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Explore How Big Is a Million?
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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
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Explore How Big Is a Million?
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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 1, Lesson 1, pages 2–3. (2)
NS 1.1
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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
© McGraw-Hill School Division
each store would need to sell in 1 day.
5. What if you were Skye? What would be your plan? Tell about your plan.
Use with Grade 4, Chapter 1, Lesson 1, pages 2–3. (3)
NS 1.1
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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
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 1, Lesson 2, pages 4–7. (4)
40 3
8,000 800 80 8
NS 1.1
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Place Value Through Millions
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 =
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 1, Lesson 2, pages 4–7. (5)
+
+
+
+
+
+
+ 10 +
Word Name
NS 1.1
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Place Value Through Millions
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?
,
,
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 1, Lesson 2, pages 4–7. (6)
NS 1.1
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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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 1, Lesson 3, pages 8–11. (7)
NS 1.2
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Compare and Order Numbers
and Money
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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 1, Lesson 3, pages 8–11. (8)
7. 50,281
$21.12
6,117
51,002
9. $285.45
$293.45
11. 832,077
822,077
NS 1.2
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Compare and Order Numbers
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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.
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 1, Lesson 3, pages 8–11. (9)
NS 1.2
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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?
© McGraw-Hill School Division
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
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Problem Solving: Reading for Math
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 1, Lesson 4, pages 12–13. (11)
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
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Problem Solving: Reading for Math
Using the Four-Step Process
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P
PRACTICE
Math Skills
Test Prep
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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 1, Lesson 4, pages 12–13. (12)
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
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Round Numbers and Money
P
PRACTICE
Round to the given place.
1. 923 to the nearest
2. $0.93 to the nearest
ten
3. $6.49 to the nearest
ten cents
4. $57.52 to the nearest
dollar
dollar
5. 862 to the nearest
6. $46.47 to the nearest
hundred
7. 4,357 to the nearest
dollar
8. $73.96 to the nearest
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
13. $34.06 to the nearest
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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 1, Lesson 5, pages 14–17. (13)
18.Joe’s class bought a bird feeder for
$38.75. To the nearest dollar, what
was the cost?
NS 1.3
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Round Numbers and Money
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 1, Lesson 5, pages 14–17. (14)
NS 1.3
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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.
© McGraw-Hill School Division
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
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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?
© McGraw-Hill School Division
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
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Problem Solving: Strategy
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
■
© McGraw-Hill School Division
■
■
■
■
■
■
■
■
■
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.
Use with Grade 4, Chapter 1, Lesson 6, pages 20–21. (17)
NS 1.2; SDP 1.3; MR 1.1, 2.3, 3.2
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R
Problem Solving: Strategy
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 1, Lesson 6, pages 20–21. (18)
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
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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
Amount given: $10.00
Amount given: $10.00
Problem Solving
13. Andy gives the cashier $5.00 to pay
for a $3.75 calendar. How much
change does he receive?
Use with Grade 4, Chapter 1, Lesson 7, pages 22–23. (19)
14. Lowanda receives 1 quarter, 2 dimes,
and 1 nickel in change. How much
money is that?
NS 1.0; MR 2.4
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Count Money and Make Change
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:
© McGraw-Hill School Division
2. Amount given: $10.00
8
8
SCHOOL MONEY
8
8
$3.79
Cost
Amount of change:
Use with Grade 4, Chapter 1, Lesson 7, pages 22–23. (20)
NS 1.0; MR 2.4
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Count Money and Make Change
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
© McGraw-Hill School Division
Clue: 19 coins, but only two kinds
7.
Clue: 3 bills, 3 coins
8.
$15.55
Clue: 2 bills, 3 coins
Use with Grade 4, Chapter 1, Lesson 7, pages 22–23. (21)
$23.00
Clue: 5 bills, 3 coins
NS 1.0; MR 2.4
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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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 1, Lesson 8, pages 24–25. (22)
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
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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.
0 is to the right of 4, so 0 4.
3 is to the right of 6, so 3 6.
Complete.
1.
2.
3.
4.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 1, Lesson 8, pages 24–25. (23)
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
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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
© McGraw-Hill School Division
2
0
1
6
3
5
Use with Grade 4, Chapter 1, Lesson 8, pages 24–25. (24)
4
NS 1.8
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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
© McGraw-Hill School Division
Discount Pet Food
Your Decision
What is your recommendation for Stacia? Explain.
Use with Grade 4, Chapter 1, Lesson 9, pages 26–27. (25)
NS 1.2; MR 1.1, 2.3
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1–9
Part
B WORKSHEET
Problem Solving: Application
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 1, Lesson 9, pages 28–29. (26)
NS 1.2; MR 1.1, 2.3, 3.3
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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?
© McGraw-Hill School Division
4. In which areas did you vary the least from your partner?
5. Why is it good to have variation in nature?
Use with Grade 4, Chapter 1, Lesson 9, pages 28–29. (27)
NS 1.2; MR 1.1, 2.3, 3.3
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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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 2, Lesson 1, pages 44–45. (28)
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
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Use Properties of Addition
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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 2, Lesson 1, pages 44–45. (29)
8. 9, 45, 54
NS 3.1; AF 1.1
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Use Properties of Addition
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.
© McGraw-Hill School Division
BB
JJ
Z0
7.
QQP
8.
0W
Write the related number sentences.
9.
ANB
Use with Grade 4, Chapter 2, Lesson 1, pages 44–45. (30)
10.
DEF
NS 3.1; AF 1.1
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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 © McGraw-Hill School Division
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?
Use with Grade 4, Chapter 2, Lesson 2, pages 46–47. (31)
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
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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.
© McGraw-Hill School Division
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
Add mentally.
3. 800 600 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
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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
© McGraw-Hill School Division
Row 3
200
Row 4
200
Row 5
200
Row 6
Row 7
200
200
Use with Grade 4, Chapter 2, Lesson 2, pages 46–47. (33)
200
400
600
200
600
1,200
200
200
200
200
NS 3.1; MR 1.1
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Add Whole Numbers and Money
P
PRACTICE
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 2, Lesson 3, pages 48–51. (34)
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
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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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 2, Lesson 3, pages 48–51. (35)
NS 3.1
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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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 2, Lesson 3, pages 48–51. (36)
NS 3.1
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Use Mental Math to Add
P
PRACTICE
Add mentally.
1. 32 45 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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 2, Lesson 4, pages 52–53. (37)
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
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Use Mental Math to Add
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
© McGraw-Hill School Division
Add mentally.
1. 62 39 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 Use with Grade 4, Chapter 2, Lesson 4, pages 52–53. (38)
NS 3.1; AF 1.1
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Use Mental Math to Add
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?
© McGraw-Hill School Division
the sum of the digits was greater than 9?
How is mental math different from estimation?
Use with Grade 4, Chapter 2, Lesson 4, pages 52–53. (39)
NS 3.1; AF 1.1
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 2, Lesson 5, pages 54–55. (40)
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
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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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 2, Lesson 5, pages 54–55. (41)
NS 2.1, 3.1; MR 2.1, 2.5
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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
© McGraw-Hill School Division
381
825
524
418,670
174
41,321
432
2.
129,600
Use with Grade 4, Chapter 2, Lesson 5, pages 54–55. (42)
645
4.
447,700
NS 2.1, 3.1; MR 2.1, 2.5
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Problem Solving: Reading for Math
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?
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 2, Lesson 6, pages 56–57. (43)
MR 1.1, 2.1, 2.3, 2.4, 2.5, 3.1, 3.2
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Problem Solving: Reading for Math
P
Estimate or Exact Answer
PRACTICE
Math Skills
Test Prep
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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 2, Lesson 6, pages 56–57. (44)
MR 1.1, 2.1, 2.3, 2.4, 2.5, 3.1, 3.2
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Problem Solving: Reading for Math
P
Estimate or Exact Answer
PRACTICE
Math Skills
Test Prep
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?
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 2, Lesson 6, pages 56–57. (45)
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
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Subtraction Patterns
P
PRACTICE
Complete the pattern.
1. 12 8 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?
Use with Grade 4, Chapter 2, Lesson 7, pages 60–61. (46)
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
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Subtraction Patterns
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.
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 2, Lesson 7, pages 60–61. (47)
10. $1,700,000 $900,000 12. 120,000 40,000 NS 3.1; MR 1.1
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Subtraction Patterns
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
© McGraw-Hill School Division
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!
Use with Grade 4, Chapter 2, Lesson 7, pages 60–61. (48)
NS 3.1; MR 1.1
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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
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 2, Lesson 8, pages 62–63. (49)
NS 3.1
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Explore Subtracting Whole Numbers
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.
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 2, Lesson 8, pages 62–63. (50)
12. 745 67 NS 3.1
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Explore Subtracting Whole Numbers
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 2, Lesson 8, pages 62–63. (51)
8
9
10
11
12
13
14
15
16
NS 3.1
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Subtract Whole Numbers and Money
P
PRACTICE
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 2, Lesson 9, pages 64–65. (52)
NS 3.1
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Subtract Whole Numbers and Money
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.
© McGraw-Hill School Division
Subtract. Check by adding.
1.
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
Use with Grade 4, Chapter 2, Lesson 9, pages 64–65. (53)
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
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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
© McGraw-Hill School Division
1,821
1,205
7,280
626
637
8
4.
3.
5.
3,750
616
Use with Grade 4, Chapter 2, Lesson 9, pages 64–65. (54)
3,650
100
4,861
2,419
6.
1,242
922
320
NS 3.1
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Regroup Across Zeros
P
PRACTICE
© McGraw-Hill School Division
Subtract. Check by adding.
1.
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?
Use with Grade 4, Chapter 2, Lesson 10, pages 66–67. (55)
NS 3.1
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Regroup Across Zeros
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
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 2, Lesson 10, pages 66–67. (56)
NS 3.1
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Regroup Across Zeros
E
ENRICH
Missing Digits
Find the missing digits.
1.
8
0
7
1
3
4.
0
1
7.
10.
6,
3,
7
2
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 2, Lesson 10, pages 66–67. (57)
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
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Problem Solving: Strategy
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:
© McGraw-Hill School Division
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:
Use with Grade 4, Chapter 2, Lesson 11, pages 68–69. (58)
NS 3.1; AF 1.1, 2.1; MR 1.1
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Problem Solving: Strategy
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
■
■
■
■
■
© McGraw-Hill School Division
■
■
■
■
■
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.
Use with Grade 4, Chapter 2, Lesson 11, pages 68–69. (59)
NS 3.1; AF 1.1, 2.1; MR 1.1
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Problem Solving: Strategy
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?
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 2, Lesson 11, pages 68–69. (60)
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
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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 © McGraw-Hill School Division
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?
Use with Grade 4, Chapter 2, Lesson 12, pages 70–71. (61)
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
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2–12 Page
Subtract Using Mental Math
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 2, Lesson 12, pages 70–71. (62)
NS 3.1; AF 2.1
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2–12 Page
Subtract Using Mental Math
E
ENRICH
Crossnumber Puzzle
Subtract mentally to complete the crossnumber puzzle.
A
4
8
E
2
G
9
B
2
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 2, Lesson 12, pages 70–71. (63)
NS 3.1; AF 2.1
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 2, Lesson 13, pages 72–73. (64)
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
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Estimate Differences
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 2, Lesson 13, pages 72–73. (65)
NS 2.1, 3.1; MR 2.1, 2.5
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Estimate Differences
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
© McGraw-Hill School Division
1C
4A
10
C
8C
4B
1A
5C
9B
5A
7A
8A
5B
t
ar
St
7A
A. 20,000
9C
A. 1,000
Use with Grade 4, Chapter 2, Lesson 13, pages 72–73. (66)
NS 2.1, 3.1; MR 2.1, 2.5
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Problem Solving: Application
Applying Addition and Subtraction
Print This Page
2–14
Part
A WORKSHEET
Decision
Making
Record your data.
© McGraw-Hill School Division
Burgers-to-Go
Ruby’s Healthy Diner
Carnival Lunch Menu
Your Decision
Where do you think The Outdoor Club should eat? Explain.
Use with Grade 4, Chapter 2, Lesson 14, pages 74–75. (67)
MR 1.1; NS 3.1
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Name
Problem Solving: Application
Which materials block a magnet?
Print This Page
2–14
Part
B WORKSHEET
Math &
Science
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
© McGraw-Hill School Division
Magnet with paper
Magnet with foil
Magnet with tape
Use with Grade 4, Chapter 2, Lesson 14, pages 76–77. (68)
NS 1.2, 3.1; MR 1.1, 3.1
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2–14
Part
B WORKSHEET
Problem Solving: Application
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
© McGraw-Hill School Division
blockers? Explain.
5. What are some other materials that you think would be bad
blockers? Explain.
Use with Grade 4, Chapter 2, Lesson 14, pages 76–77. (69)
NS 1.2, 3.1; MR 1.1, 3.1
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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 =
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 3, Lesson 1, pages 92–95. (70)
180
240
300
3
4
5
MR 1.1, 2.3
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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.
© McGraw-Hill School Division
4 15
7.
3 20
8.
Use with Grade 4, Chapter 3, Lesson 1, pages 92–95. (71)
2 50
9.
MR 1.1, 2.3
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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:
© McGraw-Hill School Division
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
Pattern: Increase by
3 :00
Pattern: Decrease by
11 12 1
2
10
3
9
4
8
7 6 5
Pattern: Increase by
Use with Grade 4, Chapter 3, Lesson 1, pages 92–95. (72)
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
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 3, Lesson 2, pages 96–97. (73)
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
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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
© McGraw-Hill School Division
12 15
5. Begin
End
6 00
6. Begin
10 30
Use with Grade 4, Chapter 3, Lesson 2, pages 96–97. (74)
3 15
End
2 15
2 35
MR 1.1, 2.3
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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?
Use with Grade 4, Chapter 3, Lesson 2, pages 96–97. (75)
MR 1.1, 2.3
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 3, Lesson 3, pages 98–99. (76)
another appointment 10 days later. On
which date is Pat’s appointment?
MR 1.1, 2.3
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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?
Use with Grade 4, Chapter 3, Lesson 3, pages 98–99. (77)
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
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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?
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 3, Lesson 3, pages 98–99. (78)
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
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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?
Use with Grade 4, Chapter 3, Lesson 4, pages 100–101. (79)
SDP 1.1
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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
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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.
© McGraw-Hill School Division
• 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
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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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 3, Lesson 5, pages 102–103. (82)
SDP 1.1, 1.2
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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
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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.
© McGraw-Hill School Division
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
Group 2’s Test Scores
Students’ Scores for Group 2
Range
18
Jason
Ann
88
Median
91
Steven
82
Karen
94
Mode
94
Melissa
94
Leroy
90
Serena
98
Carl
80
Group 3’s Test Scores
Students’ Scores for Group 3
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.
Use with Grade 4, Chapter 3, Lesson 5, pages 102–103. (84)
SDP 1.1,1.2
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Problem Solving: Reading for Math
Identify Extra and Missing Information
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3–6 Page
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?
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 3, Lesson 6, pages 104–105. (85)
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
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Identify Extra and Missing Information
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P
PRACTICE
Math Skills
Test Prep
© McGraw-Hill School Division
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
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Problem Solving: Reading for Math
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P
Identify Extra and Missing Information
PRACTICE
Math Skills
Test Prep
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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 3, Lesson 6, pages 104–105. (87)
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
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Problem Solving: Strategy
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:
Use with Grade 4, Chapter 3, Lesson 7, pages 108–109. (88)
MR 1.1, 2.3, 2.4, 3.1, 3.2, 3.3
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Problem Solving: Strategy
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
■
■
■
© McGraw-Hill School Division
■
■
■
■
■
■
■
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
Make a plan.
Choose a strategy.
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.
Use with Grade 4, Chapter 3, Lesson 7, pages 108–109. (89)
MR 1.1, 2.3, 2.4, 3.1, 3.2, 3.3
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Problem Solving: Strategy
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.?
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 3, Lesson 7, pages 108–109. (90)
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
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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?
© McGraw-Hill School Division
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
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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?
© McGraw-Hill School Division
Favorite Fruit
Fruit
Tally
Favorite Fruit
Total
Apples
9
Pears
5
Oranges
10
Plums
4
Apples
Pears
Oranges
Plums
Key: Each
Key: Each
Use with Grade 4, Chapter 3, Lesson 1, pages 110–111. (92)
stands for 2 people.
stands for 1 person.
SDP 1.1, 1.3
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 3, Lesson 8, pages 110–111. (93)
SDP 1.1, 1.3
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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
© McGraw-Hill School Division
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
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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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 3, Lesson 9, pages 112–115. (95)
Florida
France
Australia
Girls
SDP 1.1, 1.3
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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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 3, Lesson 9, pages 112–115. (96)
SDP 1.1, 1.3
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 3, Lesson 10, pages 116–117. (97)
between the city hall and the
court house. What ordered pair
names the garage’s location?
MG 2.1, 2.2, 2.3
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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?
© McGraw-Hill School Division
, 4).
What is here?
3. Start at 0. Go right 2, then up 8.
The ordered pair is
2. Start at 0. Go right 4, then up 4.
.
What is here?
4. Start at 0. Go right 6, then up 7.
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)
Use with Grade 4, Chapter 3, Lesson 10, pages 116–117. (98)
MG 2.1, 2.2, 2.3
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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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 3, Lesson 10, pages 116–117. (99)
MG 2.1, 2.2, 2.3
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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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 3, Lesson 11, pages 118–119. (100)
SDP 1.1,1.3
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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).
© McGraw-Hill School Division
• 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?
Use with Grade 4, Chapter 3, Lesson 11, pages 118–119. (101)
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
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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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 3, Lesson 11, pages 118–119. (102)
SDP 1.1, 1.3
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3–12
Part
A WORKSHEET
Problem Solving: Application
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
© McGraw-Hill School Division
Your Decision
Which activities did you choose for the Sequoia Nature Club?
Explain your choices.
Use with Grade 4, Chapter 3, Lesson 12, pages 120–121. (103)
MR 1.1, 2.3, 2.4, 2.6, 3.1
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Problem Solving: Application
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3–12
Part
B WORKSHEET
Math &
Science
Does practice make perfect?
Record your data.
Attempt
Time Needed to Complete the Puzzle
1
2
3
4
5
6
7
8
© McGraw-Hill School Division
9
10
1. Describe what happened to the time you needed as you
repeated the puzzle over and over.
Use with Grade 4, Chapter 3, Lesson 12, pages 122–123. (104)
NS 1.2; SDP 1.1, 1.3; MR 2.3, 3.2
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3–12
Part
B WORKSHEET
Problem Solving: Application
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.
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 3, Lesson 12, pages 122–123. (105)
NS 1.2; SDP 1.1, 1.3; MR 2.3, 3.2
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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 © McGraw-Hill School Division
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?
Use with Grade 4, Chapter 4, Lesson 1, pages 138–139. (106)
34. Sheila arranges her pennies in 9
rows with 6 pennies in each row.
How many pennies does Sheila have?
AF 1.1
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The Meaning of Multiplication
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.
© McGraw-Hill School Division
Find each product.
4.
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 Use with Grade 4, Chapter 4, Lesson 1, pages 138–139. (107)
AF 1.1
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The Meaning of Multiplication
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
© McGraw-Hill School Division
1. 12
Use with Grade 4, Chapter 4, Lesson 1, pages 138–139. (108)
AF 1.1
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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 © McGraw-Hill School Division
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?
Use with Grade 4, Chapter 4, Lesson 2, pages 140–141. (109)
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
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Properties of Multiplication
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 © McGraw-Hill School Division
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 Use with Grade 4, Chapter 4, Lesson 2, pages 140–141. (110)
AF 1.1; MR 1.1
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Properties of Multiplication
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.
© McGraw-Hill School Division
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
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 4, Lesson 3, pages 142–145. (112)
41. Four parents are needed on each of
9 committees. How many parents are
needed?
NS 4.1
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Multiply by 2, 3, 4, and 6
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
•••••
•••••
•••••
•••••
••••• •••••
•••••
•••••
•••••
•••••
•••••
•••••
© McGraw-Hill School Division
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 )
Use with Grade 4, Chapter 4, Lesson 3, pages 142–145. (113)
12. 8 4 (8 ) (8 )
)
NS 4.1
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Multiply by 2, 3, 4, and 6
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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 4, Lesson 3, pages 142–145. (114)
NS 4.1
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Multiply by 5 and 10
P
PRACTICE
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 4, Lesson 4, pages 146–147. (115)
54. Jan places 5 rows of 8 stars in a
rectangle to make a design. How
many stars does she use?
NS 3.2
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Multiply by 5 and 10
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 © McGraw-Hill School Division
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.
Use with Grade 4, Chapter 4, Lesson 4, pages 146–147. (116)
10
9
19.
14. 5 5 5
9
20.
10
4
NS 3.2
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Multiply by 5 and 10
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 4, Lesson 4, pages 146–147. (117)
NS 3.2
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 4, Lesson 5, pages 148–149. (118)
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
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Multiply by 7, 8, and 9
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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 4, Lesson 5, pages 148–149. (119)
3
9
4
9
17.
6
7
18.
4
8
23.
10
7
24.
9
8
NS 3.2, 4.1
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Multiply by 7, 8, and 9
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.
© McGraw-Hill School Division
glo Dro
v p
Go e in ped
3s b m
pa ack ud.
ce
s.
Puddle
Field
Markers
Start
Use with Grade 4, Chapter 4, Lesson 5, pages 148–149. (120)
NS 3.2, 4.1
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Problem Solving: Reading for Math
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4–6 Page
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,
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 4, Lesson 6, pages 150–151. (121)
MR 1.1, 2.3, 2.4, 3.2
Print This Page
Name
Problem Solving: Reading for Math
Choose an Operation
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4–6 Page
P
PRACTICE
Math Skills
Test Prep
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?
© McGraw-Hill School Division
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
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Problem Solving: Reading for Math
Choose an Operation
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P
PRACTICE
Math Skills
Test Prep
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 4, Lesson 6, pages 150–151. (123)
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
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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 © McGraw-Hill School Division
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
Use with Grade 4, Chapter 4, Lesson 7, pages 152–153. (124)
27
44
15. 4 8
18. 12 4
25 4
23
NS 4.1, 4.2, MR 1.1
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Multiplication Table and Patterns
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 4, Lesson 7, pages 152–153. (125)
NS 4.1, 4.2; MR 1.1
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Multiplication Table and Patterns
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
© McGraw-Hill School Division
7
7.
6
72
6
18
2
0
8.
56
28
16
40
15
35
18
16
24
9
0
36
18
21
6
Use with Grade 4, Chapter 4, Lesson 7, pages 152–153. (126)
42
NS 4.1, 4.2; MR 1.1
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 4, Lesson 8, pages 156–157. (127)
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
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Multiply Three Numbers
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(
© McGraw-Hill School Division
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) Use with Grade 4, Chapter 4, Lesson 8, pages 156–157. (128)
)
AF 1.3
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Multiply Three Numbers
E
ENRICH
The Search for 48
© McGraw-Hill School Division
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!
Use with Grade 4, Chapter 4, Lesson 8, pages 156–157. (129)
AF 1.3
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 4, Lesson 9, pages 160–161. (130)
NS 3.2; MR 1.1
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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
© McGraw-Hill School Division
20 5 7. 30 5
30 5 8
3. 12 3
16
16 8 5. 21 7
21 7 8. 27 9
27 9 Use with Grade 4, Chapter 4, Lesson 9, pages 160–161. (131)
4
12
12 3 6. 24 6
24 6 9. 28 4
28 4 NS 3.2; MR 1.1
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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.
© McGraw-Hill School Division
• 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
Use with Grade 4, Chapter 4, Lesson 9, pages 160–161. (132)
NS 3.2; MR 1.1
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Problem Solving: Strategy
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?
© McGraw-Hill School Division
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.
Strategy:
Use with Grade 4, Chapter 4, Lesson 10, pages 162–163. (133)
NS 3.2; MR 1.1
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Problem Solving: Strategy
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
■
■
© McGraw-Hill School Division
■
■
■
■
■
■
■
■
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.
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.
Use with Grade 4, Chapter 4, Lesson 10, pages 162–163. (134)
NS 3.2; MR 1.1
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Problem Solving: Strategy
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.
Is the solution reasonable?
Reread the problem.
Does your answer make sense?
Did you answer the question?
Yes
Yes
No
No
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 4, Lesson 10, pages 162–163. (135)
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
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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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 4, Lesson 11, pages 164–167. (136)
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
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Divide by 2 Through 12
Find 48 6.
R
RETEACH
Think: How many groups of 6 are in 48?
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 4, Lesson 11, pages 164–167. (137)
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
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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
© McGraw-Hill School Division
24
40
18
30
30
20
54
10
10
TOUCHDOWN!
50
G
35
Use with Grade 4, Chapter 4, Lesson 11, pages 164–167. (138)
NS 3.2; MR 1.1, 2.4, 3.2
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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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 4, Lesson 12, pages 168–171. (139)
NS 3.2; AF 1.1; MR 1.1
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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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 4, Lesson 12, pages 168–171. (140)
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
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4–12 Page
Fact Families
E
ENRICH
Chain Reaction
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 4, Lesson 12, pages 168–171. (141)
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
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Name
Problem Solving: Application
Applying Multiplication and Division
Print This Page
4–13
Part
A WORKSHEET
Decision
Making
Record your data.
Storage Unit
Capacity: Number
of trophies or
medals per unit
Number of
Units Used
Total Cost
Shelf
© McGraw-Hill School Division
Frame
(small or large)
Your Decision
What is your recommendation for Lily? Explain.
Use with Grade 4, Chapter 4, Lesson 13, pages 174–175. (142)
NS 3.1, 3.3; MR 1.1, 1.2
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4–13
Part
B WORKSHEET
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
© McGraw-Hill School Division
3 books
4 books
5 books
Use with Grade 4, Chapter 4, Lesson 13, pages 176–177. (143)
NS 3.4; MR 1.1, 2.3
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Name
Problem Solving: Application
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4–13
Part
B WORKSHEET
Math &
Science
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
© McGraw-Hill School Division
10-book ramp? a 20-book ramp? Explain how you made these estimates.
5. Explain the activity in terms of speed.
Use with Grade 4, Chapter 4, Lesson 13, pages 176–177. (144)
NS 3.4; MR 1.1, 2.3
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 5, Lesson 1, pages 192–193. (145)
29. A ream of paper is 500 sheets of
paper. How many sheets are in
7 reams?
NS 3.2
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Patterns of Multiplication
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
Complete the pattern.
1. 3 3 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 © McGraw-Hill School Division
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 Use with Grade 4, Chapter 5, Lesson 1, pages 192–193. (146)
NS 3.2
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Patterns of Multiplication
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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 5, Lesson 1, pages 192–193. (147)
17.
18.
21.
16.
NS 3.2
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Explore Multiplying 2-Digit Numbers
by1-Digit Numbers
P
PRACTICE
1. Multiply 4 15. Draw squares to multiply.
© McGraw-Hill School Division
Find each product.
2.
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?
Use with Grade 4, Chapter 5, Lesson 2, pages 194–195. (148)
32. Band members march in 24 rows.
There are 8 members in each row.
How many members are in the
band?
NS 3.2
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Name
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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
© McGraw-Hill School Division
Find each product.
3.
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 Use with Grade 4, Chapter 5, Lesson 2, pages 194–195. (149)
NS 3.2
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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 © McGraw-Hill School Division
H
2. 2 34 T
O
4. 5 43 H
H
3. 3 31 T
O
5. 4 212 T
O
H
Use with Grade 4, Chapter 5, Lesson 2, pages 194–195. (150)
T
H
T
O
6. 3 304 O
H
T
O
NS 3.2
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5–3 Page
Multiply 2-Digit Numbers
by 1-Digit Numbers
P
PRACTICE
© McGraw-Hill School Division
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.
31. Multiply 78 by 4.
32. Multiply 37 by 6.
33. Multiply 45 by 5.
34. Multiply 56 by 7.
35. Multiply 82 by 3.
Problem Solving
36. A rectangle is 5 tiles wide by
13 tiles high. How many tiles are
in the rectangle?
Use with Grade 4, Chapter 5, Lesson 3, pages 196–199. (151)
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
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Multiply 2-Digit Numbers by
1-Digit Numbers
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.
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 5, Lesson 3, pages 196–199. (152)
NS 3.2, 3.3
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Multiply 2-Digit Numbers
by 1-Digit Numbers
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
© McGraw-Hill School Division
4
5
4
2
5
2
5
7
7
0
5
6
6
8
5
4
Use with Grade 4, Chapter 5, Lesson 3, pages 196–199. (153)
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
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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?
Use with Grade 4, Chapter 5, Lesson 4, pages 200–201. (154)
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
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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.
© McGraw-Hill School Division
Estimate each product.
1. 2 74
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
Use with Grade 4, Chapter 5, Lesson 4, pages 200–201. (155)
9
NS 1.4, 3.2; 3.3
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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
3. Target Number: 180
S. 57 3
H. 37 4
D. 3 67
T. 52 3
I. 32 4
E. 3 61
4. Target Number: 540
5. Target Number: 420
6. Target Number: 560
S. 88 6
T. 7 62
O. 76 8
T. 83 6
U. 7 68
A. 72 8
7. Target Number: 2,700
8. Target Number: 630
9. Target Number: 4,500
T. 3 879
T. 79 9
E. 9 490
U. 3 849
U. 72 9
F. 9 430
10. Target Number: 3,600
11. Target Number: 5,600
12. Target Number: 6,000
N. 849 4
E. 770 8
L. 2,181 3
O. 889 4
F. 680 8
M. 2,898 3
13. Target Number: 6,400
14. Target Number: 7,200
15. Target Number: 2,400
I. 839 8
A. 711 9
E. 303 8
J. 899 8
B. 782 9
F. 352 8
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 5, Lesson 4, pages 200–201. (156)
12 13 14 15 16 17 18
NS 1.4, 3.2, 3.3
Print This Page
Name
Problem Solving: Reading for Math
Use an Overestimate or Underestimate
Print This
5–5 Page
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?
© McGraw-Hill School Division
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
Print This Page
Name
Problem Solving: Reading for Math
Use an Overestimate or Underestimate
Print This
5–5 Page
P
PRACTICE
Math Skills
Test Prep
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?
© McGraw-Hill School Division
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
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Name
Problem Solving: Reading for Math
Use an Overestimate or Underestimate
Print This
5–5 Page
P
PRACTICE
Math Skills
Test Prep
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?
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 5, Lesson 5, pages 202–203. (159)
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
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5–6 Page
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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 5, Lesson 6, pages 206–209. (160)
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
Print This Page
Name
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5–6 Page
Multiply Greater Numbers
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 5, Lesson 6, pages 206–209. (161)
12. $7,452
5
NS 3.2, 3.3
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5–6 Page
Multiply Greater Numbers
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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 5, Lesson 6, pages 206–209. (162)
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
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5–7 Page
Problem Solving: Strategy
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.
© McGraw-Hill School Division
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
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Problem Solving: Strategy
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.
What do you need to find?
• You need to find how many
.
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 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.
Use with Grade 4, Chapter 5, Lesson 7, pages 210–211. (164)
NS 3.2; MR 1.1, 2.4, 3.2
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Problem Solving: Strategy
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
© McGraw-Hill School Division
What other strategies could you use to solve the problem?
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?
Use with Grade 4, Chapter 5, Lesson 7, pages 210–211. (165)
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
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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.
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 5, Lesson 8, pages 212–215. (166)
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
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Functions and Graphs
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 5, Lesson 8, pages 212–215. (167)
x
0
1
y
2
4
2
AF 1.1, 1.5; SDP 2.1
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Functions and Graphs
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
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5–9
Part
A WORKSHEET
Problem Solving: Application
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
© McGraw-Hill School Division
Snack
Items
Your Decision
What is your recommendation for the menus (one breakfast, one lunch,
one dinner, and snacks)?
Use with Grade 4, Chapter 5, Lesson 9, pages 216–217. (169)
NS 1.2, 3.2; MR 1.1, 2.3, 3.1
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Problem Solving: Application
How much water do you use each day?
Print This Page
5–9
Part
B WORKSHEET
Math &
Science
Record your data.
Number of Times Amount of Water
a Day You Use This
for Each Use
Source of Water
Total Amount
of Water
© McGraw-Hill School Division
Place You
Use Water
Use with Grade 4, Chapter 5, Lesson 9, pages 218–219. (170)
NS 1.2, 3.2; MR 1.1, 3.3
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Name
Problem Solving: Application
Print This Page
5–9
Part
B WORKSHEET
Math &
Science
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?
© McGraw-Hill School Division
4. Is clean water a renewable or nonrenewable resource? Explain.
5. Give some other examples of renewable and nonrenewable resources.
Use with Grade 4, Chapter 5, Lesson 9, pages 218–219. (171)
NS 1.2, 3.2; MR 1.1, 3.3
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6-1 Page
Patterns of Multiplication
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 6, Lesson 1, pages 234–235. (172)
33.
Handy Hardware has 500 boxes of
hinges. Each box has 90 hinges. How
many hinges does the store have?
NS 3.2
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Patterns of Multiplication
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
Complete the pattern.
1. 4 3 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 © McGraw-Hill School Division
Multiply. Use mental math.
5. 3 6 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
Use with Grade 4, Chapter 6, Lesson 1, pages 234–235. (173)
4,000 50 NS 3.2
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Patterns of Multiplication
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
© McGraw-Hill School Division
Across
Down
1. 80 8,000
1. 70 90,000
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
Use with Grade 4, Chapter 6, Lesson 1, pages 234–235. (174)
NS 3.2
Print This Page
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Explore Multiplying
by 2-Digit Numbers
Print This
6–2 Page
P
PRACTICE
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 6, Lesson 2, pages 236–237. (175)
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
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Explore Multiplying
by 2-Digit Numbers
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 © McGraw-Hill School Division
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 Use with Grade 4, Chapter 6, Lesson 2, pages 236–237. (176)
15. 26 17 NS 3.2, 3.3
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Explore Multiplying by 2-Digit Numbers
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 6, Lesson 2, pages 236–237. (177)
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
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6–3 Page
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?
Use with Grade 4, Chapter 6, Lesson 3, pages 238–239. (178)
42.
A computer costs $2,345.
How much will 20 computers cost?
NS 3.2, 3.3
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Multiply by Multiples of 10
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 )
)(
)
(
)
) (
)
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 6, Lesson 3, pages 238–239. (179)
NS 3.2, 3.3
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Multiply by Multiples of 10
E
ENRICH
Missing Digits
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 6, Lesson 3, pages 238–239. (180)
6
4
5 0
3 9, 2 0 0
NS 3.2, 3.3
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Problem Solving: Reading for Math
Solve Multistep Problems
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6–4 Page
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?
© McGraw-Hill School Division
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:
Use with Grade 4, Chapter 6, Lesson 4, pages 240–241. (181)
MR 1.2, 2.4, 3.2
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Problem Solving: Reading for Math
Solve Multistep Problems
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P
PRACTICE
Math Skills
Test Prep
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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 6, Lesson 4, pages 240–241. (182)
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
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Solve Multistep Problems
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P
PRACTICE
Math Skills
Test Prep
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?
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 6, Lesson 4, pages 240–241. (183)
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
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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?
Use with Grade 4, Chapter 6, Lesson 5, pages 242–245. (184)
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
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Multiply by 2-Digit Numbers
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
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 6, Lesson 5, pages 242–245. (185)
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
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Multiply by 2-Digit Numbers
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 Use with Grade 4, Chapter 6, Lesson 5, pages 242–245. (186)
NS 3.2, 3.3
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 6, Lesson 6, pages 246–247. (187)
28. An airline ticket costs $375.
About how much will tickets cost
for a group of 25 people?
NS 3.2, 3.3
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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
© McGraw-Hill School Division
Estimate each product.
4. 37 49
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
Use with Grade 4, Chapter 6, Lesson 6, pages 246–247. (188)
NS 3.2, 3.3
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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
© McGraw-Hill School Division
6,123
R
E
Write the letters from the boxes you go through in order. What message do you find?
’
Use with Grade 4, Chapter 6, Lesson 6, pages 246–247. (189)
!
NS 3.2, 3.3
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6–7 Page
Multiply Greater Numbers
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 © McGraw-Hill School Division
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?
Use with Grade 4, Chapter 6, Lesson 7, pages 250–253. (190)
28. Pencils are packaged with 144 pencils
in a box. How many pencils are there
in 50 boxes?
NS 3.2, 3.3
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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
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 6, Lesson 7, pages 250–253. (191)
7.
8,098
66
10. 52 19,071
NS 3.2, 3.3
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Multiply Greater Numbers
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 6, Lesson 7, pages 250–253. (192)
NS 3.2, 3.3
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Problem Solving: Strategy
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;
© McGraw-Hill School Division
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.
Strategy:
Use with Grade 4, Chapter 6, Lesson 8, pages 254–255. (193)
SDP 1.1; MR 2.3, 2.4, 3.2
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Problem Solving: Strategy
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
Make a plan.
Choose a strategy.
A graph can help you compare data quickly.
Make a bar graph to solve the problem.
Use with Grade 4, Chapter 6, Lesson 8, pages 254–255. (194)
SDP 1.1; MR 2.3, 2.4, 3.2
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Problem Solving: Strategy
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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 6, Lesson 8, pages 254–255. (195)
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
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P
Multiply Using Mental Math
PRACTICE
Multiply. Use mental math.
1. 12 30 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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 6, Lesson 9, pages 256–257. (196)
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
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Multiply Using Mental Math
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)
© McGraw-Hill School Division
Multiply. Use mental math.
5. 20 45 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 Use with Grade 4, Chapter 6, Lesson 9, pages 256–257. (197)
NS 3.2, 3.3
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Multiply Using Mental Math
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
© McGraw-Hill School Division
24
16
14
40
300 22
Use with Grade 4, Chapter 6, Lesson 9, pages 256–257. (198)
NS 3.2, 3.3
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Problem Solving: Application
Print This Page
6–10
Part
A WORKSHEET
Decision
Making
Applying Multiplication
Record your data.
© McGraw-Hill School Division
Sailboats
Rowboats
Paddle boats
Canoes
Your Decision
Which boat or boats will the family rent? How long will they ride? Explain.
Use with Grade 4, Chapter 6, Lesson 10, pages 258–259. (199)
NS 1.2, 3.3; MR 1.1, 2.3
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6–10
Part
B WORKSHEET
Problem Solving: Application
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
© McGraw-Hill School Division
Each hour
Use with Grade 4, Chapter 6, Lesson 10, pages 260–261. (200)
NS 3.2, 3.3; MR 1.1, 3.3
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6–10
Part
B WORKSHEET
Problem Solving: Application
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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 6, Lesson 10, pages 260–261. (201)
NS 3.2, 3.3; MR 1.1, 3.3
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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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 7, Lesson 1, pages 276–277. (202)
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
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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 © McGraw-Hill School Division
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 Use with Grade 4, Chapter 7, Lesson 1, pages 276–277. (203)
NS 3.2, 3.4; MR 3.2
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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?
Use with Grade 4, Chapter 7, Lesson 1, pages 276–277. (204)
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.
© McGraw-Hill School Division
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
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 7, Lesson 2, pages 278–279. (205)
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
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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 © McGraw-Hill School Division
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 Use with Grade 4, Chapter 7, Lesson 2, pages 278–279. (206)
NS 3.2, 3.4
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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?
© McGraw-Hill School Division
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
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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.
28. Divide 834 by 5.
29. Divide 909 by 8.
Algebra & Functions Find each missing number.
30. 1,065 © McGraw-Hill School Division
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?
Use with Grade 4, Chapter 7, Lesson 3, pages 280–283. (208)
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
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Divide 3-Digit Numbers
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
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 7, Lesson 3, pages 280–283. (209)
NS 3.2, 3.4
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Divide 3-Digit Numbers
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 7, Lesson 3, pages 280–283. (210)
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
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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 © McGraw-Hill School Division
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?
Use with Grade 4, Chapter 7, Lesson 4, pages 284–285. (211)
41. A family of 4 spent $824 during their
vacation. If divided evenly, how much
is that per person?
NS 3.2, 3.4
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Zeros in the Quotient
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 Use with Grade 4, Chapter 7, Lesson 4, pages 284–285. (212)
NS 3.2, 3.4
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Zeros in the Quotient
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.
Use with Grade 4, Chapter 7, Lesson 4, pages 284–285. (213)
NS 3.2, 3.4
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Problem Solving: Reading for Math
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.
© McGraw-Hill School Division
Explain your thinking:
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.
Use with Grade 4, Chapter 7, Lesson 5, pages 286–287. (214)
NS 3.4; MR 1.1, 2.4, 2.6, 3.1, 3.2
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Problem Solving: Reading for Math
P
Interpret the Remainders
PRACTICE
Math Skills
Test Prep
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
to solve this problem?
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?
© McGraw-Hill School Division
5. Which of the following statements
6. How do you interpret the remainder
is false?
to solve this problem?
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.
Use with Grade 4, Chapter 7, Lesson 5, pages 286–287. (215)
NS 3.4; MR 1.1, 2.4, 2.6, 3.1, 3.2
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Problem Solving: Reading for Math
P
Interpret the Remainders
PRACTICE
Math Skills
Test Prep
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 solve this problem?
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?
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 7, Lesson 5, pages 286–287. (216)
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
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 7, Lesson 6, pages 288–289. (217)
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
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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:
© McGraw-Hill School Division
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
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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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 7, Lesson 6, pages 288–289. (219)
NS 3.2, 3.4
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Divide 4-Digit Numbers
P
PRACTICE
Divide. Check your answer.
1.
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 .
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 7, Lesson 7, pages 290–293. (220)
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
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Divide 4-Digit Numbers
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.
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 7, Lesson 7, pages 290–293. (221)
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
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Divide 4-Digit Numbers
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 7, Lesson 7, pages 290–293. (222)
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
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Divide 5-Digit Numbers
P
PRACTICE
Divide. Check your answer.
1.
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 7, Lesson 8, pages 294–295. (223)
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
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Divide 5-Digit Numbers
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
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 7, Lesson 8, pages 294–295. (224)
2 $26,856
4 52,273
9 82,445
NS 3.2, 3.4
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Divide 5-Digit Numbers
E
ENRICH
Crossnumber Puzzle
Divide to complete the crossnumber puzzle.
Then create and solve your own Across and Down clues.
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 7, Lesson 8, pages 294–295. (225)
NS 3.2, 3.4
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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?
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 7, Lesson 9, pages 298–299. (226)
NS 3.2, 3.4; MR 3.2, 3.3
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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:
© McGraw-Hill School Division
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:
Use with Grade 4, Chapter 7, Lesson 9, pages 298–299. (227)
NS 3.2, 3.4; MR 3.2, 3.3
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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!
© McGraw-Hill School Division
Item/Amount
Our Price
Greek olives:
oz
Cheddar cheese:
pounds
Cranberry juice:
boxes
Dog food:
Tuna:
Fresh pasta:
Our Unit Price
pounds
cans
inches
Use with Grade 4, Chapter 7, Lesson 9, pages 298–299. (228)
NS 3.2, 3.4; MR 3.2, 3.3
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P
Problem Solving: Strategy
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.
© McGraw-Hill School Division
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.
Strategy:
Use with Grade 4, Chapter 7, Lesson 10, pages 300–301. (229)
NS 3.4; MR 1.1, 2.3, 2.4, 3.1, 3.2
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Problem Solving: Strategy
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
What do you need to find?
• You need to find how many
.
Step 2
Plan
■
■
© McGraw-Hill School Division
■
■
■
■
■
■
■
■
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
Make a plan.
Choose a strategy.
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.
Use with Grade 4, Chapter 7, Lesson 10, pages 300–301. (230)
NS 3.4; MR 1.1, 2.3, 2.4, 3.1, 3.2
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Problem Solving: Strategy
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 7, Lesson 10, pages 300–301. (231)
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
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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:
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 7, Lesson 11, pages 302–303. (232)
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
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Explore Finding the Mean
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
Use with Grade 4, Chapter 7, Lesson 11, pages 302–303. (233)
NS 3.4; SDP 1.2
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Explore Finding the Mean
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
© McGraw-Hill School Division
63°
68°
2. Explain how you chose the temperatures.
Use with Grade 4, Chapter 7, Lesson 11, pages 302–303. (234)
NS 3.4; SDP 1.2
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 7, Lesson 12, pages 304–305. (235)
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
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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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 7, Lesson 12, pages 304–305. (236)
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
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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
© McGraw-Hill School Division
Mean:
eric
6
4
22
9
4
Total:
65
10
Team A’s
Serena
12
Total:
Total:
65
10
Total Score:
Use with Grade 4, Chapter 7, Lesson 12, pages 304–305. (237)
Mean:
13
85
Mean:
17
Mean Score per Person:
NS 3.4; SDP 1.2
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Problem Solving: Application
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7–13
Part
A WORKSHEET
Decision
Making
Applying Division
Record your data and notes.
Cost
Advantages and Disadvantages
Bus
Train
© McGraw-Hill School Division
Car
Your Decision
What is your recommendation for the club? Should they take a bus, train,
or car to the aquarium? Explain.
Use with Grade 4, Chapter 7, Lesson 13, pages 306–307. (238)
NS 3.4; MR 1.1, 2.3, 3.1
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7–13
Part
B WORKSHEET
Problem Solving: Application
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
© McGraw-Hill School Division
Paper Clip
Use with Grade 4, Chapter 7, Lesson 13, pages 308–309. (239)
NS 1.2; SDP 1.2; MR 1.1, 2.3, 3.2
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Problem Solving: Application
Do light or heavy objects fly farther?
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7–13
Part
B WORKSHEET
Math &
Science
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
© McGraw-Hill School Division
4. In your own words, explain what gravity is.
5. Explain the results of the activity in terms of gravity.
Use with Grade 4, Chapter 7, Lesson 13, pages 308–309. (240)
NS 1.2; SDP 1.2; MR 1.1, 2.3, 3.2
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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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 8, Lesson 1, pages 324–325. (241)
29. If 6,300 books are divided equally
among 90 libraries, how many
books will each library get?
NS 3.2
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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 © McGraw-Hill School Division
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 Use with Grade 4, Chapter 8, Lesson 1, pages 324–325. (242)
7. 900 30 NS 3.2
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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?
Use with Grade 4, Chapter 8, Lesson 1, pages 324–325. (243)
NS 3.2
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8–2 Page
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 8, Lesson 2, pages 326–327. (244)
20. The dividend is 160. The divisor is 12.
What are the quotient and
remainder?
NS 3.2
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Explore Dividing by 2-Digit Numbers
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 Use with Grade 4, Chapter 8, Lesson 2, pages 326–327. (245)
NS 3.2
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Explore Dividing by 2-Digit Numbers
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
.
→
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 8, Lesson 2, pages 326–327. (246)
NS 3.2
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 8, Lesson 3, pages 328–329. (247)
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
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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.
Think: How many groups of 20 are in 74?
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.
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 8, Lesson 3, pages 328–329. (248)
NS 3.2
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Divide 2-Digit Numbers by Multiples of 10
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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".
© McGraw-Hill School Division
Start
72
85
97
100
115
120
260
138
253
149
250
150
235
164
226
219
205
Use with Grade 4, Chapter 8, Lesson 3, pages 328–329. (249)
197
186
173
NS 3.2
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8–4 Page
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 8, Lesson 4, pages 330–333. (250)
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
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Divide by 2-Digit Divisors
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
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 8, Lesson 4, pages 330–333. (251)
NS 3.2
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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.
If you divide either 45 or 56 by me,
the remainder is 1.
3. I am a number between 20 and 30.
4. I am a number between 20 and 30.
If you divide either 107 or 128 by
me, the remainder is 2.
5. I am a number between 20 and 30.
If you divide either 76 or 126 by me,
the remainder is 1.
7. I am a number between 10 and 20.
If you divide either 74 or 110 by me,
the remainder is 2.
9. I am a number between 20 and 30.
© McGraw-Hill School Division
If you divide either 175 or 204 by
me, the remainder is 1.
11. I am a number between 10 and 20.
If you divide either 69 or 88 by me,
the remainder is 12.
13. I am a number between 10 and 20.
If you divide either 110 or 144 by
me, the remainder is 8.
Use with Grade 4, Chapter 8, Lesson 4, pages 330–333. (252)
If you divide either 68 or 134 by me,
the remainder is 2.
6. I am a number between 30 and 40.
If you divide either 147 or 255 by me,
the remainder is 3.
8. I am a number between 40 and 50.
If you divide either 221 or 265 by
me, the remainder is 1.
10. I am a number between 30 and 40.
If you divide either 74 or 214 by me,
the remainder is 4.
12. I am a number between 20 and 30.
If you divide either 131 or 154 by
me, the remainder is 16.
14. I am a number between 20 and 30.
If you divide either 295 or 322 by
me, the remainder is 25.
NS 3.2
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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 .
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 8, Lesson 5, pages 334–335. (253)
29. A jet flew 3,116 miles in 6 hours.
About how many miles per hour
did it fly?
NS 3.2
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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:
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 8, Lesson 5, pages 334–335. (254)
NS 3.2
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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 © McGraw-Hill School Division
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.
Use with Grade 4, Chapter 8, Lesson 5, pages 334–335. (255)
NS 3.2
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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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 8, Lesson 6, pages 336–337. (256)
34. Jason wants to save $180 in
12 months. How much should he
save each month?
NS 3.2
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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
© McGraw-Hill School Division
Divide. Check your answer.
1.
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 Use with Grade 4, Chapter 8, Lesson 6, pages 336–337. (257)
5 R3
37 223
1 R59
61 120
1 R61
63 124
11. 208 25 NS 3.2
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Adjust the Quotient
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8–6 Page
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.
© McGraw-Hill School Division
Start
sailfish
redwood
St. Bernard
hummingbird
swordfish Maple
dolphin oak
greyhound parakeet
Great Dane sparrow
Use with Grade 4, Chapter 8, Lesson 6, pages 336–337. (258)
NS 3.2
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Problem Solving: Reading for Math
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
© McGraw-Hill School Division
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
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Problem Solving: Reading for Math
P
Use an Overestimate or Underestimate
PRACTICE
Math Skills
Test Prep
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?
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 8, Lesson 7, pages 338–339. (260)
MR 1.1, 2.1, 2.4, 2.5, 3.1, 3.2
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8–7 Page
Problem Solving: Reading for Math
P
Use an Overestimate or Underestimate
PRACTICE
Math Skills
Test Prep
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.
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 8, Lesson 7, pages 338–339. (261)
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
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Problem Solving: Strategy
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?
© McGraw-Hill School Division
Strategy:
Strategy:
7. The Stadium Store sells 450 team
photos and 369 individual photos.
How many photos does it sell in all?
8. Create a problem which you could
solve by drawing a diagram or by
writing a division sentence. Share it
with others.
Strategy:
Use with Grade 4, Chapter 8, Lesson 8, pages 342–343. (262)
NS 3.2; MR 2.4
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8–8 Page
Problem Solving: Strategy
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
■
■
© McGraw-Hill School Division
■
■
■
■
■
■
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
Make a plan.
Choose a strategy.
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.
Use with Grade 4, Chapter 8, Lesson 8, pages 342–343. (263)
NS 3.2; MR 2.4
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Problem Solving: Strategy
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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 8, Lesson 8, pages 342–343. (264)
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
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8–9 Page
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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 8, Lesson 9, pages 344–345. (265)
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
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8–9 Page
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)
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 8, Lesson 9, pages 344–345. (266)
AF 1.3
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Order of Operations
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8–9 Page
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
© McGraw-Hill School Division
14. 16 – 6 + 2 = 8
In your own words describe the rules for the order of operations.
Use with Grade 4, Chapter 8, Lesson 9, pages 344–345. (267)
AF 1.3
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Problem Solving: Application
Print This Page
8–10
Part
A WORKSHEET
Decision
Making
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
© McGraw-Hill School Division
Your Decision
What is your recommendation for the hiking club? Explain.
Use with Grade 4, Chapter 8, Lesson 10, pages 346–347. (268)
NS 1.2, 3.2, 3.3, 3.4; MR 1.1, 2.4
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Problem Solving: Application
Does eating improve performance?
Print This Page
8–10
Part
B WORKSHEET
Math &
Science
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?
© McGraw-Hill School Division
2. How many more sit-ups did you do? Show your work.
Work Space
Use with Grade 4, Chapter 8, Lesson 10, pages 348–349. (269)
NS 1.2, 3.4; MR 1.1, 2.3, 3.3
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8–10
Part
B WORKSHEET
Problem Solving: Application
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?
© McGraw-Hill School Division
5. In what ways could you improve this activity?
6. Explain the activity in terms of energy conversion.
Use with Grade 4, Chapter 8, Lesson 10, pages 348–349. (270)
NS 1.2, 3.4; MR 1.1, 2.3, 3.3
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9–1 Page
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 9, Lesson 1, pages 364–365. (271)
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
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Explore Customary Length
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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 9, Lesson 1, pages 364–365. (272)
MR 1.1, 2.3
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Explore Customary Length
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 9, Lesson 1, pages 364–365. (273)
MR 1.1, 2.3
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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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 9, Lesson 2, pages 366–369. (274)
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
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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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 9, Lesson 2, pages 366–369. (275)
MR 1.1, 2.3
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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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 9, Lesson 2, pages 366–369. (276)
MR 1.1, 2.3
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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
Algebra & Functions Complete the table.
28.
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
© McGraw-Hill School Division
16
32
48
Problem Solving
32. Amy cuts a piece of ribbon 60 in.
long. How many feet long is the
piece of ribbon?
Use with Grade 4, Chapter 9, Lesson 3, pages 370–373. (277)
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
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Convert Customary Units
R
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 9, Lesson 3, pages 370–373. (278)
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
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Convert Customary Units
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
© McGraw-Hill School Division
qt
oz
in.
lb
c
ft
gal
Use with Grade 4, Chapter 9, Lesson 3, pages 370–373. (279)
yd
pt
Finish
AF 1.3; MR 1.1, 2.3
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Problem Solving: Reading for Math
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.”
© McGraw-Hill School Division
Explain your thinking:
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:
Use with Grade 4, Chapter 9, Lesson 4, pages 374–375. (280)
NS 1.2; MR 1.1, 2.3, 2.5, 3.1, 3.2
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Problem Solving: Reading for Math
P
Check for Reasonableness
PRACTICE
Math Skills
Test Prep
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?
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 9, Lesson 4, pages 374–375. (281)
NS 1.2; MR 1.1, 2.3, 2.5, 3.1, 3.2
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Problem Solving: Reading for Math
P
Check for Reasonableness
PRACTICE
Math Skills
Test Prep
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 9, Lesson 4, pages 374–375. (282)
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
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 9, Lesson 5, pages 378–379. (283)
16. One brick measures 92 mm. What is
its measurement to the nearest cm?
MR 1.1, 2.3
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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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 9, Lesson 5, pages 378–379. (284)
MR 1.1, 2.3
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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
© McGraw-Hill School Division
1. 4 cm
Use with Grade 4, Chapter 9, Lesson 5, pages 378–379. (285)
MR 1.1, 2.3
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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.
© McGraw-Hill School Division
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
Algebra & Functions Complete the table.
15.
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
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Metric Capacity and Mass
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).
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 9, Lesson 6, pages 380–383. (287)
MR 1.1, 2.3
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Metric Capacity and Mass
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 9, Lesson 6, pages 380–383. (288)
9
10
11
12
13
14
15
16
MR 1.1, 2.3
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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 .
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 9, Lesson 7, pages 384–385. (289)
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
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Convert Metric Units
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 9, Lesson 7, pages 384–385. (290)
8. 300 cm mL
cm
dm
m
10. 70 dm m
12. 40 cm dm
AF 1.3; MR 1.1, 2.3
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Convert Metric Units
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
© McGraw-Hill School Division
• 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.
Use with Grade 4, Chapter 9, Lesson 7, pages 384–385. (291)
AF 1.3; MR 1.1, 2.3
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Problem Solving: Strategy
Print This
9–8 Page
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?
© McGraw-Hill School Division
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.
Strategy:
Use with Grade 4, Chapter 9, Lesson 8, pages 386–387. (292)
MR 1.1, 2.3, 3.1, 3.2
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Problem Solving: Strategy
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
■
■
■
© McGraw-Hill School Division
■
■
■
■
■
■
■
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
Make a plan.
Choose a strategy.
Use logical reasoning to solve the problem.
You can use the difference in the amount each container
can hold to measure exactly 6 cups.
Use with Grade 4, Chapter 9, Lesson 8, pages 386–387. (293)
MR 1.1, 2.3, 3.1, 3.2
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Problem Solving: Strategy
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
Is the solution reasonable?
Reread the problem.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 9, Lesson 8, pages 386–387. (294)
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
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Temperature: Fahrenheit and Celsius
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9–9 Page
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 9, Lesson 9, pages 388–389. (295)
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
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Temperature: Fahrenheit and Celsius
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 9, Lesson 9, pages 388–389. (296)
NS 1.8; MR 1.1, 2.3
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Temperature: Fahrenheit and Celsius
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 9, Lesson 9, pages 388–389. (297)
NS 1.8; MR 1.1, 2.3
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Problem Solving: Application
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9–10
Part
A WORKSHEET
Decision
Making
Applying Measurement
Record your data.
Items
Ingredients
Amount of Each Cost of Each
Ingredient
Ingredient
Total Cost for
Item
Sandwiches
Fruit Salad
© McGraw-Hill School Division
Punch
Your Decision
How much of each item should Mr. Martin make for the birthday party? Explain.
Use with Grade 4, Chapter 9, Lesson 10, pages 390–391. (298)
MR 1.1, 2.3
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Problem Solving: Application
Which color heats up the most?
Print This Page
9–10
Part
B WORKSHEET
Math &
Science
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.
© McGraw-Hill School Division
Work Space
2. Which color heated up the most? The least?
Use with Grade 4, Chapter 9, Lesson 10, pages 392–393. (299)
NS 1.2; MR 1.2, 2.3, 2.6, 3.3
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9–10
Part
B WORKSHEET
Problem Solving: Application
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
© McGraw-Hill School Division
would you like to wear? Why?
6. Explain the results of the activity in terms of reflection or
absorption of light.
Use with Grade 4, Chapter 9, Lesson 10, pages 392–393. (300)
NS 1.2; MR 1.2, 2.3, 2.6, 3.3
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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.
© McGraw-Hill School Division
Copy and fold. Identify the 3-dimensional shape.
7.
8.
9.
10.
Algebra & Functions
11. What could the next shape be?
Use with Grade 4, Chapter 10, Lesson 1, pages 408–411. (301)
MG 3.6
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3-Dimensional Figures
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.
© McGraw-Hill School Division
Name
3Dimensional
Figure
1.
triangular
prism
2.
rectangular
prism
3.
triangular
pyramid
4.
square
pyramid
5.
cone
6.
cylinder
7.
sphere
Shape of
Base
Use with Grade 4, Chapter 10, Lesson 1, pages 408–411. (302)
Number of
Flat Faces
and Bases
Number of
Straight
Edges
Number of
Vertices
MG 3.6
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10–1 Page
3-Dimensional Figures
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.
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 10, Lesson 1, pages 408–411. (303)
MG 3.6
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2-Dimensional Figures and Polygons
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10–2 Page
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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 10, Lesson 2, pages 412–415. (304)
O
1 2 3 4 5
MG 3.8
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2-Dimensional Figures and Polygons
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
© McGraw-Hill School Division
Identify each polygon.
1.
2.
3.
4.
5.
6.
Use with Grade 4, Chapter 10, Lesson 2, pages 412–415. (305)
MG 3.8
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E
2-Dimensional Figures and Polygons
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!
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 10, Lesson 2, pages 412–415. (306)
C
MG 3.8
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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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 10, Lesson 3, pages 416–419. (307)
2
3
4
5
6
MG 3.1, 3.2
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Lines, Line Segments, and Rays
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.
© McGraw-Hill School Division
Identify each figure.
1.
2.
3.
4.
5.
6.
8.
9.
Identify the parts of a circle.
7.
Use with Grade 4, Chapter 10, Lesson 3, pages 416–419. (308)
MG 3.1, 3.2
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Lines, Line Segments, and Rays
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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 10, Lesson 3, pages 416–419. (309)
MG 3.1, 3.2
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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
© McGraw-Hill School Division
10. a 4-sided figure with 1 right angle
Use with Grade 4, Chapter 10, Lesson 4, pages 420–421. (310)
MG 3.5
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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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 10, Lesson 4, pages 420–421. (311)
MG 3.5
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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
© McGraw-Hill School Division
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
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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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 10, Lesson 5, pages 422–425. (313)
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
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Triangles and Quadrilaterals
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.
© McGraw-Hill School Division
1.
2.
3.
Identify each quadrilateral in as many ways as you can.
4.
5.
Use with Grade 4, Chapter 10, Lesson 5, pages 422–425. (314)
6.
MG 3.7, 3.8
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Triangles and Quadrilaterals
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 10, Lesson 5, pages 422–425. (315)
MG 3.7, 3.8
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10–6 Page
Problem Solving: Reading for Math
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 10, Lesson 6, pages 426–427. (316)
MG 3.1, 3.7, 3.8; MR 1.1, 2.3, 2.4, 3.2
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Problem Solving: Reading for Math
P
Use a Diagram
Math Skills
Test Prep
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?
© McGraw-Hill School Division
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
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Problem Solving: Reading for Math
P
Use a Diagram
PRACTICE
Math Skills
Test Prep
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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 10, Lesson 6, pages 426–427. (318)
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
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Congruent and Similar
P
PRACTICE
Write whether the figures are similar. Then write whether the
figures are congruent.
1.
2.
3.
4.
© McGraw-Hill School Division
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
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Congruent and Similar
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.
© McGraw-Hill School Division
Write whether the figures are similar. Then write whether the
figures are congruent. You may trace the figures.
1.
2.
3.
4.
5.
6.
Use with Grade 4, Chapter 10, Lesson 7, pages 430–433. (320)
MG 3.3, 3.4
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Congruent and Similar
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
© McGraw-Hill School Division
figures can you find in the drawing at the
right? Name each pair or set of figures.
J
N
O
Q P
M
Use with Grade 4, Chapter 10, Lesson 7, pages 430–433. (321)
K
L
MG 3.3, 3.4
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Explore Translations, Reflections,
and Rotations
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10–8 Page
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.
© McGraw-Hill School Division
7. translation
9. translation, then rotation
8. reflection
10. rotation, then reflection
Use with Grade 4, Chapter 10, Lesson 8, pages 434–435. (322)
MG 3.4
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Name
Explore Translations, Reflections, and
Rotations
Print This
10–8 Page
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.
© McGraw-Hill School Division
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
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Explore Translations, Reflections,
and Rotations
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.
Use with Grade 4, Chapter 10, Lesson 8, pages 434–435. (324)
MG 3.4
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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.
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 10, Lesson 9, pages 436–439. (325)
14.
MG 3.4
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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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 10, Lesson 9, pages 436–439 (326)
5.
MG 3.4
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Symmetry
E
ENRICH
Circle each letter that has one or more lines of symmetry.
© McGraw-Hill School Division
Draw the line or lines of symmetry.
G4_C10_L09_E01_MA01
Use with Grade 4, Chapter 10, Lesson 9, pages 436–439. (327)
MG 3.4
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10–10Page
Problem Solving: Strategy
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?
© McGraw-Hill School Division
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.
Strategy:
Use with Grade 4, Chapter 10, Lesson 10, pages 440–441. (328)
MG 3.8; MR 1.1, 2.3, 2.4, 3.2
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Problem Solving: Strategy
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10–10Page
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
Make a plan.
Choose a strategy.
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.
Use with Grade 4, Chapter 10, Lesson 10, pages 440–441. (329)
MG 3.8; MR 1.1, 2.3, 2.4, 3.2
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Problem Solving: Strategy
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
© McGraw-Hill School Division
What other strategies could you use to solve the problem?
Practice
Use data from this tessellation to solve.
1. What shapes do you see in a repeated
pattern? How are they moved?
Use with Grade 4, Chapter 10, Lesson 10, pages 440–441. (330)
2. Complete the missing pieces of the
tessellation.
MG 3.8; MR 1.1, 2.3, 2.4, 3.2
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 10, Lesson 11, pages 442–445. (331)
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
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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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 10, Lesson 11, pages 442–445. (332)
8 ft
8 ft
7m
3 ft
6.
5 cm
5 cm
6 cm
6 cm
7 cm
NS 3.1; MG 3.8
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Perimeter
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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
© McGraw-Hill School Division
Perimeter of each region: 12 units
3. Number of regions: 6
Perimeter of each region: 12 units
Use with Grade 4, Chapter 10, Lesson 11, pages 442–445. (333)
NS 3.1; MG 3.8
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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
© McGraw-Hill School Division
Find the area and perimeter of each figure.
10.
12 cm
10 cm
11. 1 m
12.
4m
Use with Grade 4, Chapter 10, Lesson 12, pages 446–449. (334)
6 mm
25 mm
MG 1.2, 1.3; AF 1.4
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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.
© McGraw-Hill School Division
8 ft
7 in.
6.
7.
8.
9 ft
4m
3 yd
6 ft
5 yd
Use with Grade 4, Chapter 10, Lesson 12, pages 446–449. (335)
6m
MG 1.2, 1.3; AF 1.4
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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
© McGraw-Hill School Division
Find the area of each polygon.
1.
2.
3.
4.
5.
6.
Use with Grade 4, Chapter 10, Lesson 12, pages 446–449. (336)
MG 1.2, 1.3; AF 1.4
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Explore Volume
P
PRACTICE
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 10, Lesson 13, pages 450–451. (337)
NS 3.1; MG 1.4
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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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 10, Lesson 13, pages 450–451. (338)
volume cm3
6.
cm3
2 cm
2 cm
5 cm
NS 3.1; MG 1.4
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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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 10, Lesson 13, pages 450–451. (339)
NS 3.1; MG 1.4
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Problem Solving: Application
Analyze Data and Make Decisions
Print This Page
10–14
Part
A WORKSHEET
Decision
Making
Record your data in the chart.
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 10, Lesson 10, pages 452–453. (340)
MG 1.1, 1.2, 1.3, 1.4; MR 1.1, 2.3
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Problem Solving: Application
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10–14
Part
B WORKSHEET
Math &
Science
How well do you make patterns?
Record your ratings.
Drawing of Structure
Rating:
1 (best)–5 (worst)
© McGraw-Hill School Division
1. How well did you follow directions? Do you have enough data to decide?
Use with Grade 4, Chapter 10, Lesson 14, pages 454–455. (341)
MG 3.3, 3.4, 3.7, 3.8; MR 1.1, 2.3, 3.2
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10–14
Part
B WORKSHEET
Problem Solving: Application
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?
© McGraw-Hill School Division
4. Make a list of words that helped you give directions.
5. Describe how a camouflage pattern gives some animals a
survival advantage.
Use with Grade 4, Chapter 10, Lesson 14, pages 454–455. (342)
MG 3.3, 3.4, 3.7, 3.8; MR 1.1, 2.3, 3.2
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Parts of a Whole
P
PRACTICE
Write a fraction for the part that is shaded.
1.
2.
3.
4.
5.
6.
7.
8.
© McGraw-Hill School Division
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
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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.
© McGraw-Hill School Division
3.
fraction
5.
fraction
6.
part shaded
parts shaded
parts shaded
parts in all
parts in all
parts in all
fraction
fraction
Use with Grade 4, Chapter 11, Lesson 1, pages 470–471. (344)
fraction
NS 1.5, 1.7
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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?
.
© McGraw-Hill School Division
Design a flag. Use red, yellow, green, and blue crayons.
2. What part of your flag is red?
green?
yellow?
blue?
Use with Grade 4, Chapter 11, Lesson 1, pages 470–471. (345)
NS 1.5, 1.7
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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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 11, Lesson 2, pages 472–473. (346)
12. Twenty of 25 students voted for class
president. What part of the class did
not vote for president?
NS 1.5, 1.7
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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.
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 11, Lesson 2, pages 472–473. (347)
5.
NS 1.5, 1.7
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E
Parts of a Group
ENRICH
Draw the Group
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 11, Lesson 2, pages 472–473. (348)
NS 1.5, 1.7
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 11, Lesson 3, pages 474–477. (349)
31. Paul caught 9 bass and 3 trout. What
fraction of the fish were trout?
NS 1.5; AF 2.2
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R
Find Equivalent Fractions and Fractions in
Simplest Form
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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 11, Lesson 3, pages 474–477. (350)
4
12
NS 1.5; AF 2.2
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Find Equivalent Fractions and Fractions in
Simplest Form
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.
© McGraw-Hill School Division
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
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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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 11, Lesson 4, pages 478–481. (352)
of a pizza. Order
NS 1.5, 1.9
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Compare and Order Fractions
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
,
Use with Grade 4, Chapter 11, Lesson 4, pages 478–481. (353)
,
,
NS 1.5, 1.9
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Compare and Order Fractions
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.
© McGraw-Hill School Division
• 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
Use with Grade 4, Chapter 11, Lesson 4, pages 478–481. (354)
NS 1.5, 1.9
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Problem Solving: Reading for Math
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:
© McGraw-Hill School Division
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
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Problem Solving: Reading for Math
Check for Reasonableness
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11–5 Page
P
PRACTICE
Math Skills
Test Prep
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
© McGraw-Hill School Division
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
4. A reasonable answer for this
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)
6. A reasonable answer for this
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
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Problem Solving: Reading for Math
Check for Reasonableness
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11–5 Page
P
PRACTICE
Math Skills
Test Prep
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
8. A reasonable answer for this
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 11, Lesson 5, pages 482–483. (357)
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
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11–6 Page
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 © McGraw-Hill School Division
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?
Use with Grade 4, Chapter 11, Lesson 6, pages 484–485. (358)
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
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11–6 Page
Explore Parts of a Group
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 © McGraw-Hill School Division
4. 3 of 15 7. 6 of 30 2
3. 3 of 6 3
6. 4 of 20 5
9. 5 of 10 Use with Grade 4, Chapter 11, Lesson 6, pages 484–485. (359)
1
1
4
NS 1.5
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Explore Parts of a Group
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 11, Lesson 6, pages 484–485. (360)
NS 1.5
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11–7 Page
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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 11, Lesson 7, pages 486–487. (361)
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
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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
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 11, Lesson 7, pages 486–487. (362)
NS 1.5, 1.9
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Mixed Numbers
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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:
2. Shade the fraction bars to show a
fraction between 2 and 3.
Fraction:
Mixed number:
3. Shade the fraction bars to show a
fraction between 2 and 3.
Fraction:
© McGraw-Hill School Division
Mixed number:
4. Shade the fraction bars to show a
fraction between 2 and 3.
Fraction:
Mixed number:
Use with Grade 4, Chapter 11, Lesson 7, pages 486–487. (363)
NS 1.5, 1.9
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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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 11, Lesson 8, pages 490–491. (364)
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
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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.
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 11, Lesson 8, pages 490–491. (365)
NS 1.5; MR 1.1; SDP 2.2
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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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 11, Lesson 8, pages 490–491. (366)
NS 1.5; MR 1.1; SDP 2.2
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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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 11, Lesson 9, pages 492–493. (367)
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
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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
© McGraw-Hill School Division
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
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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)
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 11, Lesson 9, pages 492–493. (369)
NS 1.5; SDP 1.1, 2.2
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Problem Solving: Strategy
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
© McGraw-Hill School Division
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.
Strategy:
Use with Grade 4, Chapter 11, Lesson 10, pages 494–495. (370)
SDP 2.1, 2.2; MR 1.1, 2.3, 2.4, 3.1, 3.2
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Problem Solving: Strategy
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
■
■
© McGraw-Hill School Division
■
■
■
■
■
■
■
■
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
Make a plan.
Choose a strategy.
A tree diagram can show all of the possible outcomes.
Use with Grade 4, Chapter 11, Lesson 10, pages 494–495. (371)
SDP 2.1, 2.2; MR 1.1, 2.3, 2.4, 3.1, 3.2
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Problem Solving: Strategy
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
Is the solution reasonable?
Reread the problem.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 11, Lesson 10, pages 494–495. (372)
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
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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?
3. If you spin the spinner 100 times, what
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?
6. If you spin the spinner 50 times, what
5. If you spin the spinner 50 times, what
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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 11, Lesson 11, pages 496–497. (373)
times 5 will come up when you toss a
number cube labeled 1–6?
NS 1.5; SDP 1.1, 2.1
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Explore Making Predictions
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?
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 11, Lesson 11, pages 496–497 (374)
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
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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?
© McGraw-Hill School Division
Could It Happen?
Write your own probability letter to “Could It Happen?”
Use with Grade 4, Chapter 11, Lesson 11, pages 496–497. (375)
NS 1.5; SDP 1.1, 2.1
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Problem Solving: Application
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11–12
Part
A WORKSHEET
Decision
Making
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
© McGraw-Hill School Division
Checkerboard B
Your Decision
Describe three games you would recommend to Reggie and Bianca. Explain.
Use with Grade 4, Chapter 11, Lesson 12, pages 498–499. (376)
MR1.1; NS 1.5; SDP 1.1, 2.1
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11–12
Part
B WORKSHEET
Problem Solving: Application
How does size affect how fast a solid dissolves?
Math &
Science
© McGraw-Hill School Division
Make your own chart to record the dissolving time for each
seltzer tablet.
1. Rank the seltzer tablets in order from fastest to slowest.
Use with Grade 4, Chapter 11, Lesson 12, pages 500–501. (377)
NS 1.5, 1.7; MR 1.1, 2.3, 3.3
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Part
B WORKSHEET
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
© McGraw-Hill School Division
conclusions? Explain your answer.
5. Explain the results of the activity in terms of surface area.
Use with Grade 4, Chapter 11, Lesson 12, pages 500–501. (378)
NS 1.5, 1.7; MR 1.1, 2.3, 3.3
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12–1 Page
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 12, Lesson 1, pages 516–517. (379)
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
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R
Add Fractions with Like Denominators
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
Add. Write each sum in simplest form.
1.
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 12, Lesson 1, pages 516–517. (380)
12
10
12
10
NS 1.5, 3.1
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12–1 Page
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
© McGraw-Hill School Division
• 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.
Use with Grade 4, Chapter 12, Lesson 1, pages 516–517 (381)
NS 1.5, 3.1
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 12, Lesson 2, pages 518–519. (382)
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
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Subtract Fractions with Like Denominators
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
Subtract. Write each difference in simplest form.
1.
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 12, Lesson 2, pages 518–519. (383)
NS 1.5, 3.1
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12–2 Page
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
Use with Grade 4, Chapter 12, Lesson 2, pages 518–519. (384)
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
© McGraw-Hill School Division
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
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Problem Solving: Reading for Math
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?
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 12, Lesson 3, pages 520–521. (385)
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
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Problem Solving: Reading for Math
P
Choose an Operation
PRACTICE
Math Skills
Test Prep
Choose the correct answer.
1
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?
2. Which of the following can you use
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
© McGraw-Hill School Division
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.
6. Which of the following can you use
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
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Problem Solving: Reading for Math
Choose an Operation
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12–3 Page
P
PRACTICE
Math Skills
Test Prep
Choose the correct answer.
5
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?
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 12, Lesson 3, pages 520–521. (387)
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
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Explore Adding Fractions with
Unlike Denominators
P
PRACTICE
Add. Write each sum in simplest form.
1.
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 12, Lesson 4, pages 524–525. (388)
8
4
3
9
12
8
4
8
2
4
NS 1.5, 3.1
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Explore Adding Fractions with
Unlike Denominators
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 12, Lesson 4, pages 524–525. (389)
10
3
5
9
NS 1.5, 3.1
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Explore Adding Fractions with
Unlike Denominators
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 12, Lesson 4, pages 524–525. (390)
NS 1.5, 3.1
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Add Fractions with Unlike Denominators
P
PRACTICE
Add. Write each sum in simplest form.
1.
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 12, Lesson 5, pages 526–529. (391)
NS 1.5, 3.1
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12–5 Page
Add Fractions with Unlike Denominators
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
Using Pencil and Paper
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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 12, Lesson 5, pages 526–529. (392)
1
4
1
2
6
13 6
8.
34 11.
1
2
9
10
35 12.
5
12
14
NS 1.5, 3.1
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Add Fractions with Unlike Denominators
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
© McGraw-Hill School Division
1
3
7
18
1
9
2
5
1
5
5. How did you find the magic sum in exercise 3?
Use with Grade 4, Chapter 12, Lesson 5, pages 526–529. (393)
NS 1.5, 3.1
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Problem Solving: Strategy
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.
© McGraw-Hill School Division
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.
Strategy:
Use with Grade 4, Chapter 12, Lesson 6, pages 530–531. (394)
NS 1.5; MS 1.1, 1.2, 2.4, 3.2
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Problem Solving: Strategy
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
■
■
© McGraw-Hill School Division
■
■
■
■
■
■
■
■
■
■
■
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
Make a plan.
Choose a strategy.
Use simpler numbers to make up a problem similar
to the one you need to solve. Then solve the real
problem the same way.
Use with Grade 4, Chapter 12, Lesson 6, pages 530–531. (395)
NS 1.5; MS 1.1, 1.2, 2.4, 3.2
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Problem Solving: Strategy
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 12, Lesson 6, pages 530–531. (396)
NS 1.5; MS 1.1, 1.2, 2.4, 3.2
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Name
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12–7 Page
Explore Subtracting Fractions with
Unlike Denominators
P
PRACTICE
Subtract. Write each difference in simplest form.
1.
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 12, Lesson 7, pages 532–533. (397)
NS 1.5, 3.1
Print This Page
Name
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12–7 Page
Explore Subtracting Fractions with
Unlike Denominators
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 © McGraw-Hill School Division
12
3
Use with Grade 4, Chapter 12, Lesson 7, pages 532–533. (398)
NS 1.5, 3.1
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Explore Subtracting Fractions with
Unlike Denominators
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 12, Lesson 7, pages 532–533. (399)
1
3
1
2
5
8
11
12
5
12
NS 1.5, 3.1
Print This Page
Name
12–8 Page
Subtract Fractions with Unlike DenominatorsPrint
P This
PRACTICE
Subtract. Write each difference in simplest form.
1.
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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 12, Lesson 8, pages 534–537. (400)
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
Print This Page
Name
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
Using Pencil and Paper
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 12, Lesson 8, pages 534–537. (401)
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
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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.
© McGraw-Hill School Division
• Continue taking turns until all the cards have been matched.
The player with more pairs of cards wins.
Use with Grade 4, Chapter 12, Lesson 8, pages 534–537. (402)
NS 1.5, 3.1
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Name
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12–9 Page
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
© McGraw-Hill School Division
Identity
Identity
15. 1 ( 1 1 ) 12
6
3
2
16. 3 1 Associative
Use with Grade 4, Chapter 12, Lesson 9, pages 538–539. (403)
8
2
Commutative
NS 1.5, 3.1; MR 1.1; AF 1.2, 1.3
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12–9 Page
Properties of Fractions
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 (
Use with Grade 4, Chapter 12, Lesson 9, pages 538–539. (404)
12 )
13 )
NS 1.5, 3.1; MR 1.1; AF 1.2, 1.3
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E
Properties of Fractions
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 12, Lesson 9, pages 538–539. (405)
NS 1.5, 3.1; MR 1.1; AF 1.2, 1.3
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Problem Solving: Application
Analyze and Make Decisions
Print This Page
12–10
Part
A WORKSHEET
Decision
Making
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
© McGraw-Hill School Division
Your Decision
What combinations of juices can Joseph and his sisters use to make
exactly one quart of fruit punch?
Use with Grade 4, Chapter 12, Lesson 10, pages 540–541. (406)
MR 1.1, 2.3, 3.1; NS 1.5, 3.1
Print This Page
Name
Problem Solving: Application
Which objects can hold a static charge?
Print This Page
12–10
Part
B WORKSHEET
Math &
Science
Safety Be careful when working with scissors. Wear goggles in case
the balloon bursts.
Record your observations.
Material
Observations
Balloon
Cubes
Crayons
Sock
Hand
© McGraw-Hill School Division
1. What happened to the string when a charged object came near it?
2. Which objects held a static charge? How do you know?
Use with Grade 4, Chapter 12, Lesson 10, pages 542–543. (407)
MR 1.1, 2.3, 3.1, 3.2
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Problem Solving: Application
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12–10
Part
B WORKSHEET
Math &
Science
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?
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 12, Lesson 10, pages 542–543. (408)
MR 1.1, 2.3, 3.1, 3.2
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13–1 Page
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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 13, Lesson 1, pages 558–559. (409)
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
Print This Page
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13–1 Page
Explore Fractions and Decimals
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.
© McGraw-Hill School Division
5.
Use with Grade 4, Chapter 13, Lesson 1, pages 558–559. (410)
NS 1.6
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Explore Fractions and Decimals
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.
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 13, Lesson 1, pages 558–559. (411)
NS 1.6
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13–2 Page
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.
Write each as a decimal.
2
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.
Use with Grade 4, Chapter 13, Lesson 2, pages 560–561. (412)
26.
Lora walks for five tenths of an hour.
Write the number as a decimal.
NS 1.6, 1.7
Print This Page
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13–2 Page
Tenths and Hundredths
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
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 13, Lesson 2, pages 560–561. (413)
NS 1.6, 1.7
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13–2 Page
Tenths and Hundredths
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.
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 13, Lesson 2, pages 560–561. (414)
NS 1.6, 1.7
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13–3 Page
Thousandths
P
PRACTICE
Write each as a decimal.
123
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.
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 13, Lesson 3, pages 562–563. (415)
31. Jaime bats three hundred one
thousandths for the season.
Write this as a decimal.
NS 1.6
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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
© McGraw-Hill School Division
Write each as a decimal and a fraction.
1.
2.
3.
4.
Use with Grade 4, Chapter 13, Lesson 3, pages 562–563. (416)
NS 1.6
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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.
© McGraw-Hill School Division
• 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
Use with Grade 4, Chapter 13, Lesson 3, pages 562–563. (417)
NS 1.6
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Name
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13–4 Page
Problem Solving: Reading for Math
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:
© McGraw-Hill School Division
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:
Use with Grade 4, Chapter 13, Lesson 4, pages 564–565. (418)
NS 1.2; MR 1.1, 2.4, 3.2
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Name
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Problem Solving: Reading for Math
P
Choose a Representation
PRACTICE
Math Skills
Test Prep
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
© McGraw-Hill School Division
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
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Problem Solving: Reading for Math
P
Choose a Representation
PRACTICE
Math Skills
Test Prep
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?
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 13, Lesson 4, pages 564–565. (420)
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
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Name
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13–5 Page
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?
Use with Grade 4, Chapter 13, Lesson 5, pages 568–569. (421)
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
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Name
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Decimals Greater Than 1
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 13, Lesson 5, pages 568–569. (422)
100
NS 1.6
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Name
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Decimals Greater Than 1
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 13, Lesson 5, pages 568–569. (423)
NS 1.6
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Name
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13–6 Page
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 13, Lesson 6, pages 570–573. (424)
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
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Compare and Order Decimals
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 13, Lesson 6, pages 570–573. (425)
NS 1.2, 1.6, 1.7, 1.9
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Compare and Order Decimals
E
ENRICH
Puzzles
Choose the decimal from the box that solves each puzzle. Use a
decimal only once.
© McGraw-Hill School Division
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 5
The decimal is greater
than 0.85.
It is less than 0.9.
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.
Puzzle 9
The decimal is greater
than 8.35.
It is less than 8.5.
1. Arrange the decimals in the box in order from least to greatest.
2. Explain how you found the answer to Puzzle 3.
Use with Grade 4, Chapter 13, Lesson 6, pages 570–573. (426)
NS 1.2, 1.6, 1.7, 1.9
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Problem Solving: Strategy
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?
8. Create a problem which you could
solve by drawing a diagram. Share it
with others.
Strategy:
Use with Grade 4, Chapter 13, Lesson 7, pages 574–575. (427)
NS 1.2; MR 1.1, 2.3, 2.4, 3.2
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Problem Solving: Strategy
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.
■
■
© McGraw-Hill School Division
■
■
■
■
■
■
■
■
■
■
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.
Use with Grade 4, Chapter 12, Lesson 7, pages 574–575. (428)
NS 1.2; MR 1.1, 2.3, 2.4, 3.2
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Problem Solving: Strategy
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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 13, Lesson 7, pages 574–575. (429)
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
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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
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 13, Lesson 8, pages 576–577. (430)
58. Jason weighs 152.6 lb. What is his
weight to the nearest pound?
NS 1.2, 1.3
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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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 13, Lesson 8, pages 576–577. (431)
NS 1.2, 1.3
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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.
Round me to the nearest tenth. You get 12.5.
Round me to the nearest hundredth. You get 12.48.
What number am I?
12.557
12.479
12.486
3. Round me to the nearest whole number. You get 17.
Round me to the nearest tenth. You get 16.9.
Round me to the nearest hundredth. You get 16.94.
What number am I?
16.937
16.899
16.934
4. Round me to the nearest whole number. You get 28.
Round me to the nearest tenth. You get 28.0.
Round me to the nearest hundredth. You get 28.00.
What number am I?
27.959
28.002
28.008
5. Round me to the nearest whole number. You get 124.
© McGraw-Hill School Division
Round me to the nearest tenth. You get 124.4.
Round me to the nearest hundredth. You get 124.45.
What number am I?
124.456
124.444
124.446
6. Round me to the nearest whole number. You get 203.
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.
Use with Grade 4, Chapter 13, Lesson 8, pages 576–577. (432)
NS 1.2, 1.3
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Name
Problem Solving: Application
Print This Page
13–9
Part
A WORKSHEET
Decision
Making
Applying Decimals
Record your data.
Name of Item
Number Bought
Total Cost
Items for
Business District
Items for Area
Where People Live
Your Decision
© McGraw-Hill School Division
What models should Kit and Rammel buy for the area where people
live? What models should they buy for the business district?
Explain.
Use with Grade 4, Chapter 13, Lesson 9, pages 578–579. (433)
NS 1.2; MR 1.1, 2.3
Print This Page
Name
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13–9
Part
B WORKSHEET
Problem Solving: Application
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)
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 13, Lesson 9, pages 580–581. (434)
NS 1.2, 1.6; MR 1.1, 2.3, 3.2
Print This Page
Name
Problem Solving: Application
How does distance affect how many
strikes you throw?
Print This Page
13–9
Part
B WORKSHEET
Math &
Science
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
© McGraw-Hill School Division
as a decimal.
5. Use your answer in number 3 to compare your ability to
throw strikes with Major League Baseball pitchers.
Use with Grade 4, Chapter 13, Lesson 9, pages 580–581. (435)
NS 1.2, 1.6; MR 1.1, 2.3, 3.2
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Name
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14–1 Page
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 © McGraw-Hill School Division
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?
Use with Grade 4, Chapter 14, Lesson 1, pages 596–597. (436)
29. One apple weighs 0.26 kg. Another
apple weighs 0.87 kg. How much do
the two apples weigh together?
NS 2.1
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Name
Explore Adding Decimals
Print This
14–1 Page
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.
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 14, Lesson 1, pages 596–597. (437)
NS 2.1
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Explore Adding Decimals
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 14, Lesson 1, pages 596–597. (438)
NS 2.1
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Name
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14–2 Page
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 © McGraw-Hill School Division
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?
Use with Grade 4, Chapter 14, Lesson 2, pages 598–601. (439)
36. Ben buys packing tape for $2.97 and
boxes for $6.99. How much does he
spend?
NS 2.1
Print This Page
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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
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 14, Lesson 2, pages 598–601. (440)
NS 2.1
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Name
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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
Use with Grade 4, Chapter 14, Lesson 2, pages 598–601. (441)
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
© McGraw-Hill School Division
. 2
2.
9
3
. 1
8
6 . 8
NS 2.1
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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 © McGraw-Hill School Division
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?
Use with Grade 4, Chapter 14, Lesson 3, pages 602–603. (442)
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
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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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 14, Lesson 3, pages 602–603. (443)
NS 2.1, 2.2, 3.1; MR 2.1
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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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 14, Lesson 3, pages 602–603. (444)
NS 2.1, 2.2, 3.1; MR 2.1
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Problem Solving: Reading for Math
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
© McGraw-Hill School Division
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:
Use with Grade 4, Chapter 14, Lesson 4, pages 604–605. (445)
NS 2.1; MR 1.1, 2.4, 3.2
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Problem Solving: Reading for Math
P
Choose the Operation
PRACTICE
Math Skills
Test Prep
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?
to solve this problem?
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
4. Which number sentence can you use
this problem?
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
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 14, Lesson 4, pages 604–605. (446)
NS 2.1; MR 1.1, 2.4, 3.2
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Problem Solving: Reading for Math
P
Choose the Operation
PRACTICE
Math Skills
Test Prep
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
8. Which number sentence can you use
is true?
to solve this problem?
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.
© McGraw-Hill School Division
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?
Use with Grade 4, Chapter 14, Lesson 4, pages 604–605. (447)
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
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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 © McGraw-Hill School Division
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?
Use with Grade 4, Chapter 14, Lesson 5, pages 608–609. (448)
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
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Explore Subtracting Decimals
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14–5 Page
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.
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 14, Lesson 5, pages 608–609. (449)
NS 2.1
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Explore Subtracting Decimals
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
Use with Grade 4, Chapter 14, Lesson 5, pages 608–609. (450)
5
1.6
6.5
NS 2.1
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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 © McGraw-Hill School Division
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?
Use with Grade 4, Chapter 14, Lesson 6, pages 610–613. (451)
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
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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
© McGraw-Hill School Division
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 Use with Grade 4, Chapter 14, Lesson 6, pages 610–613. (452)
NS 3.1; MR 2.2
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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
✄
© McGraw-Hill School Division
3. What method did you use to find the answer in exercise 2?
0 1
2 3 4 5 6 7 8 9
Use with Grade 4, Chapter 14, Lesson 6, pages 610–613. (453)
MR 2.2; NS 3.1
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Estimate Differences
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 © McGraw-Hill School Division
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?
Use with Grade 4, Chapter 14, Lesson 7, pages 614–615. (454)
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
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Estimate Differences
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.
© McGraw-Hill School Division
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
Use with Grade 4, Chapter 14, Lesson 7, pages 614–615. (455)
NS 2.1, 2.2, 3.1; MR 2.1
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Estimate Differences
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?
© McGraw-Hill School Division
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.
Use with Grade 4, Chapter 14, Lesson 7, pages 614–615. (456)
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
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Problem Solving: Strategy
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,
© McGraw-Hill School Division
$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.
Strategy:
Use with Grade 4, Chapter 14, Lesson 8, pages 616–617. (457)
MR 1.1, 1.2, 2.2, 2.4, 3.2
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Problem Solving: Strategy
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.
■
■
■
© 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 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.
Use with Grade 4, Chapter 14, Lesson 8, pages 616–617. (458)
MR 1.1, 1.2, 2.2, 2.4, 3.2
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Problem Solving: Strategy
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
© McGraw-Hill School Division
Look Back
Is the solution reasonable?
Reread the problem.
Does your answer make sense?
Did you answer the question?
Yes
Yes
No
No
What other strategies could you use to solve the problem?
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?
Use with Grade 4, Chapter 14, Lesson 8, pages 616–617. (459)
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
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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 © McGraw-Hill School Division
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?
Use with Grade 4, Chapter 14, Lesson 9, pages 618–619. (460)
NS 3.1; AF 1.2, 1.3; MR 2.2
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Use Properties to
Add and Subtract
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.
© McGraw-Hill School Division
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 =
Use with Grade 4, Chapter 14, Lesson 9, pages 618–619. (461)
NS 3.1; AF 1.2, 1.3; MR 2.2
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Use Properties to
Add and Subtract
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
© McGraw-Hill School Division
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
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Part
A WORKSHEET
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
© McGraw-Hill School Division
Your Decision
What is your recommendation for the Lopez family? Explain.
Use with Grade 4, Chapter 14, Lesson 10, pages 620–621. (463)
MR 1.1, 2.2; NS 3.1
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Problem Solving: Application
How would you conserve electricity?
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Part
B WORKSHEET
Math &
Science
Record data for your conservation plans in
this chart.
Plan
Activity
Time Saved
Money Saved
Plan 1
Plan 2
© McGraw-Hill School Division
Plan 3
Use with Grade 4, Chapter 14, Lesson 10, pages 622–623. (464)
NS 2.1; MR 1.1, 2.3, 3.3
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Part
B WORKSHEET
Problem Solving: Application
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
© McGraw-Hill School Division
electricity. Think about costs, energy efficiency, and stress to the environment.
Use with Grade 4, Chapter 14, Lesson 10, pages 622–623. (465)
NS 2.1; MR 1.1, 2.3, 3.3