 10 11 12 13 14 5 6 7 8 9 10 11 9 10 11 12 13 14 15 13 14 15 16 17 18 19 10 11 12 13 14 15 16 15 16 17 18 19 20 21 12 13 14 15 16 17 18 16 17 18 19 20 21 22 20 21 22 23 24 25 26 17 18 19 20 21 22 23 22 23 24 25 26 27 28 19 20 21 22 23 24 25 23 24 25 26 27 28 29 27 28 29 30 31 24 25 26 27 28 29 30 29 30 31 26 27 28 29 30 30 31

1. Jamie will start basketball practice

on the first Monday in September. She plans to buy sneakers at least two weeks before practice begins. On which date will basketball practice begin? Which is the latest date on which she can buy her sneakers?


3. George's team has its first game on

May 15. They plan to spend four Saturdays practicing. Then they will spend a week practicing every day after school. Which is the latest date on which they should start practicing?


December S M T W T F S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

2. John plans to go on a skiing trip the

third Friday in December. He must buy his ticket 14 days in advance of the flight. He wants to make the plane reservations 4 weeks before buying the ticket. Which is the latest date on which he should make his plane reservations?

4. Holly wants to run her best race the

second Saturday in June. To train, she wants to do speed workouts for 5 weeks. Before she begins speed training, she must do endurance runs for 4 weeks. Which is the latest date on which she should begin training?

MR 1.1, 2.3



Line Plots

P

PRACTICE

1. Complete the tally table and line plot for the following data.

Number of Miles Run Each Day by the Members of the Fleet-Footed Club 3 2 5 4 6 3 1 5 4 3 2 6 4 3 5 3 2 2 1 5 4 3 6 3 2 5 3 1 4 2 5 6 2 3 2 Number of Miles Run Each Day by the Members of the Fleet-Footed Club Number of Miles

Tally

Number of Miles Run Each Day by Members of The Fleet-Footed Club

Total

1 2 3 4 5 6

1

2

3

4

5

6

Use the line plot to answer the questions. 2. How many miles did the greatest number of students run? 3. How many members ran 6 miles a day? 4. How many members ran 4 miles or more a day? 5. How many more members ran 4 miles a day than ran 1 mile a day? © McGraw-Hill School Division

6. How many members are in the club?

Use the data below to make a tally table and line plot on a separate sheet of paper. Ages of Fleet-Footed Club Members 8 11 12 9 13 14 12 11 8 12 10 12 11 9 13 12 11 9 12 14 11 12 13 10 9 12 10 13 9 12 11 14 10 9 13 7. What statement can you make about the data in your line plot?


SDP 1.1



Line Plots

R

RETEACH

Marcia counted the number of letters in each word in a story. The data is shown below. 3 3 5

3 2 6

5 3 3

Number of Letters in Words in a Story 6 4 2 1 5 6 3 5 2 8 4 5 3 3 5 1 4

4 5

7 2

You can organize the data in a tally table. To compare the data, you can make a line plot. Example: For the first number, 3, make a tally mark in the table. Cross out the 3 in the data above. Then record and cross out the remaining 3s. In the line plot, use an X to stand for each word in the story. Complete the tally table and the line plot. Number of Letters in Words in a Story Number of Letters in Words

Tally

1

Total Number of Words

Number of Letters in Words in a Story 2 words had 7 words had 1 letter. 5 letters.

↓

↓ X

2

X

2 3

X

8

X

↓

X

X

X

X

X

6

X

X

X

7

1

5

6

4 5 © McGraw-Hill School Division

3 words had 6 letters.

2

3

4

7

8

8 Use the line plot. How many words had: 1. 3 letters?

2. 2 letters?

4. more than 3 letters?

3. 8 letters? 5. less than 3 letters?

6. How many letters did the greatest number of words have? Use with Grade 4, Chapter 3, Lesson 4, pages 100–101. (80)

SDP 1.1



Line Plots

E

ENRICH

Mystery Plot Use the clues below to complete the line plot. Number of Books Read in September by Students in Fourth Grade

5

6

7

Clues • There are 4 students who read 5 books a month and 3 times as many who read 7 books a month.


• The number of students who read 6 books a month is 7 less than the number of students who read 7 books a month. • The number of students who read 10 books a month is half the number who read 7 books a month.

8

9

10

• The number of students who read 8 books a month is 2 less than the number of students who read 6 and 9 books a month combined. • The number of students who read 9 books a month is twice as many as the number of the students who read 6 books a month.

Use the line plot to answer the questions. 1. How many students were surveyed? 2. How many books were read by the greatest number of students each month?

About how many was that a week? 3. How many books were read by the least number of students? Use with Grade 4, Chapter 3, Lesson 4, pages 100–101. (81)

SDP 1.1



Range, Median and Mode

P

PRACTICE

The third-grade class at Blue Hill School collects and recycles aluminum cans. The line plot shows how many cans the students collected in March. Use data from the line plot for exercises 1–3. 1. Find the range, median, and mode

from the line plot.

Number of Aluminum Cans Collected in March

Range: Median: Mode: 2. What does the mode tell you about

this data? X X 3. What does the median tell you about

X X X

X X X X

X X X X X

X X X X X X X X

X X X X X X X X X X

X X X X

X X X

X

24 25 26 27 28 29 30 31 32

this data?

Complete the table.


Data

Order Data from Least to Greatest

Range Median Mode

4. 6, 8, 8, 9, 5, 4, 8, 7, 5 5. 30, 35, 29, 42, 35, 35, 40 6. 30, 19, 21, 17, 25, 23, 25 7. 20, 80, 40, 50, 90, 60, 50 8. 78, 85, 100, 100, 95, 92, 88 9. $9, $13, $23, $15, $13


SDP 1.1, 1.2



Range, Median and Mode

R

RETEACH

You can analyze data using the range, median, and mode. Use the line plot to help you find the range, median, and mode. Time It Takes to Get to School X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 0 5 10 15 20 25 Minutes

Range: the difference between the greatest and least numbers Range: 25 5 20 Median: the middle number when the data is arranged in order from least to greatest The data in the line plot is arranged in order. There are 29 Xs, so the middle X is the 15th X. The 15th X in the line plot is above 10, so the median is 10. Mode: the number that occurs most often The greatest number of Xs is above 10, so 10 is the mode.

Order the data from least to greatest. Then find the range, median, and mode. 1. Data: 6, 4, 3, 3, 0, 5, 8 List in order from least to greatest: , , , , , , Range:

–

0

=

Median: Mode: 2. Data: 83, 96, 72, 91, 83 © McGraw-Hill School Division

List in order from least to greatest: Range: 96 –

,

,

,

,

,

,

,

=

Median: Mode: 3. Data: 56, 88, 100, 34, 96, 56, 92

List in order from least to greatest:

,

,

,

Range: Median: Mode: Use with Grade 4, Chapter 3, Lesson 5, pages 102–103. (83)

SDP 1.1, 1.2



Range, Median, and Mode

E

ENRICH

The Case of the Missing Math Tests Ms. Lee's math class is divided into three groups. Each group found the range, median, and mode of the group's scores. Use the data for each group to find the missing scores. 1.

2.


3.

Group 1’s Test Scores

Students’ Scores for Group 1

Range

18

Megan

80

Joe

90

Median

88

Stephanie

92

Chris

76

Mode

94

Gregory

84

Alison

94

Brian

86

Nancy



Range

18

Jason

Ann

88

Median

91

Steven

82

Karen

94

Mode

94

Melissa

94

Leroy

90

Serena

98

Carl

80



Range

16

Sam

Jamal

92

Median

92

Beth

92

Sally

96

Mode

92

Susan

88

Bill

82

Mario

86

Rita

92

4. Explain how you found each missing test score.


SDP 1.1,1.2


Problem Solving: Reading for Math Identify Extra and Missing Information


P

PRACTICE

Reading Skill

Circle the question that you need to answer. Cross out any extra information. Then solve or tell what information you need to solve the problem. 1. Fiona is taking a train from Boston to

Providence on May 6th. The train arrives in Providence at 3:54 P.M. How long is the train trip?

3. Marion and her daughter fly from

Atlanta to Dallas. The round-trip fare for Marion is $349. The fare for Marion’s daughter is the same. This fare costs $50 more than the fare the last time Marion flew. What was the round-trip fare the last time Marion flew?


5. Kendra wants to fly from Atlanta to

Philadelphia. Flight 17 leaves Atlanta at 11:39 A.M. and arrives in Philadelphia at 1:43 P.M. Flight 20 leaves Atlanta at 8:40 P.M. and arrives in Philadelphia at 10:54 P.M. A coach ticket on Flight 17 is $109. This is $20 more than a ticket on Flight 20. Which flight is shorter? How much shorter is it?


2. On Tuesday, September 7, Noah

bought a ticket for a flight that leaves on September 20th. The ticket cost $329. On what day of the week is Noah’s flight?

4. A train leaves Washington, D.C., at

5:45 A.M. and arrives in Philadelphia at 8:00 A.M. A train from New York City arrives in Washington, D.C., at 8:10 A.M. Which train ride takes more time?

6. A round-trip coach ticket on Flight

54 from New York City to San Francisco costs $399. A round-trip first-class ticket on Flight 54 costs $1,609. A round-trip coach ticket on Flight 98 from New York City to San Francisco costs $438. How much more expensive is a round-trip coach ticket on Flight 98 than on Flight 54?

MR 1.1, 2.3, 2.4, 3.1, 3.2, 3.3


Problem Solving: Reading for Math Identify Extra and Missing Information


P

PRACTICE



Choose the correct answer. Flight 81 leaves Salt Lake City at 2:55 P.M. and arrives in Phoenix at 4:30 P.M. Flight 62 from Salt Lake City, which is sold out, arrives in Phoenix at 3:45 P.M. Which flight is faster? 1. Which of the following statements 2. What important information is is false? missing? A Flight 81 takes less than 2 hours. F the time that Flight 81 leaves Salt Lake City B Flight 62 arrives in Phoenix after Flight 81 does. G the time that Flight 81 arrives in Phoenix C Flight 62 is sold out. H the time that Flight 62 leaves Salt D Flight 81 arrives in Phoenix before Lake City 5:00 P.M. J the time that Flight 62 arrives in Salt Lake City An express train leaves Grand Terminal at 5:05 P.M. The train arrives at the first stop at 5:21 P.M., the second stop at 5:46 P.M., and the last stop at 6:04 P.M. How long is the train ride? 3. Which extra information is not 4. How long is the train ride? needed to solve the problem? F 16 minutes A the time the train leaves Grand G 41 minutes Terminal H 59 minutes B the time the train arrives at the J 61 minutes second stop C the time the train arrives at the last stop D none of the above A train leaves Chicago at 4:20 P.M. on Wednesday, November 24. It arrives in Houston at 11:50 A.M. the next day. How long does the train ride take? 5. Which extra information is not 6. How long does the train ride take? needed to solve the problem? F 4 hours 30 minutes A the time the train leaves Chicago G 7 hours 30 minutes B the time the train arrives in H 8 hours 30 minutes Sacramento J 19 hours 30 minutes C the date the train leaves D none of the above Use with Grade 4, Chapter 3, Lesson 6, pages 104–105. (86)

MR 1.1, 2.3, 2.4, 3.1, 3.2, 3.3




P

Identify Extra and Missing Information

PRACTICE


Choose the correct answer. Ty wants to take a nonstop flight that leaves Miami at 7:25 A.M. and arrives in Cincinnati at 9:55 A.M., but the flight is sold out. Instead, he takes a 9:00 A.M. flight from Miami to Atlanta. Then Ty takes a flight from Atlanta to Cincinnati. That flight leaves Atlanta at 12:00 noon. How much later does Ty arrive in Cincinnati than he would have if he had taken a nonstop flight? 7. Which of the following statements

is false? A Ty catches a 12:00 noon flight. B Ty catches a 9:00 A.M. flight. C The nonstop flight takes less than 3 hours. D Ty’s trip to Cincinnati takes 3 hours.

8. What information do you still need

to solve the problem? F the time the 12:00 noon flight from Atlanta arrives in Cincinnati G the time the 9:00 A.M. flight from Miami arrives in Atlanta H the time the 7:25 A.M. flight from Miami arrives in Cincinnati J the time the 7:25 A.M. flight from Miami arrives in Atlanta

Solve. Identify extra or missing information in each problem. 9. A round-trip first-class ticket from St.


Louis to San Diego costs $1,600. A round-trip coach ticket costs $359. The Howards buy 3 tickets. How much do they spend?

11. A bus leaves the terminal at 6:10 P.M.

It makes its first stop at 6:30 P.M. and its second stop at 6:55 P.M. When will the bus arrive at its third stop?


10. A train leaves Rocky Mount, NC, at

1:16 P.M. The train arrives in Petersburg, VA, at 2:45 P.M. and in Richmond, VA, at 3:22 P.M. How long is the trip from Rocky Mount to Richmond?

12. Samantha takes a train to New York

City. She catches the train at 7:25 A.M. The train stops in Newark at 7:41 A.M. The train arrives in New York at 7:59 A.M. How much time does Samantha’s ride take?

MR 1.1, 2.3, 2.4, 3.1, 3.2, 3.3




P

PRACTICE

Work Backward Work backward to solve. 1. Bill wants to arrive 15 minutes early

for a movie that starts at 7:45 P.M. It will take him about 20 minutes to walk to the theater. When should Bill leave home?

3. Nick spent $21.50 on a theater ticket

and $12.50 on a meal. He has $14.25 left. How much money did Nick start with?

2. It takes Sandy 35 minutes to walk

from school to the mall. She spends 45 minutes at the mall. Sandy leaves the mall at 4:20 P.M. When did she leave school?

4. Sally spends $16.50 on gas, $2.25

on tolls, and $2.75 on a snack. She has $32.10. How much money did she start with?

Mixed Strategy Review Solve. Use any strategy. 5. Barry makes letters for a sign that

reads “Free Field Trip Sign-Up Sheet.” Which letter does Mark need to make the most of?

6. Mr. Carlson has $424. He spends

$29 on gasoline. How much money does Mr. Carlson have left?

Strategy: © McGraw-Hill School Division

Strategy:

7. Health Walking a mile burns about

110 calories. About how many calories would you burn if you walked 2 miles?

8. Create a problem which can be

solved by working backward. Share it with others.

Strategy:


MR 1.1, 2.3, 2.4, 3.1, 3.2, 3.3




R

RETEACH

Work Backward Page 109, Problem 1

Mindy wants to eat before the 7:40 P.M. show. She needs about 45 minutes to order and eat her dinner. What is the latest time she can order? Step 1

Read

Be sure you understand the problem. Read carefully. What do you know? • Mindy needs about eat her dinner.

minutes to order and

• She wants to eat before

.

What do you need to find? • You need to find the latest time that Mindy . Step 2

Plan ■

■

■


■

■

■

■

■

■

■

Make a Table or List Write a Number Sentence Work Backward Act it Out Find a Pattern Make a Graph Guess and Check Logical Reasoning Solve Simpler Problem Draw a Picture


You can work backward to solve the problem. Start at the time of the show. Then work backward to find the time that Mindy needs to order.


MR 1.1, 2.3, 2.4, 3.1, 3.2, 3.3




R

RETEACH

Work Backward Step 3

Solve

Carry out your plan. • Mindy needs about eat her dinner.

minutes to order and

• She wants to finish eating by

.

Start at 7:40 P.M. Think: Mindy wants to finish eating by 7:40 P.M. She needs to order 45 minutes before that time. Move backward 45 minutes. The latest time that Mindy can order is Step 4

Look Back

.

Is the solution reasonable? Reread the problem. Work forward to check your answer. Start with your answer. Move forward 45 minutes. Did you end at 7:40 P.M.?


What other strategies could you use to solve the problem?

Practice 1. Laurel wants to watch a show that begins at 8:30 A.M. Before she can watch TV, she has to practice piano for 1 hour 15 minutes. At what time does Laurel have to start practicing?


2. Paul plays basketball for 30 minutes

and Frisbee for 15 minutes. Then he walks home.The walk takes 20 minutes. If Paul gets home at 2:30 P.M., at what time did he start playing basketball?

MR 1.1, 2.3, 2.4, 3.1, 3.2, 3.3



Explore Pictographs

P

PRACTICE

1. Complete the table. Then use the table to complete the pictograph.

Which Modern Invention Do You Like the Most? Invention

Tally

Total

Computer

Which Modern Invention Do You Like the Most? Computer CD Player

CD Player Car

Car

Television

Television

Key: Each

stands for

people

Use the pictograph for exercises 2–5. 2. Which item do people like the most? 3. How many more people like their computers than their televisions? 4. How many people were surveyed?


5. What key would you use if 80 people were surveyed? Explain.

Use the table to make a pictograph on a separate piece of paper. Then answer each question. 6.

Favorite Lunches Lunch

7. How many more students like pizza

more than spaghetti?

Tally

Pizza Hamburgers

8. How many students took part in

the survey?

Spaghetti Chicken Use with Grade 4, Chapter 3, Lesson 8, pages 110–111. (91)

SDP 1.1, 1.3



Explore Pictographs

R

Evan and Jenny surveyed students to find out whether their favorite color is red, blue, or yellow. This is the data they collected.

Favorite Colors Red

10

Blue

11

Yellow

6

Here is how to make a pictograph of the data. Step 1: Write a title. List the categories. Step 2: Choose a picture to show the data. You can use 1 picture to represent 2 students. So, half of a picture will represent 1 student. Use the picture to make a key.

RETEACH

Favorite Colors Red Blue Yellow Key: Each

Step 3: Use the key to draw pictures to show Key: Each the data for each category.

stands for 2 students. stands for 1 student.

Use the data in the table to complete the pictograph. Answer the questions to help you. 1. How many people chose oranges?

How many faces will you draw?

2. How many people chose apples?

How many faces will you draw?


Favorite Fruit Fruit

Tally

Favorite Fruit Total

Apples

9

Pears

5

Oranges

10

Plums

4

Apples Pears Oranges Plums Key: Each Key: Each


stands for 2 people. stands for 1 person. SDP 1.1, 1.3


Explore Pictographs


E

ENRICH

Stamp Collecting Use the clues below to complete the pictograph. Sarah’s Stamp Collection Stamps of famous people Stamps of famous landmarks Stamps of famous events Stamps of birds Stamps from other countries Stamps of flowers


Key: Each

stands for 2 stamps.

Clues • Sarah has 5 fewer stamps from other countries than stamps of famous people. • Sarah has twice as many stamps of famous events as stamps from other countries. • Sarah has 3 more stamps of famous landmarks than stamps from other countries. • Sarah has 1 more than twice as many bird stamps as stamps of famous events. • If Sarah had 6 more flower stamps, she would have an amount equal to the number of bird stamps. Would you use 1 stamp to stand for 8 stamps in the key? Why or why not?


SDP 1.1, 1.3



Bar Graphs

P

PRACTICE

Complete the table below. Then use it to complete the bar graph and answer exercises 1–4. Favorite Types of Music Adults Type of Music

Tally Marks

Teenagers Total

Tally Marks

Total

Country Classical Jazz Rap Rock and roll Favorite Types of Music

Number of People

16 14 12 10 8 6 4 2 0 Country

Classical

Jazz


Adults

Rap

Rock and Roll

Teenagers

1. How many teenagers chose rock and roll?

2. Which type of music was chosen about the same number of

times by adults and teenagers? 3. Which type of music do adults like the most?

4. Did more adults or teenagers choose jazz as their favorite

music? Use with Grade 4, Chapter 3, Lesson 9, pages 112–115. (94)

SDP 1.1, 1.3



Bar Graphs

R

RETEACH

You can use single-bar graphs or double-bar graphs to show data. A single-bar graph presents one set of data. A double-bar graph presents two sets of data. When you create a double-bar graph, you need to make a key to represent each set of data. Write a title, headings for the vertical and horizontal sides, and select a scale just as you would for a single-bar graph. Remember to include different headings for both sets of data.

Use the graphs to answer the questions. 1. What is the favorite

Number of People

vacation spot? How many people chose it?

2. Did more people choose

France, Hawaii, or Greece as their favorite vacation spot?

Hawaii

4. Which vacation spot shows

the greatest difference between boys and girls?

Number of People


3. How many more boys than

girls chose Hawaii as their favorite vacation spot?

Favorite Vacation Spots

20 18 16 14 12 10 8 6 4 2 0

Greece

Florida

France

Australia

Favorite Vacation Spots

10 9 8 7 6 5 4 3 2 1 0 Hawaii

Greece Boys


Florida

France

Australia

Girls SDP 1.1, 1.3



Bar Graphs

E

ENRICH

Misleading Graphs The bar graph shows the earnings of Bayside Auto Plaza and Auto World. 1. The bar for Auto World is twice as

high as the bar for Bayside Auto Plaza. Does this mean that Auto World earns twice as much as Bayside Auto Plaza?

2. What is the actual difference in the

Earnings of Car Sales $150,000 $140,000 $130,000

earnings of the two stores? $120,000 3. Is the graph misleading? Explain.

0

130,000

150,000

Bayside Auto Plaza

Auto World

Month

40

Oct.– Dec.

0

July– Sept.

20 April– June

10 0

60

Jan.– March

20

Number of Cars Sold

30

Jan. Feb. March April May June July Aug. Sept. Oct. Nov. Dec.

Number of Cars Sold


A car salesperson made Graphs A and B to show the number of cars she sold in one year. Car Sales—Graph A Car Sales—Graph B 100 50 80 40

Months

4. Do both bar graphs show the same data? 5. Which graph do you think the salesperson showed her boss? Tell why.


SDP 1.1, 1.3



Coordinate Graphing

P

PRACTICE

Give the ordered pair for each place on the grid. 1. mall 2. library 3. park 4. school 5. video arcade

Name the place at each location.

12 11 school 10 post office 9 library 8 bank 7 park 6 5 mall fire station 4 3 video arcade 2 pool 1 0 0 1 2 3 4 5 6 7 8 9 10 1112

6. (9, 1)

7. (1, 9)

8. (4, 5)

9. (3, 8)

Give the ordered pair for each place on the grid. 10. jail 11. movie theater 12. police station 13. grocery store


Name the place at each location.

12 city hall 11 police station 10 jail 9 court house 8 pet store 7 6 movie theater 5 grocery store 4 3 2 soccer field 1 0 0 1 2 3 4 5 6 7 8 9 10 1112

14. (7, 2)

15. (8, 11)

16. (8, 9)

17. (4, 8)

18. A drive-in diner is being built

19. A parking garage is being built

3 blocks down from the pet store. What ordered pair names this location?


between the city hall and the court house. What ordered pair names the garage’s location?

MG 2.1, 2.2, 2.3



Coordinate Graphing The grid shows the location of rides at an amusement park.

R

RETEACH

10 9

Where is the Space Ride located? Start at 0. Go right 1, and then go up 2. You can write the location of the Space Ride as the ordered pair (1, 2).

8

Ferris Wheel Carousel

Sky Ride

7

In an ordered pair, the first number tells you how far to go to the right. The second number tells you how far to go up.

Paddle Boats

Swings

6

Tidal Force

5 Log Ride

4 3

Try this. Go right 5, Go up 1.

Scrambler

Shells

2

(5, 1) ← ordered pair

Roller Coaster

Space Ride

Tea Cups

1

Which ride do you find? 0

0

1

2

3

4

5

6

7

8

9

10

Complete. Use the grid above. 1. Start at 0. Go right 8, then up 3.

The ordered pair is (8,

).

The ordered pair is (

What is here?


, 4).

What is here?

3. Start at 0. Go right 2, then up 8.

The ordered pair is


.

What is here?


The ordered pair is

.

What is here?

Use the grid above to tell which is at each location. 5. (5, 8)

6. (2, 3)

7. (4, 6)

8. (1, 6)

9. (6, 4)

10. (8, 8)


MG 2.1, 2.2, 2.3



Coordinate Graphing

E

ENRICH

Find the Hidden Picture Locate each ordered pair on the grid below. Label it with the exercise number. Then connect the dots in order. 1. (17, 3)

2. (11, 7)

3. (10, 0)

4. (9, 7)

5. (3, 3)

6. (7, 9)

7. (0, 10)

8. (7, 11)

10. (9, 13)

11. (10, 20)

12. (11, 13)

14. (13, 11)

15. (20, 10)

16. (13, 9)

9. (3, 17) 13. (17, 17)

20 19 18 17 16 15 14 13 12 11 10 9


8 7 6 5 4 3 2 1 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20


MG 2.1, 2.2, 2.3



Explore Line Graphs

P

PRACTICE

Use the table to complete the line graph. Toy Sales at Toy City Amount

July

$1,700

August

$1,000

September

$1,700

October

$2,500

November

$2,700

December

$3,200

Amount

Month

Toys Sold at Toy City $3,200 $3,000 $2,800 $2,600 $2,400 $2,200 $2,000 $1,800 $1,600 $1,400 $1,200 $1,000 0

July Aug. Sept. Oct. Nov. Dec.

Month

Use the line graph to answer the questions. 1. In which month was the greatest

2.


dollar amount of toys sold at Toy City?

3. During which month did sales

the same?

4.

decrease?

5. What is the difference in sales

between the highest and lowest

In which two months were sales

During which month did sales increase the most?

6.

In how many months did Toy City sell more than $1,600 worth of toys?

points on the graph


SDP 1.1,1.3



Explore Line Graphs

R

RETEACH

A line graph shows change over a period of time. The table below shows the number of ice-cream cones sold over a year at the Ice-Cream Cottage. You can also show this information in a line graph. Ice-Cream Cone Sales Month

Number

July

800

August

900

September

700

October

650

November

350

December

100

Number of Cones Sold

Ice-Cream Cones Sold 900 800 700 600 500 400 300 200 100 0

Show the data from the table in the line graph.

July Aug. Sept. Oct. Nov. Dec.

Month

• In October, 650 cones were sold. Draw a dot across from 650 on the graph’s scale (650 is half way between 600 and 700).


• Draw a dot for each of the other month’s number of sales.

Use the line graph to answer the questions. 1. In which month was the greatest

number of ice-cream cones sold?

3. How many more ice-cream cones

were sold in July than in December?


2. How many ice-cream cones were

sold in July?

4. Between which two months did the

greatest decrease in sales take place?

SDP 1.1, 1.3



Explore Line Graphs

E

ENRICH

Population Trends Use the clues to complete the line graph. Clues • Foxwood had 200 more people in 1930 than it did in 1920. • The population was the same in 1940 as it was in 1930. • In 1950, the number of people increased by 200. • There were 1,600 people living in Foxwood in 1960. • The number of people decreased by 200 in 1970 and 100 in 1980. • The population in 1990 was 200 more than in 1980.

Number of People

Population Changes in Foxwood 2,200 2,100 2,000 1,900 1,800 1,700 1,600 1,500 1,400 1,300 1,200 1,100 0

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 Year


Write the years during which each event most likely happened. Event

Years

For the first time in 30 years, the population began growing again.

between

and

A computer factory opened. People moved to Foxwood for jobs.

between

and

The town's toy factory closed. Many people lost their jobs.

between

and


SDP 1.1, 1.3


Print This Page

3–12 Part A WORKSHEET


Decision Making

Applying Time and Data Show how the Sequoia Nature Club can spend its time. Make a schedule. Activity

Starting Time of Activity

Ending Time of Activity


Your Decision Which activities did you choose for the Sequoia Nature Club? Explain your choices.


MR 1.1, 2.3, 2.4, 2.6, 3.1



Print This Page


Does practice make perfect? Record your data. Attempt

Time Needed to Complete the Puzzle

1 2 3 4 5 6 7 8


9 10

1. Describe what happened to the time you needed as you

repeated the puzzle over and over.


NS 1.2; SDP 1.1, 1.3; MR 2.3, 3.2


Print This Page



Math & Science

Does practice make perfect? 2. How many times did you have to work the puzzle until you

mastered it?

3. What happened to your time after you mastered the puzzle?

4. Make a line graph, comparing puzzle number and time.


What happened to the line on the graph after you mastered the puzzle?

5. Explain how you used your short- and long-term memory to learn

the puzzle.


NS 1.2; SDP 1.1, 1.3; MR 2.3, 3.2



The Meaning of Multiplication

P

PRACTICE

Write a multiplication sentence for each model. 1.

2.

3.

4.

Find each product. 5.

6 6

6.

7 7

7.

3 5

8.

7 3

9.

6 0

10.

7 5

11.

5 8

12.

8 7

13.

4 6

14.

9 5

15.

6 8

16.

4 8

17. 8 8

18. 2 6

19. 9 6

20. 9 8

21. 3 3

22. 6 7

23. 2 3

24. 6 9

25. 8 6

26. 3 6

27. 1 9

28. 9 3


Algebra & Functions Find the missing number. 29. 2 (n 5) 30

30. (j 7) 4 56

31. (2 v) 6 48

32. (3 r) 8 72

Problem Solving 33. Jason practices his violin 2 hours

every day. How many hours does he practice in 7 days?


34. Sheila arranges her pennies in 9

rows with 6 pennies in each row. How many pennies does Sheila have?

AF 1.1




R

RETEACH

The numbers you multiply are the factors. The answer is the product. First factor: number of rows

5

Second factor: number in each row

6 6 ←factor

6 6 6 6 6 30

You can write 5 6 30 or 5 ←factor ↑ ↑ ↑ 30 ←product factor factor product

Complete the table. Number of Rows

Number in Number Multiplication Each Row in All Sentence

1.

2. 3.



4 3

5.

7 3

6.

6 4

7.

5 0

8.

3 5

9.

6 5

10. 2 5

11. 5 3

12. 9 3

13. 5 5

14. 4 7

15. 8 3

16. 5 9

17. 6 2


AF 1.1




E

ENRICH

Factors, Products, and Rectangles To show all the facts with a product of 6, draw as many rectangles as you can that contain 6 squares. Count the number of squares in each column and row.

List the numbers you count. Those are the factors. The factors of 6 are 1, 2, 3, and 6. 616

166

326

236

Draw as many rectangles as you can to show different facts for each product. Then list the factors. 2. 18

3. 20

4. 24


1. 12


AF 1.1



Properties of Multiplication

P

PRACTICE

Find the product. Then use the Commutative Property to write a different multiplication sentence. 1. 9 8

2. 8 7

3. 5 2

4. 9 4

5. 3 4

6. 9 2

7. 6 9

8. 2 3

9. 7 4

10. 3 9

11. 9 7

12. 5 8

13. 5 0

14. 1 8

15. 4 5


Write or to make a true sentence. 16. 6

6 36

17. 8

19

18. 3

9 27

19. 7

7 14

20. 9

09

21. 9

9 81

22. 4

39

3

23. 8

75

3

24. 6

4 12

25. 9

26

3

26. 6

79

4

27. 4

48

2 8

Problem Solving 28. Joe plants pine seedlings in 7 rows.

He puts 6 seedlings in each row. How many seedlings does Joe plant?


29. Tanya has 9 pencils in each package.

She has 6 packages. How many pencils does Tanya have in all?

AF 1.1; MR 1.1




R

RETEACH

Commutative Property The order of the factors does not change the answer.

428

248

Identity Property The product of 1 and any number is that number.

Zero Property The product of any number and zero is zero.

313

Think: 4 rows of 0 counters. 400

166

Think: 0 rows of 7 counters. 070

Find each product. Then use the Commutative Property to write another sentence. 1. 3 9


9 4. 2 8

2. 5 7

27

5 5. 1 4

3. 4 6

6

6. 0 5

Multiply. Tell which property you used. 7. 1 8

8. 0 7

9. 5 1

10. 6 0

11. 0 4

12. 1 9


AF 1.1; MR 1.1




E

ENRICH

Crack the Code! What number does each symbol in the table below stand for? Use the Commutative, Identity, and Zero properties of multiplication to help you find out. Write the number next to the symbol in the code key.

6

2. 6

7

8

5

0

6

7.

10

4. 6

5. 9

6.

9

9. If you know that

8

05

8.

10

26

90 5

1. 6

3.


4

6

,

what other multiplication fact do you know? Use with Grade 4, Chapter 4, Lesson 2, pages 140–141. (111)

AF 1.1; MR 1.1



Multiply by 2, 3, 4, and 6

P

PRACTICE

Write the multiplication sentence. 1.

2.

Multiply. 3. 7 4

4. 1 6

5. 8 2

6. 3 3

7. 9 6

8. 5 4

9. 0 6

10. 5 3

11. 5 2

12. 6 4

13. 9 4

14. 6 3

15. 2 4

16. 8 3

17. 4 2

18. 6 7

19.

4 3

20.

5 6

21.

2 2

22.

3 6

23.

4 8

24.

9 6

25.

4 4

26.

2 3

27.

2 0

28.

7 6

29.

6 2

30.

1 6

31.

4 6

32.

6 8

33.

2 5

34.

6 6

35.

3 9

36.

4 7


Algebra & Functions Find the answer. 37. If 3, then how much is

?

38. If 6, then how much is

?

39. If 4, then how much is ?

Problem Solving 40. Cars are parked in 2 rows. There are

8 cars in each row. How many cars are parked?


41. Four parents are needed on each of

9 committees. How many parents are needed?

NS 4.1




R

RETEACH

You can skip count to multiply by 2 and 3. Find 2 8. Think: Skip count by 2s eight times. 2 4 6 8 10 12 14 16

These are multiples of 2.

2 8 16 Find 7 3. Think: Skip count by 3s seven times. 3 6 9 12 15 18

21

These are multiples of 3.

7 3 21 You can double a fact you know to multiply by 4 and 6. Double a fact to multiply by 4. Double a fact to multiply by 6. 4 5 (2 5) (2 5) ↓ ↓ 10 10 20 ••••• ••••• ••••• ••••• ••••• ••••• ••••• •••••

6 5 (3 5) (3 5) ↓ ↓ 15 15 30 ••••• ••••• ••••• ••••• ••••• ••••• ••••• ••••• ••••• ••••• ••••• •••••


Skip count to find the answer. Use the models above to help you. 1. 2 7

2. 6 2

3. 2 8

4. 9 2

5. 6 3

6. 3 8

7. 9 3

8. 3 7

Double a fact to find the answer. You can use counters to help you. 9. 6 8 (3 8) (3

11. 7 6 (7

) (7

)

10. 4 7 (2

) (2

)


12. 8 4 (8

) (8

) )

NS 4.1




E

ENRICH

Triangle Math In each triangle, the number on the bottom left is the product of the middle left and the top number. The number on the bottom right is the product of the middle right and the top number. Complete the triangles. The top number must be a 2, 3, 4, or 6. 1.

2.

3.

2 1

6

12

5.

9

6.

7

9.

13.

1 3

12

16

21

5

5

15

27

28

9

20

36

16.

2

6 7

24

4

15.

4

8

12.

4 4

24

9

48

14.

3

7

3 8

36

10

3 6

8

6 6

12

8.

11.

2

3

32

6

2

16

10.

18

8

4 8

14

9 5

1

7.

7

30

4

18

2 5

42

3

3

18

6


6

3 6

2

4.

4 24

9

54

2 4

3 6

17. Explain how you found the answer to the triangle in exercise 3.


NS 4.1



Multiply by 5 and 10

P

PRACTICE


Multiply. 1. 5 4

2. 5 8

3. 6 10

4. 1 5

5. 0 5

6. 3 10

7. 7 5

8. 4 10

9. 3 5

10. 6 5

11. 5 10

12. 1 10

13. 2 5

14. 4 5

15. 9 5

16. 8 10

17. 9 10

18. 2 10

19. 8 5

20. 5 5

21. 10 6

22. 0 10

23. 5 2

24. 7 10

25.

5 6

26.

10 3

27.

5 3

28.

10 8

29.

5 2

30.

10 5

31.

10 9

32.

5 1

33.

5 5

34.

10 6

35.

10 4

36.

5 4

37.

10 7

38.

5 8

39.

5 0

40.

10 0

41.

10 2

42.

5 7

43.

10 1

44.

5 9

45.

6 5

46.

9 5

47.

8 5

48.

3 5

Tell whether the number is a multiple of 2, 5, or 10. 49. 18

50. 30

51. 35

52. 40

Problem Solving 53. Gene has 5 boxes of crayons with

10 crayons in each box. How many crayons does Gene have?


54. Jan places 5 rows of 8 stars in a

rectangle to make a design. How many stars does she use?

NS 3.2




R

RETEACH

You can skip count using nickels to multiply by 5. Find 7 5 Think: Skip count by 5s four times.

five 5

ten 10

fifteen 15

twenty 20

twenty-five 25

thirty 30

thirty-five 35

7 5 35 You can skip count using dimes to multiply by ten. Find 8 10. Think: Skip count by 10s three times.

ten 10

twenty 20

thirty 30

forty 40

fifty 50

sixty 60

seventy 70

eighty 80

8 10 80 Skip count to find the answer. 1.

2.

65

5 10


Multiply. You can use nickels and dimes to help you. 3. 4 5

4. 3 10

5. 5 10

7. 9 5

8. 6 10

9. 7 5

11. 2 5

12. 2 10

15.

10 8

16.

5 8

17.

10 5

6. 6 5 10. 7 10

13. 1 10 18.


10 9

19.

14. 5 5

5 9

20.

10 4

NS 3.2




E

ENRICH

True Sums Write multiplication sentences to make each sum true. Each multiplication sentence must have a 5 or a 10 as one of its factors. Product 1. 2

5

10 4

2. 10

20 20 40

5

1 2

Sum

5 10

5. 5

3 15 10 100

8

6 10

5

85

8.

9 10

5 8

Sum


5

10 9

6.

4 10

5 9

Product 9. 5

45 80

11. 4

5

10 10

Sum

5

1 10

5 50 55

Sum

Product

40 50 90

20 90 110 Sum

Product

30 45 75

30 80

125 Sum

Product 10. 3

Product

Product

35 50

70 40 110 Sum

Sum

110 Sum

Product

7 10

8

10 5

Product

115 Sum

7. 5

3. 7

10 10 20

Product 4.

Product

Product

12.

5 10

Sum

5 6

25 60 85

Sum

Can you follow the rules and find other numbers that will give a true sum for exercises 1 and 4?


NS 3.2



Multiply by 7, 8, and 9

P

PRACTICE

Multiply. 1. 5 7

2. 9 7

3. 1 8

4. 9 9

5. 3 8

6. 8 7

7. 4 9

8. 2 8

9. 3 7

10. 6 9

11. 7 8

12. 7 7

13. 5 8

14. 2 9

15. 0 7

16. 1 9

17. 6 8

18. 4 7

19. 8 9

20. 4 8

21.

5 9

22.

7 2

23.

9 8

24.

9 3

25.

8 0

26.

7 9

27.

8 8

28.

2 8

29.

7 1

30.

6 7

31.

9 1

32.

9 6

33.

8 4

34.

9 2

35.

7 3

36.

8 3

37.

7 5

38.

8 6

Algebra & Functions Find the rule. Then complete the table. 39.

Rule: 0

1

2

3

0

9

18

27

0

1

2

3

0

8

16

24

4

5

6

4

5

6


40.

Rule:

Problem Solving 41. Nathan puts 6 cards on each of 8

pages in an album. How many cards does he put in the album?


42. A marching band has 5 rows with

9 students in each row. How many students are in the marching band?

NS 3.2, 4.1




R

RETEACH

You can use known facts to multiply by 7, 8, and 9. Add to a known fact to multiply by 7.

Subtract from a known fact to multiply by 9.

Double a fact to multiply by 8.

Find 7 6.

Find 6 9.

Find 8 7.

Double 4 7. (4 7) (4 7) Think: Think: ↓ 35 7 is the same as 7 6. 60 6 is the same as 6 9. ↓ 28 28 56 You know 7 5 35.

You know 6 10 60.

35 7 42

60 6 54

7 6 42

6 9 54

8 7 56


Multiply. 1. 7 5

2. 8 6

3. 9 8

4. 8 8

5. 9 7

6. 7 7

7. 9 9

8. 7 9

9. 8 10

10. 3 8

11. 7 4

12. 9 2

13.

5 9

14.

8 9

15.

4 7

16.

19.

10 9

20.

4 6

21.

5 8

22.


3 9

4 9

17.

6 7

18.

4 8

23.

10 7

24.

9 8

NS 3.2, 4.1




E

ENRICH

Multiplication Game Play with a partner. Cut out the game markers. One player puts the glove on START. The other puts the baseball on START.

You will need: Two sets of number cards. Each set contains number cards from 0 through 10. Label one set A and the other set B.

Take turns. • Pick a card from A and a card from B. Find the product of the two numbers. • Have your partner check the product. If the product is correct, move forward two spaces. If the product is wrong, move back one space. The first player to get to the field wins.

Eq uip Bo me x nt

Ball is Lost in Woods. Go to equipment box.

Ball bounced in puddle. Go back to Start.

Woods

Tripped over feet. Go back 3 spaces.


glo Dro v p Go e in ped 3s b m pa ack ud. ce s.

Puddle

Field

Markers

Start


NS 3.2, 4.1




P

PRACTICE

Reading Skill

Choose an Operation Solve. Tell how you chose the operation. 1. Georgia puts coins in an album. There are 8 pages in the album. Each page

has slots for 8 coins. How many coins can Georgia put in the album?

2. Dina has 37 international dolls. Maxine has 26 international dolls.

Who has more dolls? How many more does she have?

3. Ben buys 9 packs of dinosaur stickers. There are 6 stickers in each

pack. How many stickers does Ben buy?

4. Melanie has a collection of 242 stamps. At a stamp convention, she

buys 19 more stamps. How many stamps does Melanie have now?

5. James collects model cars. He has 48 model cars. On his birthday,


James gets 7 more cars. How many model cars does James have in all?

6. Wendy has 10 flower stickers. She gives away 7 flower stickers.

How many flower stickers does Wendy have left?


MR 1.1, 2.3, 2.4, 3.2


Problem Solving: Reading for Math Choose an Operation


P

PRACTICE


Choose the correct answer. Juan buys 6 packs of stickers. Each pack has 4 stickers. How many stickers does Juan buy in all? 1. Which of the following statements

2. Which of the following can you use

is true?

to solve the problem?

A B C D

F G H J

Juan has 4 packs of stickers. Juan has 10 stickers. Juan has 24 packs of stickers. Juan has 24 stickers.

64 64 64 64

Warren has 9 silver dollars. At a coin show, he buys 3 silver dollars. How many silver dollars does Warren have now?


3. What do you have to do to solve

4. How many silver dollars does

this problem?

Warren have?

A find how many silver dollars are left B find the total of 2 unequal groups of silver dollars C find the total of 3 equal groups of silver dollars D find how many silver dollars there are when you split 9 into 3 equal groups

F G H J

3 silver dollars 6 silver dollars 12 silver dollars 27 silver dollars

Nadia collects souvenir flags. She puts the flags in her bookcase in 3 rows. There are 7 flags in each row. How many flags does Nadia have? 5. What do you have to do to solve

this problem? A find the total of 2 unequal groups of flags B find the total of 2 equal groups of flags C find the total of 3 equal groups of flags D find how many flags are left Use with Grade 4, Chapter 4, Lesson 6, pages 150–151. (122)

6. How many flags are there?

F G H J

21 flags 10 flags 4 flags 3 flags

MR 1.1, 2.3, 2.4, 3.2




P

PRACTICE


Choose the correct answer. Selena has 42 movie posters. Her brother has 26 movie posters. How many movie posters do they have in all? 7. What operation could you use to

8. How many movie posters do Selena

solve this problem?

and her brother have in all?

A addition

F 16

B subtraction

G 26

C multiplication

H 68

D division

J 78

Solve. 9. Lois sells 10 rock-star posters. She

gets $8 for each poster. How much money does Lois receive?

11. Janell has 472 baseball cards. Lou


has 397 baseball cards. How many more baseball cards does Janell have than Lou?

13. Brian displays his trophies in his

bedroom. He puts his trophies in 3 rows. There are 6 trophies in each row. How many trophies does Brian have?


10. Morris has 16 kites. He buys 4 more

kites. How many kites does Morris have now?

12. Kevin buys 7 packs of football cards.

There are 4 football cards in each pack. How many football cards does Kevin buy?

14. Barbara puts photos of France in

a photo album. The photo album can hold 94 photos. Barbara has 78 photos. How many more photos can she put in the album?

MR 1.1, 2.3, 2.4, 3.2



Multiplication Table and Patterns

P

PRACTICE

Complete the table.

0

0

0

1

0

1

2

1

2

2

2

4

3

3

3

4

5

6

7

4

9

10

11

12 21

8

27

36

20

5

15

30

6

40

50

60

36

7

12

8

9

4

8

66

7

72

77

8

16

32

96

9

54

108

10 11

22

12

24

55

88

99

84

121 132 120

144

Use the table to multiply. 1. 9 8


5.

12 8

2. 3 12 6.

12 12

7.

12 7

11. What is the pattern of odd and even

numbers in the 3 row or 3 column?

3. 11 11 8.

10 10

9.

4. 4 12

11 7

10.

12 9

12. What is the pattern of odd and even

numbers in the 4 row or 4 column?

Compare. Write , , or . 13. 6 3

33

14. 15 7

16. 9 7

6 11

17. 9 7


27 44

15. 4 8 18. 12 4

25 4 23 NS 4.1, 4.2, MR 1.1




R

RETEACH

To find 8 9, draw arrows to show where the 8 row and the 9 column meet in the table. The 8 row and the 9 column meet at 72. So, 8 9 72.

0

1

2

3

4

5

6

7

8

9

10

11

12

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

1

2

3

4

5

6

7

8

9

10

11

12

2

0

2

4

6

8

10

12

14

16

18

20

22

24

3

0

3

6

9

12

15

18

21

24

27

30

33

36

4

0

4

8

12

16

20

24

28

32

36

40

44

48

5

0

5

10

15

20

25

30

35

40

45

50

55

60

6

0

6

12

18

24

30

36

42

48

54

60

66

72

7

0

7

14

21

28

35

42

49

56

63

70

77

84

8

0

8

16

24

32

40

48

56

64

72

80

88

96

9

0

9

18

27

36

45

54

63

72

81

90

99

108

10

0

10

20

30

40

50

60

70

80

90

100 110

120

11

0

11

22

33

44

55

66

77

88

99

110 121

132

12

0

12

24

36

48

60

72

84

96

108

120 132

144


Multiply. You can use the multiplication table to help you. 1. 6 8

2. 8 12

3. 8 4

4. 7 7

5. 10 5

6. 9 11

7. 7 4

8. 3 8

9. 4 9

11. 9 9

12. 6 7

10. 7 12 13.

9 12

14.

8 7

15.

8 11

16.

9 8

17.

12 10

18.

11 7

19.

11 12

20.

8 8

21.

9 7

22.

12 12

23.

11 3

24.

11 11


NS 4.1, 4.2; MR 1.1




E

ENRICH

Twisted Tables Complete each multiplication table. Fill in the missing factors. 1.

3.

5.

2.

10

15

20

42

14

28

12

18

24

18

6

12

14

21

28

30

10

20

4.

36

42

54

24

12

28

0

8

6

7

9

4

24

56

0

16

12

14

18

8

3

7

0

2

30

35

45

20

9

21

0

6

63

42

21

6.

72 28

24 27


7

7.

6

72 6

18

2

0

8.

56

28

16

40

15

35

18 16 24

9

0

36

18

21 6


42

NS 4.1, 4.2; MR 1.1



Multiply Three Numbers

P

PRACTICE

Multiply. 1. (2 5) 4

2. 3 (2 8)

3. (4 2) 3

4. 6 (3 2)

5. 4 (4 2)

6. 7 (2 5)

7. (5 2) 4

8. (2 2) 2

9. (9 3) 0

10. (8 2) 3

11. 7 (3 3)

12. (6 2) 2

13. 2 (7 2)

14. (8 4) 2

15. (9 2) 4

16. 5 (3 3)

17. 4 (8 1)

18. 7 (2 3)

19. 9 (2 3)

20. (8 1) 9

21. 5 (3 2)

22. (8 3) 0

23. 9 (3 3)

24. (7 2) 4

25. 2 (4 3)

26. (3 3) 3

27. (7 2) 2

Complete the multiplication sentence. 28. 5 4

5


30. (9 3) 32.

27

(3 5) 9 5

29. (

8) 7 0

31. 5 6 5 (3

)

33. 4 4 2 (2

) (4 2)

Problem Solving 34. The school gives each basketball

player 2 shirts. Each shirt costs $8. What is the total cost of shirts for 6 players?


35. In a baseball game of 9 innings,

each of the 2 teams gets 3 outs per inning. How many outs are there in a game?

AF 1.3




R

RETEACH

Find: (3 5) 2 Think: 3 2 is a known fact. (5 3) 2 Use the Commutative Property to change the order. 5 (3 2) Use the Associative Property to regroup the numbers. 56

Multiply inside the parentheses first. Think: 3 twos

5 6 30 Multiply again. Think: 5 sixes

Multiply. 1. (2 5) 4

(5

)4

5(


5

2. 3 (4 3)

3( )

(

3. (2 6) 3

)

(6

)3

)4

6(

4

6

4. 2 (2 3)

5. (2 4) 3

6. (5 2) 3

7. (7 1) 3

8. (4 8) 1

9. 3 (3 2)

10. (5 4) 2

11. 9 (2 3)

12. (3 3) 3

13. (8 2) 4

14. 3 (3 5)

15. (9 2) 2

16. (9 6) 1

17. (2 7) 3

18. 5 (4 3)


)

AF 1.3




E

ENRICH

The Search for 48


Circle each combination of numbers that has a product of 48. You can multiply up to four numbers. Look across, up, down, and diagonally. Can you find all 26 combinations?

4

3

4

2

3

7

8

4

9

2

2

4

6

4

5

2

3

2

4

8

8

6

6

6

7

6

6

3

7

4

9

4

3

4

2

2

2

2

8

3

2

9

Choose one of these numbers: 24, 36, 64, or 72. Make your own number search and give it to a friend to solve. Be sure to keep a copy with the solution!


AF 1.3



Relate Multiplication and Division Facts

P

PRACTICE

Write a related multiplication fact and complete the division sentence. 1. 18 9

9

2. 15 3

18

3

18 9

3. 16 4

15

4

16

15 3

16 4

4. 6 2

5. 18 2

6. 15 5

7. 8 4

8. 27 3

9. 14 2

10. 28 7

11. 18 3

12. 63 7

13. 48 6

14. 35 7

15. 42 7

Divide.

7

16. 3 21

9

21. 5 45

7


26. 8 56

9

31. 7 63

3

17. 7 21

8

22. 7 56

5

27. 9 45

9

32. 6 54

8

18. 2 16

3

23. 8 24

9

28. 9 81

6

33. 4 24

6

19. 3 18

6

24. 9 54

4

29. 9 36

9

34. 4 36

5

20. 5 25

3

25. 3 9

8

30. 8 64

7

35. 9 63

Problem Solving 36. It takes 4 horses to pull a coach. How

37. Groups of 6 visitors can take tours of

many coaches can 20 horses pull?

an old western town. How many groups can 24 people make?


NS 3.2; MR 1.1



Relate Multiplication and Division Facts Find 15 5.

R

RETEACH

Think: How many groups of 5 are in 15?

5 ? 15 → 5 3 15 There are 3 groups of 5 in 15.

So, 15 5 3.

Write a related multiplication fact and complete the division sentence. 1. 18 6

6

2. 16 8

18

18 6 4. 20 5


20 5 7. 30 5

30 5

8

3. 12 3

16

16 8 5. 21 7

21 7 8. 27 9

27 9


4

12

12 3 6. 24 6

24 6 9. 28 4

28 4

NS 3.2; MR 1.1



Relate Multiplication and Division Facts

E

ENRICH

Word Puzzle Use the letters in the table below to complete the word puzzle. Words have to connect as they do in a crossword puzzle. Letter Values Letter

Value

Letter

Value

A

10 3 ?

L

45 5 ?

B

25 5 ?

N

49?

D

12 6 ?

O

30 3 ?

E

36?

S

55?

F

45?

T

67?

G

36 4 ?

U

42 7 ?

J

10 4 ?

Y

54 6 ?

Rules • Use each letter in the table only once.


• You cannot move the vowels in the puzzle. • Try to get the highest score you can. To find your score, complete the multiplication or division to find the value of each letter you used. For example, if you placed the letter B in the top left square, you would get 5 for that square (25 5 5). Then add to find the value of each word. Finally, add the values of all four words.

J

O

E T

G U

A

N


NS 3.2; MR 1.1




P

PRACTICE

Act It Out Use act it out to solve. 1. The Rare Book Club invites its

25 members to a dinner. Square tables seat 4 people and round tables seat 5 people. If the club wants full tables, which tables should the club use? How many of these tables will be needed?

3. Courtney is making a display of

42 shells. She arranges the shells in rows of 6. How many rows does Courtney make?


Mixed Strategy Review Solve. Use any strategy. 5. Yoki has 20 posters of science-fiction movies. She puts an equal number of these posters on each of 4 walls. How many posters does Yoki put on each wall?

Strategy: 7. Dinner starts at 6:00 P.M. It will take

Robert 45 minutes to get there. On his way, he wants to stop at the library for 30 minutes. What time does Robert need to leave to get to the dinner on time?

2. Len delivers 16 bottles of juice and

soda. A small box will hold 6 bottles and a large box will hold 8 bottles. Which box should Len use if he wants to put an equal number of bottles in each box? How many boxes will he need?

4. The Sailing Club puts 12 of its 48

trophies in a large display case. There are 6 smaller cases. How can the club arrange the rest of the trophies so that each smaller case has an equal number of trophies?

6. Art For posters, Nancy has a piece

of poster paper that is 9 feet by 2 feet. She cuts 3-foot by 1-foot rectangles from it. How many posters does she make?

Strategy: 8. Create a problem which you could

act out to solve. Share it with others.


NS 3.2; MR 1.1




R

RETEACH

Act It Out Page 163, Problem 2

For placemats, Meg is going to cut 2-foot by 1-foot rectangles from a piece of fabric with a starry background. The fabric is 4 feet wide and 3 feet long. How many placemats can she cut from one piece of fabric? Step 1

Read

Be sure you understand the problem. Read carefully. What do you know? • The placemats are

by

.

• Meg is going to cut the placemats from a piece of fabric that is by . What do you need to find? • You need to find how many . Step 2

Plan ■

■


■

■

■

■

■

■

■

■

Make a Table or List Write a Number Sentence Work Backward Act it Out Find a Pattern Make a Graph Guess and Check Logical Reasoning Solve a Simpler Problem Draw a Picture


To solve the problem, you can act it out using models. Draw a rectangle that represents the piece of fabric. A rectangle that is 4 feet by 3 feet would be very large, so draw a rectangle that is 4 centimeters by 3 centimeters to represent the piece of fabric. Make rectangles that represent the placemats. Since the placemats are 2 feet by 1 foot, cut out rectangles that are 2 centimeters by 1 centimeter.


NS 3.2; MR 1.1




R

RETEACH

Act It Out Step 3

Solve

Carry out your plan. Fill the large rectangle with small rectangles.

The large rectangle represents

.

Each small rectangle represents Meg can cut Step 4

Look Back

.

placemats from the piece of fabric.


Yes Yes

No No


What other stategies could you use to solve the problem?

Practice 1. Randy wants to cut name tags from a piece of poster paper. The poster paper is 18 inches by 24 inches. Each name tag will be 3 inches by 4 inches. How many name tags can Randy cut from the piece of poster paper?


2. Ted has 54 model train cars. He has

large boxes that will each hold 8 train cars. He has small boxes that will each hold 6 train cars. Which type of box should Ted use if he wants to put an equal number of cars in each box? How many of those boxes will he need?

NS 3.2; MR 1.1



Divide by 2 Through 12

P

PRACTICE

Divide. 1. 12 2

2. 24 3

3. 32 4

4. 35 5

5. 54 6

6. 56 7

7. 64 8

8. 81 9

9. 40 8

10. 48 6

11. 49 7

12. 27 3

13. 30 5

14. 36 4

15. 72 9

16. 90 10

17. 121 11

18. 144 12

9

6

19. 2 18

6

20. 3 18

9

21. 4 24

7

24. 7 63

7

25. 6 42

6

29. 12 72

26. 9 63

7

8

30. 11 77

31. 10 80

2

2

22. 7 14

23. 8 16

9

9

27. 5 45

28. 8 72

9

9

32. 11 99

33. 12 108

Algebra & Functions Find the rule. Then complete the table. 34.


35.

Rule: 0

9

0

1

2

3

4

5

6

2

3

4

5

6

Rule: 0

7

0

1

Problem Solving 36. There are 42 tomato plants in rows of

6 plants in each row. How many rows of tomato plants are there?


37. There are 45 tomatoes on 5 tomato

plants. Each tomato plant has the same number of tomatoes. How many tomatoes are on each plant?

NS 3.2; MR 1.1, 2.4, 3.2



Divide by 2 Through 12 Find 48 6.

R

RETEACH


6 ? 48 → 6 8 48 There are 8 groups of 6 in 48.

So, 48 6 8.

Complete the division sentence. 1.

2.

30 5

3.

24 8

16 4

Divide. Draw models if you wish. 4. 12 2

5. 21 3

6. 20 5

7. 14 7

8. 24 6

9. 16 2

10. 32 8

11. 18 3

9


13. 2 18

3

16. 5 15

3

19. 10 30

9

22. 6 54

9

25. 9 81

9

14. 4 36

6

17. 7 42

3

20. 11 33

8

23. 5 40

2

26. 12 24


12. 28 4

12

15. 3 36

5

18. 9 45

3

21. 12 36

8

24. 10 80

9

27. 11 99

NS 3.2; MR 1.1, 2.4, 3.2



Divide by 2 Through 12

E

ENRICH

Win the Division Play this division football game with a partner. You’ll need a number cube and 2 two-color counters to use as game pieces. Rules • Place your game pieces at the START positions on the 50-yard line. Each player can only move in the direction of the arrow. • Take turns rolling the number cubes. Add the number cubes to get a divisor. • If the number in the circle on the next 10-yard line can be evenly divided by the divisor, move to that circle. • Keep rolling the number cubes until one of you scores a touchdown.

16

42

TOUCHDOWN! G 28

10

15

20 36

30

12

40

Start Start


24

40 18

30

30 20

54

10 10

TOUCHDOWN!

50

G

35


NS 3.2; MR 1.1, 2.4, 3.2



Fact Families

P

PRACTICE

Complete each fact family. 1. 4 8

2. 9 5

q

3. 8 9

a

m

8 r 32

5 b 45

8 n 72

32 8 s

45 5 c

72 8 o

32 t 8

45 d 5

72 p 8

Find the missing factor. 4. 5

k 30 30 5 k

5.

7. 9

8. 9

w 54 54 9 w

h 7 56 56 7 h y 63 63 9 y

6. 9

g 72 72 9 g

9.

d 8 48 48 8 d


Write a multiplication and division fact family for each group of numbers. 10. 8, 5, 40

11. 3, 9, 27

12. 6, 7, 42

13. 9, 8, 72

14. 5, 7, 35

15. 4, 5, 20

16. 6, 9, 54

17. 5, 9, 45

Divide. What patterns do you see? 18. 4 4

88

99

66

19. 0 7

08

01

05


NS 3.2; AF 1.1; MR 1.1



Fact Families

R

RETEACH

Multiplication and division sentences that are related make up a fact family. Every sentence in a fact family uses the same numbers. Fact Family 3 4 12 4 3 12 12 3 4 12 4 3

Fact Family 5 2 10 2 5 10 10 5 2 10 2 5

Complete each fact family. 1.

2.

3 5 15 5

9

15 5 15

4

[9]

Write the fact family for each set of numbers.


3. 4, 6, 24

4. 3, 7, 21

5. 35, 7, 5

6. 54, 6, 9

Find the missing numbers. 7. 5

n 30 30 5 n n

8.

n 7 56 56 7 n n


9.

n 8 64 64 8 n n

10. 3

n 27 27 3 n n

NS 3.2; AF 1.1; MR 1.1



Fact Families

E

ENRICH

Chain Reaction


Write the missing numbers to complete each chain.

4

24

1.

24 6

6

2.

98

72

12

3.

8

6

48 4

4.

66 11

5.

5 12

60

6.

81

9

93

7.

45 9

5

6

6

1

6

12

8

3

4

30 6

5

10

69

9

45 5


0

0

48

6

8

5

9

45

6

54

3

3

40

5

9

9

9

9

81

3

27

NS 3.2; AF 1.1; MR 1.1


Problem Solving: Application Applying Multiplication and Division

Print This Page


Record your data. Storage Unit

Capacity: Number of trophies or medals per unit

Number of Units Used

Total Cost

Shelf


Frame (small or large)

Your Decision What is your recommendation for Lily? Explain.


NS 3.1, 3.3; MR 1.1, 1.2


Print This Page


Problem Solving: Application Ramp races: How does height affect distance?

Math & Science

Record your data. Ramp height

Distance traveled

Use division. How many times farther did the crayon travel on this ramp than it did on the 1-book ramp? Round to the nearest whole number.

1 book

2 books


3 books

4 books

5 books


NS 3.4; MR 1.1, 2.3



Print This Page


Ramp races: How does height affect distance? 1. On which ramp did the crayon travel the farthest? On which ramp

did the crayon travel the shortest distance?

2. Use division to calculate how many times farther the crayon

traveled for the 2-, 3-, 4-, and 5-book ramps than it did for the 1-book ramp. Do your calculations in the table and then list your answers here. Round to the nearest whole number.

3. Do you see a pattern? Describe it.

4. If the pattern continues, how far will a crayon travel if released from a


10-book ramp? a 20-book ramp? Explain how you made these estimates.

5. Explain the activity in terms of speed.


NS 3.4; MR 1.1, 2.3



Patterns of Multiplication

P

PRACTICE

Complete. 1. 3 2

a

3 b 60

c 200 600 3 2,000 d

a b c d

2. 5 8

e f g h

e

5 c 400

g 800 4,000 5 8,000 h

Multiply. Use mental math. 3.

80 6

4.

70 8

8.

400 5

9.

800 6

5.

10.

40 5

6.

700 9

11.

60 7

7.

2,000 4

12.

90 6

3,000 6

13. 90 5

14. 4 90

15. 5 600

16. 700 8

17. 9 600

18. 700 4

19. 2,000 8

20. 5,000 7

21. 8 4,000

Find each missing number. 22.

a 5 300


a 25. 3

23.

b 4 320

24. 2

a a 900

a

26. 6

c 180

c b 3,600

b

27.

c 8 72,000 c

Problem Solving 28. Stamps are sold in rolls of 100. How

many stamps are in 9 rolls?


29. A ream of paper is 500 sheets of

paper. How many sheets are in 7 reams?

NS 3.2




R

RETEACH

Using basic facts and patterns can help you multiply mentally.

2 4 ones 8 ones 248

2 4 tens 8 tens 2 40 80

2 4 hundreds 8 hundreds 2 400 800


2. 6 3

3. 4 5

3 30

6 30

4 50

3 300

6 300

4 500

3 3,000

6 3,000

4 5,000


Multiply. Use mental math. 4.

70 8

9.

200 8

5.

10.

90 4

500 7

6.

11.

70 4

3,000 8

7.

12.

60 7

8.

7,000 3

13.

800 9

6,000 8

14. 9 60

15. 6 50

16. 8 200

17. 8 800

18. 6 800

19. 5 900

20. 6 600

21. 8 400

22. 9 700

23. 4 600

24. 8 5,000

25. 3 4,000

26. 7 2,000

27. 5 6,000

28. 4 4,000


NS 3.2




E

ENRICH

History Riddles Find each missing number. Then find the letter in the table that matches that number. Solve the riddles. Write the letter in the blank above the same exercise number. 5 100

1.

2. 60

24,000 3. 7

350

4. 4

2,000

5.

9 1,800

6.

8 400

7. 7

21,000

8.

5 1,000

9.

6 3,000

11. 7

1,400

12.

6 1,200

15. 6

10. 3

1,200

13.

6 240

14. 6

480

16.

3 600

17. 9

18,000 18.

19. 6

2,400 7 2,100

22.

20

30

40

50

80

E

N

B

A

M

20.

3,000 5 100

8 4,000

21. 9

180

4,800

24. 7

210

23. 6

200 300 400 500 800 2,000 3,000 4,000 5,000 8,000 T

S

H

O

I

F

W

U

K

Y


What did Paul Revere say at the end of his ride? 7.

2.

9.

3.

Where was the Declaration of Independence signed?

6.

11.

12.

10.

1.

13.

15.

5.

8.

4.

14.

When Columbus discovered America, where did he first stand? 20.

24.

19.

23.

22.


17.

18.

21.

16.

NS 3.2



Explore Multiplying 2-Digit Numbers by1-Digit Numbers

P

PRACTICE

1. Multiply 4 15. Draw squares to multiply.



62 2

3.

38 4

4.

91 3

5.

46 5

6.

78 6

7.

98 5

8.

76 6

9.

24 9

10.

56 7

11.

48 8

12.

66 6

13.

77 7

14.

94 3

15.

59 4

16.

44 9

17.

24 7

18.

19 8

19.

67 5

20.

84 4

21.

76 7

22. 5 26

23. 37 8

24. 45 6

25. 38 4

26. 7 22

27. 9 49

28. 8 67

29. 35 4

30. 99 3

Problem Solving 31. Katy arranges oranges in 5 layers in a

crate. Each layer has 24 oranges. How many oranges does she put in the crate?


32. Band members march in 24 rows.

There are 8 members in each row. How many members are in the band?

NS 3.2



Explore Multiplying 2-Digit Numbers by 1-Digit Numbers

R

RETEACH

Find 5 21. You can draw an array to multiply. Find the total number of dots. 5 21 105

5 dots

21 dots Draw an array to multiply. 1. 4 18

2. 5 24 5 dots

4 dots 24 dots

18 dots



19 6

4.

24 5

5.

25 8

6.

13 9

7.

12 9

8.

46 3

9.

37 4

10.

58 5

11.

28 7

12.

23 6

13.

33 4

14.

21 5

15.

18 3

16.

30 6

17.

18 9

18. 4 17

19. 22 6

20. 7 14

21. 20 6

22. 5 31

23. 26 4

24. 3 13

25. 4 50

26. 5 15


NS 3.2



Explore Multiplying 2-Digit Numbers by1-Digit Numbers

E

ENRICH

The Abacus The abacus is a computing tool that is thousands of years old. To multiply 3 32 using a Russian abacus, first multiply 2 ones by 3. Move 6 beads to the bottom of the ones column to show 3 2 6.

H

T

Next, multiply 3 tens by 3. Move 9 beads to the bottom of the tens column to show 3 3 tens 9 tens.

O

H

T

O

Count the beads in each column.

There are 9 tens 6 ones, so 3 32 96. Use the abacus to find each product. Show the answer by drawing the beads you moved down. Cross out the beads you moved down from the top. 1. 4 22


H

2. 2 34

T

O

4. 5 43

H

H

3. 3 31

T

O

5. 4 212

T

O

H


T

H

T

O

6. 3 304

O

H

T

O

NS 3.2



Multiply 2-Digit Numbers by 1-Digit Numbers

P

PRACTICE


Multiply. 1.

73 3

2.

44 5

3.

31 7

4.

68 8

5.

32 9

6.

65 5

7.

33 6

8.

96 3

9.

88 4

10.

74 5

11.

85 4

12.

77 6

13.

97 2

14.

66 8

15.

94 3

16.

44 4

17.

77 7

18.

18 9

19.

38 8

20.

99 6

21. 55 5

22. 75 6

23. 8 47

24. 6 39

25. 2 98

26. 84 6

27. 4 52

28. 63 7

29. 29 9

30. Multiply 63 by 8.






Problem Solving 36. A rectangle is 5 tiles wide by

13 tiles high. How many tiles are in the rectangle?


37. Books are stacked in 3 stacks with

17 books in each stack. How many books are in the stacks?

NS 3.2, 3.3




R

RETEACH

You can multiply using models or pencil and paper. Find 4 26. Show 4 groups of 26.

You can record this way: 26 4 24

Step 1 Multiply the ones. 4 6 ones 24 ones

26 4 24 80

Step 2 Multiply the tens. 4 2 tens 8 tens

26 4 24 80 104

Step 3 Add.


Complete to find the product. You may use models to help you. 1.

23 5

2.

44 3

3.

31 8

4.

52 7

5.

45 9

6.

45 5

7.

64 6

8.

78 3

9.

86 4

10.

92 5

11. 9 52

12. 72 7

13. 68 3

14. 5 83

15. 2 88

16. 48 6


NS 3.2, 3.3




E

ENRICH

Lattice Multiplication You can use lattice multiplication to multiply. Multiply 7 48. Multiply 7 8. Write 56 in the first box.

Write 48 over the top boxes. Write 7 on the right.

4

8

4

Multiply 7 4. Write 28 in the second box. Add on the diagonals. Start at the right. Regroup as you would in any addition problem. 4

8

8

2

5

3

7

7

48 7 7 336 6

5 8

6 3

6

Use lattice multiplication to find the products. 1. 2 27

2. 5 34

2

7

3

1


4 5

4

2

5

2 5 7

7

0

5

6 6

8

5

4


2

6

2 0 2

4

4

4

6. 7 79

3

7

2 8 0

2

0

6

5 4 9

1

4

5. 8 63

3

2

1

4

4. 8 37

2

3. 4 56

4 4

8

5

4

9

6 9 5

3

7

3

NS 3.2, 3.3



Estimate Products

P

PRACTICE

Estimate each product. 1. 5 21

2. 3 39

3. 7 $46

4. 85 6

5. 17 9

6. 81 3

7. 2 $298

8. 4 305

9. 478 6

10. 5 784

11. 612 9

12. 6 556

13. 2 1,987

14. 3 $2,126

15. 7 1,905

16. 8 3,495

17. 4,723 4

18. 5 $7,118

19.

41 6

20.

28 7

21.

96 2

22.

17 8

23.

31 9

24.

255 4

25.

488 3

26.

563 5

27.

2,307 5

28.

7,596 6

Algebra & Functions 29. 2 36

1 49

30. 96 3

32. 97 1

89 2

33. 6 105

4 209 34. 396 4

106 9

6 523 36. 3 666

2 366 37. 4 712

3 412

35. 5 423 © McGraw-Hill School Division

Estimate. Write or . 68 4

31. 6 28

5 41

Problem Solving 38. The volunteer ambulance group

orders 6 first aid kits. Each kit costs $39. About how much does it cost for 6 kits?


39. An ambulance travels about 386

miles a day. About how many miles does it travel in a week?

NS 1.4, 3.2; 3.3



Estimate Products

R

RETEACH

You can round to estimate products. Round the greater factor to its greatest place and multiply using patterns. Estimate 8 287. 8 287

Round 287 to the nearest hundred.

↓

↓

8 300

287

200 210 220 230 240 250 260 270 280 290 300 Multiply using the rounded number

8 300 2,400 So, 8 287 is about 2,400.



2. 3 42

3. 6 36

4. 6 $58

5. 9 18

6. 3 71

7. 3 198

8. 2 $405

9. 4 378

10. 5 2,987

11. 8 2,126

12. 7 $2,905

13.

31 2

14.

58 3

15.

$66 4

16.

17 5

17.

51 6

18.

$454 7

19.

512 8

20.

498 9

21.

$637 4

22.

845 2

23.

7,809 6

24.

$6,047 3

25.

4,524 8

26.

$2,107 6

27.

8,596 4

28.

2,537 4

29.

5,088 2

30. $6,409

31.

3,623 8

32. $7,522

7


9

NS 1.4, 3.2; 3.3



Estimate Products

E

ENRICH

Target Practice Estimate to find the factors whose product is closer to the target number. Circle the letter of the answer. 1. Target Number: 150

2. Target Number: 160


S. 57 3

H. 37 4

D. 3 67

T. 52 3

I. 32 4

E. 3 61




S. 88 6

T. 7 62

O. 76 8

T. 83 6

U. 7 68

A. 72 8

7. Target Number: 2,700



T. 3 879

T. 79 9

E. 9 490

U. 3 849

U. 72 9

F. 9 430




N. 849 4

E. 770 8

L. 2,181 3

O. 889 4

F. 680 8

M. 2,898 3




I. 839 8

A. 711 9

E. 303 8

J. 899 8

B. 782 9

F. 352 8


16. Target Number: 25,000 17. Target Number: 32,000 18. Target Number: 35,000 Q. 4,175 5

T. 7,825 4

Y. 4,762 7

R. 4,899 5

U. 7,239 4

Z. 4,097 7

Write the circled letters above each exercise number to answer the question. “I lift my lamp beside the golden door!” Who am I?

1

2

3

4

5

6

7

8

9

10 11


12 13 14 15 16 17 18 NS 1.4, 3.2, 3.3


Problem Solving: Reading for Math Use an Overestimate or Underestimate


P

PRACTICE

Reading Skill

Form a conclusion about whether you would use an overestimate or an underestimate. Then solve each problem. 1. On Wednesday, a group of 98 students will visit the national forest.

Each student will get a nature guide fact book. These books come in boxes of 32. The park rangers have 3 boxes of fact books. Are there enough fact books so each student can get a book? Should you use an overestimate or an underestimate to solve this problem? Explain.

Are there enough fact books so each student can get a book? 2. The park charges $16 per day to use a campsite. The Nolans want

to use a campsite for 4 nights. They have $80 set aside for using a campsite. Have the Nolans set aside enough money? Should you use an overestimate or an underestimate to solve this problem? Explain.

Have the Nolans set aside enough money?


3. A total of 184 people are taking a desert hike. Each hiking group

can have up to 36 people. There are enough hike leaders and helpers to lead 6 groups. Are there enough hike leaders and helpers so that all of the people can go on a hike? Should you use an overestimate or an underestimate to solve this problem? Explain.

Are there enough hike leaders and helpers so that all of the people can go on a hike? Use with Grade 4, Chapter 5, Lesson 5, pages 202–203. (157)

MR 1.1, 2.4, 3.2




P

PRACTICE


Choose the correct answer. There are 146 students going on a trip to the desert. The school has 3 buses. Each bus can hold 48 students. Should a fourth bus be ordered for the trip? 1. Which statement is true?

A There are 48 students going on a trip to the desert. B Each bus can hold 48 students. C Three buses can hold exactly 150 students.

2. To make sure that 3 buses are enough

to hold 148 students, you should F underestimate the number of students the buses can hold. G overestimate the number of students the buses can hold. H underestimate the number of students going on the trip.

The cafeteria in the national forest visitors’ center has 23 tables. Each table seats 6 people. A group of 120 is visiting the forest. Are there enough tables so that all 120 people can eat in the cafeteria at once? 3. Which statement is not true?


A Each table can seat 23 people. B The cafeteria has 23 tables. C Each table can seat 6 people.

4. To make sure there are enough tables

to seat 120 people, you should F overestimate the number of seats. G underestimate the number of tables. H overestimate the number of tables.

There are 7 river tours per day. Each river tour has room for 48 people. Each person on the river tour receives a pamphlet. The tour leaders have 400 pamphlets. Are there enough pamphlets for a day of river tours? 5. How would you use estimation to

solve this problem? A overestimate the number of people B underestimate the number of tours C underestimate the number of people Use with Grade 4, Chapter 5, Lesson 5, pages 202–203. (158)

6. Which estimate would you use to

solve the problem? F 7 40 280 G 6 50 300 H 7 50 350

MR 1.1, 2.4, 3.2




P

PRACTICE


Choose the correct answer. The Wildlife Committee is selling books to raise $400. The committee makes $8.75 on each book it sells. If the committee sells 50 books, will that be enough to raise $400? 7. How would you use estimation to

8. Which estimate would you use to

solve this problem?

solve the problem?

A overestimate the amount made on each book

F $9 x 50 = $450

B underestimate the amount made on each book

G $8 x 50 = $400 H $8 x 40 = $320

C underestimate the number of books Solve. 9. The river tour has 4 boats. Each boat

has room for 24 people. Are there enough boats to take 76 people on a tour?


11. The forest rangers have 5 boxes of

wildlife guides. Each box contains 36 pamphlets. The rangers need 200 pamphlets. Should they order another box?

13. The motel in the national park costs

$39 per night. Nick sets aside $150 to pay for the motel. Is this enough money to pay for 5 nights?


10. There are 5 groups of 25 students

each. The rangers have 150 forest T-shirts. Do they have enough T-shirts to give a T-shirt to each student?

12. Phyllis takes 118 photos of the

desert. She buys a photo album with 24 pages. Each page can hold 6 photos. Can all the photos fit in the album?

14. It costs $89 to rent a sport utility

vehicle (SUV) for one day. Will $650 be enough to rent an SUV for a 7-day trip through the desert?

MR 1.1, 2.4, 3.2



Multiply Greater Numbers

P

PRACTICE

Multiply. Check for reasonableness. 1.

693 4

2.

907 5

3.

368 9

4.

$601 3

5.

2,901 2

6.

1,999 7

7.

8,072 8

8.

$38.88 4

9. 6 2,369

10. 7 5,786

11. 3 4,964

12. 9 $1,288

13. 5 19,091

14. 8 12,967

15. Multiply 3,687 by 8.

16. Multiply 1,096 by 9.

Algebra & Functions Complete the table. 17.


18.

Input

12

15

Output

48

60

Input

1

2

Output

37

74

18

21

24

3

4

5

Problem Solving 19. Maria made 9 trips between

New York City and Los Angeles. Each trip cost $498. How much did the 9 trips cost?


20. A company buys 8 computers. Each

computer costs $2,245. How much does the company spend on the 8 computers?

NS 3.2, 3.3




R

RETEACH

You can use models to help you multiply greater numbers. Find 2 357. Show 2 groups of 357.

You can record this way:

Step 1 Multiply the ones. 2 7 ones 14 ones Regroup. 14 ones 1 ten 4 ones

1

357 2 4

Step 2 Multiply the tens. 2 5 tens 10 tens

11

357 2 14

Add the tens. 10 tens 1 ten 11 tens Step 3 Multiply the hundreds. 2 3 hundreds 6 hundreds

11

357 2 714

Add the hundreds. 6 hundreds 1 hundred 7 hundreds


Multiply. Check for reasonableness. 1.

234 5

2.

146 3

3.

357 4

4.

$4.62 6

5.

3,548 2

6.

$6,164 7

7.

2,781 8

8.

4,862 9

9. $1,530

10.

2,681 2

11.

9,275 6

4


12. $7,452

5

NS 3.2, 3.3




E

ENRICH

Deducing Digits Find the missing digits. Write them in the boxes. 1.

3 8 184

2.

4 5 0

6.

4 6 744

10.

2

14.

5.

1

9.


17.

$5,

31

1

3

11.

7 5

25 9 5

7,

4 64

2

6,

19.

12.

7 1,666

15.

,6

22.

8.

7 434

416

4

,

9

,6

2

7.

46

18.

111

8 5

3 174

770

4,38

21.

3

3

4.

138

3 735

$1,0

3.

1

13.

1 7 98

7,

56

29,

75

74,450


5

23.

$3 $1

16.

7 9

,06

,3 3,

3 1 1,564

3 2,400

8,

20.

7

3 24. 4 32

76 ,184

0,3

9

82,472

NS 3.2, 3.3




P

PRACTICE

Find a Pattern Use find a pattern to solve. 1. Annie makes an arrangement of

chestnuts. She puts 3 chestnuts in the first row, 6 chestnuts in the second row, and 9 chestnuts in the third row. Describe the pattern. How many chestnuts will be in the fourth row?

3. Rangers examine trees that fell

during a storm. The first tree has 3 annual rings. The second tree has 9 rings. The third tree has 27 rings. The fourth tree has 81 rings. If the pattern continues, how many annual rings does the fourth tree have?

2. In one desert area, the rabbit

population is estimated at 25 in one year, 50 the next year, 100 the third year, and 200 the next year. Describe the pattern. Then estimate the rabbit population for the fifth year.

4. Stan counts robins’ nests on his

block. One year he counts 4 nests. The next year he counts 9 nests. The third year Stan counts 14 nests. The fourth year he counts 19 nests. If the pattern continues, how many nests will he count in the fifth year?

Mixed Strategy Review Solve. Use any strategy.


5. Nick took 40 photos of the desert.

6. Social Studies Colorado’s state

He has one photo album with 8 pages and another with 12 pages. Nick wants to put the same number of photos on each page. Which album should he use?

parks cover 347,000 acres. Connecticut’s state parks cover 176,000 acres. How many more acres do state parks cover in Colorado than in Connecticut?

Strategy:

Strategy:

7. Create a problem for which you

would find a pattern to solve. Share it with others. Use with Grade 4, Chapter 5, Lesson 7, pages 210–211. (163)

NS 3.2; MR 1.1, 2.4, 3.2




R

RETEACH

Find a Pattern Page 211, Problem 1

As a plant cell grows, one cell divides into two cells. Two cells divide into four cells, four into eight, and so on. Describe the pattern. How many cells will there be after seven divisions? Step 1

Read

Be sure you understand the problem. Read carefully. What do you know? • One cell divides into

cells, two cells divide into

cells, and four cells divide into

cells.


Plan ■

■

■

■


■

■

■

■

■

■

Find a Pattern Guess and Check Work Backward Make a Graph Make a Table or List Write a Number Sentence Draw a Picture Solve a Simpler Problem Logical Reasoning Act it out

Make a plan. Choose a strategy. Finding a pattern will help you solve the problem. Start 1st cell 2nd cell 3rd cell 4th cell 5th cell 6th cell 7th cell division division division division division division division Number of Cells

1

2

4

8

Find the pattern in the number of cells after the 1st, 2nd, and 3rd cell divisions. Continue the pattern to find the number of cells after the 7th cell division.


NS 3.2; MR 1.1, 2.4, 3.2




R

RETEACH

Find a Pattern Step 3

Solve

Carry out your plan. You know the number of cells after the 1st, 2nd, and 3rd cell divisions. 1st cell 2nd cell 3rd cell 4th cell 5th cell 6th cell 7th cell Start division division division division division division division Number of Cells

1

2

4

8

Find the pattern in the number of cells after the 1st, 2nd, and 3rd cell divisions. What pattern do you see?

Continue the pattern to complete the chart. If the pattern continues, there will be cells after the 7th cell division. Step 4

Look Back

Is the solution reasonable? Reread the problem. Did you find a pattern and continue it? Yes

No



Practice 1. Kate hikes 2 miles the first day,

5 miles the second day, and 8 miles the third day. If the pattern continues, how many miles will she hike the fourth day?


2. The Support-Our-Forests Fund has

goals of $3,000, $6,000, $12,000, and $24,000 for its first four fund drives. If the pattern continues, what will the goal be for the fifth fund drive?

NS 3.2; MR 1.1, 2.4, 3.2



Functions and Graphs

P

PRACTICE

Complete each table. Then write an equation. 1. Roger runs 7 miles more each week

2. One plant produces 8 times more

than another boy.

x

1

2

y

8

9

peppers than another plant. 3

4

5

3. One number is 4 less than 3 times

4

5

d

8

11

1

2

s

8

16

3

4

5

4. One number is 8 greater than 2 times

another number.

c

r

another number. 6

7

8

m

1

2

n

10

12

3

4

5

Complete each table. Then graph the function. 5. Stella works 4 times as many hours as

6. Liz swims 2 more than 2 times as

Jana does.


7.

many laps as Sunny does.

y 4x x 0

1

y

4

0

2

3

a 2b 2 b 0 1

4

a

s 2r 2

8.

r

1

2

s

0

2

3

4

5

2

2

3

4

3

4

5

4

n 3t 1 t

1

2

n

4

7

Problem Solving 9. Each of 4 people orders a $8.95

lunch. How much do the 4 lunches cost? Write and solve an equation.


10. Ben buys 3 toys that cost $3 each.

How much do the toys cost? Write and solve an equation.

AF 1.1, 1.5; SDP 2.1




R

RETEACH

The numbers in a function table relate to one another to form a pattern. One number is 1 greater than 2 times a number.

x

1

2

3

4

5

y

3

5

7

9

11

Think: How can I find the value of y? x 1 2

↓

Equation

↓

4

5

↓

↓

2x 1

2x 1

2x 1

2x 1

2x 1

3

5

7

9

11

↓

y

↓

3

↓

↓

↓

↓

In each case, multiply by 2 and add 1.

The values in the table form ordered pairs.

x

1

2

3

4

5

y 3 5 7 9 11 (x, y) (1, 3) (2, 5) (3, 7) (4, 9) (5, 11) You can graph these ordered pairs Complete each table. Then write an equation. 1. One number is 2 greater than

2. One number is 4 times another


another number. Think: Add 2 to x to get y.

x

1

2

y

3

4

3

4

number. Think: Multiply x by 4 to get y. 5

x

1

2

y

4

8

3

4

5

3

4

Complete each table. Write the ordered pairs. Then graph the function. 3.y 2x

4.y 2x 2

x

0

1

y

0

2

2

3

4


x

0

1

y

2

4

2

AF 1.1, 1.5; SDP 2.1




E

ENRICH

When Are Houses Like Books? To answer this riddle, find the points on the grid. Then write the letter for each point on the lines.

(1, 3) (7, 8) (0, 6) (7, 1)

(7, 8) (4, 7) (2, 2) (0, 6)

(3, 0) (7, 8) (0, 6) (4, 4)

(6, 5) (3, 0) (1, 1) (6, 2) (9, 5) (0, 6) (6, 5)

12 11 10 9

H

8

A

7

E

6

S

5

Y

4

W

3 © McGraw-Hill School Division

I

V

2

R

O

1

N T

0

1

2

3

4

5

6

7

8

9

10 11 12

If you are given the points (2, 2) and (6, 2), name two other points that would make a square. Use with Grade 4, Chapter 5, Lesson 8, pages 212–215. (168)

AF 1.1, 1.5; SDP 2.1


Print This Page



Decision Making

Analyze and Make Decisions Record your data. Item Name

Cost of Item per Unit

Number of Units

Total Cost of Item

Total Cost of Meal or Snack

Breakfast Items

Lunch Items

Dinner Items


Snack Items

Your Decision What is your recommendation for the menus (one breakfast, one lunch, one dinner, and snacks)?


NS 1.2, 3.2; MR 1.1, 2.3, 3.1


Problem Solving: Application How much water do you use each day?

Print This Page


Record your data. Number of Times Amount of Water a Day You Use This for Each Use Source of Water

Total Amount of Water


Place You Use Water


NS 1.2, 3.2; MR 1.1, 3.3



Print This Page


How much water do you use each day? 1. How much water do you use each day?

2. If a cup of water costs $0.10, how much money do you spend on

water each day? Show your work.

Work Space

3. How much water is being used by your whole class each day?


4. Is clean water a renewable or nonrenewable resource? Explain.

5. Give some other examples of renewable and nonrenewable resources.


NS 1.2, 3.2; MR 1.1, 3.3


Print This 6-1 Page


P

PRACTICE

Complete. 1. 6 8

s

s

2.

w 3 21

w

60 t 480

t

70 3 x

x

60 80 u

u

y 30 2,100

y

60 800 v

v

70 300 z

z


Multiply. Use mental math. 3. 60 70

4. 20 60

5. 80 800

6. 30 200

7. 50 40

8. 400 30

9. 600 50

10. 90 70

11. 20 4,000

12. 9,000 30

13. 3,000 70

14. 900 60

15. 80 5,000

16. 7,000 80

17. 40 800

18. 30 6,000

19. 20 500

20. 6,000 90

21. 700 40

22. 80 2,000

23. 50 5,000

Algebra & Functions

Find each missing number.

24. 30 j 9,000

j

25.

s 70 2,800

s

26. 60 b 24,000

b

27.

400 t 12,000

t

28. 90 q 8,100

q

29.

p 600 30,000 p

n 300 6,000 n

31.

r 800 40,000

30.

r

Problem Solving 32. ABC Hardware has 50 cartons of

nails. There are 4,000 nails in each carton. How many nails does the store have?


33.

Handy Hardware has 500 boxes of hinges. Each box has 90 hinges. How many hinges does the store have?

NS 3.2




R

RETEACH

You can use basic facts and patterns to help you multiply. 2 3 6 basic fact

4 5 20 basic fact

20 30 600 1 zero 1 zero 2 zeros

40 50 2,000 1 zero 1 zero 2 zeros

20 300 6,000 1 zero 2 zeros 3 zeros

40 500 20,000 1 zero 2 zeros 3 zeros

20 3,000 60,000 1 zero 3 zeros 4 zeros

40 5,000 200,000 1 zero 3 zeros 4 zeros


2. 7 2

40 30

70 20

40 300

70 200

40 3,000

70 2,000

3. 5 6

4. 8 5

50 60

80 50

50 600

80 500

50 6,000

80 5,000



6. 30 60

7. 30 600

8. 4 9

9. 40 90

10. 40 900

11. 80 30

12. 700 30

13. 20 50

14. 300 9

15. 80 600

16. 70 800

17. 30 8,000

18. 2,000 90

19.

20. 70 7,000

21. 7,000 60

22. 90 8,000


4,000 50

NS 3.2




E

ENRICH

Clueless Puzzle This puzzle has all the answers, but no clues. Each answer is a product of two factors. Make up clues for each answer.

1

2

3

4

5 6


Across

Down

1. 80 8,000

1. 70 90,000

2.

2.

3.

3.

4.

4.

5.

5.

6.

6.


NS 3.2


Explore Multiplying by 2-Digit Numbers


P

PRACTICE


Multiply. 1.

36 12

2.

27 41

3.

38 14

4.

23 22

5.

49 13

6.

47 34

7.

46 14

8.

17 25

9.

45 35

10.

48 20

11.

38 27

12.

32 15

13.

45 25

14.

14 15

15.

26 34

16.

32 18

17.

31 25

18.

12 46

19.

36 36

20.

28 44

21.

16 40

22.

17 17

23.

37 26

24.

19 27

25.

49 30

26. 15 23

27. 30 13

28. 14 22

29. 26 21

30. 30 24

31. 42 17

32. 63 15

33. 50 23

34. 13 13

35. 70 14

36. 32 20

37. 25 25

Problem Solving 38. The art teacher wants to decorate

each classroom with 28 balloons. How many balloons does he need for 18 classrooms?


39. There are 35 buses waiting for

students after school. Each bus carries 45 students. How many students ride the buses?

NS 3.2, 3.3




R

19 2

An array can help you multiply. Find 12 19. Think: 12 10 2 19 12 38 190 228

RETEACH

10

2 19 10 19

38 190 228 Find each product. Draw an array diagram to help you. 1.

14 15

2.

11 19


Multiply. 3.

28 14

4.

35 26

5.

42 33

6.

49 27

7.

32 18

8.

18 41

9.

23 17

10.

24 52

11.

45 28

12.

27 27

13. 32 21

14. 41 32


15. 26 17 NS 3.2, 3.3




E

ENRICH

Napier’s Bones In the seventeenth century, John Napier invented a simple calculator that multiplied by adding. It became known as Napier’s Bones. Here is a way to use Napier’s Bones to multiply 49 37. Place the strips headed 4 and 9 next to each other. Place the index beside the two strips.

Fold the strips so that the rows headed 3 and 7 on the index are next to each other. INDEX

INDEX

4

9

8 1 2 1 6 2 0 2 4 2 8 3 2 3 6

1 8 2 7 3 6 4 5 5 4 6 3 7 2 8 1

1 2 3 4 5 6 7 8 9

4

9

1 2 2 8

2 7 6 3

Add diagonally to find the product. Start at the bottom with the ones. Remember to carry. INDEX

1 3 7

4

9

1 2 2 8

2 7 6 3

1 3 7

37 49

Cut out the ten strips of Napier’s Bones below. Use them to find each product. 1. 57 34

2. 61 76

3. 85 29

4. 32 33

5. 94 65

6. 56 48

7. 39 68

8. 75 38

9. 89 21

Napier’s Bones


INDEX 1 2 3 4 5 6 7 8

8 7 6 5 4 3 2 1

1 2 3 4 4 5 6 7

6 4 2 0 8 6 4 2

1 2 2 3 4 4 5 6

4 1 8 5 2 9 6 3

1 1 2 3 3 4 4 5

2 8 4 0 6 2 8 4

1 1 2 2 3 3 4 4

8

0 5 0 5 0 5 0 5


1 1 2 2 2 3 3

2 6 0 4 8 2 6

1 1 1 2 2 2

6

4

2

9

6

3

8

4

0

5

2

6

4

7

6

8

8

9

2 5 8 1 4 7

1 1 1 1 1

NS 3.2, 3.3



Multiply by Multiples of 10

P

PRACTICE

Multiply. 1.

26 40

2.

47 30

3.

91 20

4.

87 10

5.

6.

17 80

7.

135 50

8.

207 60

9.

399 50

10.

756 30

15.

5,503 50

20.

9,075 80

11.

498 70

12.

1,038 40

13.

2,226 20

14.

16.

2,375 20

17.

4,009 40

18.

2,490 70

19.

6,967 10

21. 51 30

22. 39 80

23. 67 20

24. 325 60

25. 40 608

26. 999 10

27. 712 30

28. 10 3,116

29. 80 1,185

30. 90 4,090

31. 2,111 70

32. 50 5,549

Algebra & Functions © McGraw-Hill School Division

3,510 60

23 90

Find the missing number.

33. 34 j 680

j

34.

35. 99 a 7,920

a

36. 56 m 1,680

m

37. 861 b 77,490

b

38. 1,002 n 70,140

n

40. 898 c 53,880

c

39.

s 2,108 63,240 s

q 72 2,160

q

Problem Solving 41.

Classroom chairs cost $39. How much will 30 chairs cost?


42.

A computer costs $2,345. How much will 20 computers cost?

NS 3.2, 3.3




R

RETEACH

An expanded form can help you multiply. Find 20 37. Think: 37 30 7 20 (30 7) (20 30) (20 7) 6 0 0 1 4 0 740

37 20 740

Complete to find each product. 1. 10 28

10 ( (

2. 30 33

8) 20) (

8)

(

) (

)

4. 50 64

(20

3)

3. 80 27

(

(

(60

)

)(

)

(

) ) (

)


Multiply. 5.

34 40

6.

27 30

7.

38 40

8.

43 10

9.

18 50

10.

24 80

11.

35 20

12.

19 30

13.

22 10

14.

57 60

15. 40 18

16. 28 30

17. 30 32

18. 10 39

19. 16 30

20. 20 39


NS 3.2, 3.3




E

ENRICH

Missing Digits


Find each missing digit. 1.

7 4 1 7 4 0

2.

8 3 0 2, 4 9 0

3.

6 2 0 3, 7 2 0

4.

3 5 0 1, 6 5 0

5.

9 9 0 6, 2 1 0

6.

4 6 0 1, 8 4 0

7.

8 1 0 1, 6 2 0

8.

4 7 0 6, 5 8 0

9.

4 8 8 0 3 8, 6 4 0

10.

13.

2 1 1 0 1 0, 5 5 0

14.

17.

4 6 7 0 5 2, 2 2 0

21.

25.

11.

9 1 9 0 8 2, 0 8 0

12.

7 2 1 0 2 1, 6 3 0

3 6 0 3 3, 7 8 0

15.

6 7 3 0 2 0, 1 9 0

16.

8

6 8 0 6 6, 8 8 0

18.

8 3 4 0 3 3, 5 6 0

19.

7 8 8 0 3 8, 2 4 0

20.

5 6 9 0 5 0, 4 9 0

1 4 8 0 2 5, 1 2 0

22.

9

5 2 0 1 8, 5 0 0

23.

7 1 6 0 6 4, 4 4 0

24.

5 7 0 4 7, 2 5 0

2 5 8 0 7 4, 0 0 0

26.

5 4 4 0 2 1, 7 6 0

27.

6 3 6 0 5 7, 2 4 0

28.

7

5 8 4 0 3 5, 0 4 0 5


6

4 5 0 3 9, 2 0 0

NS 3.2, 3.3


Problem Solving: Reading for Math Solve Multistep Problems


P

PRACTICE

Reading Skill

Circle the hidden question that can help you solve the problem. Then solve the problem. 1. A group of travelers rents 5 boats for 8 hours each. Boats cost

$12 an hour to rent. What is the total fee for this rental? What is the total number of hours that the 5 boats are rented for? What is the total number of boats that are rented in a day? Solution: 2. A swimming instructor has 4 classes with 8 students in each class.

Each student pays a total of $50 for the classes for the season. How much money does the swimming instructor receive? What amount does the instructor charge per hour? How many students in all does the swimming instructor have? Solution: 3. Burke’s Bluff Beach sells 25 guest passes in one day. Condor Cove

Beach sells 2 times as many guest passes that same day. Estimate the total number of guest passes that beaches will sell in 3 days. How many guest passes does Condor Cove Beach sell in 1 day? How many guest passes will Burke’s Bluff Beach sell in 2 days?


Solution: 4. Miguel charges $30 per hour to take people on his boat. Miguel

rents his boat for 3 hours per day for 12 days. How much money does Miguel receive? How many hours in all does Miguel rent his boat? How much would Miguel receive if he rented his boat 12 hours per day? Solution:


MR 1.2, 2.4, 3.2




P

PRACTICE


Choose the correct answer. Lana and Ken rent 2 sets of scuba equipment for $16 an hour each. They rent a boat for $24 per hour. They use the boat and the equipment for 7 hours. 1. Which of the following statements

2. One “hidden question” you must

is true? A Lana and Ken pay $40 per hour to rent a boat. B Lana and Ken pay $168 to rent the boat. C Lana and Ken rent the boat and equipment for 16 hours.

solve is: F How much do they pay to rent 2 sets of scuba equipment for 7 hours? G How many hours do they use the boat? H How much do they pay for the boat each hour?

On a school trip, 3 buses of students go to Ocean Land. Each bus has 44 students. Each student spends $10 on admission and a special show. How much money do the students spend altogether? 3. Which question do you have to answer


before you can solve the problem? A How many students are in each bus? B How many hours are the students at Ocean Land? C How many students in all visit Ocean Land?

4. How much money do the students

spend altogether? F $1,320 G $440 H $10

Olive catches 3 fish in 1 hour. Her sister catches 3 times as many fish. Estimate the number of fish the girls will catch if they fish for 3 hours. 5. Which of the following statements

is true? A Olive and her sister catch 9 fish. B Olive’s sister catches 3 fish. C Olive’s sister catches 3 times as many fish as Olive does.


6. One “hidden question” you must

solve is: F How many fish did Olive catch in 1 hour? G How many fish did Olive’s sister catch in 1 hour? H How many hours have they fished so far? MR 1.2, 2.4, 3.2




P

PRACTICE


Choose the correct answer. The Beach Shack rents out 12 umbrellas for 5 hours each. Umbrellas cost $6 per hour. How much money does The Beach Shack make? 7. Which question do you have to

answer before you can solve the problem? A How much does it cost to rent 1 umbrella for 12 hours? B How much does it cost to rent 1 umbrella for 5 hours?

8. How much money does The Beach

Shack make? F $30 G $72 H $360

C How many umbrellas does The Beach Shack have? Solve. 9. The Diving Club offers 4 beginning

diving classes each day. Each class has room for 6 people. How many people can take classes in 30 days?


11. During one week, 5 sailboats are

rented for a total of 16 hours each. The rental cost is $25 per hour. Altogether, how much is paid for these rentals?

13. Amanda rents a canoe and a life

preserver from 2:00 P.M. to 5:00 P.M. A canoe costs $12 per hour. A life preserver costs $2 per hour. How much does Amanda spend?


10. A fishing guide charges $25 per

hour. He works 6 hours per day for 5 days. How much money does the guide earn?

12. The aquarium charges $12 admission

and $6 for a tour. A group of 20 people goes to the aquarium and takes the tour. How much money does the group spend?

14. Jenny rented a rowboat from

10:45 A.M. to 1:00 P.M. After lunch, she rented another rowboat from 1:45 P.M. to 4:45 P.M. For how many minutes did she rent the boat?

MR 1.2, 2.4, 3.2


Print This 6-5 Page

Multiply by 2-Digit Numbers

P

PRACTICE

Find each product 1.

26 35

2.

73 51

3.

6.

$46 35

7.

59 47

8.

11.

79 73

12.

16.

18 92

94 61

17.

13.

44 87

77 22

$0.63 58

28 19

29 19

55 15

10.

44 46

68 24

15.

51 34

$0.56 83

9.

14.

18. 86 43

19. 74 33

20. 48 26

21. 31 $0.18

22. 77 94

23. 88 62

24. 27 34

Algebra & Functions

Find each product.

25. (30 7) (10 8) n

26. (60 4) (20 9) = v

27. (80 1) (40 2) p

28. (50 6) (70 3) = r

29. (90 5) (10 1) q © McGraw-Hill School Division

5.

4.

31.

(20 8) (70 7) s

30. (60 6) (50 5) c 32. (40 3) (80 4) b

Problem Solving 33. A fence has 28 sections with

18 boards in each section. How many boards are in the fence?


34. Horses on a ranch eat 28 bales

of hay each day. How many bales do they eat in 31 days?

NS 3.2, 3.3




R

RETEACH

You can use a place-value chart to help you multiply 2-digit numbers. Multiply 47 25. Step 1 Multiply by the ones. Regroup if necessary. TH

H

T

Step 2 Multiply by the tens. O

TH

H

3

2 4 7

1

5 7 5

T

O

TH

H

T

2

2

3

3

2 4 7 0

5 7 5 0

1

1 0

TH

H

T O

5

3 8 2 6

Step 3 Add the products.

2 4 7 0 7

O

5 7 5 0 5

1 1

1 0 1

TH

H

T O

3

5 9 7 1

Complete. Find each product. 1.

H


4.

9.

14.

6

T

O

1 4

5 5 5 0

0

16 23

46 44

85 43

2.

2

2 7 4 0

5.

$15 42

6.

23 39

7.

10.

67 29

11.

59 31

12.

15.

96 35


3.

$0.27 51

$31 28

16.

5

8.

38 26

13.

72 53

9 3 7 0

$0.39 66

NS 3.2, 3.3




E

ENRICH

Patterns for Eleven Multiply 11 by a 1-digit number. 1. 2 11

2. 3 11

3. 4 11

4. 5 11

5. 6 11

6. 7 11

7. 8 11

8. 9 11

What pattern do you see?

Multiply 11 by a 2-digit number. 9.

11 31

10.

11 32

11.

11 33

12.

11 34

13.

11 53

14.

11 62

15.

11 27

16.

11 18

19.

11 38

20.

11 16

What pattern do you see?

Use the pattern to find these products. © McGraw-Hill School Division

17.

11 41

18.

11 22

21. 44 11

22. 55 11

23. 64 11

24. 72 11


NS 3.2, 3.3



P

Estimate Products

PRACTICE

Estimate each product. 1.

49 59

2.

55 65

3.

41 52

4.

18 29

5.

98 402

6.

71 874

7.

61 $216

8.

42 605

9.

81 350

10.

23 999

11.

85 1,211

12.

71 2,118

13.

19 6,302

14.

29 7,907

Algebra & Functions


15. 98 27

Estimate to compare. Write or .

3,000

16. 37 196

8,000

17. 42 84

3,200

18. 498 16

100,000

19. 21 423

8,000

20. 589 36

24,000

21. 59 689

42,000

22. 49 188

10,000

23. 224 41

8,000

24. 26 42

34 21

25. 15 47

59 68

26. 34 82

37 58

Problem Solving 27. The price of a bus ticket is $58.

About how much will tickets for a group of 62 passengers cost?


28. An airline ticket costs $375.

About how much will tickets cost for a group of 25 people?

NS 3.2, 3.3



Estimate Products

R

RETEACH

You can round to estimate products. Round each number to its greatest place. Then multiply using patterns with zeros Estimate 42 59. 42 59

40 60 2,400

Estimate 74 229. 1 zero 1 zero 2 zeros

227 74

200 70 14,000

2 zeros 1 zero 3 zeros

Estimate each product by rounding. 3.

2.

1.

54 19

788 51

$29 32



5. 23 51

6. 69 19

7. 26 $72

8. 19 315

9. 85 263

10. 72 803

11. 48 1,056

12. 92 2,228

13. 57 $5,698

14. 76 6,419

15. 12 9,058

16. 55 4,830

17. 92 1,568


NS 3.2, 3.3



Estimate Products

E

ENRICH

Estimation Maze Estimate to find your way out of the maze. First, estimate to find the box in which the answer could be 858. Start in that box. Then, in order, estimate to find and go through the boxes in which the answers are: 3,060

7,308

3,822

78 11

2,278

16,910 34 90

I 26 34

953 48 W

U

H

T 196 77

F

O 616 59

819 64 E

C 67 34

157 39

706 48

36,344

57 14

39 98

178 95

52,416

P

O

R

33,888

42 19

87 84

172 24

15,092

M

B


6,123

R

E

Write the letters from the boxes you go through in order. What message do you find? ’


!

NS 3.2, 3.3




P

PRACTICE

Multiply. Check that each answer is reasonable 1.

653 27

2.

908 43

3.

412 65

4.

714 36

5.

279 64

6.

309 32

7.

$1.26 98

8.

305 77

9.

4,084 43

10.

11.

9,148 16

12.

$50.09 31

13.

2,007 75

14. $39.85

15.

6,618 91

16.

$82.35 72

21,107 42

18. 46,118

19.

92,306 31

20.

$123.95 18

17.

7,016 25

74

27

21. 53 36,219

22. 26 $591.05

23. 36 19,962

24. 71 23,401


Algebra & Functions Given each set of digits, make the greatest and least product possible by multiplying by a 2-digit number. Use each digit one time. 25. 5, 2, 6, 1

26. 7, 9, 2, 0

Problem Solving 27. A box holds 250 ping pong balls.

How many ping pong balls can be packaged in 85 boxes?


28. Pencils are packaged with 144 pencils

in a box. How many pencils are there in 50 boxes?

NS 3.2, 3.3



Multiply by Greater Numbers

R

RETEACH

You can use a place-value chart to multiply greater numbers. Multiply 25 3,188. Estimate: 30 3,000 90,000 Step 1 Multiply by the ones. Regroup if necessary. Thousands 1.

Step 2 Multiply by the tens. Regroup if necessary.

Ones

Thousands

H T O H T O

3

Step 3 Add the products.

Ones

Thousands

H T O H T O

4

3 1 7 8 2 5 1 5 8 9 0

Ones

H T O H T O

1

1

1

1

3

4

3

4

3 1 7 8 2 5 1 5 8 9 0

6 3 5 6 0

3 1 7 8 2 5 1 5 8 9 0

6 3 5 6 0 7 9 4 5 0

Since 79,450 is close to the estimate of 90,000, the answer is reasonable. Multiply. Thousands 1.

Ones

Thousands 2.

H T O H T O

Ones

Thousands 3.

H T O H T O

Ones

H T O H T O

2

1 4 5 7 2 5


1 2 9 3 1 8

4.

$3.69 18

8.

4,484 72

5.

518 49

9. 85

2 0 0 6 1 3

6.

6,735 37

$116.95


7.

8,098 66

10. 52

19,071

NS 3.2, 3.3




E

ENRICH

Quick Check Here is a quick way to check the product for 14 1,456. Step 1 Add the digits in each number. Add again if the sum has two digits. 1,456 ← 1 4 5 6 16, 14 ← 1 4 5 20,384 ← 2 0 3 8 4 17,

167 178

Step 2

Step 3

Multiply the two numbers you got from adding the factors.

Compare the sum you got from adding the digits in the product for 14 1,456 to the sum you got in Step 2.

Then add the digits in the product. 7 5 35

8 8, so the product 20,384 is correct.

3 5 8


Use the method shown above to check each problem. Draw an X next to any incorrect product. Then find the correct product. 1.

314 57 17,896

2.

815 32 26,090

3.

742 68 50,456

4.

689 24 16,536

5.

537 49 26,213

6.

496 71 35,216

7.

2,214 88 193,832

8.

3,418 92 314,456

9.

4,372 15 65,480

11.

7,498 45 337,410

12.

9,455 76 707,580

10.

8,432 37 311,984


NS 3.2, 3.3




P

PRACTICE

Make a Graph Make a graph for the data in the table. Use data from the graph to solve problems 1 and 2. Boat Rentals at Lake Willow in July and August Type of Boat

Income from Boat Rentals

Sailboats

$1,300

Rowboats

$1,100

Paddle boats Canoes 1. Which type of boat generated the

most income?

3. A beach sells 1,000 passes in 1998;


1,200 passes in 1999; and 1,100 passes in 2000. Suppose you make a pictograph in which each symbol stands for 200 passes. How many symbols would you make for each year?

$800 $1,000 2. Which type of boat generated the

least income?

4. Suppose you make a graph for the

data in problem 3 in which each symbol stands for 100 passes. How many symbols would you make for each year?

Mixed Strategy Review Solve. Use any strategy. 5. Time Elliot returns from the beach at

4:30 P.M. He spent 2 hours at the beach. It takes 15 minutes for Elliot to travel from his home to the beach. What time did Elliot leave home to go to the beach?

6. Create a problem for which you

would make a graph to solve. Share it with others.


SDP 1.1; MR 2.3, 2.4, 3.2




R

RETEACH

Make a Graph Page 255, Problem 2

Which contest had the most people? The least?

Sandcastle Building Contests Location

Number of People

Port Aransas, TX Wenatchee, WA Seal Beach, CA Atlantic City, NJ Malibu, CA

1,250 1,675 1,775 1,525 1,375

Step 1

Read

Be sure you understand the problem. Read carefully. What do you know? • You know how many . What do you need to find? • You need to find .

Step 2

Plan © McGraw-Hill School Division

■

■

■

■

■

■

■

■

■

■

Find a Pattern Guess and Check Work Backward Make a Graph Make a Table or List Write a Number Sentence Draw a Diagram Solve a Simpler Problem Logical Reasoning Act it Out


A graph can help you compare data quickly. Make a bar graph to solve the problem.


SDP 1.1; MR 2.3, 2.4, 3.2




R

RETEACH

Make a Graph Step 3 Carry out your plan. Make a bar graph.

Solve

Sandcastle Building Contest

Location

Port Aransas,TK Wenatchee, WA Seal Beach, CA Atlantic City, NJ Malibu, CA 100

200

300

400

500

600

700

800

900 1,000 1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800

Number of People

The contest at: has the most people. has the least people. Step 4


Look Back

Is the solution reasonable? Reread the problem. Does your answer match the data given in the problem? Yes No What other kind of graph could you use to compare the data?

Practice 1. The Lakefront Swim Club had 400 members in 1970, 250 members in 1980, 600 members in 1990, and 550 members in 2000. Make a graph that displays this data.


2. In which year did the Lakefront Swim

Club have the most members? the least members?

SDP 1.1; MR 2.3, 2.4, 3.2



P

Multiply Using Mental Math

PRACTICE


2. 40 21

3. 34 11

4. 55 18

5. 60 14

6. 70 31

7. 44 22

8. 80 51

9. 90 9

10. 25 50

11. 30 26

12. 24 40

13. 44 15

14. 52 11

15. 15 16

16. 35 22

17. 61 30

18. 20 48

19. 30 19

20. 65 40

21. 48 40

22. 16 21

23. 25 28

24. 59 61

25. 50 14

26. 35 21

27. 70 49

28. 11 62

29. 90 42

30. 22 55

Algebra & Functions 31.

Rule: Multiply by 35. Input Output


32.

Complete each table.

20 700

31 1,085

42 1,470

110 3,850

130 4,550

75 1,200

100 1,600

220 3,520

Rule: Multiply by 16. Input Output

15 240

25 400

Problem Solving 33.

Teams of 16 students are helping clean the park. There are 21 teams. How many students in all are helping clean the park?


34.

Students are going on a field trip in 20 buses. Each bus carries 35 students. How many students are going on the field trip?

NS 3.2, 3.3




R

RETEACH

You can multiply using mental math. Compensation Multiply one factor by a number. Divide another factor by the same number.

Compatible Numbers Break apart one number and multiply. Then add.

25 16 (25 2) (16 2)

25 16 (25 10) (25 6)

50

400

8

250

150 400

Multiply mentally. Use compensation. 1. 35 40 (35

) (40

)

2. 60 25

(60

) (25

)

Multiply mentally. Use compatible numbers. 3. 15 16 (

16) (5

)

4. 22 30 (

30) (

30)



6. 15 28

7. 11 72

8. 75 20

9. 36 40

10. 50 23

11. 44 25

12. 70 18

13. 59 71

14. 99 10

15. 60 73

16. 45 36

17. 53 11

18. 32 26

19. 80 61

20. 70 19

21. 65 16

22. 35 90

23. 25 25

24. 80 18

25. 26 23

26. 11 37

27. 55 27

28. 75 30

29. 62 10

30. 25 45

31. 50 88


NS 3.2, 3.3




E

ENRICH

Circle Race You will need: Play with a partner. • Write each of these numbers on an index card: 12

15

18

25

30

35

10 index cards

50

60

200

400

• Mix up the cards and then place them facedown between you and your partner. Draw a card. Write the number in the center of your circle. Use mental math to multiply each number on the circle by the number in the center. The first person to complete the circle with correct answers scores 1 point. • Erase the number in the center. Repeat the activity until all the cards have been drawn. The person with the greater number of points wins.

18 33


24 16

14 40

300 22


NS 3.2, 3.3



Print This Page


Applying Multiplication Record your data.


Sailboats

Rowboats

Paddle boats

Canoes

Your Decision Which boat or boats will the family rent? How long will they ride? Explain.


NS 1.2, 3.3; MR 1.1, 2.3


Print This Page



Math & Science

How many times does your heart beat each day? Record your data in the table below. Time

Estimate

Actual Heart Beats

Each minute

Each hour

Each day

Each year

Show how you estimated the number of heart beats in each hour, each day, and each year.

Each day

Each year


Each hour


NS 3.2, 3.3; MR 1.1, 3.3


Print This Page



Math & Science

How many times does your heart beat each day? 1. Why would it be difficult to count the number of heart beats in a

day? Explain how math made your job easier.

2. Round the number of beats for a day to the nearest 10,000. Collect

the data for the whole class. What was the range of heartbeats?

What number was most common? 3. Make a bar graph to display the data


from the class.

4. Marty’s heart beats 70 times each

minute. Tamara’s heart beats 60 times each minute. How many more times does Marty’s heart beat each day? Show your work.

5. Explain how exercise can reduce the

number of times your heart beats each day.


NS 3.2, 3.3; MR 1.1, 3.3



Division Patterns

P

PRACTICE

Complete. 1. 48 6

2. 35 5

3. 16 4

480 6

350 5

160 4

4,800 6

3,500 5

1,600 4

Divide.

206 R2

50

4. 3 620

5. 5 250

$70

$90

80

9. 3 $270

8. 2 160

700

800

13. 5 3,500

12. 9 7,200

$600

400

16. 7 $4,200

17. 9 3,600

80

6. 6 $420

7. 7 560

70

60

11. 8 560

10. 4 240

700

14. 4 2,800

600

18. 3 1,800

$700 15. 6 $4,200

4,000 19. 2 8,000

20. 120 2

21. $240 3

22. 810 9

23. $450 5

24. 630 7

25. 540 9

26. 3,000 6

27. $7,200 8

28. 4,800 8

29. 3,200 8

30. 5,600 7

31. $3,600 4

Algebra & Functions Write the missing number.


32. 200

50

33. 450 5

35.

6 40

36. 200

38.

4 600

39. 1,500

34. 630

40

37.

500

90 8 80

40. 3,000 5

Problem Solving 41. There are 150 students in 3 buses. Each

bus carries the same number of students. How many students are on each bus?


42. A pet shop has 160 fish in

aquariums. Each aquarium has 40 fish. How many aquariums of fish are there?

NS 3.2, 3.4; MR 3.2



Division Patterns

R

RETEACH

You can divide mentally by using basic division facts and looking for a pattern. Divide. Count the zeros.

120 3 40 1,200 3 400

→ → →

12 3 4

Think: The basic fact is 40 8 5.

no zeros

40 8 5

1 zero

400 8 50

2 zeros

4,000 8 500

→ → →

Think: The basic fact is 12 3 4.

no extra zeros 1 extra zero 2 extra zeros

Complete. 1. 15 3

150 3

200 5

1,500 3

2,000 5

3. 32 4

4. 30 6

320 4

300 6

3,200 4

3,000 6

5. 35 5


2. 20 5

6. 45 9

350 5

450 9

3,500 5

4,500 9

7. 48 8

8. 64 8

480 8

640 8

4,800 8

6,400 8

9. 180 2

10. 360 4

11. 700 7

1 2. 360 6

13. 540 9

14. 1,400 2

15. 4,200 7

16. 2,700 9

17. 4,900 7


NS 3.2, 3.4; MR 3.2



Division Patterns

E

ENRICH

Geography Riddles Find each missing number. Solve the riddles by placing the letter from each exercise in the blank above the matching answer number.

M

1. 140 7 3. 4,200

700

5. 3,500

700

7.

3 700

O H

E

9 40

4.

2 800

6.

4 30

8. 320

400

S

10.

11. 5,600

700

S

12. 240

13. 5,400

600

L

14. 2,700 3

N

9 90

80

16. 800

17. 150 3

M

18.

7 60

19. 120 2

S

20.

8 400

C

22. 810 9

What city likes to wander?

Which people are always in a hurry?

What country is always cold?


I E

I

What state reminds you of part of a lion?

A

R

15. 720 9

5 800

A

80

9. 2,800

21.


U

2.

R

400

E I N

20

4

3

120 420

2

6

50

900

810 360 60

4,000 5

80

7 3,2001,600 90

9

8

2,100

NS 3.2, 3.4; MR 3.2



Explore Division

P

PRACTICE

Write a division sentence for each model. 1.

2.

3.

4.

5.

6.

Find each quotient. You may draw place-value models.

3 R2

7. 6 20

12 R3

11. 4 51

16 R3


15. 6 99

3 R5

9 R1

8. 8 29

9. 4 37

13 R1

13

12. 5 66

13. 6 78

14

27 R1

16. 7 98

17. 2 55

3 R6

10. 9 33

11 R6

14. 7 83

49 R1

18. 2 99

19. 41 9

20. 62 9

21. 59 7

22. 88 3

23. 73 5

24. 58 4

25. 67 6

26. 77 7

27. 43 2

Problem Solving 28. Books are packed in boxes of 9.

If 67 books are packed, how many full boxes will there be? How many books will be left over?


29. Ping pong balls are packed in boxes

of 6. If 59 ping pong balls are packed, how many full boxes will there be? How many ping pong balls will be left over?

NS 3.2, 3.4



Explore Division

R

RETEACH

You can use models to help you divide. Divide 86 3. Show 86.

Place 2 tens in each of 3 groups. Regroup the 2 tens that are left as 20 ones. You can divide the 26 ones into 3 groups of 8 with 2 left over. You can divide 86 cubes into 3 groups of 28 with 2 left over. So, 86 3 28 R2.

Divide. You may use models to help you. 1.

2.

58 4

37 2


3.

4.

49 4

68 3

Divide. 5. 43 2

6. 25 2

7. 42 4

8. 82 5

9. 48 4

10. 78 9


NS 3.2, 3.4


Explore Division


E

ENRICH

Remainder Rules You can use divisibility rules to find out if a number will have a remainder. Divisibility Rules A number is divisible by: 2 if the ones digit is 0, 2, 4, 6, or 8. 6 if it is divisible by both 2 and 3. 3 if the sum of its digits is divisible by 3. 9 if the sum of its digits is divisible by 9. 5 if the ones digit is 0 or 5. 10 if the ones digit is 0. 1. If you divide 315 by 5, will there be a remainder?

How do you know? Divide to prove your answers.

2. If you divide 691 by any 1-digit number, will there be a remainder?

How do you know?


Divide to prove your answer.

3. Think about dividing a 3-digit number by each of the following

1-digit numbers: 2, 3, 4, 5, 6, 7, 8, 9. Which divisions will have remainders? Which divisions will not have remainders? Prove your answers. Use with Grade 4, Chapter 7, Lesson 2, pages 278–279. (207)

NS 3.2, 3.4



Divide 3-Digit Numbers

P

PRACTICE

Divide. Check your work.

$135

349

1. 2 698

130 R1

2. 5 $675

3. 3 391

28 R7

111 R2

$0.67

6. 8 231

5. 5 557

11. 3 935

119 R3

361 R1

13. 7 903

15. 7 836

14. 2 723

111

$37

62 R5

17. 9 999

8. 8 995

311 R2

10. 6 $6.72

129

124 R3

7. 4 $2.68

$1.12

99 R2

9. 4 398

18. 6 377

112 R1

4. 7 785

91 R2

12. 5 457

93 R1

16. 8 745

111 R2

19. 8 $296

20. 7 779

21. 215 3

22. 367 5

23. 467 2

24. 593 4

25. 298 6

26. 506 7

27. Divide 726 by 7.



Algebra & Functions Find each missing number. 30. 1,065


33.

n 213

b 8 116

36. (250 + 14)

31.

c 4 168

34. 585

x 44

32. 690

d 195

37. (700 + y) 7 106

35.

m 345

t 9 111

38. 756 (r + 3) 126

Problem Solving 39. Morgan is planting 906 pine seedlings

in rows. She plants 8 pine seedlings in each row. How many rows are there? How many seedlings are left?


40. The school bought 2,880 tickets to

the circus. The tickets will be divided equally among 9 classes. How many tickets will each class get?

NS 3.2, 3.4




R

RETEACH

Divide 8 425 . Step 1 Divide the hundreds. Think: 4 8. There aren’t enough hundreds. 8 425

Step 2 Divide the tens. Bring down the tens. Divide the tens.

Step 3 Divide the ones. Bring down the ones. Divide the ones.

5 8 425 40 Multiply: 8 5 40 2 Subtract: 42 40 2

53 R1 8 425 40 25 24 Multiply: 8 3 24 1 Subtract: 25 24 1 The remainder is 1.

Check your answer: 53 8 1 425 Complete. 1.

2 2 8 36 8 4 6

2.

8 6 2 4 2 4 0

1 4 3 R 57 1 7 5

2

3.

8 9

R

76 2 4 5 6

2 1 2 0 1 7 1 5 2

1

6 4 6 3 1


Find each quotient.

143 R1

4. 4 573

248 R1

8. 3 745

69 R4

152 R4

5. 5 349

139

9. 7 973

6. 5 764

94 R8

10. 9 854

41 R6

7. 7 293

288 R2

11. 3 866

12. 662 5

13. 571 8

14. 927 4

15. 745 3

16. 680 5

17. 571 6


NS 3.2, 3.4




E

ENRICH

Short Division Short division is a quick way to divide. Here is how it works. Divide 6 892 . Step 1

Step 2

Step 3

Divide the hundreds. Multiply and subtract mentally. Write the difference in front of the digit in the tens place.

Divide the tens. Multiply and subtract mentally. Write the difference in front of the digit in the ones place.

Divide the ones. Multiply and subtract mentally. Write the remainder as part of the quotient.

1 6 8292 Think: 6 1 6 862

14 6 82952 Think: 6 4 24 29 24 5

1 4 8 R4 6 82952 Think: 6 8 48 52 48 4

Step 1

Step 2

Step 3

Divide the hundreds.

Divide the tens.

Divide the ones.

8 653 Think: 8 1 8, not enough hundreds.

8 8 6513 Think: 8 8 64, 65 64 1.

8 1R5 8 6513 Think: 8 1 8, 13 8 5.

Divide 8 653 .

Use short division to divide.

171

1. 2 342

164 R3


4. 5 823

111 R6

7. 8 894

72

10. 6 432

65 R2

13. 5 327

118

16. 8 944

253 R2

2. 3 761

157

5. 6 942

96 R3

8. 9 867

52 R1

11. 7 365

69 R3

14. 9 624

95 R7

17. 9 862


155 R3

3. 4 623

131 R1

6. 7 918

73 R5

9. 6 443

61 R4

12. 7 431

61 R4

15. 8 492

131 R5

18. 6 791

NS 3.2, 3.4



Zeros in the Quotient

P

PRACTICE

Divide. Check your answer. 1.

206 R2

2.

$105

6.

3 620 5.

109 R4

10.

103 R2

14.

108 R4

18.

490 R1

22.

2 981

4.

$1.09

8.

106 R6

11.

10 R8

15.

106 R7

19.

208 R3

23.

101 R4

12.

70 R1

16.

109 R3

20.

103 R6

24.

206 R3

4 827

6 657 7 727

409 R1

2 819

3 211

4 835

102

9 918

8 812

8 855

209 R3

4 839

7 $7.63

9 98

5 544 21.

7.

7 748

6 620 17.

$1.07

10 R2

9 92

8 $8.56

5 549 13.

3.

2 419

6 $630 9.

209 R1

305 R2

3 917

50 R6

8 406

25. 823 4

26. 704 5

27. 981 2

28. 920 3

29. 916 7

30. 845 6

31. 885 8

32. 954 5

33. 965 6


Find only those quotients that are greater than 200. 34. 992 3

35. 920 9

36. 619 3

37. 747 4

38. 818 2

39. 540 2

Problem Solving 40. Jenna earns $636 in 6 months by babysitting. If divided evenly, how much is that a month?


41. A family of 4 spent $824 during their

vacation. If divided evenly, how much is that per person?

NS 3.2, 3.4




R

RETEACH

Divide 3 629 . Follow the steps below. Step 1 Divide the hundreds.

Step 2 Divide the tens.

Step 3 Divide the ones.

Think: 3 2 600 The first digit is in the hundreds place.

Bring down the tens. There are not enough tens to divide. Trade 2 tens for 20 ones.

Bring down the ones. Divide the ones.

2 3 629 Multiply: 3 2 6 6 Subtract: 6 6 0 0 Compare: 0 6

20 3 629 There are not enough 6 tens to divide. Write 02 a 0 in the quotient. Compare: 0 4

209 R2 3 629 6 029 27 Multiply: 3 9 27 2 Subtract: 29 27 2

Check your answer: 209 3 2 629 Complete. 1.

3 0 8 R 39 2 6 9

2

2.

2 6 2 4 2

3.

1 0 7 66 4 2 6

2 0

R

3

71 4 3 1 4

4 2 4 2 0

3

Divide. © McGraw-Hill School Division

$204

4. 4 $816

307 R1

8. 2 615

109 R2

105 R1

5. 4 438

180 R1

9. 2 361

6. 3 316

209 R1

10. 3 628

109 R2

7. 7 765

$70

11. 3 $210

12. 912 9

13. 452 5

14. 662 3

15. 965 6

16. 905 3

17. 734 7


NS 3.2, 3.4




E

ENRICH

Pick a Winner Pick divisors from the list below to create 20 division exercises. Then complete the exercises. If you have a zero in the quotient, give yourself 2 points. If you do not have a zero in the quotient, give yourself 1 point. Divisors: 1, 2, 3, 4, 5, 6, 7, 8, 9

1.

6.

302 2 604 110 R5

7 775

106 R4 8 852

101 R4 5.

103 R1 6 619

10.

201R6 9 1,815

2.

390 R1 2 781

3.

7.

105 R3 4 423

8.

13.

3 211

14.

2 321

15.

7 354

18.

40 R3 8 323

19.

302 3 906

20.

403 2 806

11.

4 363

12.

120 R5 6 725

16.

20 R4 5 104

17.

109 5 545

90 R3

4.

170

1 170

5

509

109 R3

9.

70 R1

8 875

160 R1

50 R4

Total Points Earned: © McGraw-Hill School Division

21. Think about dividing a 3-digit number by a 1-digit number.

When will you get a quotient with a zero in the tens place? Give an example.


NS 3.2, 3.4




P

PRACTICE

Reading Skill

Interpret the Remainders Circle the correct word(s) or number(s) to make each statement true. 1. The Art Club sells T-shirts for $8. Ms. Demming has $92. Ms. Demming can buy

11

1

11 2

12

T-shirts.

If Ms. Demming buys the greatest possible number of T-shirts, she will have $ 0 $4 $8 left. Explain your thinking:

2. There are 124 people at the Howard School Sports Dinner. They sit

at tables that have 8 seats each. The school needs There are

7

15

16

7 or 8

tables.

people at each table.

Explain your thinking:

3. Manny and two friends are paid $100 for setting up a new computer

in the school’s math lab. They each do the same amount of work. Manny earns

more than

Each friend earns

the same as

more than

his friends.

less than

$30.



4. There are 75 students going to the art museum. They will ride in

vans that can hold 6 students. There will be

12

13

There are 5 5 or 6 Explain your thinking:

vans. students in each van.


NS 3.4; MR 1.1, 2.4, 2.6, 3.1, 3.2




P

Interpret the Remainders

PRACTICE


Choose the correct answer. There are 94 people who volunteer to clean the park. They will form as many groups of 4 as possible. How many groups of 4 can they make? 1. Which of the following statements

2. How do you interpret the remainder

is true?

to solve this problem?

A They will make 4 groups.

F Use only the quotient.

B Everyone can be in a group of 4.

G Use only the remainder

C There are 94 volunteers.

H Add 1 to the quotient.

The after-school baseball league wants to buy 250 baseballs. The baseballs come in boxes of 6. How many boxes will the league need? 3. How do you interpret the remainder

4. How many boxes will the


league need?

A Use only the quotient.

F 41 boxes

B Use only the remainder.

G 42 boxes

C Add 1 to the quotient.

H 43 boxes

The Computer Club has $80 to buy disks. A box of disks costs $7. There is no sales tax. How many boxes of disks can the club buy?


5. Which of the following statements

6. How do you interpret the remainder

is false?


A Each box of disks costs $7.

F Add 1 to the quotient.

B All of the money will be spent.

G Use only the quotient.

C The computer club has $80 to buy disks.

H Use only the remainder.


NS 3.4; MR 1.1, 2.4, 2.6, 3.1, 3.2




P

Interpret the Remainders

PRACTICE


Choose the correct answer. The Art Club makes $4 on each T-shirt it sells. How many shirts does the club need to sell to raise $75? 7. How do you interpret the remainder

8. How many shirts does the club need


to sell to raise $75?

A Add 1 to the quotient.

F 3 shirts

B Use only the quotient.

G 18 shirts

C Use only the remainder.

H 19 shirts

Solve. 9. There are 72 students in the Hockey

Club. How many teams of 5 can they make?

11. Paint sets cost $6. The Art Club has

$93. If the club buys as many paint sets as it can, how much money will be left over?


13. There are 64 members in the Science

Club. They travel to the science fair in cars that can hold 5 members each. How many cars are needed?

15. Each song played by a DJ is

4 minutes long. How many songs does he play in a music set that is 30 minutes long?


10. The Hockey Club buys 128 ounces of

juice. How many 7-ounce cups can they pour?

12. There are 132 students at a meeting.

The seats are arranged in rows of 8. How many rows of seats are needed?

14. There are 83 students. They will sit in

rows of 6 seats each. They will start at the front row and fill as many rows as they can. How many students will be in the last row?

16. The DJ’s assistant distributes neon

sunglasses to 50 people at a party. There are 6 glasses in a box. How many boxes should she open?

NS 3.4; MR 1.1, 2.4, 2.6, 3.1, 3.2



Estimate Quotients

P

PRACTICE

Estimate. Choose compatible numbers.

20

1.

2 43 6.

3 159

40

8 650

5 209

4 3,105

2,000

15.

5,000

16.

3 5,896


7 2,011

800

14.

6 3,124

300

12.

9 831

500

13.

9 286

90

11.

30

8.

2 131

40

10.

7 501

70

7.

70

4.

6 521

4 171

80

9.

90

3.

4 71

50

5.

20

2.

9 46,999

17. 65 3

18. 98 5

19. 22 3

20. 381 8

21. 555 6

22. 640 7

23. 468 9

24. 309 5

25. 481 7

26. 281 3

27. 349 4

28. 412 5

29. 4,124 6

30. 1,912 9

31. 1,714 2

32. 2,186 4

33. 2,904 7

34. 4,711 8

Problem Solving 35. Marta travels a total of 850 miles every

month to San Francisco for business. If she goes 3 times a month, about how many miles is each round trip?


36. Jeff went on a bike trip of

173 miles to Austin. It took him 9 days. About how many miles did he travel each day?

NS 3.2, 3.4



Estimate Quotients

R

RETEACH

Compatible numbers are numbers you can divide easily. You can use compatible numbers to estimate quotients. Estimate 351 4. Think: What basic division fact is close to 35 4? 36 4 9 360 4 90 So, 351 4 is about 90.

Estimate 435 7. Think: What basic division fact is close to 43 7? 42 7 6 420 7 60 So, 435 7 is about 60.

Complete. 1. Estimate 430 9.

2. Estimate 279 3.

Division fact: 45 9

Division fact: 27 3

Estimate: 450 9

Estimate: 270 3

3. Estimate 299 5

4. Estimate 319 4.

Division fact:

Division fact:

Estimate:

Estimate:

5. Estimate 562 6.

6. Estimate 631 8.

Division fact:

Division fact:

Estimate:

Estimate:


Estimate. Circle the letter of the division sentence with the compatible number. Then complete the division. 7. 122 4

a. 120 4

b. 100 4

8. 349 7

a. 360 7

b. 350 7

9. 272 9

a. 270 9

b. 280 9

10. 292 5

a. 300 5

b. 290 5

11. 453 9

a. 480 9

b. 450 9

Use with Grade 4, Chapter 7, Lesson 6, pages 288–289 (218)

NS 3.2, 3.4



Estimate Quotients

E

ENRICH

The Treasure State Rewrite each exercise using compatible numbers. Write the estimated quotient. 1.

7 428

60 420

2.

3 605 5.

9 8,140

900 8,100

8.

6 3,546

600 3,600

4.

7.

10.

9 98

5 5,165

10 90

200 600

4 316

1,000 5,000

500 4,000

6.

8 3,999 9.

2 196

100 200

12.

8 725

90 720

11.

80 320

3.

20 80

4 85

5 5,620

1,100 5,500

13. Write the estimated quotient beside each exercise number

below. The first one is done for you. Then cross out the letters above quotients with two digits. Circle the letters above quotients with three or more digits. H


11.

90

I 9.

T 6.

A 5.

M 8.

D 10.

O 7.

N 2.

B 1.

N 4.

P 3.

A 12.

14. Rearrange the circled letters to spell the name of the Treasure State. 15. Show how to estimate 605 3.


NS 3.2, 3.4




P

PRACTICE


2.

1,487

5 7,435 5.

$4,028

3.

431

7.

2 $8,056 6.

303

7 2,121

1,306 R3 901 R5

6 5,411

2,027 R2

3 6,083

4 5,227

8 3,448

8.

$811

9 $7,299

9. 5,647 4

10. 3,409 2

11. $6,456 8

12. 3,568 6

13. 5,598 5

14. 1,841 2

15. 9,049 7

16. $1,350 5

17. Divide $4,032 by 8.

4.

18. Divide 1,526 by 3.

19. Divide 5,732 by 9.

21. 2,814 7

22. 4,9497

Compare. Write or .


20. 1,6442

1,9323

2,4186

3,598 4

Problem Solving 23. The mountain bike club wants to

raise $4,464 for 9 new bicycles. If each bicycle costs the same amount, how much does each bicycle cost?


24. The Let’s Grow club makes and sells

hot sauce. The club grows 1,083 peppers. Each jar of hot sauce contains 3 peppers. How many jars can the club make?

NS 3.2, 3.4




R

RETEACH

When you divide 4-digit numbers, begin by deciding where to place the first digit in the quotient. You can see the quotient will have 3 digits.

Divide 3,154 6. Think: You cannot divide 3 by 6. Divide 31 by 6. Write 5 in the quotient above the 1.

5_ _ 6 3,154

Complete. 1.

5 1 6 3 1, 5 4 9 1 5

R

1

2.

1 9 1 3 4 7, 6 5 3 4

4 3 1 9 1 8 1

R

1

3.

3 6 3 6 0 5 4 1 3 1 2 1

Divide.


4.

694 R2

5.

1,159 R3

9.

5 3,472 8.

8 9,275

712 R2

6.

1,009 R1

10.

7 4,986

6 6,055

$656

2,558 R1

2 5,117

13. 7,087 5

14. 3,393 4

15. $6,426 3

R

1

1 5 1 4 1 6 1 6 0 3 2 1 7.

4 $2,624

12. 1,671 8


4 7 8 1 2 9, 5 6 3 8

457 R2

3 1,373 11.

1,090 R8

9 9,818

NS 3.2, 3.4




E

ENRICH

Greatest Remainder Game Play with a partner. Take turns. • Place your marker on START. Solve one of the exercises below. Then move your marker the same number of spaces as the remainder. • The winner is the first player to reach END.

203 R1

6 1,219

965 R3

4 3,863

967 R2

6 5,804

674 R1

4 2,697

349 R3

5 1,748

1,377 R1


7 9,640

868 R3

8 6,947

285 R7

8 2,287

606 R5

6 3,641

1,222 R5

6 7,337

877 R1

3 2,632

1,151 R2

5 5,757

T AR ST


1,165 R4

5 5,829

863 R7

9 7,774

985

653 R3

7 4,574

1,084 R3

4 4,339

451 R4

7 6,895

5 2,259

904 R3

4 3,619

709 R2

8 5,674

607 R3

5 3,038

921 R4

9 8,293

665 R5

6 3,995

430 R3

4 1,723

D

EN

NS 3.2, 3.4




P

PRACTICE


13,168

2.

4,220 R7

6.

7,073 R1

10.

2 14,147

6,447 R2

5,333

4.

26,994

2 53,988

7.

7 45,131

8 33,767

9.

3.

4 76,832

5 65,840

5.

19,208

6 $90,384

8.

$6,475

3 $19,425

11.

6 31,998

$15,064

3,056 R1

9 27,505

4,615 R4

12.

5 23,079

13. $19,328 4

14. 73,895 9

15. 54,620 5

16. 41,183 2

17. 16,697 6

18. 37,986 8

9,316 R1

7 65,213

Algebra & Functions Find each missing number. 19. $26,480

n $5,296

20. 71,910

v 7,990

21. 44,356

r 11,089


Problem Solving 22. The King School held Junior Olympic

games in its sports stadium for 3 days. Each day, every seat in the stadium was full. A total of 17,748 people sat in the stadium. How many seats does the stadium have?


23. The King School raised $75,288 by

selling Junior Olympic banners. Each banner cost $6. How many banners did the school sell?

NS 3.2, 3.4




R

RETEACH

Divide 19,834 4. Step 1: Decide where to place the first digit in the quotient. Think: You cannot divide 1 by 4. Divide 19 by 4. Write 4 in the quotient above the 9.

Step 2: Divide.

The quotient will have 4 digits.

4,958 R2 4 19,834 16 38 36 23 20 34 32 2

Step 3: Check your work. 4,958 4 19,832; 19,832 2 19,834 Divide. 1.

2.

5 68,084


5.

3.

3 94,391 6.

7 23,042

4.

7.

6 44,738

8.

5 31,619

9. 15,275 8

10. 39,021 9

11. $45,222 3

12. 19,217 3

13. 74,472 8

14. $33,496 4


2 $26,856

4 52,273

9 82,445

NS 3.2, 3.4




E

ENRICH

Crossnumber Puzzle Divide to complete the crossnumber puzzle. Then create and solve your own Across and Down clues.


Across

Down

1. 37,351 6

1. 43,393 7

31. 47,338 5

4. 20,150 4

54. 65,829 3

6. 17,037 9

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

51.

52.

53.

54.

55.

56.

57.

58.

59.

60.

61.

62.

63.

64.

65.

66.

67.

68.

69.

70.

71.

72.

73.

74.

75.

76.

77.

78.

79.

80.

81.

82.

83.

84.

85.

86.

87.

88.

89.

90.

91.

92.

93.

94.

95.

96.

97.

98.

99.

100.


NS 3.2, 3.4



Find the Better Buy

P

PRACTICE

Find each unit price. Compare to find the better buy. 1. 2 ounces for $6.80

2. 3 gallons for $59.91

4 ounces for $14.00

5 gallons for $94.90

Better buy:

Better buy:

3. 4 pounds for $10.92

4. 6 pints for $7.14

7 pounds for $19.53

9 pints for $14.31

Better buy:

Better buy:

5. 3 yards for $157.44

6. 5 inches for $48.40

4 yards for $199.80

9 inches for $78.21

Better buy:

Better buy:

7. 2 quarts for $99.50

8. 4 feet for $2.08

6 quarts for $315.00

5 feet for $2.10

Better buy:

Better buy:

Solve. Use the ad to answer exercises 9–12. 9. What is the unit price for a 2-pound

bag of wild bird seed?


10. What is the unit price for a 5-pound

bag of wild bird seed?

11. What is the unit price of a 9-pound bag

of wild bird seed?

Sa Wild le on Bird Seed ! 2-pou nd ba g $3.96 for 5-pou nd ba g for $9.4 5 9-pou nd ba g for $15.7 5

12. Which bag of wild bird seed is the best

buy?


NS 3.2, 3.4; MR 3.2, 3.3



Find the Better Buy

R

RETEACH

Products often come in different sizes. You can find the better buy by comparing the unit price of each size. Find the better buy: a 6-ounce jar of pickles for $1.92, or an 8-ounce jar of pickles for $2.80. Step 1 Find the unit prices. Divide the price by the number of ounces. $0.32 6 $1.92 18 12 12 0

$0.35 8 $2.80 24 40 40 0

Step 2 Compare the unit prices. $0.32 $0.35

Think: Write the dollar sign and the decimal point in the quotient.

So, the 6-ounce jar of pickles is the better buy.

Find each unit price. Compare to find the better buy. 1.

3 gallons of paint for $43.62

unit price:

5 gallons of paint for $75.00

unit price:


Better buy: 2. 2 pints for $2.98

3. 3 gallons for $3.69

4 pints for $4.96

5 gallons for $6.60

Better buy:

Better buy:

4. 4 yards for $12.72

5. 5 feet for $46.25

6 yards for $20.70

7 feet for $63.35

Better buy:

Better buy:

6. 3 cups for $11.22

7. 6 quarts for $55.38

8 cups for $31.52

9 quarts for $80.01

Better buy:

Better buy:


NS 3.2, 3.4; MR 3.2, 3.3



Find the Better Buy

E

ENRICH

Beat This Price! Two grocery stores, the Food Barn and Best Foods, are across the street from each other. The Food Barn placed the ad below in the newspaper.

Dog food $10.88 for a 8-pound bag

T UNA

$1.36/pound

T UNA

T UNA

$0.79/box

Three cans of tuna $4.86

NEW! Fresh pasta $3.15 for 9 inches

$1.62/can

a

Dog Food

$6.95/pound

st

$0.65/ounce

Six-pack of cranberry juice boxes $4.74

Ju ice

Cheddar cheese $34.75 for a 5-pound wheel

pa

Greek olives $2.60 for a O lives 4-ounce jar

Ju ice

Food Barn s Weekend Specials!

$0.35/inch

Best Foods says its prices are lower than the Food Barn’s prices. Find the unit price for each item in the Food Barn ad. Then create an ad for Best Foods. Use the same items, but different amounts; for example, a 7-ounce jar of Greek olives. Best Foods—Our Prices Are Always Lower!


Item/Amount

Our Price

Greek olives:

oz

Cheddar cheese:

pounds

Cranberry juice:

boxes

Dog food: Tuna: Fresh pasta:

Our Unit Price

pounds cans inches


NS 3.2, 3.4; MR 3.2, 3.3



P


PRACTICE

Guess and Check Use the guess-and-check strategy to solve. 1. Teri is putting 57 dolls in a display

case. She puts the same number on each shelf and has 3 dolls left. The case has more than 7 shelves. How many shelves does the case have? How many dolls does each shelf hold?

3. Jamal buys 59 stickers. Stickers come

in packs of 5 or 8. How many of each kind of pack does Jamal buy?

2. A group of friends choose cards

equally from a deck of 52 cards. There are more than 6 friends. After they have chosen, 4 cards are left. How many friends are there? How many cards does each friend have?

4. There are 36 students in an

auditorium. There are twice as many girls as boys. How many girls are there? How many boys are there?

Mixed Strategy Review Solve. Use any strategy.


5. Warren is making a display. He puts

6. Social Studies Each of the 50

1 photo in the first row, 4 photos in the second row, 7 in the third row, and 10 in the fourth row. If the pattern continues, how many photos will Warren put in the fifth row?

states in the United States has a state flag. Evelyn wants to make a drawing of each state flag. She has 3 more flags to draw. How many flags has Evelyn drawn?

Strategy:

Strategy:

7. Sally wants to arrive 20 minutes early

for her job. She starts work at 4:15 P.M. It will take her about 20 minutes to walk from school to the job. When should Sally leave?

8. Create a problem which can be

solved by using the guess-and-check strategy. Share it with others.


NS 3.4; MR 1.1, 2.3, 2.4, 3.1, 3.2




R

RETEACH

Guess and Check Page 301, Problem 2

Jenny is making sand art. A bottle holds 8 inches of sand. Jenny wants to have 2 inches more of red sand than blue sand. How many inches of sand will she pour?

Step 1

Read

Be sure you understand the problem. Read carefully. What do you know? • A bottle holds

inches of sand.

• There will be blue sand.

of red sand than


Plan ■

■


■

■

■

■

■

■

■

■

Find a Pattern Work Backward Use Logical Reasoning Write a Number Sentence Make a Table or List Guess and Check Make a Graph Solve a Simpler Problem Draw a Diagram Act it Out


List the information you know. Use what you know to make a guess. Guess how many inches of each color sand can be used to make a total of 8 inches. Check your guess. Revise the guess and try again if it is wrong. Guess, check, and revise until you find the answer that makes sense.


NS 3.4; MR 1.1, 2.3, 2.4, 3.1, 3.2




R

RETEACH

Guess and Check Step 3

Solve

Carry out your plan. You know that the bottle holds

inches of sand.

You know that Jenny wants to have inches of

sand than

more sand.

Guess Start with two numbers that have a sum of 8. Try 6 and 2. Check 6 + 2 = 8 inches of red sand, There are

inches of blue sand

more inches of red sand.

Does that answer fit the problem? Revise 5 + 3 = 8 inches of red sand, There are

inches of blue sand

more inches of red sand.

Does that answer fit the problem? Step 4


Look Back

Is the solution reasonable? Reread the problem. Does your answer make all of the statements true?

Practice 1. A group of friends share 30 stickers equally, with 3 stickers left over. There are more than 5 friends. How many friends are there? How many stickers does each friend get?


2. Erica bought 9 pens. Each pen costs

either $2 or $3. If the total cost was $23, how many $2 and $3 pens did Erica buy?

NS 3.4; MR 1.1, 2.3, 2.4, 3.1, 3.2



Explore Finding the Mean

P

PRACTICE

Use the connecting cubes to find the mean. Redraw the cubes so that the rows are all the same length. 1. 4, 9, 5

Mean:

2. 7, 6, 3, 4

3. 5, 6, 4, 3, 2

Mean:

Mean:


Find the mean. You may use connecting cubes. 4. 2, 2, 9, 9, 8

5. 15, 0, 6

6. 1, 9, 12, 5, 3

7. 5, 10, 15, 20, 0

8. 1, 9, 2, 8, 3, 7

9. 4, 6, 3, 7, 2, 9, 1, 8

10. 10, 10, 30, 30

11. 1, 1, 1, 9, 9, 9, 8, 2

12. 24, 36

13. 20, 15, 20, 25

14. 4, 3, 2, 5, 1, 6, 2, 9

15. 5, 5, 6, 6, 9, 9, 2

16. 5, 10, 15, 20, 30

17. 1, 2, 3, 4, 5, 6, 7, 8, 9

18. 10, 8, 6, 4, 2

Problem Solving 19. The students in Homeroom 101

collected soup labels this week. The number of labels brought in to class each day were 8, 6, 10, 6, and 5. What was the mean number of labels brought in each day?


20. Alison played in a basketball

tournament this week. She scored the following numbers of points in 5 games: 20, 17, 12, 8, and 18. What was her average point total?

NS 3.4; SDP 1.2




R

RETEACH

You can find the mean of a set of numbers by finding the sum of the numbers and then dividing the sum by the number of addends. Here is how to find the mean of 2, 3, 5, and 6 using connecting cubes. Connect cubes to represent each number.

Connect the cubes into one long row. You should have 16 cubes connected together.

Divide the cubes into 4 equal groups. You should have 4 cubes in each group.

So, the mean of 2, 3, 5, and 6 is 4. © McGraw-Hill School Division

Find the mean. You may draw cubes to help you. 1. 5, 6, 8, 1

2. 4, 8, 5, 7

3. 12, 10, 2

4. 2, 9, 3, 5, 6

5. 11, 5, 2, 2, 10

6. 5, 5, 3, 3, 9

7. 7, 6, 3, 4

8. 7, 8, 2, 4, 3, 6

9. 10, 15, 5

10. 5, 5, 0, 1, 4, 3

11. 10, 20, 40, 2, 10, 20


NS 3.4; SDP 1.2




E

ENRICH

January in Los Angeles In Los Angeles, California, from 1961 to 1990, the average, or mean, high temperature in January was 68° Fahrenheit. 1. Imagine that the average high temperature for the month below is 68°F.

Complete the calendar by writing different temperatures for the days. When you add the temperatures and divide by 31, you should have an average temperature of 68°F. January Sunday

Monday

Tuesday

Wednesday Thursday

Friday

Saturday

1

2

3

4

5

6

7

11

12

13

14

70° 8

9

10

73° 15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31


63°

68° 2. Explain how you chose the temperatures.


NS 3.4; SDP 1.2



Find the Mean

P

PRACTICE

Find the mean. 1. 8, 4, 6, 7, 5

2. 11, 18, 13, 14

3. $25, $48, $77

4. 33, 72, 67, 88

5. $120, $308, $446, $506

6. 823, 665, 482, 619, 781

7. Number of minutes Jason practiced

8. Number of miles traveled each day:

violin this week: 30, 40, 20, 40, 20.

9. Number of rolls of film used each day

to take class pictures: 6, 4, 8, 3, 2, 1, 4

11. Number of miles Dorothy ran each

day: 6, 8, 7, 9, 10, 11, 12

13. Number of books Emily read each

month: 2, 3, 5, 6, 1, 1.

15. Number of bottles of juice on


each shelf: 60, 80, 120, 40, 70, 80, 90, 140

125, 85, 115, 100, 85, 90

10. Number of gallons of gas used

each day: 8, 6, 9, 11, 11, 9

12. Number of miles a pilot flew each

day: 980, 760, 590, 910, 630

14. Height of six boys in inches: 60, 54,

62, 64, 66, 60

16. Number of boxes of cereal eaten by

campers each week: 24, 14, 18, 26, 13

Problem Solving 17. Kathy trades baseball cards.

She traded 42, 38, and 40 cards the last three Saturdays. What is the mean number of cards she trades on a Saturday?


18. From Thursday through Sunday, Pizza

Guy sold 97, 116, 208, and 151 pizzas. What is the average number of pizzas sold each day?

NS 3.4; SDP 1.2



Find the Mean

R

RETEACH

You can use connecting cubes to help you record the steps for finding a mean. Find the mean of 7, 6, 3, and 4. Using Connecting Cubes Step 1 Build each number with connecting cubes.

Connect the cubes into one long row. You should have 20 cubes connected together.

Step 2 Divide the cubes into 4 equal groups. You should have 5 cubes in each group.

Using Pencil and Paper Step 1 Add the numbers. 7 6 3 4 20 Step 2 Divide the sum by the number of addends. 5 4 20 So, the mean of 7, 6, 3, and 4 is 5.

So, the mean of 7, 6, 3, and 4 is 5.


Find the mean. 1. 4, 5, 7, 4, 5

2. 12, 10, 2

3. 16, 13, 12, 15

4. 21, 15, 12, 12, 20

5. 3, 14, 12, 11

6. 16, 15, 19, 13, 27

7. Weight of five dogs in pounds: 42,

35, 21, 38, 54

9. Number of hawks the ranger saw

each day: 19, 7, 22, 8, 9, 13, 13


8. Number of miles Lance bicycled each

day: 74, 69, 80, 57

10. Number of cars that used the parking

garage each day: 563, 709, 661, 842, 805 NS 3.4; SDP 1.2



Find the Mean

E

ENRICH

Missing Pins The computer at the bowling alley is down, so teams have to keep track of their scores on cards. The scorecards below show the scores for the first five frames, or rounds. A cat with muddy paws ran across the cards. Complete the scorecards by writing the correct numbers in the paw prints. Then fill in the team’s total score and mean score. Team A Jason

Total: Mean:

Deanna 21

13

5

10 7 8 50

18 16 5

60 Mean:

Total: Mean:

30 15 10 Total:

Mean:

80 9

Chris

Mean:

16

50

Lindsey 16 18

20

17

9

18 15 15

10 12

10

12 Team B’s

45

5 12 11 12

Total:

19

Mean Score per Person:

Annie 12 13 9 10 16

6

Total:

13

Total Score:

Team B Steven


Mean:

eric 6 4 22 9 4

Total:

65 10

Team A’s

Serena

12

Total:

Total:

65 10

Total Score:


Mean:

13

85 Mean:

17

Mean Score per Person:

NS 3.4; SDP 1.2



Print This Page


Applying Division Record your data and notes. Cost

Advantages and Disadvantages

Bus

Train


Car

Your Decision What is your recommendation for the club? Should they take a bus, train, or car to the aquarium? Explain.


NS 3.4; MR 1.1, 2.3, 3.1


Print This Page



Math & Science

Do light or heavy objects fly farther? Safety: Wear goggles to protect your eyes and work away from other people. Record your data in the table below. Distance Traveled Object

1

2

3

4

5

Mean

Paper Clip Eraser

1. Show how you found the mean or average distance for

each object. Eraser


Paper Clip


NS 1.2; SDP 1.2; MR 1.1, 2.3, 3.2


Problem Solving: Application Do light or heavy objects fly farther?

Print This Page


2. Which object traveled farther? How do you know?

3. Use division to decide how many times farther one object

traveled than the other. Show your work.

Work Space


4. In your own words, explain what gravity is.

5. Explain the results of the activity in terms of gravity.


NS 1.2; SDP 1.2; MR 1.1, 2.3, 3.2



Division Patterns

P

PRACTICE

Complete. 1. 36 9 n

2. 64 8 s

3. 18 b 6

360 90 n

640 80 s

b 30 6

3,600 90 n

6,400 80 s

1,800 30 b

36,000 90 n

64,000 80 s

18,000 30 b

360,000 90 n

640,000 80 s

180,000 30 b

Divide. Use mental math. 4.

5.

2

60 120 8.

$40

10 $400

6.

70

40 2,800 9.

500

7.

$50

11.

70 35,000 10.

$300

70 $21,000

40 $2,000

12. 150 30

13. 16,000 80

14. 2,700 90

15. 18,000 20

16. 1,200 20

17. 56,000 70

18. 810 90

19. 42,000 70

20. 3,600 40

21. 45,000 50

7,000

80 560,000

5,000

90 450,000

Algebra & Functions Find each missing number.


22. 140

25.

a2

t 60 70

23.

d 70 7

26. 28,000

24. 3,000 60

b 400

x

27. 40,000 50

y

Problem Solving 28. A box of 400 stickers is to be divided

equally among 80 students. How many stickers will each student receive?


29. If 6,300 books are divided equally

among 90 libraries, how many books will each library get?

NS 3.2



Division Patterns

R

RETEACH

To divide mentally, you can use basic division facts and look for a pattern. Find the basic division fact. Then count and subtract zeros. This will tell you how many zeros the quotient will have. The basic fact is 6 2 3. 60 20 3 → 600 20 30 → 6,000 20 300 →

1 zero 1 zero 0 zeros 2 zeros 1 zero 1 zero 3 zeros 1 zero 2 zeros

The basic fact is 20 4 5. 200 40 5 → 1 extra zero – 1 zero 0 zeros 2,000 40 50 → 2 extra zeros – 1 zero 1 zero 20,000 40 500 → 3 extra zeros – 1 zero 2 zeros Complete the pattern. Count and subtract the zeros. 1. 24 3

2. 12 4

240 30

120 40

2,400 30

1,200 40

24,000 30

12,000 40


3. 63 9

4. 30 5

630 90

300 50

6,300 90

3,000 50

63,000 90

30,000 50

5. 9 3

6. 90 30

8. 18 3

9. 180 30

10. 1,800 30

11. 42 6

12. 420 60

13. 4,200 60

14. 40 8

15. 400 80

16. 4,000 80


7. 900 30

NS 3.2



Division Patterns

E

ENRICH

Move Along Circle the correct answer for each exercise. Then use the remaining two answers to write the next division sentence. Repeat until you finish the page. 1. 8,000 10 = 800

a. 3,200

b. 800

2. 3,200 80 =

c. 80

3.

b. 4,000

c. 50

a. 4,200

b. 60

c. 50

a. 50

b. 2,800

c. 40

a. 900

b. 90

c. 81,000

a. 10

b. 10,000

c. 100,000

a. 5,000

b. 500

c. 50

4.

a. 90

b. 80

c. 4,500

5.

6.

a. 70

b. 4,000

c. 80

7.

8.

a. 54,000

b. 60

c. 70

9.

10.

a. 900,000

b. 900

c. 90

11. © McGraw-Hill School Division

a. 40

12.

a. 100,000

b. 10,000

c. 20

13. Look at exercise 12. How did you decide how many zeros were in the quotient?


NS 3.2



Explore Dividing by 2-Digit Numbers

P

PRACTICE

Divide. 1.

2.

130 10

143 30

3.

4.

121 14

156 18

Divide. You may use place-value models. 5.

6 R9

6.

13 87 9.

18 R5


16 293

9 R2

7.

15 137 10.

13 R14

7 R9

8.

12 93 11.

17 235

13 R11

19 258

8 R13

14 125 12.

17 R16

25 441

13. 135 16

14. 134 14

15. 115 15

16. 282 18

17. 230 19

18. 269 24

Problem Solving 19. The dividend is 280. The divisor is 23.

What are the quotient and remainder?


20. The dividend is 160. The divisor is 12.

What are the quotient and remainder?

NS 3.2




R

RETEACH

You can use estimation and models to help you divide. Find 148 12. Show 148 using place-value models.

Think: How many groups of 12 are there in 148? Exchange 1 hundred for 10 tens.

Divide the tens. Make as many groups of 12 as you can.

Exchange tens for ones so you can keep grouping 1 ten and 2 ones. You can make 12 equal groups of 12 with 4 ones remaining.

So, 148 12 12 R4. © McGraw-Hill School Division

Divide. You may use place-value models to help you. 1. 163 13

2. 158 10

3. 214 12

4. 285 14

5. 352 16

6. 385 15

7. 183 17

8. 268 11

9. 376 18


NS 3.2




E

ENRICH

Stick Division What if we used a number system that used symbols instead of numerals? In this Chinese system, numbers are written using the symbols shown.

1

10

2

3

20

4

50

5

60

Using these symbols, 21 is shown as Example:

426

21 8,946

6

7

70

8

90

9

100

and 8,946 is shown as

.

→


Use the number system above to create four division exercises where the divisor is a 2-digit number. Then exchange exercises with a partner and find the quotient using symbols. 1.

2.

3.

4.

5. Is it easier or harder to divide using the number system above? Explain.


NS 3.2


8–3 Page Divide 2-Digit Numbers by Multiples of 10 Print P This PRACTICE

Divide. 1. 82 20

2. 75 10

3. 51 20

4. 94 30

5. 88 20

6. 87 10

7. 93 40

8. 71 30

9. 97 20

10. 74 20

11. 52 10

12. 67 30

13. 91 10

14. 62 40

15. 94 40

16.

3 R1

17.

7 R6

21.

9 R6

25.

20 61 20.

10 96

18.

4 R15

22.

1 R29

26.

50 78

10 76 24.

1 R28

2 R1

19.

1 R24

23.

2 R4

27.

40 81

20 95

60 84

30 59

20 44

2 R3

30 63

1 R9

40 49

1 R9

50 59


Algebra & Functions Find the missing number. 28. 27

m 2 R7

29. 51

k 1 R21

30. 63

a 1 R13

31. 74

p 3 R14

32. 71

y 3 R11

33. 90

r 2 R10

Problem Solving 34. Sam needs to put 76 pencils in

packages. Each package should have 10 pencils. How many packages will there be? How many pencils will be left over?


35. Kenya needs to put 84 cans of

tennis balls in boxes. Each box should have 20 cans. How many boxes will Kenya fill? How many cans will she have left over?

NS 3.2


8–3 Page Divide 2-Digit Numbers by Multiples of 10 Print R This RETEACH

You can use models to help you divide by multiples of 10. Find 74 20.


Using Models

Using Pencil and Paper

Show 74 using place-value models.

Step 1: Divide 74 by 20.

Then make as many groups of 20 as you can.

Think: 60 20 3. 3 20 74 60 Step 2: Subtract. Write the remainder in the quotient. 3 R14 20 74 60 14

You can make 3 equal groups of 20 with 14 remaining.


Divide. You can use place-value models. 1. 63 30

2. 88 40

3. 55 10

4. 48 20

5. 74 10

6. 93 30

7. 85 30

8. 81 20

9. 76 10

10. 51 30

11. 63 50

12. 84 60

13. 90 40

14. 74 20

15. 71 20

16. 27 10

17. 59 50

18. 59 30


NS 3.2


Divide 2-Digit Numbers by Multiples of 10


E

ENRICH

Winning Start • Label the faces of a number cube 20, 30, 40, 50, 60, and 70. • Place a marker on 72, the starting position. Take turns tossing the number cube. Divide the number your marker is on by the number tossed. Find the whole number quotient. Move forward that number of spaces. • Continue moving forward until you have gone around the board once. After passing "Start", you may move forward or backward. The winner is the person who lands directly on "Start".


Start 72

85

97

100

115

120

260

138

253

149

250

150

235

164

226

219

205


197

186

173

NS 3.2



Divide by 2-Digit Divisors

P

PRACTICE

Divide. 1.

43 R6

2.

22 952 5.

11

7.

10.

96 R1

14.

4.

12 R2

11.

71

15.

17 $11.39

8.

12.

$0.89

16.

39 2,381

17. 895 24

18. 907 31

19. 367 14

20. $7.08 59

21. 814 36

22. 531 45

23. 1,467 24

24. $37.76 64

25. 4,780 77

26. $48.59 43

27. 7,900 84

28. 8,930 92

13 R9

75 984

61 R2

62 $55.18

14 R4

54 760

44 530

$0.67

51 3,621

$0.11

66 $7.26

29 496

75 R4

93 8,929

17 R3

6.

26 1,954 13.

3.

31 784

81 891 9.

25 R9

83

46 3,818

74 R6

88 6,518

Algebra & Functions Solve. 29. (1,700 53) 37

w


31. (1,900 100) 29

v

33. (2,300 70) (12 4)

n

34. (1,500 80) (11 5)

c

30. (1,000 160) 46

d

32. (1,600 240) 83

x

Problem Solving 35. Mrs. Tallo’s class made 234 ribbons for

the Sports Fair. Each student made the same number of ribbons. There are 18 students in the class. How many ribbons did each student make?


36. Mr. Willow’s class wants to sell

200 tickets to the Winter Sports Fair. There are 25 students in the class. How many tickets will each student need to sell?

NS 3.2




R

RETEACH

You can use models to help you understand dividing by 2-digit numbers. Find 165 25. Using Models Use place-value models to show 165.

Using Pencil and Paper Step 1: Divide, Think: 180 30 6 6 25 165

Exchange the one hundred for 10 tens.

Step 2: Multiply. 6 25 165 150 ← 6 25 150


Then make as many groups of 25 as you can. Exchange tens for ones. You can make 6 equal groups of 25 with 15 remaining.

Step 3: Subtract. Write the remainder in the quotient. 6 R15 25 165 150 15 ← 165 150 15

Divide. You can use place-value models. 1. 164 12

2. 174 18

3. 318 21

4. 135 14

5. 372 23

6. 243 17

7. 212 24

8. 435 16

9. 166 13


NS 3.2




E

ENRICH

What Number Am I? Solve. What number am I? 1. I am a number between 10 and 20.

2. I am a number between 10 and 20.

If you divide either 61 or 73 by me, the remainder is 1.




























NS 3.2



Estimate Quotients

P

PRACTICE

Estimate the quotient. Choose compatible numbers. 1. 19 389

2. 17 211

3. 18 586

4. 16 789

5. 49 1,585

6. 72 6,280

7. 32 8,920

8. 61 3,256

9. 68 34,912

10. 2,806 38

11. 7,903 86

12. 1,113 31

13. 7,160 93

14. 2,806 56

15. 2,210 48

16. 21 1,732

17. 63 546

18. 53 2,612

19. 41 1,512

20. 78 4,106

21. 86 1,709

Algebra & Functions Estimate to compare. Write or .


22. 396 21

914 31

23. 492 68

24. 1,947 38

2,011 48

25. 1,300 21

26. 5,106 82

6,206 91

27. 3,100 82

556 71 2,300 13 4,700 71

Problem Solving 28. Karen drove 283 miles at a speed of

46 miles per hour. About how many hours did she drive?


29. A jet flew 3,116 miles in 6 hours.

About how many miles per hour did it fly?

NS 3.2



Estimate Quotients

R

RETEACH

Compatible numbers are numbers you can divide easily. You can use compatible numbers to estimate quotients. Estimate 3,463 73. 3,463 73 Think: A basic fact that is close is 35 7. 3,500 70 50 So, 3,463 73 is about 50. Complete. 1. Estimate 1,785 31.

2. Estimate 2,880 29.

Division fact: 18 3

Division fact: 27 3

Estimate: 1,800 30

Estimate: 2,700 30

3. Estimate 5,726 72.

4. Estimate 3,952 79.

Division fact:

Division fact:

Estimate:

Estimate:


Use compatible numbers to estimate each quotient. 5. 1,482 33

6. 6,512 78

7. 7,164 89

8. 2,207 68

9. 3,512 42

10. 2,587 53

11. 3,123 64

12. 4,132 71

13. 2,712 32

14. 1,789 27

15. 2,797 43

16. 6,432 92


NS 3.2



Estimate Quotients

E

ENRICH

Box Estimation Choose the best estimate from each box to complete the sentence. Then write the answer next to the letter of the box to make a code. Use the code to answer the question. Who was the first American in space? A. 24

33

D. 63

53

E. 82

75

42

51

71

48

64

92

2,430

is about 80.

is about 70.

3,575

is about 40.

H. 27

44

L. 24

32

N. 31

42

52

38

58

44

52

28

2,277

is about 40.

12,250

is about 600. 15,880

P. 68

72

R. 68

74

84

91

47

59

25,370


4,356

is about 300. 29,790

is about 400.

S. 7

72

is about 500. 34,841

A

D

E

H

L

N

P

R

S

24

33

42

64 is about 500.

, JR.

B. 33

81

72

52

92

84

33

59

63

Explain how you estimated the divisors.


NS 3.2



Adjust the Quotient

P

PRACTICE

Divide. 1.

7 R11

2.

2 R44

6.

8 R74

10.

8 R28

14.

8 R19

18.

5 R77

22.

34 249 5.

3 R70

11.

7 R24

15.

5 R9

19.

8 R10

23.

4 R34

8.

5 R35

12.

5 R86

16.

3 R52

20.

8 R35

24.

3 R49

63 238

7 R11

25 186

92 546

3 R75

88 339

65 247

22 186

8 R39

41 367

39 230

24 129

81 482

4.

79 350

69 507

44 371 21.

7.

75 295

56 476 17.

7 R38

8 R21

56 469

84 626

92 810 13.

3.

26 189

51 146 9.

7 R7

4 R56

57 284

45 395

8 R11

36 299

Algebra & Functions Divide only those with quotients between $5.00 and $8.00. 25.

$5.25

26.

$7.15

30.


18 $94.50 29.

13 $92.95

$6.15

27.

16 $98.40

no

11 $99.11

no

28.

no

32.

14 $60.90 31.

15 $56.25

no

25 $93.75

$7.76

12 $93.12

Problem Solving 33. Candy wants to walk 220 miles in

30 days. If she walks 7 miles every day, will she meet her goal?


34. Jason wants to save $180 in

12 months. How much should he save each month?

NS 3.2



Adjust the Quotient

R

RETEACH

When you divide, sometimes your first estimate is too high or too low. Then you must adjust the quotient. Divide 125 43. Step 1:

3 43 125

Estimate: 120 40 3 Step 2: Use your estimate to divide.

3 43 125 129 ← Multiply: 3 43 129

Compare: 129 125. You cannot subtract. The estimate of 3 is too high. Step 3: Adjust your estimate and divide.

Multiply to check the answer.

2 R39 43 125 86 ← Multiply: 2 43 86 39 Subtract: 125 86 39 Compare: 39 43

43 2 86 39 125



4 R14

2.

6 R8

6.

24 110 5.

57 350

9. 173 19

7 R1

3.

8 R1

7.

27 190

4.

6 R1

8.

29 148

16 129

10. 293 44


5 R3

37 223

1 R59

61 120

1 R61

63 124

11. 208 25

NS 3.2


Adjust the Quotient


E

Hi Lo

ENRICH

Estimate each quotient. Write your estimate. Then divide. If your estimate was too high, circle "Too High." If your estimate was too low, circle "Too Low." Use the circled answers to complete the maze below. 1.

5.

3 R71

2.

9 R10

3.

7 R30

4.

$3.25

73 290

65 595

31 247

21 $68.25

Too High Down

Too High Left

Too High Down

Too High Left

Too Low Up

Too Low Right

Too Low Up

Too Low Right

6 R2

6.

$2.13

7.

7 R7

8.

7 R2

88 530

91 $25.56

48 343

26 184

Too High Down

Too High Right

Too High Up

Too High Left

Too Low Up

Too Low Left

Too Low Down

Too Low Right

What is the fastest fish, the tallest tree, the biggest dog, and the smallest bird? To find out, begin at Start. Move one space in the direction given next to each circled answer.


Start

sailfish redwood St. Bernard hummingbird swordfish Maple

dolphin oak

greyhound parakeet

Great Dane sparrow


NS 3.2




P

PRACTICE

Reading Skill

Use an Overestimate or Underestimate Form a conclusion about whether you would overestimate or underestimate. Then solve the problem. 1. A group of 118 people have signed up for the 5-kilometer run. Each person will receive a special cap. Caps are sold in boxes of 36. How many boxes are needed? Should you overestimate or underestimate to solve this problem? Explain.

How many boxes are needed? 2. The Flying Disk Club has saved $90 to buy Disks for its

members. A package of 2 Disks costs $8. How many packages of Disks can the club buy? Should you overestimate or underestimate to solve this problem? Explain.

How many packages of Frisbees can the club buy? 3. Trophies cost $9 each. The tournament organizers have $60


budgeted for trophies. How many trophies can they buy? Should you overestimate or underestimate to solve this problem? Explain.

How many trophies can they buy? 4. A group of 24 students is playing catch. They share 7 softballs.

What is the least number of students who can share each softball? Should you overestimate or underestimate to solve this problem? Explain.

What is the least number of students who can share a softball? Use with Grade 4, Chapter 8, Lesson 7, pages 338–339. (259)

MR 1.1, 2.1, 2.4, 2.5, 3.1, 3.2




P

Use an Overestimate or Underestimate

PRACTICE


Choose the correct answer. There are 95 volunteers working at the marathon. Each volunteer will get a water bottle. A box contains 24 water bottles. How many boxes are needed? 1. Which of the following statements

2. To be sure there are enough water

is true?

bottles for the volunteers, you should:

A There are not enough water bottles for the volunteers.

F underestimate the number of volunteers.

B A box contains 24 water bottles.

G overestimate the number of volunteers and underestimate the number of boxes needed.

C There are 95 water bottles. D Four water bottles are needed.

H underestimate the number of boxes needed. J overestimate the number of boxes needed.

At the game, there are 44 color guards. Each color guard will help carry flags. There are 21 flags on 6-foot poles. What is the greatest number of students that will have to share a flag?


3. Which of the following is not

4. To find the greatest number of students

important to solving the problem?

who will share a flag, you should:

A There are 44 students carrying flags.

F overestimate the number of students per flag.

B Each color guard will help carry a flag. C There are 21 flags. D The flags are on 6-foot poles.

G underestimate the number of students per flag. H overestimate the number of flags and underestimate the number of students. J underestimate the number of flags per student.


MR 1.1, 2.1, 2.4, 2.5, 3.1, 3.2




P

Use an Overestimate or Underestimate

PRACTICE


Choose the correct answer. The sports committee buys a piece of fabric that is 60 feet long. Underestimate the number of 9-foot banners that can be made from the fabric. 5. To underestimate the number of

banners that can be made, you: A use 63 feet for the length of the fabric. B round down the length of the fabric to 50 feet. C round up the length of each banner to 10 feet. D use 6 feet for the length of each banner. Solve. 7. Travis is making first-place ribbons for Sports Day. He has 111 inches of blue ribbon. Each blue ribbon will be 8 inches long. Underestimate the number of ribbons he can make.


9. There are 152 people at the Sports

Night Dinner. There are 33 tables. What is the greatest number of people that can sit at a table? Explain.

11. A pack of 3 pennants costs $8.

Maryanne has $30. Is this enough to buy 4 packs of pennants? Explain.


6. How many 9-foot banners can be

made from the fabric? F 5 G 6 H 7 J 8

8. The soccer club makes 100 cups of

fruit drink. There are 46 students in the soccer club. Is there enough fruit drink for each student to have 2 cups? Explain.

10. Mark wants to buy baseball shirts of

different teams. Each shirt costs $18. Mark has $62. How many shirts can he buy? Explain.

12. A box of gold medals costs $56. The

Sports Committee has $185 to spend on medals. How many boxes can the committee buy? Explain.

MR 1.1, 2.1, 2.4, 2.5, 3.1, 3.2




P

PRACTICE

Choose a Strategy Choose a strategy. Use it to solve the problem. 1. The Sports Committee buys 30 yards

of material. The material will be cut into banners that are 5 feet long. How many banners can be made?

3. Liam is building a fence around his

backyard. The backyard is 24 feet wide and 60 feet long. If Liam uses sections of fencing that are 12 feet long, how many sections will he need?

Mixed Strategy Review Solve. Use any strategy. 5. Art Tina makes a display of 36 autographed baseballs. She puts 12 baseballs in a large display case. Tina also has 4 smaller display cases. How can she arrange the baseballs in the smaller cases so that each smaller case has an equal number of baseballs?

2. The Sand Trap Golf Shop has 132 golf

balls in stock. The golf balls are packed in tubes of 6. How many tubes of golf balls does the store have?

4. There are 115 students who want to

go to the basketball tournament. One bus can carry 26 students. How many buses will be needed?

6. Francine uses a pattern to make a

window display for a sneaker store. The first row has 2 sneakers, the second row has 6 sneakers, the third row has 10, and the fourth row has 14. How many sneakers will be in the fifth row?


Strategy: Strategy: 7. The Stadium Store sells 450 team

photos and 369 individual photos. How many photos does it sell in all?


solve by drawing a diagram or by writing a division sentence. Share it with others.

Strategy:


NS 3.2; MR 2.4




R

RETEACH

Choose a Strategy Page 343, Problem 1

Camille wants to practice sharper turns. She uses the same 20-yard distance in the driveway and begins at the starting line. This time she places the cones 3 feet apart. How many cones will she use? Step 1

Read

Be sure you understand the problem. Read carefully. What do you know? • The total distance is

yards.

• Camille will start at the starting line and place cones feet apart. What do you need to find? • You need to find the number of feet in

yards.

• You need to find how many

.

Step 2

Plan ■

■


■

■

■

■

■

■

Find a Pattern Work Backward Use Logical Reasoning Write a Number Sentence Make a Table or List Guess and Check Make a Graph Solve Simpler Problem


To find the answer, you may draw a diagram. Find the number of feet in 20 yards. Show a distance that is that many feet long. Count by 3s to see how many cones Camille will use if they are placed 3 feet apart. To find the answer, you can also write a number sentence. All the cones are the same distance apart. Use division to find how many cones Camille will use.


NS 3.2; MR 2.4




R

RETEACH

Choose a Strategy Step 3 Carry out your plan.

Solve

How many feet are in 20 yards? 1 yard 3 feet 20 3 60 Draw a diagram. Show a 60-foot distance. Count by 3s to see how many cones Camille will use. 0

3

6

9

12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60

Count. Camille will use a total of

cones.

Write a number sentence. The distance is feet. There will be 1 cone every Write a division sentence.

Camille will use a total of

cones

feet.

Step 4

Look Back

Is the solution reasonable? Reread the problem.


Does your answer make sense? Yes No Which method do you prefer? Explain.

Practice 1. The parks department builds stands next to a baseball field. There will be 5 rows of stands. Each row will be 20 feet long. How many 10-foot long boards will they need to build the stands?


2. Ed has 4 packs of sports stickers.

There are 24 stickers in each pack. He divides the stickers among 3 friends. How many stickers does each friend get?

NS 3.2; MR 2.4



Order of Operations

P

PRACTICE

Write which operation should be done first. 1. 2 8 7

2. 2 3 9

3. 4 10 2

4. 9 2 3

5. (3 2) 9

6. 8 (2 2)

7. 6 2 1

8. 1 3 5

9. 10 5 2

10. 7 8 2

11. (12 4) 2

12. 9 2 6


Simplify. Use order of operations. 13. 3 2 7

14. 10 2 1

15. 9 6 2

16. 24 2 8

17. (2 6) 7

18. 12 12 3

19. (4 6) 5

20. 12 3 9

21. 20 5 2

22. 18 9 6

23. 2 8 4

24. 20 5 4

25. 2 6 4 3

26. 20 2 3 6

27. (2 9) (7 3)

28. 4 (14 6) 2 5

29. 2 9 10 5 (3 2)

Problem Solving 30. Tamara buys 6 apples for $0.40 each.

She has a $0.50 off coupon. Write an expression and simplify to find her final cost.


31. Steven has 126 photos to put in an

album. He finds 18 more photos. Each page holds 12 photos. Write an expression and simplify to find how many pages Steven will fill.

AF 1.3



Order of Operations

R

RETEACH

Always use the order of operations to simplify expressions. The rules for the order in which you should perform operations are given below. Simplify (20 8) 4 2. Step 1:

Step 2:

Step 3:

Do the operations in parentheses first.

Multiply and divide from left to right.

Add and subtract from left to right.

(20 8) 4 2

28 4 2

72

28 4 2

72

5

Which operation should you do first? 1. 12 4 2

2. 4 (10 2)

3. 2 8 4

4. (3 7) 2

5. 9 3 2

6. 8 2 4

7. 6 (8 5)

8. 8 4 2

9. 12 (2 2)


Simplify. Use the order of operations. 10. 3 (2 5)

11. 14 7 2

12. 9 (6 2)

13. 4 2 5

14. 8 2 2

15. 10 8 4

16.12 3 2

17. (1 5) 4

18. 8 8 4

19. (5 5) 2

20. 14 10 2

21. 16 4 2


AF 1.3


Order of Operations


E

ENRICH

Order Counts Rewrite each number sentence. Put in parentheses to make each number sentence true. 1. 3 8 2 1 21 2. 5 x 16 + 14 + 6÷ 2 = 153 3. 6 ÷ 9 – 8 = 6 4. 22 – 3 x 5 + 2 = 1 5. 18 ÷ 2 + 1 + 1 = 7 6. 6 x 5 + 9 ÷ 3 = 28 7. 5 x 10 + 1 ÷ 11 = 5 8. 3 + 40 ÷ 8 x 5 = 4 9. 10 – 6 ÷ 4 = 1 10. 4 x 5 – 2 = 12 11. 40 ÷ 10 – 2 = 5 12. 20 + 8 ÷ 4 = 7 13. 6 + 2 x 7 = 56


14. 16 – 6 + 2 = 8

In your own words describe the rules for the order of operations.


AF 1.3



Print This Page


Applying Multiplication Record your data. Cost to the club

Profit per bar for the club at a sale price of $1

Sales needed to reach goal for $110 in profits

Home-made hiker bars

Boxed hiker bars


Your Decision What is your recommendation for the hiking club? Explain.


NS 1.2, 3.2, 3.3, 3.4; MR 1.1, 2.4


Problem Solving: Application Does eating improve performance?

Print This Page


Safety: Wait at least 30 minutes after eating before doing vigorous exercise. Record your data. Number of Sit-ups Student

Before Lunch

After Lunch

1. Did you do more sit-ups before or after lunch?


2. How many more sit-ups did you do? Show your work.

Work Space


NS 1.2, 3.4; MR 1.1, 2.3, 3.3


Print This Page



Math & Science

Does eating improve performance? 3. How many times more sit-ups did you do? Round to the nearest

whole number. Show your work.

Work Space

4. Can you conclude that the food from lunch gave you more energy?

Why or why not?


5. In what ways could you improve this activity?

6. Explain the activity in terms of energy conversion.


NS 1.2, 3.4; MR 1.1, 2.3, 3.3



Explore Customary Length

P

PRACTICE

Estimate and then measure. Tell what unit and tool you use. 1. length of a pencil 2. height of a desk 3. width of the classroom 4. length of a book 5. distance you go in a stride


Circle the letter of the correct estimate. 6. distance you can ride your bike

A. 2 mi

B. 2 ft

C. 2 yd

7. length of a car

A. 10 in.

B. 10 ft

C. 10 yd

8. height of a fourth-grader

A. 4 in.

B. 4 ft

C. 4 yd

9. height of a tree

A. 40 mi

B. 40 yd

C. 40 ft

10. height of a cat

A. 1 yd

B. 1 mi

C. 1 ft

11. length of a worm

A. 3 in.

B. 3 ft

C. 3 yd

12. height of a refrigerator

A. 2 ft

B. 2 yd

C. 2 mi

13. length of a crayon

A. 4 ft

B. 4 yd

C. 4 in.

14. length of a football field

A. 100 ft

B. 100 yd

C. 100 mi

Problem Solving 15. Jane can walk a mile in about

15 minutes. About how long would it take her to walk 5 miles?


16. Marta measures the length of her

notebook. To the nearest quarter 3 inch, it is 12 4 in. What does it measure to the nearest inch?

MR 1.1, 2.3




R

An inch (in.) is used to measure short lengths in the customary system.

Customary Units of Length 1 foot (ft) 12 inches (in.)

You can use a ruler to measure in inches. 0

1

2

RETEACH

1 yard (yd) 3 feet (ft)

3

1 mile (mi) 1,760 yards (yd) 1 mile (mi) 5,280 feet (ft) 3 14 in. The foot (ft) and yard (yd) are used to measure larger units in the customary system. 1 yd 1 ft Use an inch ruler to measure each object. Measure to the nearest 14 inch. 1.

2.


3.

4.

Circle the letter of the correct estimate. 5. length of a person’s foot

A. 8 in.

B. 8 ft

C. 8 yd

6. length of a bed

A. 6 in.

B. 6 ft

C. 6 yd


MR 1.1, 2.3




E

ENRICH

Early Measurements In early times, distances were measured using fingers, hands, and arms. digit

span

cubit

digit: the width of a finger

span: the width of a stretched hand

cubit: the distance from fingertip to elbow


Choose digit, span, or cubit as the appropriate unit of measure. Then estimate. 1. width of your desk

2. thickness of your math book

3. length of your notebook

4. diameter of an apple

5. height of the classroom

6. length of a car

7. your friend’s height

8. length of your foot

9. What is an advantage of this system? What is a disadvantage?

10. What kinds of distance would be difficult to measure using this system

of measurement?


MR 1.1, 2.3



Customary Capacity and Weight

P

PRACTICE

Estimate and then measure the capacity of each object. 1. a water glass 2. a large pot 3. a cereal bowl

4. a milk carton

5. Order the objects above from least to greatest capacity.

Estimate and then measure the weight of each object. 6. an apple 7. four potatoes 8. two envelopes

9. a pencil

10. Order the objects above from least to greatest weight.


Circle the letter of the correct estimate. 11.

A. 5 c

B. 5 pt

C. 5 gal

12.

A. 1 c

B. 1 pt

C. 1 qt

13.

A. 6 c

B. 6 qt

C. 6 gal

14.

A. 2 fl oz

B. 2 c

C. 2 pt

15.

A. 500 oz

B. 500 lb

C. 500 T

16.

A. 3 oz

B. 3 T

C. 3 lb

Problem Solving 17. A box of Krispy Krunch cereal holds 20 oz. Kyle pours 3 oz of cereal into his bowl. How much cereal is left in the box?


18. Sarah buys a 48 fl oz bottle of apple

juice. How many cups of juice can she pour from the bottle?

MR 1.1, 2.3



Customary Capacity and Weight Capacity is the measure of dry or liquid volume of a container. Pour water into empty milk cartons to model the equivalent units of capacity shown below.

2 cups 1 pint (c) (pt)

R

RETEACH

Customary Units of Capacity 8 fluid ounces (fl oz) 1 cup (c) 2 cups (c) 1 pint (pt) 2 pints (pt) 1 quart (qt) 4 quarts (qt) 1 gallon (gal)

2 pints 1 quart (pt) (qt)

Weight is the measure that tells how heavy an object is.

A card and envelope weigh about 1 ounce.

4 quarts 1 gallon (qt) (gal)

Customary Units of Weight 16 ounces (oz) 1 pound (lb) 2,000 pounds (lb) 1 ton (T)

A book weighs about 1 pound.


Circle the letter of the correct estimate. 1. weight of an apple

A. 5 oz

B. 2 lb

C. 12 T

2. weight of a fourth grader

A. 12 T

B. 20 oz

C. 60 lb

3. amount of water in a bathtub

A. 25 qt

B. 25 gal

C. 25 pt

4. weight of a refrigerator

A. 100 oz

B. 100 lb

C. 5 T

5. amount of water in a pail

A. 5 qt

B. 50 gal

C. 500 c


MR 1.1, 2.3



Customary Capacity and Weight

E

ENRICH

Reasonable Measure Maze Shade each box that contains a reasonable measure. The shaded boxes will form a path from start to finish.

Finish

A living room is 6 yards long.

Your smile is 1 yard wide.

In an hour, an airplane flew 1,780 miles.

A horse weighs 827 oz.

A pizza weighs 144 oz.

A song is about 3 minutes long.

A goldfish bowl holds 18 cups of water.

An automobile might weigh 2,545 lb.

The pitcher holds 3 qt of lemonade.

A football field

A frog can jump 475 feet.

A girl’s braid was 3 yards long.

A dog can jump 17 yards.

Jen held her breath for 63 seconds.

The gate is 40 inches high.

A gallon of paint is enough to paint a large wall.

The kitten drank an ounce of milk.

The movie lasted 107 minutes.

A TV commercial lasts about 600 seconds.

A bathtub holds 18 pints of water.

The train was 125 yd long.


You could walk a mile in 20 seconds.

1 is 4 mile long.

The punch bowl holds 24 cups of punch.

Pat rode his bike 12 mph.

The climbing rope to the tree fort was 37 inches long.

The diving pool was 4 yd deep.

The subway sandwich was 12 yd long.

A light bulb weighs 2 ounces.

It took about 3 yards of fabric to make a cape.

The newborn baby drank 7 oz of milk.

A banana is 9 inches long.

Beth ran a distance of 10,525 ft.

A sneaker weighs 40 oz.

Start

How did you decide if running a distance of 10,525 feet was reasonable?


MR 1.1, 2.3



Convert Customary Units

P

PRACTICE

Complete. 1. 7 ft

in.

4. 60 in.

ft

2. 21 ft

yd

3. 2 mi

yd

5. 13 yd

ft

6. 2 mi

ft

9. 3 pt

c

7. 8 qt

gal

10. 36 ft

yd

11. 4 ft

in.

12. 12 ft

yd

13. 12 pt

qt

14. 2 lb

oz

15. 48 oz

lb

16. 3 T

ft

17. 10,000 lb

lb

19. 3 gal

8. 144 in.

qt

T 18. 2 c

20. 2 qt

fl oz

21. 10 c

pt

pt

22. 1 lb 10 oz

oz 23. 1 gal 2 pt

pt 24. 10 ft

yd

25. 4 T 800 lb

lb 26. 5 ft 8 in.

in. 27. 13 qt

gal

ft qt


Gallons

29.

1

Quarts Pints

1

Feet

12

9

Inches

16

Cups 30.

Yards

72

64

Ounces

Pounds 1 2 3 4

31.

Tons Pounds

1 6,000


16 32 48 Problem Solving 32. Amy cuts a piece of ribbon 60 in.

long. How many feet long is the piece of ribbon?


33. The 6 members of the Brown family

drink a total of 3 gallons of milk each week. How much is that per person?

AF 1.3; MR 1.1, 2.3




R


You can use tables to help you convert customary units of measure. To convert a larger unit to a smaller unit, multiply. Think: 2 gallons 4 8 quarts Cups Pints Quarts To convert a smaller unit to a larger unit, 2 1 divide. Think: 8 quarts 4 2 gallons 4

2

1

6

3

24

2

8

4

36

3

10

5

48

4

12

6

60

5

14

7

72

6

16

8

4

84

7

Ounces

Cups

Pounds

96

8

8

1

108

9

3

16

2

Feet

Yards

Miles

24

3

5,280

1,760

1

32

4

10,560

3,520

2

40

5

15,840

5,280

3

48

6

Inches

Feet

12

Yards

1

2

RETEACH

Gallons

1

2

3

1

1

2

3

Complete. 1. 3 ft

in.

4. 5 yd

ft

7. 12 qt 10. 3 pt

gal c

2. 24 in. 5. 8 c 8. 3 mi 11. 2 lb


ft pt yd oz

3. 6 ft 6. 12 pt 9. 2 qt 12. 48 oz

yd qt pt lb AF 1.3; MR 1.1, 2.3




E

ENRICH

Can You Convert? Play with a partner. Take turns. • For each turn, roll one number cube. Move that many spaces. • Then roll two number cubes. Convert that number to a larger or smaller unit of measure. For example, you land on a qt square. You roll a 1 and a 7. You can convert 17 or 71 quarts to cups, pints, or gallons, or a combination of units. • If your answer is correct, move ahead 1 space. If it is incorrect, move back 1 space. • The player who reaches FINISH first wins.

Start

qt

oz

in.

lb

c ft

gal yd pt


qt oz in. lb c

ft

gal


yd

pt

Finish

AF 1.3; MR 1.1, 2.3




P

PRACTICE

Reading Skill

Check for Reasonableness Circle the statement that is reasonable. 1. Robert and Anthony ran 3 miles.

Robert says, “We ran about 30,000 feet.” Anthony says, “We ran about 15,000 feet.” Explain your thinking:

2. The distance from April’s home to the school is 10,560 feet.

April says “Our home is about 3,500 yards from the school.” April’s sister says, “Our home is about 30,000 yards from the school.” Explain your thinking:

3. A running track is 3,600 yards.

Pablo says, “The track is less than 2 miles long.” John says, “The track is more than 2 miles long.”



4. A cooler holds 8 gallons of sports drink.

Brian says, “The cooler holds 2 quarts.” Rachel says, “The cooler holds 32 quarts.” Explain your thinking:


NS 1.2; MR 1.1, 2.3, 2.5, 3.1, 3.2




P

Check for Reasonableness

PRACTICE


Choose the correct answer. The stage is 31 feet long. The director says the stage is more than 10 yards long. Is this statement reasonable? 1. Which of these statements is true?

2. The director’s statement is

A The stage is 11 yards long.

reasonable because

B The stage is 12 yards long.

F 30 feet is less than 10 yards.

C The stage is 31 feet long.

G 30 feet equals 10 yards.

D The stage is 36 inches long.

H 31 feet equals 10 yards. J 31 feet equals 11 yards.

The television cabinet is 78 inches high. Mary says this is more than 7 feet high. Is this statement reasonable? 3. Which of these statements is true?

4. Mary’s statement is not reasonable

A The cabinet is 7 feet high.

because

B The cabinet is 8 feet high.

F 78 inches is less than 7 feet.

C The cabinet is more than 8 feet high.

G 78 inches is equal to 7 feet.

D None of the above

J 78 inches is greater than 8 feet.

H 78 inches is greater than 7 feet.

The refreshment stand sells 36 quarts of punch. Ms. Spencer says the stand sells 9 gallons of punch. Is this statement reasonable?


5. Which of the following is important

6. Ms. Spencer’s statement is

to solving this problem?

reasonable because

A There are 2 gallons in a quart.

F You divide quarts by 2 to find gallons.

B There are 4 gallons in a quart. C There are 2 quarts in a gallon. D There are 4 quarts in a gallon.

G You divide quarts by 4 to find gallons. H You multiply quarts by 2 to find gallons. J You multiply quarts by 4 to find gallons.


NS 1.2; MR 1.1, 2.3, 2.5, 3.1, 3.2




P

Check for Reasonableness

PRACTICE


Choose the correct answer. The theater is 75 feet wide. The theater is twice as long as it is wide. Ned says the theater is 225 yards wide. Is this statement reasonable? 7. Which of these statements is false?

A B C D

The theater is 75 feet wide. The theater is 75 feet long. The theater is 150 feet long. The theater is twice as long as it is wide.

Solve. Explain your answer. 9. Tyler walks 4 miles from his home to the movie theater. He says he walks more than 20,000 feet. Is his statement reasonable?

11. Tammy’s sled is 65 inches long. She


says the sled is more than 5 feet long. Is her statement reasonable?

13. The popcorn stand sells 100 ounces

of popcorn. Ben says this is 1,600 pounds of popcorn. Is his statement reasonable?


8. Ned’s statement is not reasonable

because F You need to divide 75 by 3 to find the width in yards. G You need to multiply 75 by 3 to find the width in feet. H You need to divide 225 by 3 to find the width in yards. J You need to multiply 150 by 3 to find the width in feet. 10. A movie star is 6 feet tall. Meg says

that the movie star is more than 80 inches tall. Is her statement reasonable?

12. Earl’s house is 1,200 yards from the

bus stop. Earl says that is 3,600 feet. Is his statement reasonable?

14. The refreshment stand sells 144

ounces of peanuts. The manager says that this is more than 10 pounds of peanuts. Is his statement reasonable?

NS 3.2; MR 1.1, 2.3, 2.5, 3.1, 3.2



Explore Metric Length

P

PRACTICE

Estimate and then measure. Tell what unit and tool you use. 1. the width of your classroom 2. the largest step you can take 3. the width of a window in your classroom 4. the distance from the tip of your hand

to the elbow 5. thickness of a nickel


Circle the letter of the correct estimate. 6. the distance from Sue’s house to school

A. 2,000 mm B. 200 cm

C. 2 km

7. the length of a piece of chalk

A. 6 cm

B. 6 dm

C. 6 km

8. the height of a fourth-grader

A. 140 mm

B. 30 dm

C. 140 cm

9. the height of a door

A. 30 cm

B. 3 m

C. 300 mm

10. the length of a classroom

A. 7 cm

B. 7 m

C. 7 km

11. the distance from Chicago to New York

A. 1,200 km B. 5,000 m

C. 2,000 dm

12. the thickness of a book

A. 3 dm

B. 3 cm

C. 3 mm

13. the width of a pencil point

A. 1 dm

B. 1 cm

C. 1 mm

14. the length of Ben’s foot

A. 20 cm

B. 20 dm

C. 20 m

Problem Solving 15. Norma bicycles 1 km in 4 minutes.

About how many kilometers will she bicycle in 60 minutes?


16. One brick measures 92 mm. What is

its measurement to the nearest cm?

MR 1.1, 2.3



Explore Metric Length A centimeter (cm), millimeter (mm), decimeter (dm), and kilometer (km) are used to measure lengths in the metric system. 1cm

1 mm

R

RETEACH

Metric Units of Length 10 millimeters (mm) 1 centimeter (cm) 10 centimeters (cm) 1 decimeter (dm) 100 centimeters (cm) 1 meter (m) 1,000 meters (m) 1 kilometer (km) 1 dm

A kilometer measures large distances such as the distance from your school to a school in another town or city. Use a centimeter ruler to measure each object. Write the length. 1.

2.


3.

4.

Circle the letter of the correct estimate. 5. the width of a button

A. 18 cm

B. 18 mm

C. 2 mm

6. the length of a dollar bill

A. 15 dm

B. 15 mm

C. 15 cm


MR 1.1, 2.3



Explore Metric Length

E

ENRICH

Connect the Dots Use a centimeter ruler to connect only those dots that are the given distance apart. 2. 2 cm

3. 5 cm

4. 3 cm


1. 4 cm


MR 1.1, 2.3



Metric Capacity and Mass

P

PRACTICE

Estimate and then measure the capacity of each object. 1. a water glass

2. a large pot

3. a cereal bowl

4. a milk carton

5. Order the objects above from least to greatest capacity.

Estimate and then measure the mass of each object. 6. a box of crayons

7. a book

8. a paper clip

9. a pencil

10. Order the objects above from least to greatest mass.


Circle the letter of the correct estimate. 11.

A. 15 mL

B. 15 L

C. 2 L

12.

A. 3 mL

B. 31 L

C. 310 mL

13.

A. 200 mL

B. 200 L

C. 2 mL

14.

A. 15 g

B. 150 g

C. 15 kg


Liters Milliliters

1

2

1,000

Problem Solving 16. Sally buys 1 kg of grapes. She packs 200 g of grapes in her lunch. How many grams of grapes are left? Use with Grade 4, Chapter 9, Lesson 6, pages 380–383. (286)

3 4,000

17. Jim buys 1 L of milk. He drinks

300 mL for breakfast. How many milliliters of milk are left? MR 1.1, 2.3




R

Milliliters and liters measure capacity in the metric system.

1cm

RETEACH

Metric Units of Capacity 1,000 milliliters (mL) 1 liter (L)

1cm 1cm 1 Liter

A cube 1 centimeter (cm) long, 1 centimeter wide, and 1 centimeter high will hold 1 milliliter (mL) of water.

This bottle holds 1 liter (L) or 1,000 milliliters (mL) of water.

Mass is the amount of matter that makes up an object.

The mass of a paper clip is about 1 gram (g).

Metric Units of Mass 1,000 grams (g) 1 kilogram (kg)

The mass of the book is about 1 kilogram (kg) or 1,000 grams (g).


Circle the letter of the correct estimate. 1. mass of a bar of soap

A. 120 g

B. 120 kg

C. 12 kg

2. mass of an iron

A. 1 g

B. 100 g

C. 1 kg

3. amount of water in a bathtub

A. 100 mL

B. 100 L

C. 1,000 mL

4. mass of a horse

A. 500 g

B. 500 kg

C. 1,000 g

5. a bottle cap

A. 3 mL

B. 300 mL

C. 3 L


MR 1.1, 2.3




E

ENRICH

Who Invented It? Compare. Choose >, <, or . 1. 50 mL

5L

G

W

4. 1 L

B

B

7. 12 L

5. 8 L

T

H

10. 400 g

R

13. 1 kg

H

I

16. 10,000 g

R

C

M

I

U

C

I

8L

O 14. 7 kg

J

H

B

D

9. 5 kg

R

M

F

N 11 L

C

5,000 g M

12. 6,000 g

6,900 g

E

M

6. 10,000 mL

C 80 L

400 mL

L

7,500 mL

11. 8,400 mL

70 g

3. 3 L

8. 75,000 mL

E

4 kg

U

B

A

12,000 mL

T

3L

A

70 mL

L


2. 4,000 mL

R 15. 5 kg

G

P

A 6 kg

S

T

69,000 g R

S

12 kg S

T

Your backpack or windbreaker is probably made out of nylon. Who invented nylon? To find out, write the code letter for each answer. Write the letters in the order of the exercises. H. 1

2

3

4

5

6

7

8


9

10

11

12

13

14

15

16

MR 1.1, 2.3



Convert Metric Units

P

PRACTICE

Complete. 1. 5 m

2. 2 L

cm

4. 10 mm

5. 5 kg

cm

7. 3,000 mL

3. 7 kg

g

g

6. 2 m

dm

8. 300 cm

L

10. 6,000 mL

mL

L 11. 40 kg

13. 700 cm

14. 10 L

m

16. 10,000 g

12. 40 cm

mL

15. 2 km

m

18. 4 m

mm

22. 10 m

m

20. 3 dm

mm cm

mm

21. 5 L

23. 5 cm

mm

dm

mL

24. 600 mm

cm

25. 8,000 mm

26. 4,000 m

km

27. 7,000 mL

L

L

29. 70,000 g

kg

28. 20,000 mL

kg

g

kg 17. 6,000 cm

19. 20 cm

9. 4,000 g

m

cm

Compare. Write >, <, or .


30. 5,000 g

5 kg

31. 20 L

33. 60 cm

6m

34. 300 cm

36. 3 km

300 m

37. 900 mm

39. 500 dm

5 dm

40. 7 dm

200 mL 3m 9 cm 7,000 mm

32. 50 cm

6 dm

35. 2,500 mL 38. 13 L

2L 1,300 mL

41. 18,000 mL

18 L

Problem Solving 42. Dottie has 1 kg 200 g of food for her

cat. How many grams of cat food does she have?


43. A 1 L bottle of water is half full. How

many milliliters of water are in the bottle?

AF 1.3; MR 1.1, 2.3




R

RETEACH

You can convert metric units to compare. Metric Units Length

1 centimeter (cm) 10 milliliters (mm) 10 centimeters (cm) 1 decimeter (dm) 10 decimeters (dm) 1 meter (m) 1,000 meters (m) 1 kilometer (km)

Mass

1 kilogram (kg) 1,000 grams (g) 1 gram (g) 1,000 milligrams (mg)

Capacity

1 liter (L) 1,000 milliliters (mL)

Convert 9 dm to centimeters (cm).

Convert 6,000 mg to grams (g).

To convert a larger unit to a smaller unit, multiply.

To convert a smaller unit to a larger unit, divide.

Think: 1 dm 10 cm

Think: 1 g 1,000 mg

9 dm ? cm 9 dm 9 10 cm 9 dm 90 cm

6,000 g ? mg 6,000 g 6,000 1,000 mg 6,000 g 6 mg


Complete. 1. 5 m

cm

2. 8 L

3. 6 kg

g

4. 70 mm

5. 8 dm 7. 2,000 mL 9. 9 cm 11. 5,000 g

6. 2 m

cm L mm kg


8. 300 cm

mL cm dm m

10. 70 dm

m

12. 40 cm

dm

AF 1.3; MR 1.1, 2.3




E

ENRICH

Metric Match Game Use index cards to make the cards shown below.

10 mm

1 cm

5 km

500 cm

1,000 mm

1m

100 cm

1 km

10 cm

100 mm

1m

20 m

40 m

5m

200 dm

4 dm

5,000 m

1m

1,000 m

10 dm

20L

20,000 mL

5L

5,000 mL

500g

0.5 kg

59 kg

59,000 g

150,000 g

150 kg


• Mix up the cards and place them facedown. Players take turns turning over two cards. • If all players agree that the measurements on the two cards are equivalent, the player that turned them over keeps the cards and takes another turn. If the cards are not equivalent, turn them facedown again. The next player turns over two cards. • Play until there are no more cards left. The player with the most pairs of cards wins.


AF 1.3; MR 1.1, 2.3




P

PRACTICE

Logical Reasoning Use logical reasoning to solve each problem. 1. An aquarium worker needs to fill a tank with 10 gallons of water. He has an 8-gallon pail and a 6-gallon pail. How can he use the pails to get exactly 10 gallons of water in the tank?

3. The parrot house has 2 times as

many birds as the toucan house. The toucan house has 3 more birds than the jay house. The jay house has 6 birds. How many birds do the other houses have?


Mixed Strategy Review Solve. Use any strategy. 5. Language Arts Kenny writes a 740-word review of a play. The review needs to be cut so that it is 500 words. How many words have to be cut? Strategy: 7. A bandstand is 40 feet wide by 80 feet long. It is built from wood planks that are 5 feet wide by 10 feet long. How many planks wide will the platform be? How many planks long?

2. Simon needs to put 9 cups of sea

salt into a saltwater tank. He has a 10-cup container and a 7-cup container. How can Simon use the containers to measure 9 cups?

4. The parrots get food 20 minutes before

the toucans. The toucans get food 15 minutes after the jays. The jays get food 30 minutes after Bird World opens. Bird World opens at 10:00 A.M. When does each kind of bird get food?

6. There are 24 cars in the theater

parking lot. There are 3 times as many 4-door cars as 2-door cars. How many of each kind of car are there? Strategy: 8. Create a problem which you could solve by using logical reasoning. Share it with others.


MR 1.1, 2.3, 3.1, 3.2




R

RETEACH

Logical Reasoning Page 387, Problem 1

Dan needs to put 6 cups of sea salt into the saltwater tank. He has a 7-cup container and a 5-cup container. How can he use the containers to measure 6 cups? Step 1

Read

Be sure you understand the problem. Read carefully. What do you know? • Dan needs to put

cups of sea salt in a saltwater tank.

• Dan has containers that hold

cups and

cups.

What do you need to find? • You need to find how to use the containers to measure cups. Step 2

Plan ■

■

■


■

■

■

■

■

■

■

Make a Table or List Write a Number Sentence Work Backward Act it Out Find a Pattern Make a Graph Guess and Check Logical Reasoning Solve a Simpler Problem Draw a Diagram


Use logical reasoning to solve the problem. You can use the difference in the amount each container can hold to measure exactly 6 cups.


MR 1.1, 2.3, 3.1, 3.2




R

RETEACH

Logical Reasoning Step 3 Carry out your plan.

Solve

Complete the table. It will show how to use the 7-cup container and the 5-cup container to measure exactly 6 cups. Sea Salt in Sea Salt in 7-cup Container 5-cup Container

Steps

Sea Salt in Tank

1. Fill the 7-cup container.

0

0

2. Fill the 5-cup container

5 cups

0

from the 7-cup container. 3. Pour what is left in the

7-cup container into the tank. 4. Repeat steps 1–3. How much sea salt is in the tank now? 5. Repeat steps 1–3. How much sea salt is in the tank now?

0

5 cups

0

5 cups

0

5 cups

Step 4

Look Back



How can you check your answers?

Practice 1. A worker has a 4-gallon pail and a 9-gallon pail. How can he use pails to fill a 10-gallon tank with water?


2. Marcia arrives at the theater

10 minutes before Sam. Sam arrives 25 minutes after Lynn. Paul arrives 10 minutes before Lynn. Lynn gets to the theater at 6:30 P.M. When do the others arrive at the theater?

MR 1.1, 2.3, 3.1, 3.2


Temperature: Fahrenheit and Celsius


P

PRACTICE

Give a reasonable temperature for each. Then use Fahrenheit and Celsius thermometers to measure each temperature. 1. warm water

2. temperature in freezer

3. cool water

4. temperature in cafeteria

5. temperature outside

6. temperature in classroom


Circle the letter of the correct estimate. 7. to go skiing

A. 20°C

B. 20°F

8. to swim in the swimming pool

A. 80°C

B. 80°F

9. to go to the beach

A. 30°C

B. 30°F

10. to sleep comfortably

A. 20°C

B. 20°F

11. to work in the garden

A. 70°C

B. 70°F

12. to shiver without a coat

A. 20°C

B. 20°F

13. to picnic in the park

A. 25°C

B. 25°F

14. to rake leaves

A. 10°C

B. 10°F

15. to go sledding in the snow

A. 30°C

B. 30°F

16. to walk your dog

A. 65°C

B. 65°F

Problem Solving 17. The temperature of a can of soup on

the shelf is 45°F. Joy heats the soup to 25°F above its shelf temperature. What is the soup’s temperature now?


18. At noon the temperature of the

water in a swimming pool was 25°C. At 9:00 P.M. the temperature was 17°C. By how much did the water temperature drop?

NS 1.8; MR 1.1, 2.3




R

RETEACH

Temperature is measured in degrees Celsius (°C) or in degrees Fahrenheit (°F). Compare the two scales shown at the right.

230 220 210 200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0 –10 –20 Fahrenheit Celsius 110

100

90

80

70

60

50

40

30

20

10

0

– 10

– 20

–30

Write the temperature in degrees Celsius (°C) and degrees Fahrenheit (°F). 1.

2.

10

0

– 10

– 20

10

0

– 10

4. 170

160

150

140

130

70

60

50

– 10

– 20

– 20

Circle the letter of the correct estimate. 5. the temperature of cold water

120

20

10

0

–10 –20


40

30

20

10

0

60

50

40

30

20

3.

A. 10°C

B. 10°F

6. the temperature of warm water

A. 100°C

B. 100°F

7. the temperature of a fever

A. 39°C

B. 39°F

8. room temperature

A. 70°C

B. 70°F

9. temperature at an outdoor ice rink

A. 20°C

B. 20°F

10. temperature on a hot beach

A. 30°C

B. 30°F

11. comfortable outdoor temperature

A. 10°C

B. 10°F


NS 1.8; MR 1.1, 2.3




E

ENRICH

Predicting Temperatures Label the thermometers below with the following temperatures: 10°C 20°C 30°C 40°C 50°F 68°F 86°F 104°F 70

0°C

70

60

60

50

50

40

40

30

30

20

20

10

10

0

0

– 10

– 10

– 20

– 20

– 20

– 20

150 140 130 120 110 100 90 80 70

150 140 130 120 110 100 90 80 70

60 50 40 30 20 10 0

60 50 40 30 20 10 0 –10 –20

–10 –20

100°F

32°F

Fahrenheit

Celsius


The thermometers are drawn so that equivalent measures are the same height on both scales. 1. Write the equivalent temperatures in degrees Fahrenheit. Use the thermometers above to help you. 10°C

20°C

30°C

40°C

2. When the Celsius temperature changes 10 degrees, how much

does the Fahrenheit temperature change? 3. What pattern do you see that will help you predict Fahrenheit

temperatures based on Celsius temperatures?


NS 1.8; MR 1.1, 2.3



Print This Page


Applying Measurement Record your data. Items

Ingredients

Amount of Each Cost of Each Ingredient Ingredient

Total Cost for Item

Sandwiches

Fruit Salad


Punch

Your Decision How much of each item should Mr. Martin make for the birthday party? Explain.


MR 1.1, 2.3


Problem Solving: Application Which color heats up the most?

Print This Page


Record the temperature of each thermometer. Start Temperature Finish Temperature

Difference

Black Paper

White Paper

Aluminum Foil

1. Find the difference between each start and finish temperature.

Show your work.


Work Space

2. Which color heated up the most? The least?


NS 1.2; MR 1.2, 2.3, 2.6, 3.3


Print This Page



Math & Science

Which color heats up the most? 3. Use subtraction to find how many more degrees the hottest

thermometer changed than the coolest. Show your work. Is this a big difference?

Work Space

4. Why did you have to put the thermometers under the sun or a lamp?

5. If you were playing outside on a sunny day, which color clothing


would you like to wear? Why?

6. Explain the results of the activity in terms of reflection or

absorption of light.


NS 1.2; MR 1.2, 2.3, 2.6, 3.3



3-Dimensional Figures

P

PRACTICE

Identify the 3-dimensional figure the object looks like. Tell how many faces, edges, and vertices it has. 1.

2.

3.

4.

5.

6.


Copy and fold. Identify the 3-dimensional shape. 7.

8.

9.

10.

Algebra & Functions 11. What could the next shape be?


MG 3.6




R

RETEACH

A 3-dimensional figure usually rests on one of its faces, which is called a base. Look at the cube below. Count the number of faces, vertices, and edges it has.

face

edge

A cube has 6 faces.

A cube has 12 edges.

vertices A cube has 8 vertices.

Complete the chart.


Name 3Dimensional Figure

1.

triangular prism

2.

rectangular prism

3.

triangular pyramid

4.

square pyramid

5.

cone

6.

cylinder

7.

sphere

Shape of Base


Number of Flat Faces and Bases

Number of Straight Edges

Number of Vertices

MG 3.6




E

ENRICH

Polyhedrons The 3-dimensional figures shown below are called polyhedrons. • Each face of a polyhedron is the same size and shape. • Each edge of a polyhedron is the same length. • Each angle of each face is equal.

Cube

Tetrahedron

Dodecahedron

Icosahedron

Octahedron

Look at the cube. • It has 6 square faces. • Each square face has 4 edges. • Since 2 sides meet at each edge, a cube has (6 4) 2 12 edges. Use the information about polyhedrons to complete the sentences. 1. A tetrahedron has 4 triangular faces.


Each triangular face has edges. (4 A tetrahedron has edges. 2. An octahedron has

Each triangular face has An octahedron has 3. A dodecahedron has

Each pentagonal face has A dodecahedron has

)2

triangular faces. edges. edges. pentagonal faces. edges. edges.

4. An icosahedron has 20 triangular faces.

Each triangular face has An icosahedron has

edges. edges.


MG 3.6


2-Dimensional Figures and Polygons


P

PRACTICE

Tell whether each figure is open or closed. Is it a polygon? If so, classify the figure. 1.

2.

3.

4.

5.

6.

Draw the figure and identify it. Use a separate sheet of paper. 7. a 4-sided figure that is not a square

9. a 6-sided figure

8. a 5-sided figure

10. an 8-sided figure

Algebra & Functions Locate each set of points. Then connect the points to make a geometric figure. Identify the figure.


11. (2, 2), (4, 3), (3, 5)

12. (2, 2), (5, 2), (5, 3), (2, 3)

5 4 3 2 1

5 4 3 2 1 O

1 2 3 4 5


O

1 2 3 4 5

MG 3.8




R

RETEACH

A polygon is a closed 2-dimensional figure that has straight sides. These figures are not polygons. Open Figures

Closed Figures

These figures are polygons.

square 4 straight sides

rectangle 4 straight sides

triangle 3 straight sides

pentagon 5 straight sides

hexagon 6 straight sides

octagon 8 straight sides


Identify each polygon. 1.

2.

3.

4.

5.

6.


MG 3.8



E


ENRICH

Tangrams A tangram is a Chinese puzzle that is made of 2-dimensional figures. The figures can be put together to form different shapes— sometimes even animal shapes!


Cut out the five figures at the bottom of the page. Use all five figures to form each of the large polygons shown below.

1. tangram 1

2. tangram 2

3. tangram 3

4. tangram 4

Tangrams:

G


C

MG 3.8



Lines, Line Segments, and Rays

P

PRACTICE

Identify each figure. 1.

B

A

2. C

3. D

4. I

L

K

J

5.

Q S

l

T

R

6. M

N

O

P

Identify the parts of a circle. 7.

8.


G

O

9.

H K

T V S

Algebra & Functions Locate the set of points. Then connect the points to draw line segments. Classify the lines as perpendicular or parallel. 10. Line segment OP:

6

(1, 4) (2, 4) (3, 4) (4, 4)

5

Line segment QR: (1, 2) (2, 2) (3, 2) (4, 2)

4 3 2 1 1


2

3

4

5

6 MG 3.1, 3.2




R

RETEACH

A line goes on forever in both directions

A line segment is part of a line. It has two endpoints.

A ray has one endpoint.

Parallel lines never meet.

Intersecting lines meet.

Perpendicular lines form square corners.

A chord is a line that connects two points on a circle.

A diameter is a chord that goes through the center of the circle.

A radius is the distance from the center of a circle to every point on a circle.


Identify each figure. 1.

2.

3.

4.

5.

6.

8.

9.

Identify the parts of a circle. 7.


MG 3.1, 3.2




E

ENRICH

Can You Trace a Figure Without Lifting Your Pencil? 1. Look at Figure A and Figure B below. Can you trace each figure

without lifting your pencil or retracing any line? Vertex 2 E O Vertex 3

Vertex 1 O

E Vertex 2

Vertex 1 E

E Vertex 4

Vertex 5 E

E Vertex 3

Vertex 4 E

Figure A

Figure B

2. Can you trace Figure B without lifting your pencil if you start at any vertex?

3. Can you trace Figure A without lifting your pencil if you start at any vertex?

4. In Figure A, Vertex 4 has an even number of lines that meet at that point.

This vertex can be called an even vertex. Vertex 3 has an odd number of lines meeting at that point. Vertex 3 can be called an odd vertex. Label each vertex in the figures. Write E for an even vertex and O for an odd vertex. 5. Can you trace the figures below without lifting your pencil or retracing any

line? Label each vertex even or odd. O

O

E

O

O

O


E O

Figure C

E

E

O

E

Figure D

O

Figure E

6. What conclusion can you draw about whether you can trace a figure

without lifting your pencil? Hint: Think about the types of vertices a figure has.


MG 3.1, 3.2



Angles

P

PRACTICE

Write acute, obtuse, or right for each angle. 1.

2.

3.

4.

5.

6.

Write the degree measure and fraction of a turn for each angle. 7.

8.

9.

Draw each figure. 11. a 3-sided figure with 3 acute angles


10. a 4-sided figure with 1 right angle


MG 3.5



Angles

R

RETEACH

Angles are formed by two rays that have the same endpoint.

A right angle forms a square corner.

An acute angle is less than a right angle.

An obtuse angle is greater than a right angle.

Identify each angle. Write acute, obtuse, or right. Use the corner of a sheet of paper to help you. 1.

2.

3.

4.

5.

6.

7.

8.


Complete. 9.

10.

This triangle has 3

11.

This kite has 2

angles.

This pentagon has

angles and

2

angles,

angles.

2

angles, and

1

angle.

2


MG 3.5



Angles

E

ENRICH

Angle Sums What is the sum of the angles of a triangle? The sum will always be 180º or a straight line. Follow the steps below. 1

1 1

3

2

3

2

2

3

Step 1:

Step 2:

Step 3

Draw a triangle. Then draw lines to show each angle. Shade and number the 3 angles.

Cut along the lines.

Place the corners of the pieces together to form a straight line.

Follow Steps 1–3 for each triangle below. 1.

2.

3.

2 1

1

3

3

2 1

Triangle 1

Triangle 2

3

2

Triangle 3


4. What do you think the sum of the angles of a quadrilateral is?

5. Draw a quadrilateral. Draw lines to show the 4 angles. Then shade

the corners, cut them out, and put them together to see if you are correct.

Use with Grade 4, Chapter 10, Lesson 4, pages 420-421. (312)

MG 3.5



Triangles and Quadrilaterals

P

PRACTICE

Classify each triangle as equilateral, isosceles, or scalene. Then classify each triangle as right, acute, or obtuse. 1.

2.

3.

5.

6.

Identify each quadrilateral. 4.

Tell if each statement is true or false. Explain why. 7. All rectangles are parallelograms.

8. All squares are rhombuses.

9. Some right triangles are also equilateral triangles.


Problem Solving 10. Sue’s desk has equal sides of 20

inches and 4 right angles. Nancy’s desk has two sides of 20 inches, two sides of 30 inches, and 4 right angles. Both say their desks are rectangles. Who is correct?


11. Mike makes a square out of wooden

sticks. He pushes one corner of the square and makes a rhombus. How are the square and rhombus alike? How are they different?

MG 3.7, 3.8




R

RETEACH

You can classify a triangle by the lengths of its sides or the measures of its angles. An equilateral triangle has three sides of equal length.

An isosceles triangle has at least two sides of equal length.

A scalene triangle has no sides of equal length.

An acute triangle has three acute angles (less than 90º).

An obtuse triangle has one obtuse angle (greater than 90º and less than 180º).

A right triangle has one right angle (exactly 90º).

All quadrilaterals have 4 sides and 4 angles. A square has 4 equal sides and 4 right angles.

A rectangle has 4 right angles. Its opposite sides are equal and parallel.

A rhombus has 4 equal sides. Its opposite sides are parallel.

A trapezoid has 1 pair of parallel sides.

A parallelogram has opposite sides that are equal and parallel.

Classify each triangle by its sides and angles.


1.

2.

3.

Identify each quadrilateral in as many ways as you can. 4.

5.


6.

MG 3.7, 3.8




E

ENRICH

Geometry Bingo Play this bingo game with 2–3 players. • Work together to make the bingo game. On an index card, write each of the names for geometric figures shown in the box below. • Then draw each figure in one of the squares on the bingo card below. Be sure to mix up the names. • Shuffle the index cards and place them face down. • Players take turns drawing index cards. Each player places a game marker on the matching figure drawn on the bingo card. • The first player to have markers that fill any row, column, or diagonal wins. parallel lines parallelogram radius rhombus hexagon isosceles triangle


B

intersecting lines ray right angle octagon acute triangle obtuse triangle

I

perpendicular lines chord acute angle cube equilateral triangle right triangle

N

G

line segment diameter obtuse angle pentagon trapezoid scalene triangle

O

FREE


MG 3.7, 3.8




P

PRACTICE

Reading Skill

Use a Diagram Use the illustration to solve problems 1–2.

1. Howie used the above figure in a painting. Describe the figure in

more than one way.

2. What shape could Howie add to the right side of the figure so that

the figure becomes a trapezoid? Add the shape to the figure.

Use the illustration below to solve problems 3–4. 4 ft

4 ft


4 ft 6 ft

4 ft 3. Phyllis designed this doorway. What two shapes make up

this doorway?

4. What is the length of the missing side of the doorway?


MG 3.1, 3.7, 3.8; MR 1.1, 2.3, 2.4, 3.2




P

Use a Diagram


Choose the correct answer. This figure is composed of a parallelogram and an equilateral triangle. What is the length of Side A of the triangle? 1. Which statement is true?

A All sides of the figure are the same length. B Side A has the same length as one side of parallelogram. C The length of Side A must be greater than 6 inches.

PRACTICE

6 in. 4 in. A 2. What is the length of Side A?

F 4 inches G 6 inches H 12 inches

4 in.

This figure is composed of a rhombus and a triangle. Can the length of side B be 8 inches long?

B 4 in.

3. Which statement is true?


A The length of side B must be greater than 8 inches. B The length of side B must be less than 8 inches. C The length of side B must be equal to 8 inches. This figure is composed of an isosceles triangle and a rectangle. What is the length of Side C? 5. You can find the length of Side C

because A two sides of an isosceles triangle are equal. B the length of Side C is greater than the lengths of the other two sides of the triangle. C no two sides of the triangle have equal lengths. Use with Grade 4, Chapter 10, Lesson 6, pages 426–427. (317)

4. Can the length of side B be

8 inches long? F Yes G No H The answer cannot be found using the information in the diagram.

C

10 cm

3 cm 6 cm 6. What is the length of Side C?

F 3 centimeters G 6 centimeters H 10 centimeters MG 3.1, 3.7, 3.8; MR 1.1, 2.3, 2.4, 3.2




P

Use a Diagram

PRACTICE


Choose the correct answer. This figure is a parallelogram. Suppose you draw a line segment from point A to point C. The length of this segment is 5 cm. How would you describe the two new figures you made? 7. Which of these statements is true?

A You cannot tell the lengths of the unlabeled sides of the parallelogram. B Only two sides of the parallelogram have a length of 2 centimeters. C Each side of the parallelogram has the length of 2 centimeters.

A

B

2 cm D

C

6 cm

8. How would you describe the two

new figures you made? F They are scalene triangles. G They are isosceles triangles. H They are equilateral triangles.

Solve. Use data from the illustration to answer problems 9–10. 9. Orson designed this picture frame.

What shapes make up the frame? What shape is made by the outer edge of the frame?

10. Suppose Robert added 2 feet to the


height of the frame, but kept the width the same. What shape would be made by the outer edge of the frame?

12. Robert drew a square. Then he divided

the shape into two parts by drawing a line from one corner of the square, through the center, to the opposite corner. Name two ways to describe the two smaller shapes he created.


3 ft

3 ft

11. Wendy drew a triangle in which

three angles were less than 90°. What kind of triangle did she draw?

13. Max draws a rectangle with sides of

6 inches and 9 inches. He uses one of the short sides of the rectangle as a side of a scalene triangle. Can the lengths of the other two sides of the triangle be 6 inches? Explain.

MG 3.1, 3.7, 3.8; MR 1.1, 2.3, 2.4, 3.2



Congruent and Similar

P

PRACTICE

Write whether the figures are similar. Then write whether the figures are congruent. 1.

2.

3.

4.


Copy the figure on a separate piece of dot paper. Then draw one congruent figure and one similar figure. 5.

6.

7.

8.

9.

10.

Algebra & Functions Use separate grid paper. 11. Draw a figure on a coordinate grid. Then draw a similar figure

that is one half the size of the original. Write the ordered pairs for all vertices. 12. Draw a figure on a coordinate grid. Then draw a similar figure

that is two times the size of the original. Write the ordered pairs for all vertices. Use with Grade 4, Chapter 10, Lesson 7, pages 430–433. (319)

MG 3.3, 3.4




R

RETEACH

Similar Figures

Congruent Figures

Not congruent Not similar

• same shape • may be different sizes

• same shape • same size

• not the same shape • not the same size

To see if figures are congruent, trace one figure. If you can make it fit exactly on top of the other figure, the figures are congruent.


Write whether the figures are similar. Then write whether the figures are congruent. You may trace the figures. 1.

2.

3.

4.

5.

6.


MG 3.3, 3.4




E

ENRICH

Shape Detective Can you find the similar and congruent figures in the drawings below? Each figure in the drawings can be named with one or more letters. Look at the first drawing. Figure A is the rectangle in the upper left corner. Figure AB is the top rectangle. Complete the sentences. The first one is done for you. 1. Figure B is similar to Figure ABCD. 2. Figure C is congruent to Figure

A

B

D

C

.

3. Figure BC is congruent to Figure

.

4. Figure EF is similar to Figure

.

F G 5. Figure F is congruent to Figure

and Figure

E

H

.

I 6. Figure I is

to Figure EF.

7. How many sets of congruent and similar


figures can you find in the drawing at the right? Name each pair or set of figures.

J

N

O Q P M


K L

MG 3.3, 3.4


Explore Translations, Reflections, and Rotations


P

PRACTICE

Write translation, reflection, or rotation to describe how the figure was moved. 1.

2.

3.

4.

5.

6.

Draw the movement of each figure on the dot paper.


7. translation

9. translation, then rotation

8. reflection

10. rotation, then reflection


MG 3.4




R

RETEACH

You can move figures in different ways.

You can slide a figure across a line to show a translation.

You can flip a figure over a line to show a reflection.

You can turn a figure around a point to show a rotation.


Write translation, reflection, or rotation to tell how each figure was moved. 1.

2.

3.

4.

5.

6.

7.

8.

9.

Use with Grade 4, Chapter 10, Lesson 8, pages 434-435 (323)

MG 3.4




E

ENRICH

Shape Art Cut out the shape cards and turn them face down. Then cut out the movement cards. Place those cards face down in another pile. Choose one shape card. On another sheet of paper, trace that shape. Then choose a movement card. Follow the instructions on that card. Return the movement card to the bottom of the pile, and choose another movement card. Repeat until you have chosen 4 movement cards. Trade your artwork with a partner. Try to guess which movement cards your partner chose to create the drawing. Movement Cards Translation

Reflection

Rotation

Slide your shape 1 inch to the right. Trace it again.

Flip over your shape to the right. Trace it again.

Turn your shape around a point. Trace it again.

Shape Cards

Sample Artwork © McGraw-Hill School Division

Which cards were chosen to draw this artwork?

Create another shape and another rule for a movement cards.


MG 3.4



Symmetry

P

PRACTICE

Is the dotted line a line of symmetry? 1.

2.

3.

4.

5.

6.

Is the figure symmetrical? If yes, draw its lines of symmetry. 7.

8.

9.


10. On a separate sheet of paper, draw a figure with rotational symmetry.

11. On a separate sheet of paper, draw a figure with bilateral symmetry.

Complete the drawing to make it symmetrical. 12.

13.


14.

MG 3.4



Symmetry

R

RETEACH

Follow these steps to find out if a figure has bilateral symmetry. Step 1: Trace Figure A and cut it out. Step 2: Fold it along one of the dashed lines.

The two halves match. The dashed line is a line of symmetry. The figure has bilateral symmetry. Step 3: Unfold the figure. Step 4: Fold the figure along the other

dashed lines. The halves match, so all the lines are lines of symmetry.

Figure A

Follow these steps to find out if Figure B has rotational symmetry. Step 1: Trace Figure B and cut it out. Step 2: Place it on top of the original

Figure B. Put your pencil point on the dot in the center. Step 3: Turn the top figure 90º. The top

figure matches the original figure. Step 4: Turn the top figure 180º. The

figures match. Figure B has rotational symmetry.

Figure B


1. Place Figure A you traced on top of original Figure A.

Put your pencil point in the center. Turn the top of figure 180º. Does the top figure match the original? Does Figure A have rotational symmetry? 2. Fold Figure B you traced to find its lines of symmetry.

How many lines of symmetry does Figure B have? Look at each figure. Is the dashed line a line of symmetry? Then trace each figure. Turn it to see if it has rotational symmetry. 3.

4.


5.

MG 3.4



Symmetry

E

ENRICH

Circle each letter that has one or more lines of symmetry.


Draw the line or lines of symmetry.

G4_C10_L09_E01_MA01


MG 3.4


Print This 10–10Page


P

PRACTICE

Find a Pattern Use data from this tessellation to solve problems 1–4. 1. What shapes do you see in a repeated pattern?

2. How are the shapes moved?

3. Complete the missing pieces of the

pattern. 4. Suppose you extend this design. You

have a total of 20 small right triangles. How many rhombuses will there be in all?


Mixed Strategy Review Solve. Use any strategy. 5. Aaron buys 5 Picasso T-shirts for his family. A large T-shirt costs $15 and a small T-shirt costs $12. Aaron spends $69. How many large T-shirts does he buy? How many small T-shirts does he buy?

Strategy: 7. Mr. Ervin has 32 jars of paint. He has

small boxes that will hold 4 jars and a large box that will hold 6 jars. Which box should Mr. Ervin use if he wants to put an equal number of jars in each box? How many boxes will he need?

6. Art On May 15, 1990, a painting by

Van Gogh sold for $75,000,000. Two days later, a painting by Renoir sold for $4,000,000 less than that amount. How much did Renoir’s painting sell for?

Strategy: 8. Create a problem which involves

finding a pattern in a tessellation. Share it with others.


MG 3.8; MR 1.1, 2.3, 2.4, 3.2




R

RETEACH

Find a Pattern Page 441, Problem 1

What shapes do you see in a repeated pattern? How are the figures moved?

Step 1

Read

Be sure you understand the problem. Read carefully. What do you know? • The illustration shown is a tessellation. What do you need to find? • You need to identify .

Step 2

Plan © McGraw-Hill School Division

■

■

■

■

■

■

■

■

■

■

Find a Pattern Guess and Check Work Backward Make a Graph Make a Table or List Write a Number Sentence Draw a Diagram Solve a Simpler Problem Logical Reasoning Act It Out


Looking for a pattern will help you solve the problem. Find shapes that look familiar. Look for a pattern to see how these shapes have been moved.


MG 3.8; MR 1.1, 2.3, 2.4, 3.2




R

RETEACH

Find a Pattern Step 3

Solve

Carry out your plan.

Look for shapes you know. What shapes do you see?

To find how these shapes have been moved, look for examples of rotations, translations, and reflections. What is one way to describe how the figures moved?

Step 4

Look Back

Is the solution reasonable? Reread the problem. Did you answer the question?

Yes

No



Practice Use data from this tessellation to solve.

1. What shapes do you see in a repeated

pattern? How are they moved?


2. Complete the missing pieces of the

tessellation.

MG 3.8; MR 1.1, 2.3, 2.4, 3.2



Perimeter

P

PRACTICE

Find the perimeter of each figure. 1.

2.

10 cm

3.

10 mm

8 mm 8 mm

5 cm

9 mm

7 cm 4 cm

11 mm

6 mm

4.

8 mm

11 mm

5.

11 mm

6.

Algebra & Functions Find the length of each missing side. 7.

8. 8 in.

8 in.

9.

8 ft

11 yd 11 yd

4 ft

11 yd 11 yd

perimeter 24 in.

perimeter 24 ft

perimeter 55 yd


Problem Solving 10. Gerry plans a rectangular garden

plot that is 30 ft long and 15 ft wide. What is the perimeter of the garden plot?


11. A fence around a rectangular corral

has a length of 180 ft and a width of 90 ft. What is the perimeter of the fence?

NS 3.1; MG 3.8



Perimeter

R

RETEACH

Perimeter is the distance around a closed figure. To find the perimeter, add the lengths of all the sides. To find the perimeter of the rectangle, add the lengths of the sides. 10ft 15ft 10ft 15ft 50ft

15 ft 10 ft

10 ft 15 ft

The perimeter of the rectangle is 50 ft.

Find the perimeter of each figure. 1.

2. 4 in.

5 in.

4 in.

5 in.

5 in.

5 in.

4 in.

3.

4. 4 ft

4 ft

7m 5m


7.

6 dm 6 dm

6 dm

6 dm

6 dm 6 dm

5.

8 ft 8 ft

5m

8.

4 in. 5 in. 3 in. 6 in.


8 ft 8 ft

7m

3 ft

6.

5 cm

5 cm

6 cm

6 cm 7 cm

NS 3.1; MG 3.8


Perimeter


E

ENRICH

Create a Perimeter Each square at the right is divided into three regions. Each region has a perimeter of 8 units.

The square at the right is divided into two regions. Each region has a perimeter of 10 units.

Divide each square below into the number of regions and the perimeter given. Try to do this in two different ways. 1. Number of regions: 4

Perimeter of each region: 10 units

2. Number of regions: 5



3. Number of regions: 6



NS 3.1; MG 3.8



Area

P

PRACTICE

Find the area of each figure. 1.

4.

4 ft

2.

3.

5.

6.

2 yd

2 in. 5 yd

4 ft 2 in.

Use graph paper to draw each figure. Tell what the figure is and find the area. 7. length: 5 cm

width: 8 cm

8. length:7 cm

9. length: 7 cm

width: 7 cm

width: 4 cm


Find the area and perimeter of each figure. 10.

12 cm 10 cm

11. 1 m

12. 4m


6 mm 25 mm

MG 1.2, 1.3; AF 1.4



Area

R

RETEACH

Area is the number of square units needed to cover a region or figure. You can use these two ways to find the area of a rectangle or square. • Count the number of square units. There are 25 square units. The area is 25 square units. • Multiply the length times the width. 5 5 25 The area is 25 square units. Complete. 1.

2.

length:

units

length:

units

width:

units

width:

units

area

square units

area

square units

Find the area of each figure. 3.

4.

5. 4 in.

3 ft

2 in. 4 in.


8 ft

7 in.

6.

7.

8.

9 ft

4m

3 yd

6 ft 5 yd


6m

MG 1.2, 1.3; AF 1.4



Area

E

ENRICH

Pick’s Law Pick’s law can be used to find the area of any polygon. Draw the polygon on dot paper. Use this formula:

A

1 2 (number of dots on the polygon) 1 (number of dots inside the polygon)

Here’s how to use the formula to find the area of this polygon below.

A ( 12 12) 1 3 A (6 1) 3 A53 A8


Find the area of each polygon. 1.

2.

3.

4.

5.

6.


MG 1.2, 1.3; AF 1.4



Explore Volume

P

PRACTICE


Find the volume of each rectangular prism. 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13. length: 9 in.

14. length: 5 m

15. length: 7 cm

16. length: 10 ft

width: 5 in.

width: 8 m

width: 2 cm

width: 12 ft

height: 4 in.

height: 6 m

height: 8 cm

height: 5 ft


NS 3.1; MG 1.4



Explore Volume

R

RETEACH

Volume is the amount of space a 3-dimensional figure encloses. Volume is measured in cubic units. You can use these two ways to find the volume of a rectangular or square prism. • Count the number of cubes in one layer. The bottom layer has 12 cubes. There are 3 layers. 12 12 12 36 The volume of the cube is 36 cubic units. • Multiply: length width height V length width height V 4 3 3 36 The volume is 36 cubic units.

3 4 3

Find the volume of each rectangular prism.


1.

2.

3.

length:

length:

length:

width:

width:

width:

height:

height:

height:

volume

volume

cm3

4.

5.

2 cm

3 cm

4 cm 4 cm

2 cm

6 cm


volume

cm3

6.

cm3

2 cm 2 cm 5 cm

NS 3.1; MG 1.4



Explore Volume

E

ENRICH

Volume Patterns 1. What is the volume of Prism A? 3 cm 2 cm 4 cm

Prism A 2. What do you think will happen to the

volume if you double the length, width, and height of Prism A?

6 cm

4 cm 8 cm

Prism A Doubled 3. Find the volume of Prism A doubled.

Was your answer to exercise 2 correct?

4. Complete the table.


Original Rectangular Prism Length 2 cm 2 cm 1 cm 2 cm

Width 2 cm 3 cm 2 cm 2 cm

Height 1 cm 3 cm 3 cm 2 cm

Volume

Doubled Rectangular Prism Length 4 cm 4 cm 2 cm 4 cm

Width 4 cm 6 cm 4 cm 4 cm

Height 2 cm 6 cm 6 cm 4 cm

Volume

5. Compare the volumes of the original and doubled prisms. What

pattern do you see?


NS 3.1; MG 1.4


Problem Solving: Application Analyze Data and Make Decisions

Print This Page


Record your data in the chart.


Size of Garden

Perimeter of Garden

Cost of Fencing Material

Cost of Fencing and Installation

Your Decision What is your recommendation for Mr. Harris’s garden? Explain.


MG 1.1, 1.2, 1.3, 1.4; MR 1.1, 2.3



Print This Page


How well do you make patterns? Record your ratings. Drawing of Structure

Rating: 1 (best)–5 (worst)


1. How well did you follow directions? Do you have enough data to decide?


MG 3.3, 3.4, 3.7, 3.8; MR 1.1, 2.3, 3.2


Print This Page



Math & Science

How well do you make patterns? 2. What was easy or hard when giving directions?

3. What was easy or hard when following directions?


4. Make a list of words that helped you give directions.

5. Describe how a camouflage pattern gives some animals a

survival advantage.


MG 3.3, 3.4, 3.7, 3.8; MR 1.1, 2.3, 3.2



Parts of a Whole

P

PRACTICE

Write a fraction for the part that is shaded. 1.

2.

3.

4.

5.

6.

7.

8.


Draw a rectangle with the fraction shaded. 9. 1 3

10. 4 5

11. 5 7

12. 4 8

13. 4 9

14. 5 6

Use with Grade 4, Chapter 11, Lesson 1, pages 470-471. (343)

NS 1.5, 1.7



Parts of a Whole

R

RETEACH

A fraction can name parts of a whole.

4 parts shaded 7 parts in all 4 7 shaded

2 parts shaded 5 parts in all 2 5 shaded

parts shaded → 4 → numerator parts in all → 7→ denominator

parts shaded → 2 → numerator parts in all → 5 → denominator

Complete to write a fraction for the part that is shaded. 1.

2.

part shaded

parts shaded

parts shaded

parts in all

parts in all

parts in all

fraction 4.


3.

fraction 5.

fraction 6.

part shaded

parts shaded

parts shaded

parts in all

parts in all

parts in all

fraction

fraction


fraction

NS 1.5, 1.7



Parts of a Whole

E

ENRICH

Fraction Design Design a quilt. Use red, white, blue, and purple crayons to color the squares below.

1. What part of your quilt is red?

blue?

purple?

white? .


Design a flag. Use red, yellow, green, and blue crayons.

2. What part of your flag is red?

green?

yellow?

blue?


NS 1.5, 1.7



Parts of a Group

P

PRACTICE

Write a fraction that names what part is shaded. 1.

2.

3.

4.

5.

6.

Draw a picture, and then write a fraction. 7. Six of eleven balloons are blue.


9. All of five kittens are smiling.

8. Four out of seven hats have stars.

10. One of four animals is a chimpanzee.

Problem Solving 11. Five of 12 students are in the school

chorus. What part of the students are in the chorus?


12. Twenty of 25 students voted for class

president. What part of the class did not vote for president?

NS 1.5, 1.7



Parts of a Group

R

RETEACH

A fraction can name part of a group. There are 7 squares in all. 3 7

are shaded.

4 7

are not shaded.

5 8

are shaded.

3 8

are not shaded.

There are 8 circles in all.

Complete.


1.

2.

shapes shaded

shapes shaded

shapes in all

shapes in all

fraction that is shaded

fraction that is shaded

fraction that is not shaded

fraction that is not shaded

Write a fraction that names what part is shaded. 3.

4.


5.

NS 1.5, 1.7



E

Parts of a Group

ENRICH

Draw the Group


Each fraction tells what part of a group the shaded figure or figures represent. Complete the group for each fractional part. 1. 2 5

4 2. 16

3. 1 3

4. 5 6

5. 3 8

6. 1 2

7. 4 7

8. 2 8

9 9. 10

10. How did you decide how many triangles to draw in exercise 1?


NS 1.5, 1.7



Find Equivalent Fractions and Fractions in Simplest Form

P

PRACTICE

Draw an equivalent fraction for each. 1.

2.

1 2 1 6

1 6

1 4

1 6

1 4

3.

1 4

1 1 1 1 1 1 8 8 8 8 8 8

1 5

1 5

1 5

1 5

1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10

Complete to find equivalent fractions. 4.

42 10

8. 4 5

2

10

5.

1 28

6.

16

9. 1 6 2

22 8

1

7.

1 54

10. 4 1

11. 9

14. 6

15. 4

4

12

20

4

Name an equivalent fraction for each. 12. 3 7

13. 4 5

15

12

Write each fraction in simplest form. 16. 4

17. 6

18. 3

19. 6

20. 8

21. 3

22. 10

23. 8

24. 5

25. 9

26. 12

27. 24

10

12


15

12

21

24

18

30

24

18

20

32

Complete the pattern of equivalent fractions. 28.

1 4 8 12 16 20 24

29.

1 3 6 9 12 15 18

Problem Solving 30. A box contains 6 red pencils and 8

black pencils. What fraction of the pencils are red?


31. Paul caught 9 bass and 3 trout. What

fraction of the fish were trout?

NS 1.5; AF 2.2



R


RETEACH

Equivalent Fractions

Simplest Form

Equivalent fractions name the same part. To find an equivalent fraction, multiply the numerator and denominator by the same number.

When a fraction is in simplest form, its numerator and denominator have only 1 as a common factor. Show

12 32

So, 13,

13 33

2 6

2 3 6, 9,

and

4 12

3 9

14 34

4 12

6 8

in simplest form.

1. Find the greatest common factor

of the numerator and denominator. factors of 6: 1, 2, 3, 6 factors of 8: 1, 2, 4 The greatest common factor is 2. 2. Divide the numerator and denominator by the greatest common factor. So, the simplest 6 62 3 8 4 82 form of 68 is 34 .

are equivalent

fractions.

Complete to find equivalent fractions. 1.

2.


3 4

4. 3 3 4 4

3.

3 5

8

3 6

10

5. 3 3 5 5

6. 3 3 6 6

12

Write each fraction in simplest form. 7.

8.

4 8

9.

2 10


4 12

NS 1.5; AF 2.2




E

ENRICH

Which Does Not Belong? Look at the fractions in each exercise. Cross out the fraction that does not belong. Then write a fraction that does belong. 1.

4.


7.

3 8

5 8

6 7

7 8

2 8

3 12

4 16

5 25

5 9

3 5

5 12

5 6

2.

5.

8.

1 3

2 7

5 6

1 12

2 3

6 9

4 7

8 12

2 3

5 5

8 8

1 1

3.

6.

9.

1 2

5 9

4 8

3 6

6 8

8 12

10 16

3 4

1 3

3 7

4 6

5 8

Cross out each fraction in simplest form and the letter below it. 1 3

4 6

3 7

6 9

8 10

5 8

3 9

10 20

6 13

2 12

8 16

5 6

9 12

15 30

8 15

B

E

N

X

C

K

E

L

P

L

E

T

N

T

Y

Write the letters that are left. Use with Grade 4, Chapter 11, Lesson 3, pages 474–477. (351)

NS 1.5; AF 2.2



Compare and Order Fractions

P

PRACTICE

Complete. Write , , or . 1. 1 2

1 3

2. 2 5

3. 4 9

2 3

4. 2 5

3 4

7 5. 10

4 5

6. 3 4

2 3

7. 4 5

12 15

8. 1 5

4 20

9. 1 5

2 15

5 10. 12

1 4

11. 3 4

13 16

12. 8 9

7 8

7 13. 12

5 6

3 14. 10

4 9

15. 7 8

3 4

9 16. 10

4 5

17. 1 4

5 16

18. 3 5

7 10

2 7

Order from least to greatest. 1 1 19. 1 4, 2, 5

,

1 3 21. 5 7 , 7 , 20

, ,

,

3 3 20. 7 8, 4, 8

,

,

1 2 22. 4 9, 3, 3

,

,

2 5 24. 4 9, 9, 9

,

,

Order from greatest to least. 2 3 23. 1 2, 3, 4


3 3 25. 1 4 , 4 , 16

,

, ,

,

7 3 26. 5 6 , 12 , 4

,

,

Problem Solving 1 27. Sandra eats 1 6 of the cake. Pat eats 3

2 28. Karl eats 1 2 of a pizza. Tim eats 3 of a 3 4

of the cake. Who eats more cake?

pizza. Chris eats

Explain.

the amounts from greatest to least.


of a pizza. Order

NS 1.5, 1.9




R

RETEACH

You can use equivalent fractions to compare and order fractions. Order the fractions from least to greatest: 16 , 23 , 36 . Step 1

Step 2

Write each fraction as an equivalent fraction with the same denominator.

Compare the numerators. Put the fractions in order from least to greatest.

1 6

1 6

1 6

1 6

2 3

4 6

3 6

3 6

3 6

3 6

4 6

2 3

From least to greatest, the fractions are 16 , 36 , 23 . Complete. Write , , or . 1.

2.

3 4

2 4

4.

5 10

3 10

5.

4 8 © McGraw-Hill School Division

3.

1 2

2 3

1 3

1 4

3 8

6.

2 3

5 6

Write the fractions in order from least to greatest. 2 5 7. 6 6, 6, 6

,

5 3 8. 3 4, 8, 8

,

,

1 1 9. 2 3 , 4 , 12

,


,

,

NS 1.5, 1.9




E

ENRICH

Fraction War Play this game with a partner. • Cut out the cards below. Shuffle them and then place them facedown in a pile in front of you. Your partner will do the same thing. • Each player draws a card at the same time from his or her pile. The player who draws the greater fraction takes both cards. If both fractions are equal, each player draws another card. The player with the greater fraction also takes the fraction cards that were equal.


• When the piles of cards are gone, the player with the greater number of cards wins. 1 2

1 3

1 4

1 5

1 6

1 8

1 9

1 12

1 18

2 3

2 4

2 5

2 6

2 8

2 9

2 12

2 18

3 8

3 9

3 10

5 8

3 15

3 6

5 12

8 10

4 12

7 12

6 15

5 6

7 8

5 9

3 4


NS 1.5, 1.9




P

PRACTICE

Reading Skill

Check for Reasonableness Circle the statement that helps you solve the problem. Then solve the problem. 1 1. Jack spends 1 hour in an amusement park. He spends 4 of his time

waiting in lines. How many minutes does Jack wait in lines? There are 24 hours in 1 day.

There are 60 minutes in 1 hour.

Solution: 1 2. Two dozen students went to the amusement park. A group of 3 of

those students went on the roller coaster. How many students went on the roller coaster? 1 1 3 is greater than 4 .

A dozen is the same as 12. Solution:

3. At the amusement park, Vivian buys a bag of popcorn. The bag holds 14 pound of popcorn. How many ounces is that?

Two thousand pounds equal 1 ton.

One pound equals 16 ounces.

Solution:


4. A flag at the amusement park is 4 yards long. The width of the flag 2 is 3 of its length. How many feet wide is the flag?

One yard is the same as 3 feet.

A yard is a measure of length.

Solution: 5. Leora buys a quart container of iced tea to share with her friends. 1 Each friend drinks 4 of the iced tea. How many ounces did

each friend drink? One quart equals 32 ounces.

One cup equals 8 ounces.

Solution: Use with Grade 4, Chapter 11, Lesson 5, pages 482–483. (355)

MR 1.1, 2.3, 3.1, 3.2


Problem Solving: Reading for Math Check for Reasonableness


P

PRACTICE


Choose the correct answer. A group of 18 students goes to the amusement park. Of these students, 5 6 go on the bumper cars. How many students go on the bumper cars? 1. What prior knowledge do you need

2. A reasonable answer for this

in order to solve this problem?

problem would be

A 56 means 5 of 6 equal parts.

F greater than 18.

B 56 is less than 1.

G less than 3.

C 56 is greater than 16 .

H greater than 3 but less than 9.

D 18 is divisible by 9.

J greater than 9 but less than 18.

Fun Time International has 16 amusement parks. Of these amusement parks, 34 are in the United States. There is a Fun Time Amusement Park in France. How many Fun Time Amusement Parks are in the United States? 3. Which information is not needed in


order to solve the problem? A Fun Time has 16 amusement parks. B Of Fun Time’s amusement parks, 3 4 are in the United States. C Fun Time has an amusement park in France. D All of the above


problem would be that Fun Time has F 16 amusement parks in the United States. G 12 amusement parks in the United States. H 4 amusement parks in the U.S J no amusement parks in the U.S.

Nick spends 2 hours in the amusement park. He spends 23 of his time on rides. How many minutes does Nick spend on rides? 5. Which of the following information

is important to solve the problem? A There are 24 hours in 1 day. B Nick goes on 4 rides. C There are 60 minutes in an hour. D There are 36 rides in the amusement park. Use with Grade 4, Chapter 11, Lesson 5, pages 482–483. (356)


problem would be F 2 hours. G more than 60 minutes but less than 120 minutes. H greater than 20 minutes but less than 1 hour. J less than 20 minutes. MR 1.1, 2.3, 3.1, 3.2


Problem Solving: Reading for Math Check for Reasonableness


P

PRACTICE


Choose the correct answer. 3

A group of 40 students goes to the amusement park. If 4 of the students go on the Water Slide and 25 of the students go on the Space Shot, how many students go on the Space Shot? 7. What prior knowledge do you need


in order to solve this problem?

problem would be

A 20 25

F 40 students.

3

B 4 means 3 4 2

C 5 means 2 of 5 equal groups 3

D 4 1

G 24 students. H 20 students. J 16 students.

Solve. 9. There are 32 rides at an amusement park. Norman goes on 38 of the rides.

How many rides does he go on?

11. A dozen students go to the


amusement park. A group of 31 of these students goes on the Super Cycle. How many students go on the Super Cycle?

13. Each car of the Sling Shot can hold 15 people. A car is 25 full. How many

people are in the car?


10. Donna took 18 rides. She went on the roller coaster 23 of the time.

How many roller-coaster rides did Donna take?

12. There were 25 students at the

amusement park. Of these students, 2 5 were there for the first time. How many students were there for the first time?

14. An amusement park has 36 rides. Bobby goes on 12 of them. How

many rides does he go on?

MR 1.1, 2.3, 3.1, 3.2



Explore Parts of a Group

P

PRACTICE

Use the squares to help you find the fraction of each group. 1.

2.

1 3

3.

3 4

of 6

4.

of 16

5.

3 4

of 18

4 5

of 15

6.

2 3

of 20

2 3

of 24

Find the fraction of each number. 1

8. 3 of 15

5

11. 7 of 14

2

14. 10 of 40

5

17. 3 of 21

2

20. 6 of 36

3

23. 7 of 49

7. 2 of 18 10. 6 of 12 13. 9 of 18 16. 8 of 40 19. 5 of 30


22. 7 of 28

2

9. 5 of 30

3

3

12. 8 of 32

1

15. 7 of 21

1

18. 4 of 20

1

21. 8 of 16

6

24. 10 of 60

1 4 1 3

7

Problem Solving 25. Of the 24 fourth graders in Mrs. 1 4

Williams’ class, participate in sports. How many fourth-grade students participate in sports?


26. Steven practices cello 15 hours a

week. On Monday he practices 15 of that time. How many hours does Steven practice cello on Monday?

NS 1.5




R

RETEACH

You can use counters to find a part of a group. Suppose you have 20 counters. You want to find 2 5 of 20 counters. The denominator tells you how many equal groups to make. Divide the 20 counters into 5 equal groups.

There are 8 counters in 2 groups. So,

2 5

of 20 is 8.

Complete. Circle the part of each group. 1

2. 5 of 10

2

5. 4 of 12

1

8. 6 of 18

1. 2 of 8


4. 3 of 15

7. 6 of 30

2

3. 3 of 6

3

6. 4 of 20

5

9. 5 of 10


1

1

4

NS 1.5




E

ENRICH

Cooking with Fractions Use the grocery list to answer each question. 3

1. Barb adds salt and pepper to 4 of the

ground beef. How much ground beef is that?

Grocery List 12 pounds of ground beef 9 pounds of ground turkey

2

2. Mark uses 3 of the ground turkey to

15 pounds of potatoes

make meatballs. How many pounds does he use?

36 eggs 16 loaves of bread 18 pounds of chicken

3

3. Melanie uses 5 of the potatoes for

potato salad. How many pounds does she use?

20 pounds of sausage

5

4. George boils 6 of the eggs. How many eggs does he boil? 3

5. Sam slices 4 of the bread. How much is that? 1


6. Sarah uses 8 of the bread for stuffing. How much is that? 3

7. Jon barbecues 4 of the sausage and uses the rest for appetizers.

How many pounds does he barbecue? How many pounds does he use for appetizers? 1

1

8. Jan grills 2 of the chicken. Bob cooks 6 of the chicken for chicken salad.

How much chicken is left?


NS 1.5



Mixed Numbers

P

PRACTICE

Rename as a mixed number or fraction in simplest form. 8

9

1. 7

7

2. 2

2

6. 38

22

10. 6

2

14. 28

40

18. 4

5. 66 9. 10 13. 56 17. 6

10

3. 2

6

7. 45

21

11. 2

2

15. 36

30

19. 6

4. 3

1

8. 17

5

13

12. 4

2

16. 84

64

20. 5

19

3

48

Algebra & Functions Use the number line to compare. Write , , or .

1 8

0

1 6

1 4

3 4

1 2

5 8

3 4

21. 1 1 6

1 18

22. 1

24. 1 1 4

1 58

25. 1 1 8

7 8

1

1 18

8 8

1

16

1

14

3

14

1

5

7

2

1 78

23. 2

1 12

3

12 18 14 18

26. 1 3 4

1 78

Problem Solving


27. Ben measures ten one-fourths of a

1

28. Claudia ran 43 miles on Monday. On

cup of water. What is this as a mixed

Tuesday she ran 412 miles. On which

number?

day did Claudia run a longer distance? Explain.

29. Jared drank 7 cups of juice. Aida

drank

9 6

4

cups. Who drank more juice?

Explain.


30. Mary worked 81 hours on Monday 2

and 835 hours on Tuesday. On which day did she work longer? Explain.

NS 1.5, 1.9



Mixed Numbers

R

13 4

You can use models to help you write

13 4 13 4 13 4

RETEACH

as a mixed number.

4 4

4 4

4 4

1

1

1

3 14

1 4 1 4

You can also use multiplication and addition to write a mixed number as a fraction. Step 1. Multiply the whole number by the denominator. Step 2. Add the numerator to the product. 1 35 =

(5 1) 3 5

=

53 5

=

8 5

Write the fraction as a mixed number or whole number. 1. 7 4

9


4. 4

2. 7 3

11

5. 3

3. 31 8

8

6. 8

Write the mixed number as a fraction. 7. 1 1 4

8.6 3 5

10. 8 2 3

11. 4 1 3

12.5 2 7

13. 3 5 6


NS 1.5, 1.9


Mixed Numbers


E

ENRICH

Fractions Between Shade the fraction bars to show a fraction between the two whole numbers given. Write both the fraction and the mixed number.

1. Shade the fraction bars to show a

fraction between 1 and 2. Fraction: Mixed number:




fraction between 2 and 3. Fraction:


Mixed number:




NS 1.5, 1.9



Likely and Unlikely

P

PRACTICE

Describe the probability of picking a certain shape from the bag. Use the words likely, equally likely, certain, unlikely, or impossible. 1.

2.

3.

4. or

,

,or

Describe the probability of spinning the number.

2

5. spinning 2

3 2

4

6. spinning 3

2

1

7. spinning 6

2

2 2

8. spinning 1

2

4

3

9. spinning 3 or 4 10. spinning 1, 2, 3, or 4

Describe the probability. 11. The month after September will be November. 12. It will be sunny or rainy tomorrow.


13. It will snow in Alaska this year.

Problem Solving 14. A bag contains 3 red and 7 white

balls. Is it unlikely, more likely, or equally likely you will pick a red ball?


15. A box contains 6 red pencils and

6 black pencils. Is it unlikely, less likely, or equally likely you will pick a red pencil?

NS 1.5; MR 1.1; SDP 2.2



Likely and Unlikely

R

The chance, or likelihood, that something will happen is called probability.

6

Look at the spinner at the right. You could spin 1, 2, 3, 4, 5, or 6. There are 6 possible outcomes. • The probability of spinning each

1

5

2 4

number is equally likely. • It is impossible to spin an 8. • It is certain that you will spin a number greater than 0.

Look at the spinner at the right.

RETEACH

3

7

8

8

8

• The probability of spinning a 7 is unlikely. • The probability of spinning an 8 is likely.

Look at the spinner at the right. Use the words likely, equally likely, certain, unlikely, or impossible to describe the probability. 1. The probability of spinning 12

2. It is

that you will land on a number greater than 2.


3. It is

that you will land on a number less than 2.

4. It is

that you will land on a number less than 9.

8

1

7

2

6

3 5

4

5. It is

that you will land on an odd or even number.

6. It is

to land on a

number greater than 8.


NS 1.5; MR 1.1; SDP 2.2



Likely and Unlikely

E

ENRICH

Guess the Number • Play this game with a partner. Partner A chooses a secret 4-digit number and writes it on a sheet of paper. • Player B guesses a 4-digit number and writes in the first row of the guess chart. • Player A looks at the 4-digit number and then fills in the second chart. He or she writes the number of digits that are correct. Player A also writes the number of digits that are in the correct position. Example: The secret number is 1,093. The first guess is 6,198. The number of correct digits is 2. The number of digits in the correct position is 1. • Based on that information, Player B makes a second guess. • Continue playing until the secret 4-digit number is guessed, or until 10 guesses have been used. • Players then switch roles.


Guess

Number of Correct Numbers

1.

1.

2.

2.

3.

3.

4.

4.

5.

5.

6.

6.

7.

7.

8.

8.

9.

9.

10.

10.

Number of Digits in the Correct Position

What strategy did you use in guessing the numbers?


NS 1.5; MR 1.1; SDP 2.2



Explore Probability

P

Find the probability of spinning the number.

4

PRACTICE

3 3

1 1. 3

3. 4

2. 1

4. 2

4

4

4

4 2 4

5. 3 or 4

2

2

6. 5

Find the probability of picking the shape. 7. circle

9. square

11. hexagon

8. triangle

10. pentagon

12. triangle or square

Find the probability of picking the color.


13. blue

14. red

15. green

16. purple

17. red or blue

18. blue or green

red

blue

red

blue

red

blue

red

green

Problem Solving 19. Greg has a coin in one of his closed

hands. What is the probability that Greg’s friend will pick the hand the coin is in?


20. Karen turns over 5 paper cups. She

hides a coin under one of them. What is the probability that Steven will guess which cup the coin is under?

NS 1.5; SDP 1.1, 2.2



Explore Probability

R

RETEACH

You can use a fraction to show a probability. Probability number of favorable outcomes number of possible outcomes You can use probability to predict an outcome. If you pick one of these counters without looking, there are 5 possible outcomes. The probability of picking a

is 25 .

The probability of picking a

is 15 .

The probability of picking a

is 25 .

Find the probability of picking each shape. 1.

2.

3.

4.

Find the probability of picking each letter. 5. A

6. B

7. C

8. D

A B C C D B C C C B


Find the probability of picking each item. 9. a pencil

10. a pen

11. an eraser

12. a pair of scissors

13. a pad of paper

14. a crayon Use with Grade 4, Chapter 11, Lesson 9, pages 492–493. (368)

NS 1.5; SDP 1.1, 2.2



Explore Probability

E

ENRICH

Experimental Probability 1. What if you toss a number cube numbered 1–6 120 times?

About how many times do you think you will toss the number 1? Explain.

2. Toss two number cubes numbered 1–6 120 times. Use tally

marks to record your results in the table below. Number Cube (120 tosses) 1

2

3

4

5

6

3. You get the sums 2–12 when you toss two number cubes

and add the numbers. What if you toss two number cubes 72 times? Record your sums in the table below. Sum of Numbers on Two Number Cubes (72 tosses)


2

3

4

5

6

7

8

9

10

11

12

4. What if you toss 3 numbers cubes? What sums would

be least likely to come up? Explain.


NS 1.5; SDP 1.1, 2.2




P

PRACTICE

Draw a Tree Diagram Use a tree diagram to solve. 1. You spin a spinner with 4 equal

sections marked 1–4. Then you spin another spinner with 3 equal sections colored red, blue, and yellow. What are all of the possible outcomes?

3. The Boardwalk Shop sells souvenir


shirts. The shirts come with long sleeves or short sleeves. The shirts come in white, gray, and blue. What are all of the different kinds of shirts?

Mixed Strategy Review Solve. Use any strategy. 5. The Target Toss Game has 6 rings. The first ring is worth 4 points, the second ring is worth 8 points, and the third ring is worth 12 points. If the pattern continues, what is the sixth ring worth?

Strategy: 7. Marnie brought $75 to the

amusement park. She has $39 left. How much money did Marnie spend?

2. Karen throws a dart at a target with

5 equal sections marked 1–5. She then throws a dart at a target with two equal sections colored green and blue. What are all of the possible outcomes?

4. Boardwalk Burgers sells burgers made

from beef, turkey, chicken, or soy. Burgers can have no cheese, Swiss cheese, or American cheese. How many different choices are there?

11 6. Social Studies In a recent year, 100

of all U.S. vacations included time at 6 the beach, 100 included time at 8 included time sports events, and 100 at theme parks. Write these activities in order from least to most popular.

Strategy: 8. Create a problem which can be

solved by drawing a tree diagram. Share it with others.


SDP 2.1, 2.2; MR 1.1, 2.3, 2.4, 3.1, 3.2




R

RETEACH

Draw a Tree Diagram Page 495, Problem 1

What are all of the possible outcomes of tossing a number cube and flipping a coin?

Step 1

Read

Be sure you understand the problem. Read carefully. What do you know? • When you toss a number cube, you can toss a , , , , . • When you flip a coin, you can get

or

,

.

What do you need to find? • You need to find

Step 2

Plan ■

■


■

■

■

■

■

■

■

■

Find a Pattern Guess and Check Work Backward Make a Table or List Write a Number Sentence Use Logical Reasoning Solve a Simpler Problem Make a Graph Act it out Draw a Diagram


A tree diagram can show all of the possible outcomes.


SDP 2.1, 2.2; MR 1.1, 2.3, 2.4, 3.1, 3.2




R

RETEACH

Draw a Tree Diagram Step 3

Solve

Carry out your plan. Number Cube

Make branches to show all of the possible outcomes for tossing the number cube. Then make branches to show all of the possible outcomes for flipping the coin. List each outcome.

1

Coin

Outcome

heads

1-heads

tails

1-tails

2 heads tails 4 heads tails 6

Step 4

Look Back



How can you check to make sure your answer is correct?

Practice 1. The amusement park offers discount tickets for 5 rides, 10 rides, or 20 rides. The tickets come as adult tickets or child’s tickets. What are all of the possible discount tickets?


2. Pia wants a fruit drink. She can choose

strawberry, banana, orange, grapefruit, or mango. Drinks come in small, medium, or large. What are all of the possible combinations?

SDP 2.1, 2.2; MR 1.1, 2.3, 2.4, 3.1, 3.2



Explore Making Predictions

P

PRACTICE

Use the spinner for exercises 1–6. 1. If you spin the spinner 100 times, what

is the probability you will land on A?

2. If you spin the spinner 50 times, what

C

is the probability you will land on B?


is the probability you will land on C?

B

A

A

C

B C

4. If you spin the spinner 100 times,

A

A

A

what is the probability you will land on a shaded section?



is the probability you will land on an A or a B?

is the probability you will land on an unshaded section?

Use a number cube with the sides labeled 1–6 for problems 7–10.


7. Predict the number of times 3 will

8. If you toss the number cube 60 times,

come up if you toss the number cube 30 times.

9. Is it reasonable to predict that you will

how often might 4 come up?

10. Can you predict exactly how many

toss a 4 on the number cube 2 out 12 tosses?


times 5 will come up when you toss a number cube labeled 1–6?

NS 1.5; SDP 1.1, 2.1




R

RETEACH

Suppose you toss a coin. There are 2 possible outcomes, heads or tails. You can predict that 1 out of 2 times you will toss heads. As an experiment, you can toss a coin 10 times and record your results. Compare the results with your prediction. Suppose you spin this spinner. You can predict that 2 out of 8 times the spinner will land on 5. There are 2 favorable outcomes and 8 possible outcomes. The probability of spinning a 5 is 2 1 8 , or 4 . You can spin a spinner for 10 or 20 times to check your prediction.

5

1

4

3

3

1 2

5

Use the spinner below to answer the questions. Write true or false. Explain. 1. Is it reasonable to predict that the

spinner will land on a shaded section 1 out of 5 times?

2. Is it reasonable to predict that the

spinner will land on a dotted section 5 out of 15 times?


3. The probability of landing on a striped

section is 2 out of 5.

4. The probability of landing on a red

section is 1 out of 5.


5. Is it reasonable to predict that the

spinner will land on a section that is not shaded 6 out of 30 times?

NS 1.5; SDP 1.1, 2.1




E

ENRICH

Could It Happen? The letters below have been sent to an advice column called “Could It Happen?” Write a response to each letter. Include information about probability in your response. Dear Could It Happen?

Dear Could It Happen?

My school is having a raffle for a

There are 30 people trying out for 15

computer. Each ticket costs $3.00. My

parts in the school play. I don’t want to

friend says that if each student in our

try out unless I have a pretty good chance

class buys a ticket our class has a great

of getting a part. What do you think

chance of winning the computer for our

the chances are that I will get the part?

classroom. What do you think?

Regards,

Sincerely,

Broadway Bound

Mouse Potato Could It Happen?


Could It Happen?

Write your own probability letter to “Could It Happen?”


NS 1.5; SDP 1.1, 2.1



Print This Page


Applying Probability Record your data. Game

Fair or unfair? Why?

If the game is unfair, how can you change it to make it fair?

Spinner A

Spinner B

Spinner C

Spinner D

Cards A

Cards B

Checkerboard A


Checkerboard B Your Decision Describe three games you would recommend to Reggie and Bianca. Explain.


MR1.1; NS 1.5; SDP 1.1, 2.1


Print This Page


Problem Solving: Application How does size affect how fast a solid dissolves?

Math & Science


Make your own chart to record the dissolving time for each seltzer tablet.

1. Rank the seltzer tablets in order from fastest to slowest.


NS 1.5, 1.7; MR 1.1, 2.3, 3.3


Print This Page


Problem Solving: Application How does size affect how fast a solid dissolves?

Math & Science

2. What would happen if you broke the seltzer tablet into

eighths? Why?

3. Describe a plan to make the seltzer tablet dissolve as fast

as possible.

4. Did you collect enough data in this activity to make any strong


conclusions? Explain your answer.

5. Explain the results of the activity in terms of surface area.


NS 1.5, 1.7; MR 1.1, 2.3, 3.3



Add Fractions with Like Denominators

P

PRACTICE

Add. Write each sum in simplest form. 1.

7.

1 3 1 3

1 6 2 6

2 4 2 4

2.

3 9 2 9

8.

3.

9.

2 7 2 7

4.

2 8 4 8

2 12 4 12

10.

3 5 3 5

5.

3 15 3 15

11.

6.

7 9 6 9

12.

13. 2 2

14. 3 2

15. 3 3

16. 1 7

17. 3 3

18. 5 4

19. 3 3

20. 5 5

21. 13 12

22. 7 8

23. 5 7

24. 9 3

16

8

4

16

10

8

9

4

12

8

12

10

18

9

8

8

11

3 12 5 12

18

8

16

11

6 10 8 10

15

16

15


Algebra & Functions Compare. Write , , or . 3 25. 1 4 4

1

2 26. 6 7 7

6 28. 2 9 9

1

2 7 29. 10 10

3 27. 1 6 6

1 1

8 5 30. 12 12

1 1

Problem Solving 1

31. You need at least 1 4 yards of paper

for a mural. You tape together 2 pieces of paper that are 34 yard each. Do you have enough paper now? How long is your piece of paper?


32. You want to make some salt ceramic

dough. The recipe calls for 23 cup of salt. If you want to double the recipe, how much salt will you need?

NS 1.5, 3.1



R


RETEACH

You can use fraction strips to add fractions with like denominators. 1 1 6 6

1 1 6 6

1 1 1 1 6 6 6 6 1 3

2 6

2 6

1 3

4 6

2 3


1 8 1 8

4.

3 8

7.

1 1 6 6 2 6

3 6

1 6

5.

1 6

8.

1 1 4 4

2 4

1 4

4 10

6.

1 3

1 3

1 1 10 10 2 10

1 1 1 1 1 10 10 10 10 10 5 10

1 1 3 3 2 3

1 4

3.

1 4 1 4

1 1 1 6 6 6

1 4 1 4

1 1 1 1 6 6 6 6 4 6


2.

1 1 1 8 8 8

3 10

1 1 1 10 10 10

1 1 1 1 10 10 10 10

9. 1 2

10. 1 4

11. 3 4

12. 2 5

13. 2 4

14. 2 6

5

12

5

12

8 8

8 8


12 10

12 10

NS 1.5, 3.1




E

ENRICH

Hexagon Roll Game Play with a partner to form hexagons. You will need two number cubes and triangle and hexagon pattern blocks.

2 6 2 6

5 6 5 6

• Write the following fractions on each side of two number cubes: 0, 16 , 26 , 36 , 46 , 56 . • Each triangle pattern block stands for stands for 1.

1 6

and each hexagon


• The first player rolls the two number cubes and shows the fractions with the triangle pattern blocks. Then he or she finds the sum of the fractions by combining the pattern blocks. That player should also write a number sentence that shows the addition. • If the triangle pattern blocks form a whole hexagon, call out “Hexagon!” to score 1 point. • Take turns and continue playing for 5 rounds. The player with more points wins the game. Which fractions would you like to roll each time? Explain.


NS 1.5, 3.1



P

Subtract Fractions with Like Denominators

PRACTICE

Subtract. Write each difference in simplest form. 1.

7.

4 5 2 5

2.

7 10 2 10

8.

5 7 3 7

3.

6 10 4 10

9.

5 8 1 8

4.

7 12 1 12

10.

8 9 2 9

5 6 1 6

5.

4 15 1 15

11.

6.

8 11 4 11

12.

13. 7 2

14. 5 1

15. 7 3

16. 5 4

17. 8 1

18. 4 3

19. 7 5

20. 7 4

21. 10 5

22. 11 8

23. 9 5

24. 7 3

25. 2 2

26. 8 2

27. 9 8

9

7

9

7

12

9

12

12

3

16

16

9

12

12

9

5

11

10

8

9

11 12 8 12

8

5

12

10

3

8

4 9 1 9

11

8

11

11

Algebra & Functions Compare. Write , , or . 28. 5 2

3 9

30. 5 1

12

7 12

32. 7 6

7 11


9

12

11

6 9

9

11

29. 7 3

10

8 10

2 10

5 12

31. 11 10 15

14 15

13 15

5 11

33. 12 5

9 13

2 13

10

15

13

13

Problem Solving 34. At lunch you cut a sandwich into

4 parts and eat 3 of the parts. What fraction of the sandwich is left?


35. For breakfast and lunch you drink 2 3

of a quart of milk. How much of the quart is left?

NS 1.5, 3.1




R

RETEACH

You can use fraction strips to subtract fractions with like denominators. 1 5 4 5

1 5 1 5

1 5

1 5

3 5


1 1 1 4 4 4 3 4

4.

1 4

7.

2 8

3 8

8.

1 3

1 8

1 1 1 1 1 6 6 6 6 6 5 6

1 1 1 1 1 1 1 8 8 8 8 8 8 8 7 8

1 1 1 1 1 1 1 8 8 8 8 8 8 8 7 8

5.

3.

1 3

1 3 2 3

1 1 1 1 1 8 8 8 8 8 5 8


2.

6.

1 1 1 1 1 10 10 10 10 10 5 10

4 6

1 10

1 1 1 1 1 1 1 1 1 12 12 12 12 12 12 12 12 12 9 12

1 12

Subtract. Write each difference in simplest form. 1 9. 3 4 4 7 1 12. 12 12

2 10. 3 3 3

3 11. 5 5 5

7 3 13. 16 16

8 5 14. 10 10


NS 1.5, 3.1




E

ENRICH

Fraction Subtraction Riddle When is it bad luck to have a black cat follow you? Subtract. Write each difference in simplest form. To solve the riddle, find the letter that goes with each difference. Write the letters on the lines below.

E

A 5 8

2 8

4 10

7 16

3 12

Y

2 8

4 16

5 8

1 4

3 10

4 15

7 8

5 12

3 5

13 15

2 5


1 16

2 24

6 10

5 10

18 20

2 20

11 12

6 12

U

A 13 16

1 3

1 24

23 24

M 13 24

O 7 12

5 16

S 7 8

N

5 10

W 7 16

H 11 16


3 16

9 10

E 15 16

E

1 10

4 16

U 7 10

O

R 5 16

3 8

4 5

9 16

3 4

1 2

1 8

NS 1.5, 3.1




P

PRACTICE

Reading Skill

Choose an Operation Solve. Tell how you chose the operation. 1. Kerstin cuts a pie into a dozen

pieces. Her friends eat 7 pieces. What part of the pie is left?

of raisins than nuts are needed?

3. A recipe calls for 3 cup of 8 macadamia nuts and 58 cup of

4. Kevin uses 1 stick of butter for 8 one recipe and 58 stick of butter for

5. Mary makes a batch of 16 muffins.

6. Nick buys 3 pound of roast beef and 4 1 4 pound of ham. How many pounds

cashew nuts. What is the total amount of nuts in the recipe?

She sells 9 of them. What part of the batch is left?


2. A recipe calls for 3 cup of raisins and 4 1 cup of nuts. How many more cups 4

7. Nicole drinks 1 quart of orange juice 8 and 38 quart of water. How much did

she drink in all?


another recipe. How much butter does he use altogether?

of meat does Nick buy?

8. Michael fills 10 bowls with fruit salad.

He serves 8 bowls to his guests. What part of the bowls is left?

MR 1.1, 2.3, 2.4, 3.1, 3.2




P

Choose an Operation

PRACTICE



3

A recipe calls for 8 cup of beef broth and 8 cup of water. How much liquid does it call for in all? 1. Which of these statements is true?


to solve the problem?

A The recipe uses more water than beef broth.

3

1

3

1

3

1

F 88

1

G 88

B The recipe uses 8 cup of beef broth.

H 88

1

C The recipe uses 8 cup of water 3

1

Tim buys 4 pound of provolone cheese and 4 pound of Swiss cheese. How much more provolone cheese than Swiss cheese does Ted buy? 3. What do you have to do to solve

4. How much more provolone cheese

this problem?

than Swiss cheese does Ted buy?

A Find the difference between two amounts.

F 1 pound

B Find the total of two equal amounts.

3

G 4 pound 1

H 2 pound


C Find the total of two unequal amounts. Ashley cuts a cake into 16 squares. Her family eats 10 squares. What part of the cake is left? 5. Which statement is true?

A There is a total of 10 squares of cake. B There is a total of 16 squares of cake.


to solve the problem? 16

10

16

10

10

6

F 16 16 G 16 16 H 16 16

C Ashley’s family eats 16 squares of cake. Use with Grade 4, Chapter 12, Lesson 3, pages 520–521. (386)

MR 1.1, 2.3, 2.4, 3.1, 3.2




P

PRACTICE



7

Janell uses 8 cup of pine nuts and 8 cup of peanuts. What is the total amount of nuts she uses? 7. What operation would you use to

8. What is the total amount of nuts

solve this problem?

she uses?

A addition

F 1 2 cups

B subtraction

G 2 cup

C multiplication

H 4 cup

1

1 1

Solve. 7 9. Max buys 8 pound of apples and 3 pound of grapes. What is the total 8

amount of fruit he buys?

15 cookies to her friends. What part of the 20 cookies is left?

5 11. Chen buys 8 pound of American cheese and 7 pound of Swiss cheese. 8

12. Kathryn uses 3 tablespoon of nutmeg 4 and 34 tablespoon of cocoa. How

13. Amy buys 1 pound of turkey and 1 pound of4 honey-roasted ham. How 4

14. Marge cuts a cherry pie into 8 slices.

15. A recipe for pudding uses 7 cup 8

3 16. Patrick bought 4 pound of cookies. He ate 14 pound of the cookies. How

How much more Swiss cheese than American cheese does he buy?


10. Adela makes 20 cookies. She gives

much meat did she buy altogether?

of milk. A recipe for custard uses 3 cup of milk. How much more milk 8 does the pudding use than the custard recipe?


many tablespoons of nutmeg and cocoa does she use altogether?

She eats one slice. What part of the pie is left?

much of the cookies is left?

MR 1.1, 2.3, 2.4, 3.1, 3.2



Explore Adding Fractions with Unlike Denominators

P

PRACTICE


1 2

1 4

2. 1 6

1 1 4 4

1 4

1 6

1 2

1 4

2 4

1 4

4.

1 1 6 6

1 6

1 3

1 6

2 6

1 2

111 888

5. 1 1 1 10 10 10

1111 8888

111 888

111 10 10 10

1 2

3 8

4 8

3 8

1 6

1 5

1 5

1111 10 10 10 10

3 10

2 5

3 10

4 10

1 2 1 1 1 6 6 6

1 6

1 2

1 6

3 6

1 4

1 4

6.

1 4

111 888

111111 888888 3 4

3 8

6 8

3 8

111 888

7. 3 5

8. 7 1

10. 5 1

11. 1 5

12. 1 1

13. 1 3

14. 1 2

15. 1 1

16. 2 5

17. 2 7

18. 3 1

19. 2 1

20. 1 3

21. 3 7

1 22. 3 3 2 5 10

23. 1 1 1

24. 1 1 1

12

6

12


3. 1 6

1 3

5

3

3

4

10

6

6

9

4

6

3

3

8

3

3

2

12

10

8

9. 2 2

3

5

4

2


8

4

3

9

12

8

4

8

2

4

NS 1.5, 3.1




R

RETEACH

You can use fraction strips to find equivalent fractions before you add. 3 4

Add

1 12 .

1 1 4

Compare fourths to twelfths: 9 12

is equivalent to

9 12

Add the twelfths. 3 4

1 12

1 4

1 12

1 1 1 1 1 1 1 1 1 1 12 12 12 12 12 12 12 12 12 12

3 4.

1 6

So,

1 4

1 6

1 12

1 6

1 6 10 12

1 6

5 6

is 56 .

Add. You may use fraction strips to help you. Write each answer in simplest form. 1. 3 2

2. 1 2

3. 1 1

4. 3 2

5. 2 1

6. 1 1

7. 3 1

8. 4 1

9. 1 5

5

10


12

4

6

8

6

3

12

2

10

2

6

4

2

2

2

12

10. 2 2

11. 3 1

12. 1 3

13. 1 1

14. 5 1

15. 2 1

9

6

3

3

8

8

2

4


10

3

5

9

NS 1.5, 3.1




E

ENRICH

Hidden Sentences The squares contain hidden addition sentences. Look from left to right and top to bottom to find the hidden addition sentences. Circle each addition sentence you find. Each sum is in simplest form. 1.

2. 1 3

2 8

5 8

7 8

2 8

3 8

5 10

1 4

1 3

3 5

3 5

2 5

4 8

1 8

2 10

1 3

2 3

1 5

1 5

2 5

3 4

1 2

7 10

3 5

1 5

4 5

2 5

4 5

3 10

2 10

1 2

4 10


3.

4. 3 4

5 12

2 3

1 4

1 3

3 10

1 10

2 5

3 8

1 12

1 8

1 3

1 6

1 3

3 4

1 4

1 18

1 2

1 2

2 3

1 2

1 4

3 4

3 8

3 4

3 4

1 12

1

1 4

3 4

1

5 8


NS 1.5, 3.1



Add Fractions with Unlike Denominators

P

PRACTICE


7.

1 4 1 8

2 3 1 2

1 3 2 5

2.

1 6 2 3

8.

3.

9.

2 3 3 4

5 6 1 3

1 2 5 6

4.

1 2 3 5

10.

5.

1 5 2 15

6.

1 2 7 8

11.

12.

13. 1 1

14. 3 1

15. 1 5

16. 1 3

17. 1 2

18. 2 1

19. 3 3

20. 7 1

21. 1 5

22. 10 3

23. 1 5 1

2

4

4

12

4

10

8

4

8

9

4

2

2

6

3

6

3 5 7 10

12

5

3

1 6 1 4

3

4

12

24. 1 1 3

3

8

2

4


Algebra & Functions Compare. Write , , or . 9 25. 1 4 12

1 4

2 27. 12 14

3 12

2 3

1 26. 2 6 6 1 6

4 28. 3 5 10

1 2

1 2

1 4

1 3

Problem Solving 1

29. Your family ate 2 of a box of cereal

1

30. At 6:00 P.M., 6 of the passengers

one day and 34 the next. Did you eat

boarded the plane. At 6:10 P.M., 23 of

more or less than 1 box of cereal?

the passengers boarded. What fraction

Explain.

of the passengers are on the plane?


NS 1.5, 3.1




R

RETEACH

You can use fraction strips to help you record the steps when you add unlike fractions. Add

2 3

16 .

Using Fraction Strips 1 3

1 3

1 6 1 6

Find equivalent fractions.

1 6

1 1 1 1 6 6 6 6

2 3 4 6


2 3

1 6

Add the numerators. Use the common denominator.

4 6

4 6 1 6 5 6

Write the answer in simplest form if necessary.

5 6

Find each equivalent fraction. Then add. Write the sum in simplest form. You may use fraction strips to help you add. 1.

1 8

8

34 8

5.

6 10

10


7 12 26

12

3 4

6.

1 3 1 6

10

4.

2 10 10

9

7 8

7.

16 2

10.

4 5

3.

7 12 12

15 10

9.

1 3

2.


1 4 1 2

6

13 6

8.

34

11.

1 2

9 10

35

12.

5 12 14

NS 1.5, 3.1




E

ENRICH

Fraction Magic Squares In a magic square, the sum of each row, column, and diagonal is the same. Complete each magic square. 4 1. The magic sum is 1 11 .

2. The magic sum is 15 16 .

8 11

1 4

9 11

1 16

7 11

7 16

6 11

3. What is the magic sum?

1 8

4. What is the magic sum?

3 5

1 6 1 2


1 3

7 18

1 9

2 5

1 5

5. How did you find the magic sum in exercise 3?


NS 1.5, 3.1




P

PRACTICE

Solve a Simpler Problem Solve using a simpler problem. 1. Sandwiches cost $4.95. Drinks cost

$0.99. How much does it cost to buy 2 sandwiches and 3 drinks? 1 3. Recipe A uses 2 cup of chicken broth and 41 cup of water. Recipe B uses 1 1 3 cup of chicken broth and 3 cup of

water. Which recipe uses more liquid?

2. A customer pays $3.95 for 5 pounds

of apples. What is the price for 1 pound of apples?

4. Tracy buys 3 pound of roast beef, 1 pound of4turkey, and 3 pound of 2 8 ham. Ken buys 41 pound of roast beef, 1 pound of turkey, and 3 pound of 2 8

ham. Who buys more meat? How much more does that person buy?

Mixed Strategy Review Solve. Use any strategy. 5. There are 24 plants in a garden.


There are 4 more tomato plants than red pepper plants. There are twice as many red pepper plants as green pepper plants. How many of each kind of plant is in the garden?

Strategy: 7. Health An ounce of cheddar cheese

has 114 calories. An ounce of brie cheese has 95 calories. How many more calories does an ounce of cheddar cheese have than an ounce of brie cheese?

6. The Yogurt Cart has the following 3

flavors: chocolate, vanilla, and strawberry. Yogurt comes in a cup or a cone. You can have no sprinkles, chocolate sprinkles, or rainbow sprinkles. How many different choices are there?

Strategy: 8. Create a problem for which you

could use a simpler problem to help you find the answer. Share it with others.


NS 1.5; MS 1.1, 1.2, 2.4, 3.2




R

RETEACH

Solve a Simpler Problem Page 531, Problem 1

Josh buys a 5-pound watermelon at $0.49 per pound and 2 pounds of grapes at $1.29 per pound. Sabrina buys an 8-pound watermelon at $0.29 per pound and 3 pounds of grapes at $0.99 per pound. Who spends more money? How much more? Step 1

Read

Be sure you understand the problem. Read carefully.

What do you know? • Josh buys

pounds of watermelon at

He also buys • Sabrina buys She also buys

pounds of grapes at pounds of watermelon at pounds of grapes at

per pound. per pound. per pound. per pound.

What do you need to find? • You need to find Step 2

Plan ■

■


■

■

■

■

■

■

■

■

■

■

■

Make a Table Write a Number Sentence Work Backward Act It Out Find a Pattern Make a Graph Guess and Check Choose a Strategy Make a Graph Logical Reasoning Draw a Tree Diagram Solve a Simpler Problem Draw a Diagram


Use simpler numbers to make up a problem similar to the one you need to solve. Then solve the real problem the same way.


NS 1.5; MS 1.1, 1.2, 2.4, 3.2




R

RETEACH

Solve a Simpler Problem Step 3

Solve

Carry out your plan. Josh: watermelon: $0.50 per lb

grapes: $1.30 per lb

5 $0.50 $2.50 $2.50 $2.60 $5.10 Sabrina: watermelon: $0.30 per lb 8 $0.30 $2.40 $2.40 $3.00 $5.40

2 $1.30 $2.60 grapes: $1.00 per lb 3 $1.00 $3.00

Now solve the real problem the same way. Josh: 5 lb $0.49 $2.45

2 lb $1.29 $2.58

$2.45 $2.58 $5.03 Sabrina: 8 lb $0.29 $2.32

3 lb $0.99 $2.97

$2.32 $2.97 $5.29 $5.29 $5.03 $0.26

Sabrina spends $0.26 more.

Step 4


Look Back

Is the solution reasonable? Reread the problem. Does your answer make sense? Explain.

Practice 1. Robert buys 4 pounds of apples for $0.89 per pounds and 3 pounds of grapes for $1.09 per pounds. Which fruit does he spend more on? How much more?

7 2. Kostas buys 8 pound of cashew nuts, 5 1 pound 8 pound of walnuts, and 2 of peanuts. Jane buys 38 pound of cashew nuts, 21 pound of walnuts, 3 and 8 pound of peanuts. Who buys

more nuts? How much more?


NS 1.5; MS 1.1, 1.2, 2.4, 3.2



Explore Subtracting Fractions with Unlike Denominators

P

PRACTICE


2.

1 4

1 3

3.

1 3

1 2

1 1 1 1 6 6 6 6

11 88

1 1 1 6 6 6

1 2 1 4

1 8

2 8

1 8

4.

2 3

1 6

4 6

1 6

5.

1 2 111111 12 12 12 12 12 12

1 2

1 3

3 6

2 6

6.

1 5 11 10 10

1 6 11 12 12

1 3 1 2

6 12

2 12

2 12

1 5


1 7. 1 4 6

2 10

1 6

1 10

1 10

1 12

2 1 12 12

1 8. 1 2 5

1 9. 1 4 12

10. 7 1

2 11. 7 9 3

5 12. 12 14

1 13. 5 6 3

1 14. 3 4 3

1 15. 1 2 12

3 16. 1 2 10

1 17. 5 6 12

3 18. 1 2 8

1 19. 2 3 6

1 20. 4 5 10

1 21. 3 4 8

12

3


NS 1.5, 3.1




R

RETEACH

You can use fraction strips to find equivalent fractions before you subtract fractions with unlike denominators. Subtract

1 4

18 .

1 4

Compare fourths to eighths: 2 8

is equivalent to

1 1 8 8

1 4.

Subtract the eighths. 2 8

So,

1 4

1 8 1 8

1 1 8 8

1 8

18 .

Subtract. You may use fraction strips to help you. Write each difference in simplest form. 2 1. 1 2 12

1 2. 1 5 10

1 3. 3 4 2

4. 7 1

5 5. 10 12

1 6. 5 6 3

3 7. 1 2 10

5 8. 5 6 12

3 9. 1 2 8

1 10. 2 3 6

1 11. 4 5 10

1 12. 7 9 3

5 13. 3 4 8

3 14. 4 5 10

5 15. 11 12 6

7 16. 10 35

1 17. 2 3 6

5 18. 5 6 12


12

3


NS 1.5, 3.1




E

ENRICH

Fraction Wheels Subtract the fraction in the center from each fraction in the inner circle. Write the difference in simplest form in the outer circle. 1.

2. 1 12 7 12 5 9

1 18

1 2

5 6

1 2

2 3

1 4

1 6

1 6

3.

1 12

5 6 2 3

3 4

7 12

4. 7 10 9 10

1 2


5 12

1 3

7 10

1 5

3 10 4 5

1 2

1 8

3 5

5.

5 8

1 4

1 10

3 8

1 4

7 8 7 12

1 3

6. 1 2

1 6 2 3

5 12

7 12

1 6

1 8

1 4

1 3

3 4

1 2

5 6

1 3


1 3

1 2

5 8 11 12

5 12

NS 1.5, 3.1


12–8 Page Subtract Fractions with Unlike DenominatorsPrint P This PRACTICE


7.

1 3 1 12

2.

9 10 35

3 4 5 12

8.

3 4 1 2

3.

9.

1 5 2 15

3 5 3 10

4.

7 10 15

10.

5.

5 9 1 3

11 12 56

11.

2 3 2 9

5 6 2 3

3 4 1 8

6.

12.

1 13. 5 8 4

1 14. 2 3 6

1 15. 1 4 12

7 16. 4 5 10

1 17. 4 9 3

3 18. 4 5 10

1 19. 1 2 6

1 20. 3 8 4

1 21. 7 9 3

7 22. 12 16

1 23. 1 2 4

5 24. 2 3 12

7 25. 12 12

7 26. 10 25

1 27. 1 2 5

Algebra & Functions Find each missing number.


1 28. 7 8 2

8

1 31. 1 13 2

1 29. 5 23 6

2 30. 3 4 12 3

1 32. 2 3 6 2

1 33. 5 29 9

Problem Solving 34. Pam has 7 yard of ribbon. She uses 8

1 2

yard. How much ribbon does Pam

have left?


35. Joe has 5 yard of fabric. He uses 6

2 3

yard to make a kite. How much

fabric does Joe have left?

NS 1.5, 3.1


12–8 Page Subtract Fractions with Unlike DenominatorsPrint R This RETEACH

You can use fraction strips to help you record the steps when you subtract unlike fractions. 7 10

Subtract

25 .

Using Fraction Strips


1111111 10 10 10 10 10 10 10

Find equivalent fractions.

1 1 5 5

7 10

1111 10 10 10 10

2 5

1111111 10 10 10 10 10 10 10 7 10

2 5

7 10

4 10

Subtract the numerators. Use the common 7 10 denominator. 4 10

7 10

3 10

4 10

Write the answer in simplest form if necessary.

3 10

Find each equivalent fraction. Then subtract. Write the difference in simplest form. You may use fraction strips to help you subtract. 7 8

1.

8


34 8

4 5

5.

3 10

1 2 1 5

9.

10

7 12

2.

12

26 12

3 4

6.

10.

1 2 1 3

8

9

7.

7 9


6 10 15

6

16 6

2 3

8.

13

11.

2 3

4.

18 8

16 2

10

1 2

3.

4 12

12.

4 5 1 2

NS 1.5, 3.1


12–8 Page Subtract Fractions with Unlike DenominatorsPrint E This ENRICH

Fraction Memory Game How good is your memory? Play this memory game with a partner. • Make up 12 subtraction sentences with unlike denominators on cards like the sample below. Write each subtraction sentence on a separate index card. Also write each difference, in simplest form, on a separate index card. You should have 24 cards. 3 4

1 8

5 8

• Place the 24 cards facedown. Mix them up. Then arrange the cards in 4 rows of 6 cards each. • Take turns turning over two cards. If a player turns over a subtraction sentence and its matching difference, then he or she keeps the cards and takes another turn. If there is no match, the player turns over both cards. The other player takes a turn.


• Continue taking turns until all the cards have been matched. The player with more pairs of cards wins.


NS 1.5, 3.1



Properties of Fractions

P

PRACTICE

Use properties to find each missing number. 7 1. 10

7 10

1 1 1 2. ( 1 2 3) 4 2 (

3 4 4 3. 10 17 17

( 47 59 ) ( 34 47 )

5. 7. 1 3

3 5

1 3

4.

5 9

0

2 3

1 2

6. 8 9

14 )

8 9

1 2 4 8. ( 4 5 2) 3 5 (

23 )

Add. Then use the property to write a different number sentence. 1 10. 1 ( 1 3 2) 3

9. 1 3 4

8

Commutative

1 12. 1 ( 1 3 4) 2

11. 2 1 9

Associative

3

Commutative

13. 2 3 5

Associative

14. 1 2

10

4


Identity

Identity

15. 1 ( 1 1 ) 12

6

3

2

16. 3 1

Associative


8

2

Commutative

NS 1.5, 3.1; MR 1.1; AF 1.2, 1.3




R

RETEACH

You can use the Commutative, Identity, and Associative properties to help you add fractions. Commutative Property The order of the addends does not change the sum. 1 4

1 4

1 4

11 11 11 88 88 88 3 4

1 8

=

1 8

1 8

1 8

1 8

7 8

0

1 4

1 4

11 11 11 88 88 88

1 8

Identity Property The sum of 0 and any fraction is that fraction. 4 5

1 4

3 4

=

7 8

Associative Property The way you group the fraction addends does not change the sum. (3 1)

4 5

8

8

4 8

3 8

(1 4) 1 8

8

Add. Then use the property to write a different number sentence. 1 1. 1 ( 1 4 2) 8

2. 3 1 8

Associative

Commutative

1 3 4. ( 1 3 6 ) 12

3. 3 3 5

10

Identity © McGraw-Hill School Division

2

Associative

Use the properties to find each missing number. 5. 4 7

4 7

7. 1 8

3 4

3 9. 12

1 1 1 6. ( 1 3 6) 2 3 (

1 2

1 8

8.

3 12

0

9 10

1 1 2 10. ( 2 5 2) 3 5 (


12 )

13 )

NS 1.5, 3.1; MR 1.1; AF 1.2, 1.3



E


ENRICH

Crossword Property Puzzle Identify the property in each clue. Write it in proper place in the crossword puzzle. Then write a fraction as an example for each property in each clue. 2

3

4

A

A

S S O

C

S O C S M I 1 C O M M U T A T

6

5

I

I D V E

C I

U T

T I

D E

N T

A

A

V

N

I

T

T

E

T

T

I

I

I

Y

V E

V E

T Y


Across a

c

c

a

1. b d d b

Down a

c

e

r

t

v

m

o

o

a

c

e

2. ( b d ) f b ( d f )

r

t

v

3. s ( u w ) ( s u ) w

m

4. n p p n

g

g

5. h 0 h

x

x

6. y 0 y


NS 1.5, 3.1; MR 1.1; AF 1.2, 1.3


Problem Solving: Application Analyze and Make Decisions

Print This Page


Record your data. Add Other Juices to This Juice

Possible Combinations and Total Amounts of Juice

Orange Juice Pineapple Juice Grapefruit Juice Cranberry Juice Grape Juice Apple Juice Mixed Berry Juice Mixed Citrus Juice


Your Decision What combinations of juices can Joseph and his sisters use to make exactly one quart of fruit punch?


MR 1.1, 2.3, 3.1; NS 1.5, 3.1


Problem Solving: Application Which objects can hold a static charge?

Print This Page


Safety Be careful when working with scissors. Wear goggles in case the balloon bursts. Record your observations. Material

Observations

Balloon

Cubes

Crayons

Sock

Hand


1. What happened to the string when a charged object came near it?

2. Which objects held a static charge? How do you know?


MR 1.1, 2.3, 3.1, 3.2



Print This Page


Which objects can hold a static charge?

3. What fraction of the objects held a static charge? Construct a circle graph to

display your results.

4. What fraction of all the objects in the world do you think hold a static charge?


Think about how the objects you used represent all things in the world.

5. Explain the results of the activity in terms of static electricity.


MR 1.1, 2.3, 3.1, 3.2



P

Explore Fractions and Decimals

PRACTICE

Write a fraction and a decimal for each shaded part. Then write the fraction in simplest form. 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.


Write each as a decimal. 70

78

13. 100

14. 100

8 17. 10

18. 10

3

21. 10 4

25. 10 4

29. 5

5

66

22. 100 1

26. 2 10

30. 50


13

15. 100 1

19. 100 7

23. 10 10

27. 25 3

31. 4

27

16. 100 4

20. 100 90

24. 100 5

28. 20 2

32. 5 NS 1.6




R

RETEACH

You can use models to show decimals.

This model shows 1.

This model shows 1 divided into 10 equal parts. You can shade the model to 1 1 show 10 . You can write 10 as a decimal: 0.1.

This model shows 1 divided into 100 equal parts. You can shade the model to 1 1 show 100 . You can write 100 as a decimal: 0.01.

Look at each model. Circle the fraction and the decimal for the shaded part. 1.

2. 4 10

4 100

3.

4.

0.4 0.04

7 10

7 100

52 100

0.7 0.07

5 10

8 10

0.5 0.52

8 100

0.8 0.08

Look at each model. Write a decimal for each shaded part. 6.

7.

8.


5.


NS 1.6




E

ENRICH

Riddle Fun Match each of the ten fractions and decimals below with its word name at the right. Write the number of the exercise on the blank. 7

1. 10

C three hundredths

2. 0.5

A eleven hundredths

63

3. 100 4.

O ninety-nine hundredths

90 100

I five tenths

2

5. 10

A twenty-two hundredths

6. 0.89

T eight tenths

11 7. 100

P sixty-three hundredths

8. 0.03

T eighty-nine hundredths

9. 0.22

N ninety hundredths

10. 0.99

O seven tenths

11. 0.17

F two tenths

12. 0.8

A seventeen hundredths

To solve the riddle below, write the letters above the numbers. The first one is done for you.


What kind of coat can be put on only when wet? A 7

8

1

9

6

10

5

3

11

2

4

12

13. Write the decimals in the left-hand column above as fractions.

14. Write the fractions in the left-hand column above as decimals.


NS 1.6



Tenths and Hundredths

P

PRACTICE

Write a fraction and a decimal for each part that is shaded. Then write the fraction in simple form. 1.

2.

3.

4.


7

5. 5

1

6. 10

1

1

9. 2

7

7. 4

8. 100 2

10. 10

96

11. 100

12. 100

13. two tenths

14. fifteen hundredths

15. six hundredths

16. three tenths

17. five tenths

18. seventeen hundredths

19. ninety-nine hundredths

20. two tenths

Write a fraction and a decimal for each point. Tell if it is close to 0, 12, or 1.

A

B 1 2

0 © McGraw-Hill School Division

C

D 1

21. A

22. B

23. C

24. D

Problem Solving 25.

Peter’s house is 0.78 mile from school. Write the number in words.


26.

Lora walks for five tenths of an hour. Write the number as a decimal.

NS 1.6, 1.7




R

RETEACH

You can use a model and a place-value chart to read and write decimals. A model and a place-value chart can also help you write a fraction for a decimal. Using Models

Using Paper and Pencil Ones 0

Think:

5 10

12

•

Tenths 5

Think: 0.5 Ones 0

•

5 10

60 100

6 10

12

Tenths 6

Think: 0.60 Think:

Hundredths

6 100

Hundredths 0

6 10

35

35


Write a fraction and a decimal for each shaded part. Then write the fraction in simplest form. 1.

2.

3.

4.

5.

6.

7.

8.


NS 1.6, 1.7




E

ENRICH

Decimal History Other symbols for decimals were used in England and Europe before the eighteenth century. Here are some examples of different ways to show 0.45. A. 0.4’ .5"

B.

0|45

(1) (2) C. 0.4 .5

D.

0,45

Write the decimals using each of the notations shown above. A

B

C

D

(1) 1.

0.6 (1)

2.

0.4 (1)

3.

0.9 (1)

4.

5.


6.

7.

8.

0.5 (1)

(2)

(1)

(2)

(1)

(2)

(1)

(2)

0.61 0.95 0.78 0.67

9. Which notation is most like the one we use today? Which notation

did you find the most difficult to use? Explain.


NS 1.6, 1.7



Thousandths

P

PRACTICE


370

1. 1,000

17

6. 1,000

6 1,000

10. 1,000

120

4. 1,000

36

1

7. 1,000

24

8. 1,000

3

12

11. 1,000

999

13. 1,000

4

3. 1,000

225

5. 1,000

9.

25

2. 1,000

12. 1,000

9

14. 1,000

60

15. 1,000

16. 1,000

17. sixteen thousandths

18. twenty-five thousandths

19. nine thousandths

20. three hundred twenty-nine thousandths

21. five hundred thousandths

22. six hundred ninety thousandths

23. ninety-five thousandths

24. two thousandths

25. eleven thousandths

26. four thousandths

27. seventy-two thousandths

28. one hundred ninety-nine thousandths

Algebra & Functions Complete.


29.

meters

decimeters

centimeters

millimeters

0.06

0.6

6

0.009 14 Problem Solving 30. Joe weighs 0.625 g of rice. Write

this in words.


31. Jaime bats three hundred one

thousandths for the season. Write this as a decimal.

NS 1.6



Thousandths

R

RETEACH

You can use models and a place-value chart to read and write decimals. Using Models

The first decimal square is divided into hundredths. Think of dividing each hundredth into 10 equal parts. The second decimal square shows thousandths. Think:

7 1,000

0.007

The first decimal square is divided into hundredths. Think of dividing each hundredth into 10 equal parts. The second decimal square shows thousandths. Think:

513 1,000

= 0.513

Using Paper and Pencil Ones

•

Tenths Hundredths Thousandths

0 Think:

0 7 1,000

0

Ones

Tenths Hundredths Thousandths

0

7

0.007

•

Think:

5 513 1,000

1

3

0.513


Write each as a decimal and a fraction. 1.

2.

3.

4.


NS 1.6



Thousandths

E

ENRICH

Decimal Memory Game Play this memory game with a partner. • Cut out the cards below. Mix them up and place them facedown in six rows of six. • The first player turns over two cards. If the cards show an equivalent fraction and decimal, he or she keeps the cards. If the cards do not match, the cards are turned over again and left in the same position. • Try to remember which fractions and decimals have been turned over. • Players take turns until all the cards have been matched.


• The player with more cards wins.

0.5

0.3

0.2

0.7

0.8

0.9

1 2

3 10

1 5

7 10

4 5

9 10

0.35

0.85

0.25

0.75

0.40

0.50

35 100

85 100

1 4

3 4

2 5

1 2

5 1,000

255 1,000

10 1,000

600 1,000

345 1,000

850 1,000

0.005

0.255

0.01

0.600

0.345

0.850


NS 1.6




P

PRACTICE

Reading Skill

Choose a Representation Circle the word fraction or decimal to tell how you will represent the numbers in the problem. Write both numbers in that form. Then compare the data to solve the problem. 1. A survey question asked people how they got to work most often. 4 Of those who answered, 0.3 said bus and 10 said subway. Do more

riders take the bus or the subway? fraction

decimal

4 10

0.3

Answer: 2. A survey question asked bus riders how often they took the bus. Of those who answered, 41 said 5 or more times per week and 0.75

said fewer than 5 times per week. Which answer got the greater number of responses? fraction 1 4

decimal

0.75

Answer:


4 3. Ashley takes the subway to work 5 of the time. Lauren takes the

subway to work 0.7 of the time. Who takes the subway to work the greater part of the time? fraction 4 5

decimal

0.7

Answer:


NS 1.2; MR 1.1, 2.4, 3.2




P

Choose a Representation

PRACTICE


Choose the correct answer. In a survey, 10 out of 20 people say they ride the subway at least once a week. Is it reasonable to say that 0.5 of the people surveyed ride the subway? 1. Which statement is true?

A Twenty people say they ride the subway at least once a week. B Ten out of 20 people say they ride the subway at least once a week.

2. The statement is reasonable because

F 10 20. 1

1

1

G 1 2 2 , and 2 0.5. 10

1

1

H 20 2 , and 2 0.5.

C Ten percent of the people ride the subway at least once a week. Tonya takes the subway 8 out of 10 days. Max takes the subway 0.7 of the time. Max says he takes the subway a greater part of the time than Tonya does. Is his statement reasonable? 3. Which of the following plans can

help you solve this problem? 8

4. Max’s statement is not reasonable

because 8

A Write a decimal for 10 , and compare it to 0.7.

F 10 0.7.

B Write a fraction for 0.7 and 2 compare it to 10 .

H 0.7 10 , and 10 10 .

8

G 10 0.8, and 0.8 0.7. 7

7

8


C Subtract 10 7. In a survey, 10 out of 40 people say they never walk to work. Is it reasonable to say that 0.4 of the people never walk to work? 5. Which statement is true?

A Ten out of 40 people say they never walk to work. B Four out of 10 people never walk to work.

6. The statement is not reasonable

because 10

1

1

F 40 4 , and 4 0.25, not 0.4. 1

3

3

G 1 4 4 , and 4 0.75, not 0.4. 10

4

4

H 40 10 , and 10 0.4.

C Thirty out of 40 people say they never walk to work. Use with Grade 4, Chapter 13, Lesson 4, pages 564–565. (419)

NS 1.2; MR 1.1, 2.4, 3.2




P

Choose a Representation

PRACTICE


Choose the correct answer. A survey question asks people which is faster, the train or the bus. Of the people surveyed, 34 said the train and 0.1 said the bus. The rest of the people said that neither was faster. Which answer got more responses, the train or the bus? 7. Which statement is true?

A Of the people surveyed, 14 said neither was faster. B Of the people surveyed, 0.1 said the train was faster. C Of the people surveyed, 0.1 said the bus was faster.

8. Which of the following plans can

help you solve this problem? 1

F Write a decimal for 4 , and compare it to 0.1. G Write a fraction for 0.1 and 3 compare it to 4 . 1

H Subtract 4 from 1, and write it as a decimal.

Solve. 9. George walks to work 6 out of 10

days. Janice walks to work 0.7 of 10 days. Who walks to work a greater part of the time?


11. In a survey, 0.5 of the people who

answer say that they are very satisfied with subway service. Four tenths of the people say that they are somewhat satisfied. Are more people very satisfied or somewhat satisfied?

13. Alfredo walks to work 15 out of 20

days. He says he walks to work 0.9 of those days. Is his statement reasonable?


10. Train Q is on time or early 0.4 of the 1 time. Train Y is on time or early 2 of

the time. Which train is on time or early a lesser part of time?

12. Colleen takes the bus 18 of the days 7 in June. Rita takes the bus 10 of the

days in June. Who takes the bus more days? [HINT: June has 30 days.]

14. The express bus is late 0.2 of the

time. A reporter says that the express 2 bus is late 10 of the time. Is the reporter’s statement reasonable?

NS 1.2; MR 1.1, 2.4, 3.2



Decimals Greater Than 1

P

PRACTICE

Write as a mixed number in simplest form and a decimal to tell how much is shaded. 1.

2.

3.

Write as a decimal. 4. 7 10

3

5. 1 100

25

2

9. 17 10

8. 6 100

1

13. 2 10

98

16. 18 100

6

20. 6 100

4

24. 24 100 © McGraw-Hill School Division

7

9

12. 9 10

5

7. 8 1,000

5

11. 3 1,000

21

15. 25 1,000

6. 9 100

10. 8 1,000

14. 27 100

5

17. 13 1,000

12

18. 10 1,000

375

22. 23 10

1

26. 9 100

21. 19 1,000

25. 11 100

28. eight and three tenths

8

19

125

37

16

3

19. 11 100

60

23. 76 1,000

26

27. 6 100

29. seven and seventy hundredths

Problem Solving 30. Out of 100 pairs of shoes in a sporting

goods store, 53 are running shoes. What decimal shows the number of running shoes?


31. Out of 1,000 backpacks, 25 are red

and the rest are green. What decimal shows the number of red backpacks?

NS 1.6




R

RETEACH

A mixed number is made up of a whole and a part of a whole. You can use models to help you write mixed numbers as decimals. 7

Mixed Number: 1 10 Decimal: 1.7 Read: one and seven tenths

36 Mixed Number: 2 100 Decimal: 2.36 Read: two and thirty-six hundredths


Look at each model. Write a mixed number and a decimal to tell how much is shaded. 1.

2.

3.

4.

Write a decimal and the word name. 5. 1 9

10

6. 3 5


100

NS 1.6




E

ENRICH

Decimal Crossword Complete the decimal crossword puzzle. Write the decimal for the fraction or word name given in the ACROSS and DOWN clues below. Each decimal point has a space of its own. 1.

5

.

2.

6.

4

.

7.

3

4

4

.

.

5

8

7

.

8.

.

2

3

.

3

14.

6

.

16.

.

5

1

7

7 3

1

1

.

6

21.

9

9

6 5 10


8 3. 37 10 9 6. 44 10

7.

5 3 10

5 8. 3 100 7 11. 12 10 75

14. 6 100 37 15. 38 100

28 17. 3 100

18. thirty-five

and twenty-one hundredths 19. eleven and

six tenths 20. seventy-eight and

seventy-nine hundredths 21. ninety-nine and sixty-

5

1

.

5

2

.

.

2

8

6

3 Down

Across 1.

9.

8

2

9

5

7

7

17.

7

19.

.

0

13.

. .

7 .

.

2

3

8

2

12.

. 20.

5.

8

9

1

18.

3

4.

0

11.

3

. 3

.

4

10.

6 15.

7

3

.

3

8

3.

6

48

1. 53 100 2.

43 6 100 51

3. 34 100 37

4. 80 100 5. 27

12. two and thirty- five

hundredths 13. fifteen and eight

tenths 15. thirty-three and

seven tenths 16. seven and nineteen

28

9. 57 100

hundredths

8

10. 36 10

three hundredths


NS 1.6



Compare and Order Decimals

P

PRACTICE

Compare. Write , , or . 1.

0.2

5. 0.106 9. 9.06

0.02

2.

0.7

0.70

0.160 6. 5.117 9.16

10. 6.5

5.107 5.9

3.

1.78

7. 11.99 11. 2.1

13. 16.75

16.57 14. 14.44

14.54 15. 18.01

17. 21.12

22.13 18. 16.06

16.6

21. 9.01

9.10

22. 14.03

19. 1.1

13.99 23. 2.22

1.87 12.1 0.2

4.

12.16

8. 11.1

2.11

10.1

12. 10.3

18.11 16. 9.1 1.11

12.160

10.300 9.09

20. 9.9

10.0

24. 19.99

18.99

Write in order from greatest to least. 25. 1.78, 1.08, 1.87

26. 0.88, 0.08, 0.98

27. 1.11, 1.21, 0.22

28. 10.02, 9.9, 10.12

29. 7.7, 8.8, 7.07

30. 1.001, 1.011, 1.111


Write in order from least to greatest. 31. 0.01, 0.1, 0.001

32. 2.22, 2.02, 2.12

33. 6.07, 5.99, 6.17

34. 1.06, 1.16, 0.99

35. 11.17, 10.99, 9.99

36. 16.6, 16.61, 16.1

Problem Solving 37. On Monday Ken ran 100 meters in

11.2 seconds. On Tuesday he ran 100 meters in 10.9 seconds. On which day did Ken run faster?


38. Jadwin Bridge is 1.6 km long.

Seely Bridge is 1.06 km long. Which bridge is longer?

NS 1.2, 1.6, 1.7, 1.9




R

RETEACH

You can use models to compare and order decimals. Order the numbers from least to greatest.

3.63

3.68

2.75

Compare the decimals.

Order the decimals.

Since 2 3, 2.75 3.63 and 3.68.

Think: 2.75 3.63 3.68.

Since

63 100

68 100 , 3.63 3.68.

The order from least to greatest is 2.75 3.63 3.68.

Compare. Write , , or . 1.

2.

0.75

0.7


4.

3.

0.66

0.77

5.

0.29

0.25

0.06

0.60

0.03

0.30

6.

0.24

0.33

Write the decimals in order from least to greatest. 7. 0.75, 0.66, 0.7 9. 0.29, 0.25, 0.24

8. 0.06, 0.77, 0.60 10. 0.33, 0.03, 0.30


NS 1.2, 1.6, 1.7, 1.9




E

ENRICH

Puzzles Choose the decimal from the box that solves each puzzle. Use a decimal only once.


10.79

8.08

0.84

8.01

0.89

10.25

8.43

10.33

10.8

Puzzle 1 The decimal is greater than 0. It is less than 0.85

Puzzle 2 The decimal is less than 10.8. It is greater than 10.75.

Puzzle 3 The decimal is greater than 8.02. It is less than 8.1.

Puzzle 4 The decimal is less than 10.30. It is greater than 10.


Puzzle 6 The decimal is greater than 10. It is less than 10.85.

Puzzle 7 The decimal is greater than 8. It is less than 8.07.

Puzzle 8 The decimal is less than 10.4. It is greater than 10.25.


1. Arrange the decimals in the box in order from least to greatest.

2. Explain how you found the answer to Puzzle 3.


NS 1.2, 1.6, 1.7, 1.9




P

PRACTICE

Draw a Diagram Draw a diagram to solve. 1. CD World is 1.8 miles east of the

school. William lives 1.4 miles west of the school. Sound City is 2.9 miles east of William. Is William closer to CD World or to Sound City?

3. Ed walks up 2 floors from his office to

the storeroom. He walks down 6 floors to the cafeteria. How many floors away is the cafeteria from Ed’s office?

2. Silver Hills is 3.9 miles north of Bay

Edge. East Ridge is 1.3 miles south of Silver Hills. East Ridge is 2.8 miles north of Hightown. How far is Bay Edge from Hightown?

4. A cab driver leaves his garage. He

goes north 9 blocks, south 6 blocks, and north 8 blocks. How many blocks is he from his garage?

Mixed Strategy Review Solve. Use any strategy. 5. The City Sports Center offers season

tickets, 20-game tickets, or single game tickets. Seats are available for the lower deck, middle deck, or upper deck. You can buy an individual seat or a pair of seats. How many choices do you have?

6. Social Studies In 1996, Abilene,

Texas, had a population of 122,130. Amarillo, Texas has a population that was 83,885 greater than the population of Abilene. What was the population of Amarillo?

Strategy: © McGraw-Hill School Division

Strategy: 7. There are 48 people at a dinner at

City Hall. You want to use small tables that seat 5 people and large tables that seat 8 people. To have full tables, which tables should be used? How many of these tables will be needed?


solve by drawing a diagram. Share it with others.


NS 1.2; MR 1.1, 2.3, 2.4, 3.2




R

RETEACH

Draw a Diagram Page 575, Problem 1

Kendra wants to go to a mall. The Loews Mall is 3.9 miles east of her town. The Bergen Mall is 1.8 miles west of the Loews Mall. King’s Mall is 2.9 miles east of Bergen Mall. Which mall is the closest to Kendra’s town? the farthest from her town? Step 1

Read

Be sure you understand the problem. Read carefully. What do you know? • Loews Mall is • Bergen Mall is • King’s Mall is

miles east of Kendra’s town. miles west of the Loews Mall. miles east of Bergen Mall.

What do you need to find? • You need to find . Step 2

Make a plan.

Plan

Choose a strategy.

■

■


■

■

■

■

■

■

■

■

■

■

Make a Table Write a Number Sentence Work Backward Act It Out Find a Pattern Make a Graph Guess and Check Choose a Stategy Logical Reasoning Draw a Tree Diagram Solve Simpler Problem Draw a Diagram

Drawing a diagram can help you see the solution to a problem. Draw a line segment to show the distance between Kendra’s town and Loews Mall. Along that line, show the distance between Bergen Mall and Loews Mall. Then show the distance between Bergen Mall and King’s Mall. Extend the line in either direction if you need to. Use your drawing to solve the problem.


NS 1.2; MR 1.1, 2.3, 2.4, 3.2




R

RETEACH

Draw a Diagram Step 3

Solve

Carry out your plan. Draw a diagram. Use 1 cm to show 1 mile. Loews Mall

3.9 miles 3.9 cm

Bergen Mall

1.8 miles 1.8 cm

King’s Mall

2.9 miles 2.9 cm N

Kendra‘s Town

Bergen Mall

Loew‘s Mall

King‘s Mall

W

E S

3.9 cm 1.8 cm 2.9 cm

Mall is closest to Kendra’s town. Mall is farthest from her town. Step 4


Look Back

Is the solution reasonable? Reread the problem. Does your answer make sense? Did you check your answer?

Practice 1. Allison lives 2.6 miles west of the beach. Jerry lives 1.2 miles east of Allison. Phil lives 1.7 miles west of Jerry. Who is farthest from the beach?


2. Norma goes up 4 floors from her

office to her manager’s office. She then goes down 7 floors to the copy room. Randi is in the copy room. Randi goes up 1 floor to her office. How many floors away is Randi’s office from Norma’s?

NS 1.2; MR 1.1, 2.3, 2.4, 3.2



Round Decimals

P

PRACTICE

Round to the nearest whole number. 1. 9.47

2. 2.8

3. 6.01

4. 9.09

5. 1.1

6. 3.51

7. 4.62

8. 1.5

9. 13.61

10. 25.09

11. 37.8

12. 52.4

13. 93.56

14. 88.48

15. 19.71

16. 63.44

Round to the nearest tenth. 17. 7.24

18. 9.43

19. 6.58

20. 8.89

21. 3.25

22. 1.27

23. 3.98

24. 7.24

25. 31.26

26. 71.64

27. 12.55

28. 64.93

29. 47.96

30. 87.54

31. 29.69

32. 36.97

33. 53.84

34. 19.46

35. 61.07

36. 78.85


Round to the nearest hundredth. 37. 8.236

38. 4.186

39. 9.275

40. 1.123

41. 6.008

42. 2.055

43. 7.266

44. 3.199

45. 17.246

46. 26.981

47. 78.006

48. 91.115

49. 53.102

50. 66.666

51. 32.333

52. 45.999

53. 13.462

54. 51.277

55. 90.409

56. 45.555

Problem Solving 57. A vitamin pill weighs 2.346 g. What is

its weight to the nearest hundredth of a gram?


58. Jason weighs 152.6 lb. What is his

weight to the nearest pound?

NS 1.2, 1.3



Round Decimals

R

RETEACH

You can use a number line to help you round decimals. To round a decimal to the nearest whole number, look at the digit in the tenths place. If the ones digit is 5 or greater, round up to the nearest one. If the ones digit is less than 5, round down to the nearest one. 8.0 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9.0 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 10.0

Round 8.3 to the nearest whole number. Think: 8.3 is closer to 8 than 9. So, 8.3 rounds down to 8.

Round 9.8 to the nearest whole number. Think: 9.8 is closer to 10 than 9. So, 9.8 rounds up to 10.

To round to the nearest tenth, look at the digit in the hundredths place. If the hundredths digit is 5 or greater, round up to the nearest tenth. If the hundredths digit is less than 5, round down to the nearest tenth. 1.50 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.601.61 1.62 1.63 1.64 1.65 1.66 1.67 1.68 1.69 1.70

Think: 1.56 is closer to 1.6 than 1.5. So, 1.56 rounds up to 1.6.

Think: 1.61 is closer to 1.6 than 1.7. So, 1.61 rounds down to 1.6.


Round each decimal to the nearest whole number. Use the number line above to help you. 1. 8.6

2. 9.1

3. 8.2

4. 9.3

5. 9.8

6. 8.4

7. 9.5

8. 8.7

Round to the nearest tenth. Use the number line above to help you. 9. 1.52

10. 1.64

11. 1.59

12. 1.63

13. 1.55

14. 1.68

15. 1.51

16. 1.66


NS 1.2, 1.3



Round Decimals

E

ENRICH

Decimal Detective Use the clues to solve each riddle. Circle the mystery number. 1. Round me to the nearest whole number. You get 5.

Round me to the nearest tenth. You get 5.3. Round me to the nearest hundredth. You get 5.32. What number am I?

5.316

5.295

5.334

2. Round me to the nearest whole number. You get 12.


12.557

12.479

12.486



16.937

16.899

16.934



27.959

28.002

28.008




124.456

124.444

124.446


Round me to the nearest tenth. You get 203.5. The sum of my digits is 20. What number am I?

203.456

203.458

203.566

7. Create you own mystery number puzzle.

Exchange your puzzle with a friend to solve.


NS 1.2, 1.3



Print This Page


Applying Decimals Record your data. Name of Item

Number Bought

Total Cost

Items for Business District

Items for Area Where People Live

Your Decision


What models should Kit and Rammel buy for the area where people live? What models should they buy for the business district? Explain.


NS 1.2; MR 1.1, 2.3


Print This Page



Math & Science

How does distance affect how many strikes you throw? Record your data. Distance

Attempts

1.5 m

10

3m

10

4.5 m

10

6m

10

Strikes

Strikes Thrown (as a decimal)


1. At which distance was it easiest to make strikes? Explain your answer.

In ten tries, how many strikes do you think you will be able to throw from 1.5 meters away?


NS 1.2, 1.6; MR 1.1, 2.3, 3.2


Problem Solving: Application How does distance affect how many strikes you throw?

Print This Page


2. How did the results compare to what you thought the

results would be?

3. Order the decimals in the table from least to greatest. If you

made a lot of strikes, was the decimal bigger or smaller than the other numbers?

4. What fraction of all throws are strikes? Write the fraction


as a decimal.

5. Use your answer in number 3 to compare your ability to

throw strikes with Major League Baseball pitchers.


NS 1.2, 1.6; MR 1.1, 2.3, 3.2



Explore Adding Decimals

P

PRACTICE

Use the models to find each sum. 1.

2.

1.56 0.43

3.

1.7 1.2

0.76 0.45


Find each sum. 4.

0.3 0.4

5.

0.5 0.4

6.

0.6 0.7

7.

0.8 0.9

8.

0.4 0.6

9.

0.99 0.88

10.

0.62 0.53

11.

0.71 0.59

12.

0.44 0.79

13.

0.86 0.13

14.

2.7 3.8

15.

0.5 1.9

16.

2.6 1.8

17.

1.7 2.8

18.

0.4 0.9

19. 0.85 2.17

20. 2.76 1.32

21. 3.46 1.78

22. 2.96 2.23

23. 0.67 2.98

24. 0.12 2.2

25. 1.5 2.49

26. 2.14 1.9

27. 2.3 1.92

Problem Solving 28. Two strips of paper, 3.6 cm long and

2.8 cm long, are taped together. How long is the entire strip of paper?


29. One apple weighs 0.26 kg. Another

apple weighs 0.87 kg. How much do the two apples weigh together?

NS 2.1




R

RETEACH

You can use models to help you add decimals. Add 1.7 0.85. Write a decimal to show the total number of shaded squares. 2.55 Color 1.7 dark gray.

Color 0.85 with stripes.

So, 1.7 0.85 2.55.


Add. Draw 10 by 10 grids to help you. 1. 0.65 0.34

2. 1.3 1.5

3. 2.4 1.36

4. 1.52 0.31

5. 0.77 0.24

6. 0.84 0.39

7. 1.8 0.5

8. 2.5 0.62

9. 2.75 0.45


NS 2.1




E

ENRICH

Magic Boxes and Mazes Fill in the boxes so that each row, column, and diagonal adds up to the same sum. 1.

2.

0.9 0.6

1.0

0.8

0.8 0.7 0.4

0.7 3.

4.

0.5 0.7

0.1

1.0

1.2

0.9

0.6 1.1

1.3 1.3

0.5

0.3

1.6


Move through the maze from start to finish by adding numbers that will give you the finish number. You may move across, down, up, or diagonally. Start ↓

Start ↓

5.

6.

2.3

3.1

0.6

0.9

1.4

1.2

0.7

4.1

1.2

2.4

0.3

2.1

2.8

1.7

8.2

7.9

0.6

3.2

↑ Finish

↑ Finish


NS 2.1



Add Decimals

P

PRACTICE

Add. 1.

0.36 0.25

2.

0.29 0.44

3.

0.60 0.70

4.

6.

4.2 6.4

7.

1.2 8.3

8.

0.697 9.262

1.67 1.45

5.

2.67 1.38

9.

23.604 10. 5.408

32.75 12.30

11.

25.97 12. 0.12

12.32 13. 1.74

13.407 14. 26.708

21.151 15. 4.774

6.373 5.602

16.

2.874 17. 8.129

36.215 18. 9.759

12.948 19. 7.267

0.254 20. 12.259

3.187 6.975

21.

11.3 22. 6.7 21.6

8.25 23. 4.30 9.20

4.142 24. 8.167 2.94

4.567 25. 7.0 13.621 9.288 21.984 12.6

26. 12.5 11.35

27. 2.7 2.73

28. 3.36 5.031

29. 3.869 9.3 7.76

30. 7.35 8.2 17.314

31. 12.42 7.687 19.3

32. 8.0 4.343 10.5


Find the number you need to add to complete the pattern. 33. 1.3, 1.9, 2.5, 34. 4.12, 4.125,

,

,

, 4.135,

Add ,

Add

Problem Solving 35. Lora spends $2.64 on stamps and

$1.39 on envelopes. How much does she spend?


36. Ben buys packing tape for $2.97 and

boxes for $6.99. How much does he spend?

NS 2.1



Add Decimals

R

RETEACH

You can use models to help you add decimals. Add 1.34 1.28. Using Models Regroup Color 1.34 dark gray. Color 1.28 with stripes. Count the number of squares you shaded.

Using Paper and Pencil Add each place. Regroup if needed. 1

1.34 1.28 2.62


Find each sum. Draw 10 by 10 grids to help you. 1. 1.7 1.4

2. 0.5 0.8

3. 2.25 1.03

4. 0.9 0.8

5. 0.85 0.15

6. 1.24 0.38

7. 1.5 1.35

8. 1.52 0.35

9. 0.6 1.85


NS 2.1



Add Decimals

E

ENRICH

Digit Detective Find the missing digits. . 2

1.

6

1. 4

1 .

5.

9

5. 4

.7

6. $

10. 8 .

7.

. 1

6 9 . 2

. 9

1 .

6 . 5 . 3

7 22.

2

. 1 6

7 7.

1

$2 . 1

4

3 .

6

4 3

. 4

3

. 1 8

$ 23. 4

2 . 9 8 .

0 . 4

1 6

1 . 2 1


1 8 . 4 12. 6 .

1 5 . 8 7 16.

. 3 7 . 7 6 . 2

6

8

3 . 2 . 9 0 .

4 3

4

7 .

24.

3 . 4

2

4 .

20.

. 0

8 6 .

2 3

2

7

7

. 5

. 4

5

. 3 7

3. 3

19.

1

1

. 4

3. 8 6

15.

2 . 3

5

4

2 .

6

7 . 8 5

3 1 .

3 .

2 2 . 1

1 .

5

6 . 6

18.

1 .

2

9 .

8.

1 . 9 9

11. 7 7 .

. 1 3

$

.5

$

3

$10

17. 6 9 .

21.

8

2 . 7

1

8

$7 6 . 2

. 6 7

4. $ 6

.3 3

7. $ 8

. 0

14.

1 0 . 3

4 .6 6 .

1 4 . 9

13. 5 9 .

$ 6 2.

9. 2

1

5

8.

9.

3.

4. 7

3 .6 4

1 0

2

9. 6

1 3 .9


. 2

2.

9 3

. 1 8 6 . 8

NS 2.1



Estimate Sums

P

PRACTICE

Estimate. Round to the nearest whole number. 1. 5.1 9.4

2. 6.7 8.4

3. 1.9 3.8

4. $6.35 $5.95

5. 7.45 8.56

6. 4.32 7.59

7. 9.3 2.6

8. 22.63 3.46

9. 31.06 9.98

10. 45.92 4.18

11. $33.19 $9.50

12. 6.67 21.15

Add. Estimate to check for reasonableness. 13. 19.76 9.55

14. $10.25 $3.25

15. 19.67 9.94

16. 3.7 5.2 4.6

17. 4.1 9.6 1.9

18. 2.9 6.7 7.3

19. $3.75 $9.90 $8.75

20. 4.76 9.15 8.95

21. 8.12 4.79 7.15

22. $6.30 $7.95 $8.10

23. 7.75 8.90 9.90

24. 2.178 6.472 8.015


Algebra & Functions Compare. Write or . 25. 3.7 2.5

1.9 4.2 26. 4.9 1.6

5.1 3.1 27. 6.9 7.1

3.8 8.3

28. 9.2 3.6

2.6 9.1 29. 5.5 6.3

8.2 5.2 30. 9.4 2.7

6.8 6.1

31. 1.6 2.9

3.1 1.1 32. 7.7 7.2

8.1 9.1 33. 8.7 9.6

9.1 8.6

Problem Solving 34. The odometer on a new car shows

17.7 miles. Sean drives the car 12.9 miles. About what does the odometer show now?


35. Lenny buys one CD for $12.75 and

another CD for $18.90. About how much does Lenny pay for the two CDs?

NS 2.1, 2.2, 3.1; MR 2.1



Estimate Sums

R

RETEACH

To estimate the sums of decimals, round each decimal to the nearest whole number. Then add the rounded numbers. Estimate 22.52 4.49. ↓ ↓ Round each number 23 4 to the nearest whole number. Add.

23 4 27

So, 22.52 4.49 is about 27.

Estimate $7.95 $9.25 ↓ ↓ Round each number $8.00 $9.00 to the nearest dollar. Add.

$8.00 $9.00 = $17.00

So, $7.95 $9.25 is about $17.00.

Circle the digits in the place to which you will round each number.


Estimate each sum. Show how you rounded. 1. $ 5 . 8 9 $ 4 . 2 9

2. 1 7 . 3 5 . 6 7

3. 8 . 4 8 3 . 0 7

4.

5. $ 1 5 . 9 5 $ 2 . 5 9

6. 2 5 . 7 8 . 9

7. 1 5 . 7 5 1 2 . 3 4

8.

9.

11.

6. 7 3.2

9.9 7 8.4

5.6 3 1 8.4 7

10. $ 6 . 5 2 $ 1 . 7 5

4.4 7 6.7 4

12. $ 8 . 5 0 $2 4 . 3 8


NS 2.1, 2.2, 3.1; MR 2.1



Estimate Sums

E

ENRICH

Four for 16 Use estimation to try to choose four numbers that will have a sum close to 16. • Player 1 chooses a number from below and writes it in the first box for that round. He or she crosses out the number below. • Player 2 chooses any number that is not crossed out and follows the same steps. • Players take turns until each player has four numbers. • Add the numbers. Then find the difference between each sum and 16. You may check your results with a calculator. • The player with the sum closer to 16 wins that round. Round

Players

1

Player 1

Numbers

Sum

How Close to 16?

Player 2 2

Player 1 Player 2

3

Player 1 Player 2

4

Player 1


Player 2 5

Player 1 Player 2

3.38

3.56

1.08

4.5

6.75

2.03

2.58

4.61

3.23

4.89

2.47

4.19

8.48

3.96

4.91

5.57

7.59

2.19

2.64

1.18

1.77

2.63

5.72

5.63

4.24

3.27

5.13

3.76

2.30

4.55

3.69

3.31

4.16

6.89

7.81

7.35

8.74

0.99

3.49

3.98


NS 2.1, 2.2, 3.1; MR 2.1




P

PRACTICE

Reading Skill

Choose the Operation Circle the number sentence you would use to solve the problem. Then tell how you decided whether to use addition or subtraction. 1. Chico bikes 4.6 miles. Tom bikes 3.7 miles. How much farther does

Chico bike than Tom? 4.6 3.7 8.3 4.6 3.7 0.9 Explain:

2. Keiko rode her bike 8.4 miles last week. This week, she rode

4.35 miles more than last week. How far did Keiko ride this week? 8.4 4.35 12.75 8.4 4.35 4.05 Explain:

3. Rachel bikes 3.2 miles to the mall. Then she bikes 2.7 miles to the

park. How many miles does she bike? 3.2 2.7 5.9 3.2 2.7 0.5


Explain:

4. Mark is biking around a 9.2-mile loop. He has biked 4.5 miles so far.

How many miles does Mark have left to finish the loop? 9.3 4.5 13.8 9.3 4.5 4.8 Explain:


NS 2.1; MR 1.1, 2.4, 3.2




P

Choose the Operation

PRACTICE


Choose the correct answer. Mikio rides his bike 4.25 miles from home to school. Then he rides 2.9 miles to the park. How far does Mikio ride? 1. Which of the following statements

2. Which number sentence can you use

is true?


A Hiroshi walks to school.

F 4.25 2.9 7.15

B Hiroshi rides 4.25 miles in all.

G 2.9 2.9 5.8

C The ride from school to the park is 2.9 miles.

H 4.25 2.9 1.35

It is 5.6 miles from Sarah’s house to the museum. She has completed 1.75 miles of the trip so far. How many miles does Sarah have left? 3. What do you have to do to solve


this problem?


A Add to find the total amount of miles that Sarah travels to the museum.

F 5.6 5.6 11.2

B Subtract to find the number of miles Sarah has left.

G 5.6 1.75 7.35 H 5.6 1.75 3.85


C Add to find the total number of miles in the round trip. Michael takes the train for 8.4 miles. Then he walks 0.6 miles. How many miles does Michael travel? 5. Which could you use to solve

6. How many miles does Michael

the problem?

travel?

A 8.4 0.6

F 16.8 miles

B 8.4 0.6

G 9 miles

C 8.4 8.4

H 8.4 miles


NS 2.1; MR 1.1, 2.4, 3.2




P

Choose the Operation

PRACTICE


Choose the correct answer. Roland bikes 8.24 miles. Paul bikes 4.62 miles. How much farther does Roland bike than Paul? 7. Which of the following statements


is true?


A Paul bikes farther than Roland.

F 8.24 4.62 3.62

B Roland bikes 4.62 miles.

G 4.62 4.62 9.24

C Paul bikes 4.62 miles.

H 8.24 4.62 12.86

Solve. 9. The train trip from Springfield to

Morris Hill is 6.2 miles. The next stop, Peapack, is 3.2 miles from Morris Hills. How long is the train trip from Springfield to Peapack?

11. Daniel biked 6.24 miles last week.


This week he biked 1.65 miles less than last week. How far did he bike this week?

13. Eddie rode 1.9 miles more today

than he did yesterday. He rode 5.75 miles yesterday. How far did Eddie ride today?


10.The train trip from Point Dume to

Snug Harbor is 8.31 miles. The road from Point Dume to Snug Harbor is 9.6 miles. How much longer is the train trip than the road?

12. Myra bikes 3.25 miles from home

to the record store. Then she bikes 1.1 miles to the movie theater. How many miles does she bike altogether?

14. Shore Road is 6.3 miles long. Nicole

has biked 2.2 miles along Shore Road so far. How many miles does she have left?

NS 2.1; MR 1.1, 2.4, 3.2



Explore Subtracting Decimals

P

PRACTICE

Use the models to find each difference. 1.

2.

0.68 0.35

3.

1.12 0.7

1.8 1.1


Find each difference. 4.

0.9 0.3

5.

1.2 0.6

6.

2.7 0.9

7.

2.5 1.6

8.

2.1 1.7

9.

1.67 0.48

10.

1.6 1.48

11.

3.11 1.12

12.

3.7 2.91

13.

1.2 1.13

14.

3.6 1.47

15.

2.02 1.79

16.

0.95 0.67

17.

0.8 0.25

18.

0.74 0.59

19.

1.7 0.35

20.

2.04 1.69

21.

1.03 0.6

22.

0.80 0.54

23.

2.0 1.06

24. 2.7 1.6

25. 0.8 0.5

26. 7.66 2.34

27. 1.52 0.57

28. 0.73 0.57

29. 0.70 0.34

30. 0.8 0.07

31. 0.4 0.14

32. 3.7 0.16

Problem Solving 33. A board is 2.12 m long. A piece

1.55 m long is cut from it. How much of the board is left?


34. A piece of wire is 2.6 cm long. A

piece 1.9 cm long is cut from it. How much of the wire is left?

NS 2.1




R

RETEACH

You can use models to help you subtract decimals. Subtract 1.85 0.9. Write a decimal to show how many squares are not crossed out. 0.95 Shade 1.85.

Cross out 0.9.

So, 1.85 0.9 0.95.


Subtract. Draw 10 by 10 grids to help you. 1. 1.6 1.3

2. 0.8 0.3

3. 1.22 0.55

4. 1.9 0.56

5. 0.80 0.57

6. 1.35 1.07

7. 0.8 0.09

8. 1.85 1.49

9. 1.7 0.45


NS 2.1




E

ENRICH

Magic Triangles In a magic triangle, each side of the triangle has the same sum. Choose numbers from the box so each side of the triangle has a sum of 22.4. 3.8

5.19

6.88

7.22

5.19

0.73

1.6

2.48

4

4.85

5.35

4.3

4

3.6

6.88

2.08

Choose numbers from the box so each side of the triangle has a sum of 24.5. 5.8

0.73 © McGraw-Hill School Division

4.9

5

4.9

4.85

5.05

2

4

8.92

4.3

7.22

2.67

5.84

4

5.35

2.48


5

1.6

6.5

NS 2.1



Subtract Decimals

P

PRACTICE

Subtract. Check each answer. 1.

0.7 0.4

2.

6.3 0.7

3.

9.1 2.3

7.

0.44 0.22

8.

7.04 3.66

9.

13.

9.04 7.50

14.

19.

8.154 20. 2.075

4.5 2.7

1.2 0.7

6.

0.43 0.26

15.03 10. 4.12 11. 3.12 1.27

9.00 12. 0.09

7.17 2.70

6.00 15. 8.20 16. 5.34 17. 4.70 4.96 4.67

1.67 18. 0.50

19.83 3.60

4.

5.

17.076 21. 5.258 22. 8.000 23. 1.755 24. 6.024 0.027 3.129 2.974 0.896 2.402

25. 6.7 2.4

26. 7.6 2.07

27. 8.5 3.08

28. 9.03 3.775

29. 7.44 3.867

30. 4.627 2.88

31. 3.6 2.79

32. 8.36 3.248

33. 4.556 0.93

34. 34.0 2.097


Algebra & Functions Find each missing number. 35. 7.97 n 0.52

36. h 4.64 2.31

37. 5.25 b 10.46

38. a 7.08 18.5

Problem Solving 39. Christine buys a pair of socks for

$8.35. What is her change from a $10 bill?


40. Matt buys a pencil for $0.35, a pen

for $2.75, and a ruler for $4.36. What is his change from a $20 bill?

NS 3.1; MR 2.2



Subtract Decimals

R

RETEACH

You can use models to help you subtract decimals. Subtract 1.7 1.59. Using Models Color 1.7. Cross out 1.59. Count the number of squares not crossed out.

Using Paper and Pencil Subtract each place. Regroup if necessary. Write zero as a 1.70 ← placeholder. 1.59 0.11 6 10


Find each difference. Draw 10 by 10 grids to help you. 1. 1.8 1.2

2. 0.9 0.5

3. 1.25 0.18

4. 0.8 0.25

5. 1.35 1.08

6. 1.7 0.48

7. 0.5 0.05

8. 1.65 1.3

9. 1.06 0.88


NS 3.1; MR 2.2



Subtract Decimals

E

ENRICH

Problem Generator • • • •

Cut out the numbered cards below. Mix them up and place them face down. Turn over 8 cards and place them into a. and b. Then solve. Record your work. Repeat several times.

a.

b.

•

•

•

•

1. Turn over all the cards. Using b., what is the greatest possible

sum you can make?

2. Using a., what is the greatest possible difference you can make

without using the zeros?

✄ 0 1

2 3 4 5 6 7 8 9

✄


3. What method did you use to find the answer in exercise 2?

0 1

2 3 4 5 6 7 8 9


MR 2.2; NS 3.1




P

PRACTICE

Estimate. Round to the nearest whole number. 1. 6.3 2.6

2. 7.1 4.8

3. 8.7 5.2

4. 9.0 3.9

5. 4.6 1.5

6. 7.34 5.78

7. 8.57 3.52

8. 17.26 13.78

9. 26.14 12.95

11. 25.60 11.55

12. 47.15 17.11

10. $34.95 $12.20

Subtract. Estimate to check for reasonableness. 13. 7.1 2.70

14. 9.8 4.6

15. 8.5 6.3

16. 5.6 1.75

17. 36.62 23.13

18. 24.35 10.4

19. 77.36 15.93

20. $16.12 $12.80

21. 94.32 22.80

22. $54.10 $34.89

23. 13.4 6.79

24. 47.65 17.93

25. $14.75 $6.90

26. 63.5 18.27


Algebra & Functions Compare. Write or . 27. 7.2 3.5

8.8 5.4 28. 9.9 4.8

6.4 1.7 29. 7.6 2.2

5.6 1.3

30. 8.3 6.6

4.2 2.3 31. 9.1 8.7

2.1 1.1 32. 7.2 4.5

6.8 5.8

33. 5.2 2.3

9.7 7.9 34. 9.3 3.8

9.9 3.1 35. 8.1 4.6

7.2 5.1

Problem Solving 36. Jake has $25.75. He spends $13.15

on magazines. About how much money does Jake have left?


37. Nancy ran a total of 5.7 miles today.

She ran 3.2 miles this morning. About how many miles did Nancy run this afternoon?

NS 2.1, 2.2, 3.1; MR 2.1




R

RETEACH

To estimate differences of decimals, round each decimal to the nearest whole number. Then subtract the rounded numbers. Estimate 12.25 5.79. ↓ ↓ Round each number 12 – 6 to the nearest whole number.

Estimate $6.25 $4.79. ↓ ↓ Round each number $6.00 $5.00 to the nearest dollar.

Subtract.

Subtract.

12 – 6 = 6

So, 12.25 5.79 is about 6.

$6.00 $5.00 $1.00

So, $6.25 $4.79 is about $1.00.

Circle the digits in the place to which you will round each number.


Estimate each difference. Show how you rounded. 1. $ 7 . 2 4 $ 3 . 6 9

2. 2 7 . 3 1 5 . 7 6

3. 1 2 . 4 3 . 7

4. 1 2 . 7 4 . 8

5. $ 2 5 . 7 5 $ 7 . 8 0

6. 2 5 . 8 7 7 . 2

7. 1 4 . 2 5 7 . 8 4

8. 1 0 . 9 7 7 . 4

9. 3 . 6 2 1 . 8 7

11. $1 0 . 5 4 $ 7 . 8 1

10. $1 0 . 2 5 $ 3 . 4 5

12. 4 3 . 7 2 0 . 4 8


NS 2.1, 2.2, 3.1; MR 2.1




E

ENRICH

Dollars and Sense scissors

$7.49

T-Shirt

markers

$2.89

sweatshirt

$3.29

notebook jeans

$14.95

paper

$0.89

$8.98 $12.98 $11.99

backpack

$29.99

sneakers radio

$14.98

ruler

$0.99

glue

$1.59

pencils clock pen

$1.29 $5.98 $1.19

About how much more would Group A cost than Group B?


Group A

Group B

Difference

1. paper, glue

notebook, ruler

2. sweatshirt, jeans

T-Shirt, jeans

3. backpack, pencils

clock, pen

4. markers, sneakers

radio, scissors

5. clothing and shoes

everything but clothing and shoes

Estimate to solve. 6. Andy buys a box of markers. He gives

the clerk $20. He receives $18.11 in change. Is the amount of change reasonable? Explain.


7. Heidi buys a clock. She gives the clerk

$10. She receives $4.02 in change. Is the amount of change reasonable? Explain.

NS 2.1, 2.2, 3.1; MR 2.1




P

PRACTICE

Solve Simpler Problems Solve using a simpler problem. 1. The tennis team travels to a statewide

contest. They buy 8 student bus tickets at $6.95 each and 2 adult bus tickets at $9.50 each. How much does the team spend for tickets?

2. A bus ticket costs $8.75. A train

ticket for the same ride costs $12.50. Suppose you buy 4 tickets. How much money would you save by taking the bus instead of the train?

3. A bus driver earns $16.40 per hour

4. The Silver Eagle Express has a dining

for the first 7 hours of work each day. She earns $24.60 per hour for each hour over 7 hours. How much does she earn in a 9-hour day?

car. Sandwiches cost $5.95. Drinks cost $1.49. How much does a family pay for 3 sandwiches and 4 drinks?

Mixed Strategy Review Solve. Use any strategy. 5. Sam spends $18.40 on a train ticket,


$5.90 on a cab, and $11.20 on dinner. He has $30 left. How much money did Sam have when he started?

6. Science The first steam-powered

railroad engine was built in England 1804. Thomas Edison tested an electricpowered railroad engine 76 years later. When did Edison test his engine?

Strategy: 7. Teri has 17 model trains. She has a

long shelf that can hold 7 trains. She also has 2 smaller shelves. How can she arrange the trains on shelves so that each smaller shelf has an equal number of trains?

Strategy: 8. Create a problem for which you

could use a simpler problem to help you find the answer. Share it with others.


MR 1.1, 1.2, 2.2, 2.4, 3.2




R

RETEACH

Solve Simpler Problems Page 616, Problem 2

A train conductor earns $18.45 an hour. A ticket checker earns $12.95 an hour. How much do both workers earn in an 8-hour day?

Step 1

Read

Be sure you understand the problem. Read carefully. What do you know? • A train conductor works an hour. • A ticket checker works an hour.

hours for hours for

What do you need to find? • You need to find how much

Step 2

Make a plan.

Plan

Choose a strategy.

■

■

■


■

■

■

■

■

■

■

Find a Pattern Guess and Check Work Backward Make a Graph Make a Table or List Write a Number Sentence Draw a Picture Solve a Simpler Problem Logical Reasoning Act it Out

Use simpler numbers to make up a problem similar to the one you need to solve. Then solve the real problem the same way.


MR 1.1, 1.2, 2.2, 2.4, 3.2




R

RETEACH

Solve Simpler Problems Step 3

Solve

Solve this simpler problem. • A conductor works 8 hours for $18 an hour. The conductor earns 8

or

.

• A ticket checker works 8 hours at $13 an hour. The ticket checker earns 8

or

The total amount is

.

.

Now solve the real problem the same way. • A conductor works 8 hours at

an hour.

The conductor earns 8

or

.

• A ticket checker works 8 hours at

an hour.

The ticket checker earns 8

or

The total amount is

.

Step 4


Look Back


Yes Yes

No No


Practice 1. The Sheppards buy 2 adult tickets for $8.70 each and 3 children’s tickets for $4.35 each. How much money do they spend?


2. Gina buys 3 model planes for

$14.95 each and 4 model trains for $7.29 each. How much money does Gina spend?

MR 1.1, 1.2, 2.2, 2.4, 3.2



Use Properties to Add and Subtract

P

PRACTICE

Add or subtract mentally. 1. 3.56 0.04

2. 4.12 1.7

3. 4.5 4.5

4. 1.7 1.3

5. 8.87 0.03

6. 5.08 0.9

7. 6.04 6

8. 7.86 1.06

9. 17.23 0

10. 12.13 0.14

11. 11.22 10.02

12. 15.66 10.44

13. 17.01 9.99

14. 10.17 8.18

15. 15.44 3.22

16. 3.6 4.7 0.4

17. 13.1 5.6 3.9

18. 7.9 2.8 0.9

19. 7.5 6.3 4.5

20. 9.3 2.6 4.4

21. 6.3 5.5 1.7

22. 8.7 2.9 5.7

23. 9.1 4.7 9.1


Algebra & Functions Find each missing number. 24. 4.9 b 6.0

25. (f 1.5) 3.5 5

26. 2.7 c 2.7

27. 10.6 d 5

28. 14.12 m 0

29. 3.7 h 6.3 3.7

30. 6.3 w 6.3

31. 4.2 t 10

32. 2.7 9.3 9.3 n

33. a 7.9 0

Problem Solving 34. It takes Anita 11.6 seconds to sprint

35. Fernando expected to run the mile in

the first 100 m and 12.3 s to sprint the second 100 m. How long does it take Anita to sprint the 200 m?

5.6 minutes. Because of an injury, he ran the mile in 6.3 minutes. How much slower than expected did Fernando run the mile?


NS 3.1; AF 1.2, 1.3; MR 2.2




R

RETEACH

You can use the Commutative, Associative, and Identity properties to add and subtract mentally. Look for compatible numbers. (1.3 4.2) 1.7 (4.2 1.3) 1.7 4.2 (1.3 1.7) 4.2 3.0 7.2

Look for zeros.

Think: 1.3 and 1.7 are compatible. 5.35 0 5.35 Use the Commutative Property. 3.29 0 3.29 Use the Associative Property. Add the compatible numbers. Look for the same number. Find the sum. 0.85 0.85 0 16.5 0 16.5

Remember: Associative Property: When adding, the grouping of the numbers does not affect the sum. Commutative Property: When adding, the order of the numbers does not affect the sum. Identity Property: In addition, the sum of 0 and a number is the number.


Use mental math to add or subtract. 1. 2.6 0.4 =

2. 4.75 0 =

3. 1.5 3.2 1.5 =

4. 2.7 2.7 =

5. 6.78 6 =

6. 4.7 0 5.3 =

7. 12.24 6.12 =

8. 10.10 5.01 =

9. 1.8 2.2 1.3 =

10. 3.3 3.3 =

11. 2.3 3.5 =

12. 8.9 2.9 8 =

13. 14.6 0 5.4 =

14. 4.44 4.44 =


NS 3.1; AF 1.2, 1.3; MR 2.2




E

ENRICH

Crack the Code Use the symbols below to write the top numbers in exercises 1–6. Use the code and properties to add or subtract the bottom number using mental math. Write the answers using numbers and the code symbols. Check your symbol answers with a friend. Use the code to write all the numbers in exercises 7–9 before you check by adding.

0

1

2

3

Example:

2.5

4

5

6

7

8

9

←Think: 0.0


2.5 1.

2.

3.

4.

5.

6.

7.

8.

9.

10. Which problem can you solve without using numbers? Use with Grade 4, Chapter 14, Lesson 9, pages 618–619. (462)

NS 3.1; AF 1.2, 1.3; MR 2.2


Print This Page


Problem Solving: Application Applying Adding and Subtracting Decimals

Decision Making

Record your data and notes. Route (List all stops and highways used.)

Miles Traveled

Costs

Other Notes


Your Decision What is your recommendation for the Lopez family? Explain.


MR 1.1, 2.2; NS 3.1


Problem Solving: Application How would you conserve electricity?

Print This Page


Record data for your conservation plans in this chart. Plan

Activity

Time Saved

Money Saved

Plan 1

Plan 2


Plan 3


NS 2.1; MR 1.1, 2.3, 3.3


Print This Page



Math & Science

How would you conserve electricity?

1. Which of your three plans would you prefer to use?

Explain your answer.

2. Which of your three plans might you actually use?

Explain your answer.

3. Look at the plan you liked best. How much money would you save

in a month? in a year?

4. Compare the advantages and disadvantages of the different ways to produce


electricity. Think about costs, energy efficiency, and stress to the environment.


NS 2.1; MR 1.1, 2.3, 3.3

Math Worksheets

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