Workout
Mathematics
Grade
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Workout, Mathematics, Grade 3
238NA
ISBN-10: 1-59823-950-3
ISBN-13: 978-1-59823-950-8
Cover Image: © SWP Incorporated/Brand X Pictures/Jupiter Images
Triumph Learning® 136 Madison Avenue, 7th Floor, New York, NY 10016
A Haights Cross Communications, Inc. company
© 2008 Triumph Learning, LLC
All rights reserved. No part of this publication may be reproduced in whole or in part, stored
in a retrieval system, or transmitted in any form or by any means, electronic, mechanical,
photocopying, recording or otherwise, without written permission from the publisher.
Printed in the United States of America.
10 9 8
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Dear Student,
Are you a math champion?
You will be when you use
Workout!
Getting in shape is easy. Just complete
the lessons inside.
So, on your mark, get set –
Work OUT!
This book belongs to ______________________________
238NA_Mth_G3_SE_FM_PDF_.indd 3
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Table of Contents
Numbers and Operations
Lesson 1
Understanding Place Value. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
Lesson 2
Even and Odd Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
Lesson 3
Comparing and Ordering Whole Numbers . . . . . . . . . . . . . . . . . . . . . .14
Lesson 4
Models for Fractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
Lesson 5
Coins and Making Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22
Lesson 6
Addition-Subtraction Fact Families . . . . . . . . . . . . . . . . . . . . . . . . . . . .26
Lesson 7
Multiplication as Repeated Addition . . . . . . . . . . . . . . . . . . . . . . . . . . .30
Lesson 8
How to Solve Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34
Lesson 9
Solving Problems by Adding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38
Lesson 10
Solving Problems by Subtracting . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42
Lesson 11
Solving Problems with Multiplication. . . . . . . . . . . . . . . . . . . . . . . . . . .46
Lesson 12
Rounding to the Nearest 10 or 100 . . . . . . . . . . . . . . . . . . . . . . . . . . .50
Lesson 13
Using Estimation to Solve Problems. . . . . . . . . . . . . . . . . . . . . . . . . . .54
Measurement
Lesson 14
Units of Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58
Lesson 15
Estimating Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62
Lesson 16
Estimating Weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66
Lesson 17
Estimating Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70
Lesson 18
Using Rulers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74
Lesson 19
Comparing and Ordering Objects. . . . . . . . . . . . . . . . . . . . . . . . . . . . .78
Lesson 20
Telling Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .82
Lesson 21
Elapsed Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86
4
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Geometry
Lesson 22
Two-Dimensional Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .90
Lesson 23
Three-Dimensional Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .94
Lesson 24
Symmetry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .98
Algebraic Concepts
Lesson 25
Patterns with Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102
Lesson 26
Patterns with Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .106
Lesson 27
Completing Number Sentences . . . . . . . . . . . . . . . . . . . . . . . . . . . . .110
Lesson 28
Solving Problems with Number Sentences. . . . . . . . . . . . . . . . . . . . .114
Statistics and Probability
Lesson 29
Bar Graphs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .118
Lesson 30
Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .122
Math Words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .126
5
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Numbers and Operations
LESSON
1
Understanding
Place Value
When you use place value, remember these
words:
expanded form writing numbers by
adding the values of the digits
place value the value of a position in a
number
standard form writing numbers with
digits
745 is in standard form
700 40 5 is in expanded form
Write 3,924 in expanded form.
Step 1
Step 2
REMEMBER A place
value-chart shows the value
of each digit in a number.
Write the number in a place-value chart.
thousands
hundreds
3
9
tens
ones
Use the chart to write the value of each number.
thousands
hundreds
tens
ones
3
9
2
4
3,000
900
THINK 9 is in the hundreds place.
9 hundreds = 900
So, the number in expanded
form is
.
6
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Write these numbers in standard
form.
1.
300 4
3.
2,000 500 60 1
4.
two hundred nine
5.
one thousand, eight hundred sixty-seven
6.
2.
700 80 5
five thousand, two hundred twenty
1.
Numbers and Operations
Lesson 1: Understanding Place Value
What digit is in
the tens place?
0, 3, or 4?
7.
How can
you show 8
hundreds?
800, 80, or 8?
Write these numbers in expanded form.
7.
8.
816
7,950
Write the number in words.
9.
9.
Say the number
softy to yourself.
What is the
thousands part?
5 thousand or 54
thousand?
2,704
10.
Solve.
10.
In 2006, the population of Forest County,
Pennsylvania was six thousand, five hundred six
people. What is this number in standard form?
In a 4-digit
number, where
is the thousands
place?
1st or 4th?
7
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Numbers and Operations
Circle the answer for each question.
1.
2.
3.
How many tens are there in
1,475?
4.
How do you say the number
7,003?
A.
5 tens
A.
seven thousand, three
B.
4 tens
B.
seven thousand, thirty
C.
7 tens
C.
seventy-three
D.
75 tens
D.
seven oh three
Which number shows 6,000 500 20 8?
5.
What is the value of the 4 in
4,316?
A.
6,825
A.
4
B.
6,582
B.
40
C.
6,528
C.
400
D.
6,258
D.
4,000
There are five hundred sixtytwo students at Robinson
School. Which shows this
number in standard form?
6.
Trevor said this number: five
thousand, seven hundred
thirty-two. Which shows Trevor’s
number?
A.
265
A.
5,723
B.
526
B.
5,732
C.
560
C.
5,733
D.
562
D.
5,700,032
8
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7.
The principal said four hundred eight cans were collected during the can
drive. Write this number in standard form.
8.
Kara wrote this number in expanded form:
Numbers and Operations
Lesson 1: Understanding Place Value
6,000 20 9
Part A.
Write the number in standard form.
Part B.
Explain how you used place value to write the number in
standard form.
Math
Words
Fill in the blanks.
9.
The number 352 is written in
10.
In the number 8,624, the digit 8 is in the
11.
2,000 800 10 9 is the
form.
place.
form of 2,819.
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Numbers and Operations
LESSON
Even and Odd Numbers
2
When you use even and odd numbers, remember
these words:
even numbers end in 0, 2, 4, 6, or 8
odd numbers end in 1, 3, 5, 7, or 9
8, 24, and 78 are all even numbers
5, 37, and 89 are all odd numbers
Find the odd numbers between 64 and 74.
Step 1
Write the numbers between 64 and 74.
65, 66, 67, 68, 69, 70, 71, 72, 73
Step 2
Circle the odd numbers.
Step 3
Count how many numbers you circled.
There are
So, there are
THINK Count
by 1’s to write the
missing numbers.
REMEMBER Any numbers
that end in 1, 3, 5, 7, or 9 are
odd numbers.
circled numbers.
odd numbers between 64 and 74.
10
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Write odd or even for each number.
1.
58
2.
3.
73
26
1.
Numbers and Operations
Lesson 2: Even and Odd Numbers
Is 8 odd or
even?
4.
12
5.
65
6.
87
7.
41
8.
90
9.
39
Write if the sum or difference of each problem
is odd or even.
10.
10.
25 42
11.
54 28
Solve.
12.
13.
What is the
ones digit in the
sum?
6 or 7?
How many even numbers are between 41 and 53?
12.
Mr. Wilson’s class is learning about odd and even
numbers. Jeremy says that 83 is an even number. Is
Jeremy right? Explain.
What digits do
all even numbers
end in?
0, 2, 4, 6, 8
or
1, 3, 5, 7, 9?
11
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Numbers and Operations
Circle the answer for each question.
1.
2.
3.
Which is an odd number?
4.
How many odd numbers are
between 38 and 50?
A.
50
B.
65
A.
7
C.
28
B.
6
D.
34
C.
5
D.
4
Which is an even number?
A.
19
B.
57
C.
83
D.
96
5.
Which sentence best describes
this group of numbers?
84, 32, 70, 68, 42
A.
They are not in standard
form.
B.
They are all odd.
C.
They are all even.
D.
Some are even and some
are odd.
6.
How many even numbers are
between 61 and 71?
A.
4
B.
5
C.
6
D.
7
73 is an odd number because it
ends in 3. What kind of number
comes right after 73?
A.
even number
B.
odd number
C.
cannot tell
D.
a number ending in 0
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7.
Greta is given number cards for the numbers between 25 and 40.
Part A.
List all of the odd numbers in Greta’s set of number cards.
Part B.
Use what you know about even and odd numbers to explain
why your answer is correct.
Math
Words
Numbers and Operations
Lesson 2: Even and Odd Numbers
Choose words from the box to label each column
of the table.
even numbers
even and odd numbers
odd numbers
numbers in expanded form
8.
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Numbers and Operations
Comparing and Ordering
Whole Numbers
LESSON
3
When you compare whole numbers, remember
these symbols:
is greater than
is less than
is equal to
Order 3,351, 3,263, and 3,347 from least to greatest.
Step 1
Write the numbers in three rows with their places lined up.
3 , 3
3 , 2
5
6
1
3
,
THINK Always
Step 2
Compare the thousands digits.
The thousands digit of all three numbers is 3.
So, you cannot order the numbers yet.
Step 3
Compare the hundreds digits.
The number with the least hundreds digit is 3,263.
is the least number.
Step 4
Compare the tens digits of the two remaining numbers.
The tens digit of 3,351 is
.
The tens digit of 3,347 is
.
That means the greatest number is
.
So, from least to greatest, the numbers are
.
compare numbers
from left to right.
,
,
14
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Compare. Write , , or .
1.
3.
4,581
3,824
2.
5,488
4.
3,824
8,763
4,035
8,495
1.
3,045
Which symbol
means less than?
, , or ?
Numbers and Operations
Lesson 3: Comparing and Ordering Whole Numbers
Order the numbers from least to greatest.
5.
6.
5.
485, 398, 424
To compare
numbers, where
do you start?
Left or right?
2,091; 2,910; 2,190
Order the numbers from greatest to least.
7.
8.
7.
583, 576, 972
8,165; 6,184; 8,976
Use the table for Questions 9 and 10.
Day
Water Park Visitors
Monday
Tuesday
Wednesday
Thursday
5,785
5,690
5,609
5,734
9.
On which day did the greatest number of people
go to the water park?
10.
On which day did fewer people go to the water
park than on Tuesday?
Which digits
will you compare
first?
Hundreds or
ones?
9.
Which digits
will you compare
first?
Thousands, tens,
or ones?
15
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Numbers and Operations
Circle the answer for each question.
1.
2.
Which of the following
numbers is the greatest?
Which set of numbers is in
order from least to greatest?
A.
3,519
A.
8,073; 7,084; 7,809
B.
3,915
B.
7,800; 7,084; 8,073
C.
3,159
C.
7,084; 8,073; 7,809
D.
3,951
D.
7,084; 7,809; 8,073
Which symbol makes the
number sentence true?
5,683
3.
4.
5.
What is the greatest number that
can be made with these digits?
5,615
5
4
A.
A.
5,427
B.
B.
7,245
C.
C.
7,542
D.
D.
2,457
Jake says there are between
7,660 and 7,668 students in
his school district. How many
students could be in Jake’s
school district?
A.
7,606
B.
7,639
C.
7,663
D.
7,686
6.
7 2
The Nile River in Africa is
4,160 miles long. The Chang
River in Asia is 3,940 miles
long. The Amazon River in
South America is 4,000 miles
long. Which shows the rivers in
order from longest to shortest?
A.
Chang, Amazon, Nile
B.
Nile, Amazon, Chang
C.
Amazon, Nile, Chang
D.
Nile, Chang, Amazon
16
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7.
What is the least number that can be made using these digits?
Use each digit only once.
6
8.
5
1
8
Numbers and Operations
Lesson 3: Comparing and Ordering Whole Numbers
Macy needs to order these numbers from greatest to least:
4,823
4,832
4,382
Part A.
Order the numbers from greatest to least.
Part B.
Explain how you used place value to order the numbers.
-ATH
7ORDS
Draw a line to match each symbol to its meaning.
9.
is equal to
10.
is less than
11.
is greater than
17
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Numbers and Operations
LESSON
Models for Fractions
4
When you model fractions, remember these
words:
fraction names part of a whole or part
of a set
numerator the top number of a
fraction
denominator the bottom number of
a fraction; it tells the number of equal
parts
_3
4
numerator
denominator
Write a fraction to name the shaded part of the set.
Step 1
Step 2
Count the total number of circles.
REMEMBER Count both
There are 5 circles.
the white circles and the
shaded circles.
Count the number of shaded circles.
There are
Step 3
shaded circles.
Write the fraction.
Number of Shaded Circles
__________________
___
Total Number of Circles
So, the fraction
names the shaded part of the set.
18
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Write a fraction for the shaded part.
1.
2.
1.
Numbers and Operations
Lesson 4: Models for Fractions
How many
equal parts are
there?
2 or 4?
3.
4.
Color each picture to show the fraction.
5.
5.
_1
3
6.
_5
8
Solve.
7.
8.
There are 5 red apples and 3 green apples in a
bowl. What fraction shows the number of green
apples?
The Murphy family buys a 10-slice pizza for dinner.
They eat 7 slices. What fraction shows how much
pizza they ate?
What is the
numerator of the
fraction?
1 or 3?
7.
What is the
total number of
apples?
3, 5, or 8?
19
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Numbers and Operations
Circle the answer for each question.
1.
2.
3.
What fraction of the figure is
shaded?
4.
What fraction of the circles are
shaded?
A.
_2
5
C.
_5
5
A.
_1
6
C.
_5
6
B.
_3
5
D.
_5
2
B.
_3
6
D.
_6
6
What fraction of the stars are
shaded?
A.
_3
1
B.
_2
3
C.
_3
3
D.
_1
3
A sandwich is cut into 4 equal
pieces. Melody eats 3 pieces.
What fraction shows the amount
of the sandwich Melody ate?
A.
_1
4
C.
_4
1
B.
_3
4
D.
_4
3
5.
6.
What fraction of the figure is
shaded?
A.
_1
2
C.
_2
2
B.
_2
1
D.
_3
2
There are 6 green peppers and
4 red peppers at the store. What
fraction shows the number of
red peppers?
A.
_2
6
C.
4
__
10
B.
_4
6
D.
6
__
10
20
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7.
Izzy drew a circle.
Part A.
Shade _64 of Izzy’s circle.
Part B.
Use words and/or numbers to explain your answer.
Math
Words
Numbers and Operations
Lesson 4: Models for Fractions
Label the diagrams using words from the box.
8.
3
_
8
fraction
9.
3
_
8
denominator
10.
3
_
8
numerator
21
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Numbers and Operations
LESSON
Coins and Making Change
5
When counting on to find the value of a set of
money, start with the bill or coin of the greatest
value.
Nathan bought a board game for $3.47. He paid with a $5 bill.
Find the bills and coins Nathan will get back as change.
Find how much change Nathan will get back.
$5. 0 0
REMEMBER To find change,
subtract the cost of the item
from the amount used to pay
for the item.
– $3. 4 7
$
$ .
$ .
$ .
UNUM •
UNIT
CEN
T
UNIT
$1.25
•
NE
O
$1 .00
CEN
•
ICA
ICA
O
NE
ATES oF
STE PLURIBUS A
ER
UNUM •
ER
•
M
•
M
ATES oF
STE PLURIBUS A
ED
Make the change with bills and coins.
ED
Step 2
.
T
Step 1
$ .
total
So, Nathan will get
dollar bill,
pennies back as change.
quarters, and
22
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Find the value of each set.
1.
BU S U N
URI
UM
PL
UNITED
ERICA
M O N T I C E L L O
D
E
DIM
FI
VE CENT
S
What is the
value of 1 quarter
and 1 dime?
30¢ or 35¢?
CA
IT
UN
•O
NE
EP
LUR1 9 9 9 NUM
ABUS U
E
M
VIRTUE
LIBERTY
INDEPENDENCE
ATES OF A
ST
ER
I
SYLVAN
NN
IA
PE 1787
E•
1.
Numbers and Operations
Lesson 5: Coins and Making Change
M
STA
TES OF A
total
BU S U N
URI
UM
PL
ATES oF
STE PLURIBUS A
•
E
CA
S
M
STA
TES OF A
NE
CEN
T
VE CENT
ER
I
FI
O
IT
UN
M O N T I C E L L O
D
ICA
UNIT
UNUM •
ER
•
M
E
ED
2.
total
Find the total amount of change. List the bills
and coins that could be given as change.
3.
5.
Price: $1.25
Amount given: $2.00
4.
Price: $4.18
Amount given: $5.00
6.
Price: $7.83
Amount given: $10.00
Do you add or
subtract to find
the amount of
change?
Price: $7.55
Amount given: $10.00
Solve.
7.
3.
Robin bought a book for $11.49. She paid using
three $5 bills. What bills and coins could Robin get
back?
7.
What is the
value of three $5
bills?
$5, $10, or $15?
23
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Numbers and Operations
Circle the answer for each question.
1.
What is the value of this set of
money?
Samantha bought a carton of
juice for $2.29. She paid with a
$5 bill. Which choice shows the
bills and coins he could receive
as change?
A.
ATES oF
STE PLURIBUS A
•
ICA
UNIT
UNUM •
ER
•
M
ED
SYLVAN
NN
IA
PE 1787
VIRTUE
LIBERTY
INDEPENDENCE
3.
EP
LUR1 9 9 9 NUM
ABUS U
2.
A.
$3.62
B.
$2.67
C.
$2.62
D.
$2.57
B.
CEN
T
O
NE
C.
D.
What is the value of this set of
money?
•
DIM
ICA
BU S U N
URI
UM
PL
Jeff paid $2.38 for a pair of
gloves with three $1 bills. Which
choice lists the coins he could
have received?
CEN
IT
UN
M O N T I C E L L O
E
D
A.
$1.41
B.
$1.36
C.
$5.36
D.
$5.41
FI
VE CENT
S
CA
T
O
NE
E
ER
I
UNIT
UNUM •
ER
•
M
ED
•O
NE
ATES oF
STE PLURIBUS A
E•
ERICA
UNITED
M
ATES OF A
ST
4.
M
STA
TES OF A
A.
2 quarters, 1 dime, and
2 pennies
B.
2 dimes, 2 pennies, and
1 quarter
C.
1 nickel, 1 dime, 2 pennies,
and 1 quarter
D.
2 pennies, 3 dimes, and
4 nickels
24
238NA_Mth_G3_SE_Less 01-09_PDF_.24 24
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5.
Cherisa pays $3.35 for a hamburger with a $5 bill.
Part A.
Name the bills and coins Cherisa could receive as change.
Part B.
Use what you know about making change to explain why your
answer is correct.
Math
Words
Numbers and Operations
Lesson 5: Coins and Making Change
Fill in the blanks.
6.
To find change,
pay for the item.
7.
$2.96 can be shown using
and
penny.
8.
Two $1 bills, 2 quarters, 1 nickel, and 3 pennies equals
$
.
.
the cost of the item from the amount used to
$1 bills,
quarters,
dimes,
25
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Numbers and Operations
Addition-Subtraction
Fact Families
LESSON
6
When you use fact families, remember this word:
fact family a set of related addition and subtraction number sentences
Find the three facts related to 7 4 11.
Step 1
will have 2 addition and 2
subtraction facts.
Find the other addition fact.
4
Step 2
THINK This fact family
11
Write the subtraction facts.
11 7 4
REMEMBER The missing
11 Step 3
numbers are the other two
numbers from the addition facts.
Check that four facts use the same numbers.
The numbers are
,
, and
So, the three facts related to 7 4 11 are
, and
.
.
,
26
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Write an addition-subtraction fact
family for each set of numbers.
1.
2.
3, 9, 12
7, 8, 15
1.
Numbers and Operations
Lesson 6: Addition-Subtraction Fact Families
Which number
will be the sum?
3 or 12?
Find the missing number in each fact family.
3.
5
12
4.
5 12
12 5 12 67
3.
76
What number
plus 5 equals 12?
7, 8, or 9?
7 6
5
6 7
Write a related subtraction fact for each
addition fact.
5.
84
6.
89
Write a related addition fact for each
subtraction fact.
7.
15 6 8.
14 5 7.
What number
do you add to 6
to equal 15?
5, 7, or 9?
27
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Numbers and Operations
Circle the answer for each question.
1.
Which addition fact is related to
this subtraction fact?
4.
Which subtraction fact is related
to this addition fact?
13 8 2.
3.
48
A.
13 8 21
A.
844
B.
8 4 12
B.
12 4 8
C.
7 6 23
C.
12 6 6
D.
5 8 13
D.
12 3 9
Which set of numbers can
be used to make an additionsubtraction fact family?
A.
5, 7, 9
C.
5, 7, 12
B.
3, 9, 11
D.
4, 8, 8
What are the other members of
the fact family that includes the
addition fact 9 2 11?
A.
2 9 11, 11 2 9,
11 9 2
B.
2 9 11, 9 2 7,
725
C.
2 11 13, 13 9 4,
11 2 9
D.
2 9 11, 11 2 13,
2 11 13
5.
and
are numbers in
The
the fact family shown below.
17 17 17
17
A.
6 and
7
B.
7 and
8
C.
8 and
9
D.
9 and
10
28
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6.
Kendra wrote an addition-subtraction fact family using the numbers 3, 8,
and 11. Write the facts in her fact family.
7.
The fact family 3 3 6 and 6 3 3 only has two number
sentences.
Part A.
Write another addition-subtraction fact family that only has
two number sentences.
Part B.
Explain why there are only two number sentences in your fact
family.
Math
Words
8.
Numbers and Operations
Lesson 6: Addition-Subtraction Fact Families
Write fact family next to the set of facts that shows a fact
family. Cross out the set of facts that does not show a fact
family.
8 5 13
5 8 13
13 8 5
13 5 8
9.
7 3 10
5 5 10
10 3 7
10 5 5
29
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Numbers and Operations
Multiplication as
Repeated Addition
LESSON
7
You can use arrays to model multiplication facts.
What multiplication fact does the array show?
Step 1
REMEMBER Rows
Count the number of rows.
go across.
There are 4 rows.
Step 2
Count the squares in each row.
There are 5 squares in one row.
Step 3
Use repeated addition to find the total.
THINK The array
5555
Step 4
shows 4 groups of 5.
Write the multiplication fact.
rows
So, the array shows
squares in
each row
total
number
.
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Complete each set.
1.
groups of
2.
1.
Numbers and Operations
Lesson 7: Multiplication as Repeated Addition
How many
groups are
there?
3, 4, or 12?
groups of
Write a repeated addition sentence and a
multiplication sentence for each array.
3.
3.
How many
groups are
there?
6, 7, or 42?
4.
5.
Write a multiplication sentence for each.
5.
8 8 8 24
6.
33333
3 18
How can you
draw a picture
to solve this
problem?
31
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Numbers and Operations
Circle the answer for each question.
1.
Which array shows
2 6 12?
3.
Which multiplication fact does
the array show?
A.
B.
C.
D.
2.
Which tells how many hearts
are in the array?
4.
A.
4 7 28
B.
4 8 32
C.
7 3 21
D.
7 5 35
Which is another way to show
3 3 3 3 3?
A.
35
B.
33
A.
55
C.
55
B.
22
D.
53
C.
55
D.
22
5.
Which is another way to show
2 3?
A.
33
B.
23
C.
22
D.
333
32
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6.
Topher used the array shown below.
Part A.
Write an addition sentence and a multiplication sentence for
Topher’s array.
Part B.
Explain why the number sentences you wrote are correct.
-ATH
7ORDS
Numbers and Operations
Lesson 7: Multiplication as Repeated Addition
Fill in the blanks with add, subtract, or multiply.
7.
To find the total of groups of different sizes,
8.
To find a difference,
9.
To find the total when given equal groups,
.
.
.
33
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Numbers and Operations
LESSON
How to Solve Problems
8
When you solve problems, remember these
words:
add to find the total number when you
join groups of different sizes
multiply to find the total when given
equal groups
subtract to compare or find a difference
There are 274 third graders and 329 fourth graders at Tanglewood
School. How many third and fourth graders are there at
Tanglewood School?
Step 1
Read the problem.
Write a sentence telling what you are asked to find.
Step 2
Decide if you should add, subtract, or multiply.
What operation will you use?
Step 3
Use the operation to solve the problem.
274 329 Step 4
Check your work.
How can you check your answer?
So, there are
Tanglewood School.
THINK You need to find
the total number of third
and fourth graders.
third and fourth graders at
34
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Write add, subtract, or multiply to
name the operation you will use to
solve the problem. Then solve each
problem.
1.
Rory has 80¢. She spends 43¢ on a granola bar.
How much money does Rory have left?
2.
Henry scored 2 points in each soccer game. He has
played in 7 soccer games. How many points has
Henry scored in all of the games?
3.
Joe displays his collection of model cars on 3
shelves. There are 8 cars on each shelf. How many
model cars does Joe have?
4.
Libby’s family drove 283 miles on Friday and 152
miles on Saturday. How many miles did they travel
both days?
5.
Brecken has a book that is 123 pages long. He has
read 64 pages. How many more pages does he need
to read to finish the book?
6.
Mrs. Rios grew tomato plants in 5 rows of her
garden. There were 8 tomato plants in each row.
How many tomato plants did Mrs. Rios grow?
Numbers and Operations
Lesson 8: How to Solve Problems
1.
How can you
find how much
money is left?
Subtract or
divide?
4.
How can you
find the total of
two groups of
different sizes?
Add or subtract?
35
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Numbers and Operations
Circle the answer for each question.
1.
2.
3.
A roll of mints has 10 pieces.
How can you find how many
mints there are in 4 packages?
A.
Subtract 4 from 10.
B.
Add 10 and 4.
C.
Multiply 10 by 4.
D.
Divide 10 by 4.
Which operation would best
solve this problem? There are 63
houses on Patrick’s paper route.
He has delivered the paper to
19 houses so far. How many
more houses does he need to
deliver the paper to?
4.
5.
Pedro had 142 toy cars. He then
bought 29 toy cars at a garage
sale. Which operation can you
use to find how many toy cars
Pedro now has?
A.
addition
B.
subtraction
C.
multiplication
D.
division
Rini walked 18 minutes to her
friend’s house. They then walked
25 minutes to the park. Which
number sentence could you
use to find out how many total
minutes Rini walked?
A.
addition
B.
subtraction
A.
25 18 C.
multiplication
B.
18 25 D.
division
C.
25 18 D.
18 25 Rosa has saved $37 to buy an
MP3 player for $93. How much
more money does she need to
save?
A.
$130
C.
$64
B.
$120
D.
$56
36
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7.
Connor bought 5 packs of pencils. Each pack has 10 pencils. How many
pencils did Connor buy?
Part A.
Write and solve a number sentence to solve the problem.
Part B.
Explain how you knew what operation to use to solve this
problem.
-ATH
7ORDS
Numbers and Operations
Lesson 8: How to Solve Problems
Draw a line to match.
8.
to find the total when
given equal groups
add
9.
to find a difference
subtract
10.
to find the total of
groups of different sizes
multiply
37
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Numbers and Operations
Solving Problems by
Adding
LESSON
9
When you add whole numbers, remember these
words:
addend a number added
sum the answer to an addition problem
Mrs. Roberts’ class collected 318 cans and Mr. Torres’ class collected
456 cans for the can drive. How many cans did both classes collect?
Step 1
Step 2
Circle which operation to use.
I will (add / subtract) to solve the problem.
THINK You need to find
the total number of cans.
Set up the problem.
REMEMBER Line up the
numbers by place value.
Step 3
Step 4
Add the ones.
1
318
4 5 6
4
THINK 8 6 14.
Regroup 14 as 1 ten 4 ones.
Add the tens. Then add the hundreds.
1
3 1 8
4 5 6
4
So, the two classes collected
cans.
38
238NA_Mth_G3_SE_Less 01-09_PDF_.38 38
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Find the sum.
1.
43
89
2.
3.
675
132
4.
509
321
5.
224
397
6.
386
427
8.
407 392 7.
57 68 9.
316 485 132 10.
912 219 347 27
32
1.
Numbers and Operations
Lesson 9: Solving Problems by Adding
How can you
regroup 12?
1 ten 2 ones
or
2 ones 1 ten?
7.
Do you need to
regroup the sum
of 7 8?
Yes or no?
Solve.
11.
12.
Carrie drove 185 miles on Friday and 237 miles on
Saturday. How many miles did she drive both days?
11.
Do you add or
subtract to join
two numbers?
Miguel read 45 pages of a book before school and
72 pages of the same book after school. How many
pages of the book did Miguel read in all?
39
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Numbers and Operations
Circle the answer for each question.
1.
2.
3.
53 29 4.
436 217 A.
24
A.
553
B.
72
B.
643
C.
76
C.
653
D.
82
D.
743
39
47
5.
154
628
A.
66
A.
772
B.
76
B.
782
C.
86
C.
882
D.
96
D.
1,268
Collin bought a new video
game for $56 and a used video
game for $17. How much did
Collin spend for both video
games?
6.
There were 312 visitors to
the zoo Friday morning and
493 visitors to the zoo Friday
afternoon. How many visitors
came to the zoo on Friday?
A.
$73
A.
815 visitors
B.
$72
B.
805 visitors
C.
$63
C.
605 visitors
D.
$39
D.
181 visitors
40
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7.
On a farm, there are 127 horses and 245 cows.
Part A.
Show how to find how many horses and cows there are in all
on the farm.
Part B.
Explain the steps you used to find the answer to Part A.
Math
Words
8.
Numbers and Operations
Lesson 9: Solving Problems by Adding
Label the diagram using words from the box.
67
24
91
sum
HINT You need to use
addend
a word more than once!
41
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Numbers and Operations
Solving Problems
10 by Subtracting
LESSON
When you subtract whole numbers, remember
this word:
difference the answer to a subtraction problem
Carrie is thinking of a number. It is 216 less than 423. Find
Carrie’s number.
Step 1
Circle which operation to use.
I will (add / subtract) to solve the problem.
Step 2
Set up the problem.
REMEMBER Line
up the numbers by
place value.
Step 3
Subtract the ones.
THINK 6 3, so
1 13
423
216
7
Step 4
regroup 2 tens 3 ones as
1 ten 13 ones to subtract.
Subtract the tens. Then subtract the hundreds.
1
13
4 2 3
2 1 6
7
So, Carrie’s number is
.
42
238NA_Mth_G3_SE_Less 10-19_PDF_.42 42
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Find the difference.
1.
74
56
2.
3.
863
548
4.
218
85
5.
434
297
6.
307
215
7.
95 46 8.
50 29 9.
317 184 10.
832 173 31
17
1.
Numbers and Operations
Lesson 10: Solving Problems by Subtracting
How can you
regroup 74?
7 tens 14 ones
or
6 tens 14 ones?
9.
What place
do you regroup
to subtract the
tens?
ones, tens, or
hundreds?
Solve.
11.
12.
Trevor wanted to ride his bike for 45 minutes. He
has been riding his bike for 18 minutes. How much
longer does Trevor have to ride his bike to meet his
goal?
11.
Will you add or
subtract to solve?
There are two sea turtles at the aquarium. The male
sea turtle weighs 342 pounds. The female sea turtle
weighs 194 pounds. How much more does the
male sea turtle weigh than the female sea turtle?
43
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Numbers and Operations
Circle the answer for each question.
1.
2.
3.
83 45 4.
526 259 A.
32
A.
267
B.
38
B.
273
C.
42
C.
333
D.
48
D.
367
71
54
5.
902
178
A.
27
A.
876
B.
23
B.
824
C.
17
C.
734
D.
7
D.
724
Melody had 82¢. She spent 39¢.
How much money does Melody
have left?
6.
A.
57¢
B.
53¢
C.
47¢
There were 716 people at the
school play on Friday night.
On Saturday, there were 805
people at the school play. How
many more people were at the
school play on Saturday than on
Friday?
D.
43¢
A.
89 people
B.
99 people
C.
101 people
D.
189 people
44
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7.
Rosewood School had a two week read-a-thon. During the first week,
Maria read 56 pages. During the second week she read 81 pages. How
many more pages did Maria read during the second week than during the
first week?
8.
Jin has two puzzles. A sailboat puzzle has 425 pieces. A balloon puzzle
has 380 pieces. How many more pieces does the sailboat puzzle have than
the balloon puzzle?
Math
Words
Numbers and Operations
Lesson 10: Solving Problems by Subtracting
Fill in the blanks.
9.
The result of an addition problem is the
10.
3 tens 4 ones can be
11.
The result of a subtraction problem is the
12.
In 14 16 30, 14, and 16 are
.
as 2 tens 14 ones.
.
.
45
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Numbers and Operations
Solving Problems
with Multiplication
LESSON
11
Carefully read word problems to find the
question you need to answer and the information
in the problem.
There is a type of bamboo that grows 12 inches in one day! How
many inches will the bamboo grow in one week?
Step 1
Write a multiplication sentence.
THINK There are
7 days in one week.
number of
inches
12
Step 2
number of
days
total number
of inches
Solve.
12 7 So, the bamboo plant will grow
inches in one week.
46
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Write a multiplication sentence to
solve each problem.
1.
Jacey’s team scored 3 points in each of the last 7
hockey games he has played. How many points did
Jacey’s team score in all?
2.
Jenn is peeling carrots for a salad. She peels 2
carrots each minute. How many carrots does she
peel in 4 minutes?
3.
Farrah’s mom bought 9 packs of juice boxes at the
store. Each pack has 3 juice boxes in it. How many
juice boxes did Farrah’s mom buy?
4.
The state tree of Pennsylvania is the hemlock tree.
In one park, there are 5 rows of hemlock trees.
Each row has 4 trees. How many hemlock trees are
in the park?
5.
1.
Numbers and Operations
Lesson 11: Solving Problems with Multiplication
What is
3 7?
11 or 21?
4.
What number
do you multiply
by 5?
4 or 5?
In warm water, coral reefs can grow 2 feet each
year. How many feet can a coral reef grow in 8
years?
47
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Numbers and Operations
Circle the answer for each question.
1.
Debbie buys 3 boxes of granola
bars. Each box has 6 granola
bars in it. How many granola
bars does Debbie buy in all?
4.
3.
A.
76 laps
A.
9 granola bars
B.
42 laps
B.
12 granola bars
C.
36 laps
C.
18 granola bars
D.
13 laps
D.
24 granola bars
5.
2.
Eric runs 7 laps around the
track each day. How many laps
does Eric run in 6 days?
There are 4 boxes of crayons.
Each box has 10 crayons. How
many crayons are there in all?
A.
6 crayons
B.
14 crayons
C.
20 crayons
D.
40 crayons
Mrs. Green baked muffins for
the bake sale. She set 8 muffins
on each of 3 plates. How many
muffins did she bake?
6.
Jae used 6 pages of his
scrapbook for pictures
of a vacation to Hershey,
Pennsylvania. He put 4 pictures
on each page. How many
pictures does Jae have of his
vacation?
A.
10 pictures
B.
14 pictures
C.
20 pictures
D.
24 pictures
A.
24 muffins
B.
18 muffins
C.
15 muffins
Sierra earned $4 an hour for
babysitting. She babysat for 4
hours on Saturday. How much
money did Sierra earn on
Saturday?
D.
11 muffins
A.
$8
C.
$16
B.
$12
D.
$20
48
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7.
Ahmed has 3 packs of trading cards. Each pack has 8 cards. How many
cards does Ahmed have in all?
8.
Ben needs 4 tickets for each ride at the fair.
Part A.
If he goes on 7 different rides, how many tickets does he need?
Part B.
Explain how you used multiplication to solve the problem.
Math
Words
Numbers and Operations
Lesson 11: Solving Problems with Multiplication
Fill in the blanks.
9.
To find the total when given equal groups I can
10.
To compare two groups I can
11.
To find the total of different-sized groups I can
.
.
.
49
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Numbers and Operations
Rounding to the
12 Nearest 10 or 100
LESSON
When you round numbers, remember this word:
round to estimate a number to the nearest 10 or 100
47 rounds to 50
Example 1 Round 176 to the nearest 100.
Step 1
0
Place 176 on a number line marked off by 100’s.
100
Step 2
200
300
400
500
600
700
800
900
THINK 176 is between
Decide if 176 is closer to 100 or 200.
100 and 200.
So, 176 rounded to the nearest 100 is
.
Example 2 Round 176 to the nearest 10.
Step 1
100
Place 176 on a number line marked off by 10’s.
110
Step 2
120
130
140
150
160
Decide if 176 is closer to 170 or 180.
So, 176 rounded to the nearest 10 is
170
180
190
200
THINK 176 is between
170 and 180.
.
50
238NA_Mth_G3_SE_Less 10-19_PDF_.50 50
8/6/07 8:40:57 AM
Round to the nearest 10.
1.
74
2.
93
3.
7
4.
25
5.
38
6.
41
7.
19
8.
55
9.
63
Round to the nearest 10 and 100.
284
11.
149
12.
637
13.
316
14.
851
15.
733
593
17.
475
Which number
is 74 closer to on
a number line?
70 or 80?
4.
10.
16.
1.
Numbers and Operations
Lesson 12: Rounding to the Nearest 10 or 100
18.
When the ones
digit is 5, do
you round up or
down?
10.
805
Solve.
19.
A reindeer can run 32 miles per hour. What is this
number rounded to the nearest 10?
20.
There are 365 students in the school. What is this
number rounded to the nearest 100?
Which places
change to zero
when you round
to the nearest
hundred?
Tens, ones, or
both?
19.
What number
is 32 closer to?
30 or 40?
51
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Numbers and Operations
Circle the answer for each question.
1.
2.
3.
Round 48 to the nearest 10.
4.
Round 268 to the nearest 100.
A.
30
A.
200
B.
40
B.
260
C.
45
C.
270
D.
50
D.
300
Round 314 to the nearest 10.
5.
Round 93 to the nearest 100.
A.
300
A.
0
B.
310
B.
90
C.
320
C.
100
D.
400
D.
200
Trevor has 137 leaves in his
collection. To the nearest 10,
how many leaves does Trevor
have?
6.
Alfredo lives 364 miles away
from his grandmother. To
the nearest 100, how far
does Alfredo live from his
grandmother?
A.
100 leaves
B.
130 leaves
A.
300 miles
C.
140 leaves
B.
360 miles
D.
200 leaves
C.
370 miles
D.
400 miles
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7.
Adam and Jenn went hiking in the Pocono Mountains. Their hiking trip
was 26 miles long. To the nearest 10, how many miles did Adam and Jenn
hike?
8.
Write a 3-digit number that, when rounded to the nearest hundred,
rounds to 400. Explain how you know your answer is correct.
Math
Words
Numbers and Operations
Lesson 12: Rounding to the Nearest 10 or 100
Fill in the blanks.
9.
375
10.
894 rounded to the nearest
is 890.
to the nearest 10 is 380 and rounded to the nearest
is 400.
is 900 and rounded to the nearest
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Numbers and Operations
Using Estimation
13 to Solve Problems
LESSON
When you estimate answers, remember this word:
estimate a number that is close to the exact number
The table shows the number of apples picked by three friends.
Friend
Number of Apples
Gina
Andy
James
36
47
31
About how many apples did the friends pick?
Step 1
THINK About
usually means you
can find an estimate.
Decide if you need an estimate or exact answer.
The question asks “About how many,” so you can use an estimate.
Step 2
Round the number of apples each friend picked to the nearest 10.
36 rounds to 40.
47 rounds to 50.
31 rounds to
Step 3
.
Use mental math to add the rounded numbers.
40 50 So, the friends picked about
apples.
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Estimate the sum or difference.
1.
64 28 2.
29 62 3.
147 389 4. 425 150 5.
505 271 6.
What does 64
round to?
50 or 60?
853 209 The table shows the driving distances the
Chang family traveled when visiting family in
Pennsylvania. Use the table for Questions 7–10.
7.
1.
Numbers and Operations
Lesson 13: Using Estimation to Solve Problems
Day
Distance Driven
Tuesday
Wednesday
Thursday
187 miles
203 miles
251 miles
About how many miles did the Chang family drive
on Tuesday and Wednesday?
8.
About how many more miles did the Chang family
drive on Thursday than on Tuesday?
9.
About how many more miles did the Chang family
drive on Thursday than on Wednesday?
10.
About how many miles did the Chang family travel
in all?
4.
What place will
you round to?
Hundreds or
tens?
7.
Will you
estimate a sum
or difference to
solve?
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Numbers and Operations
Circle the answer for each question.
1.
2.
There are 87 students signed up
for soccer. There are 63 students
signed up for swimming. About
how many more students are
signed up for soccer than
swimming?
A.
150 students
B.
140 students
C.
40 students
D.
30 students
Grover School put on a concert.
On Friday night, 212 people
came. On Saturday night, 295
people came. Round each
number to the nearest hundred
to find about how many people
came to the concert in all.
A.
400 people
B.
500 people
C.
600 people
D.
700 people
Use the table to answer
Questions 3 and 4.
3.
4.
Grade
Number of Students
Second
Third
Fourth
212
165
143
To the nearest hundred, about
how many students are in all
three grades?
A.
300 students
B.
400 students
C.
500 students
D.
600 students
Which number sentence could
you use to estimate the number
of students in second grade and
third grade?
A.
200 100 B.
200 100 C.
200 200 D.
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5.
Joshua has 132 stickers in his collection. 45 of the stickers are puffy
stickers. The rest are regular stickers. About how many regular stickers
does Joshua have in his collection?
6.
Derek wants to buy a book for $18 and a board game for $31. Derek
estimates he needs $40. Is his estimate correct? Explain why or why not.
If his estimate is not correct, find the correct estimate.
Math
Words
Numbers and Operations
Lesson 13: Using Estimation to Solve Problems
Write the meaning for each in your own words.
7.
round
8.
estimate
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LESSON
Measurement
14 Units of Measurement
When finding units of measure, first decide if
you need to find units of length, weight, mass, or
capacity. Then select the size of the unit.
Which unit would be best to measure the capacity of a mug?
grams
cups
meters
ounces
REMEMBER Capacity
is a measure of how much
something can hold.
Step 1
Look at the chart. Find the column for capacity.
customary
units
metric units
measurement
tools
Step 2
length
weight and mass
inch, foot, yard,
mile
ounce, pound, ton
centimeter,
gram, kilogram
meter, kilometer
ruler, yardstick, scale, pan balance
measuring tape
Find a unit that measures capacity.
So, the best unit to measure the
capacity of a mug is
.
capacity
teaspoon, tablespoon,
cup, pint, quart, gallon
liter, milliliter
teaspoon, tablespoon,
measuring cup
THINK Which answer
choice is in the capacity
column of the table?
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Lesson 14: Units of Measurement
Circle the best unit of measurement
for each.
1.
2.
capacity of a sink
grams
feet
centimeters
gallons
length of a piece
of paper
4.
1.
Which unit is in
the mass column
of the chart?
Grams or
centimeters?
Measurement
3.
mass of an apple
distance from your
house to school
centimeters
kilograms
teaspoons
miles
Circle the best measuring tool for each.
5.
7.
length of your
math book
6.
capacity of a juice
glass
ruler
teaspoon
yardstick
measuring cup
weight of a child
8.
length of the
chalkboard
scale
yardstick
measuring tape
ruler
5.
Which is best
for measuring
short objects?
Ruler or
yardstick?
6.
Which makes
more sense?
Using a teaspoon
many times
or using a
measuring cup
one time?
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Circle the answer for each question.
Measurement
1.
2.
3.
What does a liter measure?
4.
What does a gram measure?
A.
length
A.
length
B.
weight
B.
time
C.
capacity
C.
capacity
D.
time
D.
mass
Which unit can be used to find
the length of a feather?
5.
Which unit can be used to
measure the capacity of a
bathtub?
A.
centimeter
B.
gram
A.
ounces
C.
cup
B.
gallons
D.
pound
C.
tons
D.
hours
Shawn needs to measure the
mass of a puppy. Which of the
following measurement tools
should he use?
A.
teaspoon
B.
scale
C.
measuring tape
D.
yardstick
6.
Margot is making curtains for
a large window. She needs to
measure 8 feet of fabric. Which
measurement tool should
Margot use?
A.
scale
B.
ruler
C.
measuring cup
D.
yardstick
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Lesson 14: Units of Measurement
7.
Shelley needs to measure flour for a recipe.
What measurement tool should Shelly use? Explain your
choice.
Part B.
Will Shelley measure the flour in ounces, grams, or cups?
Explain your choice.
Math
Words
Measurement
Part A.
Fill in the blanks.
8.
Teaspoon, liter, and quart are units used to measure
9.
Gram and kilogram are units used to measure
10.
Inch, centimeter, yard, and meter are units used to measure
11.
A ruler is a tool used to measure
12.
A ton is a unit used to measure
.
.
.
.
.
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LESSON
15 Estimating Length
Measurement
When you estimate length, remember these units:
customary units of length
unit
benchmark
inch
the length of a small paper
clip
foot
the length of this page from
top to bottom
yard
the length of a baseball bat
mile
about how far a person can
walk in 20 minutes
metric units of length
unit
benchmark
millimeter the width of a pencil
point
centimeter the width of your
thumb
meter
a little more than 1 yard
kilometer about how far a person
can walk in 12 minutes
Which measurement best describes the height of your desk?
3 inches
Step 1
3 feet
3 yards
3 miles
Think about 3 inches.
3 inches is (too short / about right / too long).
THINK It would take
Step 2
Think about 3 feet.
3 feet is (too short / about right / too long).
Step 3
Think about 3 yards and 3 miles.
3 yards and 3 miles are (too short / about right / too long).
you about 60 minutes
to walk 3 miles.
So, the best estimate for the height of your desk is
about 3
.
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Lesson 15: Estimating Length
Circle the better estimate.
1.
5.
7.
2.
length of a pencil
3 inches
15 centimeters
3 feet
15 meters
distance from
Pittsburgh to
Philadelphia
4.
height of the
classroom
300 yards
4 meters
300 miles
4 kilometers
length of a football
field
6.
30 millimeters
100 yards
30 centimeters
8.
About how long
is a paper clip?
1 inch or 1 foot?
4.
Which unit is
about the length
of a baseball
bat?
Meter or
kilometer?
length of a pin
100 inches
height of a third
grader
1.
Measurement
3.
length of a classroom
window
length of a hiking trail
4 feet
3 meters
4 yards
3 kilometers
8.
Which unit
shows a distance
you would walk?
Meter or
kilometer?
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Circle the answer for each question.
Measurement
1.
Which measurement best
describes the height of the
classroom door?
4.
65 inches
2 kilometers
B.
65 feet
B.
2 meters
C.
65 yards
C.
2 centimeters
D.
65 miles
D.
2 millimeters
About how long is a chalkboard
eraser?
Which is the best estimate for
the height of a store ceiling?
A.
10 millimeters
A.
5 inches
B.
10 centimeters
B.
5 feet
C.
10 meters
C.
5 yards
D.
10 kilometers
D.
5 miles
6.
3.
A.
A.
5.
2.
Which is a reasonable height for
an adult?
Which is the best estimate for
the distance from Harrisburg,
Pennsylvania, to Washington,
D.C.?
A.
120 inches
B.
120 feet
C.
120 yards
D.
120 miles
Which of the following is
a reasonable distance for a
running race?
A.
5 millimeters
B.
5 centimeters
C.
5 meters
D.
5 kilometers
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Lesson 15: Estimating Length
7.
Which metric unit would you use to measure the length of a classroom?
8.
Look at the door to your classroom.
Part A.
What is a reasonable estimate for the height of the door?
Measurement
7 inches, 7 feet, 7 yards, or 7 miles?
Part B.
-ATH
7ORDS
Explain how you made your estimate.
Match the benchmark to the unit of measure.
9.
the length of a paper
clip
a yard
10.
the length of a baseball
bat
a mile
11.
the length of this page
a foot
12.
the distance traveled on
a 20-minute walk
an inch
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LESSON
16 Estimating Weight
Measurement
When you estimate weight, remember this word:
weight how heavy something is
Mary weighs the items in the list using ounces
or pounds. Find the item she should measure
in ounces.
Step 1
Step 2
Think about objects that weigh about 1 pound
and about 1 ounce.
ounce
pound
a strawberry
a bunch of grapes
Mary’s List
desk
math book
marker
globe
Compare each item in Mary’s list to the table in Step 1.
Write each item in the table under the best unit of measure.
ounces
pounds
desk
REMEMBER Heavier
objects are measured in
pounds. Lighter objects
are measured in ounces.
So, the
should be measured in ounces.
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Lesson 16: Estimating Weight
Write the best unit to weigh each
item. Write ounces or pounds.
1.
a handful of blueberries 2.
a bicycle
1.
a watermelon
4.
a piece of chalk
5.
a computer
6.
a bag of potatoes
5.
Measurement
3.
Which
describes a
handful of
blueberries?
Heavy or light?
Is a computer
heavy or light?
7.
a glue stick
9.
a cat
8.
10.
a pack of gum
a toothbrush
Solve.
11.
12.
The weight of a cell phone is 14 units. Were ounces
or pounds used to measure the weight?
11.
Is a cell phone
heavy or light?
The weight of a book is 2 units. Were ounces or
pounds used to measure the weight?
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Circle the answer for each question.
Measurement
1.
2.
3.
Which classroom object would
best be measured in ounces?
4.
Which object would be best to
measure in pounds?
A.
the garbage pail
A.
a leaf
B.
a desk
B.
an insect
C.
a chair
C.
a rock
D.
chalkboard eraser
D.
a piece of bark
The weight of a bag of oranges
is 8 units. Which unit was used
to measure the weight?
5.
Which unit should you use to
measure the weight of a hair
brush?
A.
pounds
A.
inches
B.
ounces
B.
pounds
C.
feet
C.
cups
D.
inches
D.
ounces
Which object should you
measure in pounds?
6.
The weight of a pair of
sunglasses is 5 units. Which unit
was used to measure the weight?
A.
a bracelet
B.
a backpack
A.
pounds
C.
a sandwich
B.
ounces
D.
a pencil
C.
feet
D.
inches
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Lesson 16: Estimating Weight
7.
Look at this list of camping supplies.
pocket flashlight
canoe
hiking boots
map
tent
Sort these supplies into two groups: supplies that you would
measure in ounces and supplies you would measure in pounds.
ounces
Part B.
Math
Words
pounds
Explain how you decided which supplies would be best
measured using ounces.
Fill in the blanks.
8.
9.
Measurement
Part A.
is the measure of how heavy something is.
Heavier items are measured in units called
measured in units called
.
. Lighter items are
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LESSON
17 Estimating Capacity
Measurement
When you estimate capacity, remember this
vocabulary word:
capacity how much a container can hold
Find the unit of measure that would be best
for measuring the capacity a fish tank.
Step 1
Name the units of capacity.
cup
Step 2
pint
quart
gallon
Compare each unit of capacity to the fish tank.
Cross out units that are too small or too big.
THINK A fish
Circle the best unit.
tank holds a lot of
water. You should
choose a large unit
of capacity.
cup
pint
quart
gallon
So, the best unit for measuring the capacity of
the fish tank is
.
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Lesson 17: Estimating Capacity
Circle the better estimate.
1.
2.
1.
Which unit
holds more?
Pint or gallon?
3.
Measurement
5 pints
5 gallons
30 pints
30 gallons
4.
2 cups
2 quarts
3 cups
3 quarts
Write the best unit to measure the capacity of
each item. Write cup, pint, quart, or gallon.
5.
5.
a soup bowl
6.
a bathtub
7.
a saucepan
8.
a drinking glass
Does a soup
bowl hold about
a pint or about a
gallon?
9.
Solve.
9.
The capacity of a bathroom sink is 5 units. Were
pints or gallons used to measure the capacity?
10.
The capacity of a punch bowl is 4 units. Were cups
or quarts used to measure the capacity?
Does a
bathroom sink
hold a small
amount of
water or a large
amount of water?
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Circle the answer for each question.
What is the best unit to
measure the capacity of a
kitchen sink?
4.
The capacity of a fish bowl is
1 unit. What unit was used to
measure its capacity?
Measurement
1.
2.
3.
A.
cup
B.
quart
C.
gallon
D.
pint
5.
What is the best estimate of the
capacity of the pitcher?
A.
1 gallon
B.
1 quart
C.
1 pint
D.
1 cup
Which object would be best to
measure using cups?
6.
A.
cup
C.
quart
B.
pint
D.
gallon
What is the best estimate of the
capacity of a coffee mug?
A.
1 gallon
B.
1 quart
C.
1 pint
D.
1 cup
Kendra is filling her car’s gas
tank with gasoline. She fills the
tank with 12 units of gasoline.
What unit was used to measure
the capacity of the gas tank?
A.
cereal bowl
B.
punch bowl
A.
gallons
C.
bathtub
B.
cups
D.
eye dropper
C.
quarts
D.
pints
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Lesson 17: Estimating Capacity
7.
Dylan has cards with the measurements shown below.
9 gallons
9 quarts
5 cups
9 cups
9 pints
Show the cards in order from least capacity to greatest capacity.
Part B.
Explain how you know your answer is correct.
Measurement
Part A.
-ATH
7ORDS
Draw a line to match.
8.
the measure of how
heavy something is
length
9.
the measure of how
much something holds
capacity
10.
the measure of the
distance of an object
from end to end
weight
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LESSON
18 Using Rulers
Measurement
When you measure length, remember these
words:
length the distance of an object from
end to end
ruler a tool used to measure length
Find the length of the pen to the nearest _21-inch.
Inches
1
2
3
4
5
6
Step 1
Line up the beginning of the ruler with the left side of the pen.
Step 2
Look at the right end of the pen.
REMEMBER
The end of the pen is between
and
Step 3
The numbers on the
ruler show inches.
.
Look at the marks between 5 and 6.
1
Is the end of the pen closest to 5, 5 _2 , or 6?
So, the pen is
inches long.
THINK The mark
halfway between two whole
numbers shows _21 .
5
1
5 __
2
6
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Lesson 18: Using Rulers
Measure to the nearest _21-inch.
1.
1.
1
2
3
1
2
3
Measurement
Inches
What whole
number is the
right end closest
to?
2 or 3?
2.
Inches
For Questions 3-5, use your ruler to measure
the objects to the nearest _21-inch.
3.
4.
4.
5.
What whole
numbers are the
right end closest to?
4 and 5 or
5 and 6?
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Circle the answer for each question.
Measurement
1.
To the nearest _21-inch, what is
the length of this barrette?
1
Inches
2.
A.
1 inch
B.
1
1 _2 inch
C.
2 inches
D.
1
2 _2 inches
3.
Use your ruler to measure the
length of the ribbon to the
nearest half inch.
2
Use your ruler to measure the
length of the ant to the nearest
half inch.
4.
A.
2 inches
B.
2 _2 inches
C.
3 inches
D.
3 _2 inches
1
1
Use your ruler to measure
the length of the ticket to the
nearest half inch.
MOVIE
TICKET
A.
2 inches
B.
1 _2 inches
C.
1 inch
D.
_1 inch
2
1
A.
2 inches
B.
2 _2 inches
C.
3 inches
D.
3 _2 inches
1
1
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Lesson 18: Using Rulers
What is the length of this marker to the nearest half inch?
6.
What is the length of this glue stick to the nearest half inch?
Measurement
5.
Glue Stick
Math
Words
Circle the word that completes the sentence.
7.
A (thermometer / ruler) is a tool used to measure length.
8.
An (inch / pound) is a unit to measure length.
9.
(Length / Capacity) is a distance from the beginning to the end of an
object.
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Comparing and Ordering
19 Objects
Measurement
LESSON
When you compare and order objects using
measurements, first make sure all of the units are
the same.
Omar weighs these four boxes.
Box A
Box B
Box C
Box D
4 pounds
1 pounds
2 __
3 pounds
1 pounds
3 __
2
2
He wants to place them in order from heaviest to lightest.
Find how Omar can order the boxes.
THINK Since all
of the units are the
same, pounds, you can
compare the numbers.
Step 1
Compare the weights to order the boxes.
Step 2
Find the heaviest box first.
Box A has the greatest weight. It weighs 4 pounds.
Step 3
Find the box that comes next.
1
Box
comes next. It weighs 3 _2 pounds.
Step 4
Find the box that comes next.
Box C comes next. It weighs
Step 5
THINK The box
pounds.
with the least weight
is the lightest box.
Find the lightest box.
1
Box
has the least weight. It weighs 2 _2 pounds.
So, the boxes in order from heaviest to lightest are
Box
, Box
, Box
, and Box
.
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Lesson 19: Comparing and Ordering Objects
Use , , or to compare the
objects.
1.
Jeff planted a tree that is 6 feet tall and Mary
planted a tree that is 3 feet tall.
6 feet
Carson’s cat weighs 12 pounds and his puppy
weighs 14 pounds.
12 pounds
3.
6.
5 ounces
Graham has a string that is 15 inches long and a
string that is 12 inches long.
15 inches
5.
14 pounds
Naomi bought an apple that weighs 5 ounces and a
plum that weighs 5 ounces.
5 ounces
4.
Which symbol
means greater
than?
or ?
Measurement
2.
3 feet
1.
12 inches
The school nurse measures the heights of four
students. Justin is 52 inches tall, Sophia is 48 inches
tall, Taylor is 47 inches tall, and Catherine is 53
inches tall. What is the order of the students from
tallest to shortest?
5.
Who is
taller, Justin or
Catherine?
Kyan has three bags of marbles. The blue bag
weighs 17 ounces, the red bag weighs 15 ounces,
and the green bag weighs 19 ounces. What is the
order of the bags from heaviest to lightest?
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Circle the answer for each question.
Measurement
1.
2.
Liam cuts two pieces of string
for his kite. String A is 34 inches
long. String B is 37 inches long.
Which of the following best
compares the two pieces of
string?
3.
A bag of oranges weighs 6 _21
pounds and a bag of apples
weighs 5 _21 pounds. Which of
the following best compares the
weights of the bags of fruit?
A.
apples oranges
A.
String A String B
B.
B.
String A String B
apples oranges
C.
C.
String B String A
oranges apples
D.
D.
String B String A
oranges apples
Carmen measures the length of
three worms.
A
3 inches
B
5 inches
C
4 inches
Which of these shows the
worms in order from longest to
shortest?
A.
B, C, A
B.
A, B, C
C.
A, C, B
D.
B, A, C
4.
Carol has four ribbons. The
blue ribbon is 5 inches long, the
red ribbon is 3 _21 inches long,
the green ribbon is 4 _21 inches
long, and the yellow ribbon is
4 inches long. Which shows the
ribbons in order from shortest
to longest?
A.
red, green, yellow, blue
B.
red, yellow, green, blue
C.
blue, green, yellow, red
D.
yellow, red, green, blue
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Lesson 19: Comparing and Ordering Objects
5.
The vet weighs 4 dogs.
Rover
47 pounds
Cricket
Buster
Bailey
42 pounds
36 pounds
39 pounds
Put the dogs in order of their weights from greatest to least.
Part B.
Use what you know about comparing weights to explain why
your answer is correct.
Math
Words
Measurement
Part A.
Fill in the missing symbols.
6.
The symbol
means is less than.
7.
The symbol
means is greater than.
8.
The symbol
means is equal to.
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LESSON
20 Telling Time
Measurement
Remember when telling time that the hour hand
is shorter than the minute hand.
What time does the clock show?
11
12
1
2
10
9
3
8
4
7
6
5
Read the hour.
Step 1
The hour hand is between 10 and 11.
So, the hour is
Step 2
Read the minutes. Count by 5s. Then count by 1s.
5
11
:
12
10
1
2
10
9
REMEMBER In 5
15
minutes, the minute hand
moves from one number to
the next. In 1 minute, the
minute hand moves from
one mark to the next.
3
8
4
7
6
5
So, the time is
:
.
REMEMBER You can
say this time as twentytwo minutes after ten.
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Lesson 20: Telling Time
Read and write each time.
1.
11
12
2.
1
2
10
9
11
12
8
4.
1
9
12
2
3
8
4
7
5
How many
minutes after 6
is it?
7, 12, or 17?
1
9
4
6
11
6
5
10
3
8
4
7
2
7
3
5
10
2
Measurement
3.
6
1.
1
9
4
7
12
10
3
8
11
6
5
Write the time on the clock.
5.
7.
quarter after 12
eighteen minutes
after 9
6.
8.
thirty-two minutes
after 4
5.
How long is one
quarter of an
hour?
15 minutes or
30 minutes?
half past 3
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Circle the answer for each question.
Measurement
1.
What is another way of writing
“fifty-five minutes after 3?”
A.
3:05
B.
3:35
C.
3:55
D.
4:55
4.
Which clock shows 8:52?
11
A.
2
9
3
8
4
7
11
12
1
2
B.
9
3
8
4
7
6
5
1
2
10
9
3
8
11
6
C.
5
9:28
B.
9:33
C.
9:53
D.
10:28
2
3
8
4
11
6
12
5
1
2
10
D.
9
3
8
4
7
Julia spent 60 minutes at soccer
practice. How many hours long
was soccer practice?
1
9
7
A.
12
10
4
7
3.
6
5
10
What time does the clock
show?
12
1
10
11
2.
12
5.
6
5
What is another way of writing
“quarter past 7”?
A.
4 hours
A.
6:45
B.
3 hours
B.
7:30
C.
2 hours
C.
7:45
D.
1 hour
D.
7:15
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Lesson 20: Telling Time
The clock shows the time that Connie leaves for play practice.
6.
11
12
1
2
10
9
3
8
4
7
6
5
Write the time Connie leaves for play practice.
Part B.
Connie finishes play practice at 6:15. Draw this time on the
clock below.
11
12
1
2
10
9
3
8
4
7
Math
Words
11
Measurement
Part A.
6
5
Label the clock using words from the box.
12
7.
1
2
10
9
8.
hour hand
3
8
4
7
6
5
minute hand
quarter hand
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LESSON
21 Elapsed Time
Measurement
When you find elapsed time, remember this
word:
elapsed time the amount of time that passes between two events
A concert starts at 6:15 P.M. and ends at 8:45 P.M. Find how long
the concert lasted.
Step 1
Count the hours.
THINK Another whole
6:15 to 7:15 1 hour
hour would bring the time
to 9:15 P.M., which is later
than 8:45 P.M.
7:15 to 8:15 1 hour
whole hours from 6:15 P.M. to 8:15 P.M.
There are
Step 2
Count the minutes from 8:15 P.M. to 8:45 P.M.
11
12
1
minutes
minutes
9
3
8
minutes
There are
Step 3
REMEMBER You
can skip count by 5s
to count the minutes.
2
10
4
7
6
5
5 minutes
10 minutes
15 minutes
minutes from 8:15 P.M. to 8:45 P.M.
Combine the hours and minutes to find the total elapsed time.
So, the concert is
hours
minutes long.
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Lesson 21: Elapsed Time
Find the elapsed time.
1.
2.
Start Time: 8:00 A.M.
End Time: 11:45 A.M.
Elapsed Time:
4.
Start Time: 1:45 P.M.
End Time: 4:15 P.M.
Elapsed Time:
Start Time: 7:15 A.M.
End Time: 9:30 A.M.
Elapsed Time:
7.
How many
whole hours are
there from 4:00
to 6:30?
1, 2, or 3?
2.
Find the end time for each.
5.
1.
Measurement
3.
Start Time: 4:00 P.M.
End Time: 6:30 P.M.
Elapsed Time:
Start Time: 3:30 P.M. 6.
Elapsed Time: 2 hours
15 minutes
End Time:
Start Time: 2:15 P.M.
Elapsed Time: 1 hour
45 minutes
End Time:
Start Time: 8:00 A.M. 8.
Elapsed Time: 3 hours
30 minutes
End Time:
Start Time: 9:45 A.M.
Elapsed Time: 1 hour
30 minutes
End Time:
How many
minutes from
3:45 to 4:15?
15, 20, or 30?
5.
What time is 2
hours after 3:30?
4:30 or 5:30?
Solve.
9.
10.
Tanner spends 1 hour 45 minutes jogging each
Saturday morning. If he starts at 7:15 A.M., at what
time will he finish?
Amanda started her homework at 6:45 P.M. She
finished at 7:30 P.M. How long did it take Amanda
to do her homework?
9.
What do you
need to find?
Elapsed time or
end time?
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Circle the answer for each question.
Measurement
1.
James is going to a bowling
party at 4:00 P.M. His watch says
that it is 1:15 P.M. How much
longer does James have to wait
before the bowling party begins?
4.
9:30 A.M.
2 hours 45 minutes
B.
9:45 A.M.
B.
3 hours 15 minutes
C.
10:00 A.M.
C.
3 hours 45 minutes
D.
10:45 A.M.
D.
2 hours 15 minutes
Bianca is taking a 2 hour and 30
minute trip to see her sister. She
left at 2:30 P.M. At what time
should she arrive at her sister’s?
Kelly started painting a picture
at 1:15 P.M. She stopped at
2:30 P.M. For how long was she
painting?
A.
15 minutes
A.
4:30 P.M.
B.
1 hour
B.
5:30 P.M.
C.
1 hour 15 minutes
C.
4:00 P.M.
D.
1 hour 30 minutes
D.
5:00 P.M.
6.
3.
A.
A.
5.
2.
Anthony and his sister played
a game for 30 minutes. If they
started at 9:15 A.M., at what
time did they finish?
Aaron’s band concert was 2
hours 15 minutes long. The
concert ended at 9:00 P.M. At
what time did the concert start?
It takes April 1 hour and
30 minutes to drive to her
grandmother’s house. If she
leaves at 4:45 P.M., what time
will she arrive?
A.
6:45 P.M.
A.
6:00 P.M.
B.
7:00 P.M.
B.
6:15 P.M.
C.
7:15 P.M.
C.
6:45 P.M.
D.
7:45 P.M.
D.
7:15 P.M.
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Lesson 21: Elapsed Time
7.
Rob was at a friend’s house from 1:15 P.M. to 4:30 P.M.
Part A.
How long was Rob at his friend’s house?
Part B.
Use what you know about elapsed time to explain why your
answer is correct.
Measurement
Math
Words
Fill in the blanks.
8.
The
an activity.
time is the amount of time from the start to the end of
9.
On a clock face, the
hand is the shorter hand.
10.
On a clock face, the
hand is the longer hand.
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LESSON
22 Two-Dimensional Figures
When you work with two-dimensional figures,
remember these figures:
circle
triangle
rectangle
Geometry
pentagon
square
octagon
hexagon
Name this figure.
Step 1
Count the sides of the figure.
There are 6 sides.
Step 2
Count the vertices.
There are
Step 3
THINK Make a mark
on each side as you
count it. This way you
will not forget a side, or
count a side two times.
vertices.
THINK Vertices are
the corners of a figure.
Compare your answers to the pictures above.
So, the figure is a
.
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Lesson 22: Two-Dimensional Figures
Write the number of sides and
vertices for each figure. Then name
the figure.
1.
1.
2.
sides
verticies
Which figure
has 3 sides?
Triangle or
square?
sides
verticies
4.
3.
5.
sides
verticies
How many sides
does the figure
have?
0, 1, or 2?
Geometry
sides
verticies
4.
6.
sides
verticies
sides
verticies
7.
Solve.
7.
Cody draws a figure with six sides and six verticies.
What figure did he draw?
What does the
figure look like
when you draw
it?
or
?
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Circle the answer for each question.
1.
Which of the following figures
is a pentagon?
3.
A.
B.
4.
Geometry
C.
Which figure has 4 corners,
4 square vertices, and opposite
sides that are the same length?
A.
circle
B.
pentagon
C.
trapezoid
D.
rectangle
Trent drew three triangles.
Which of these is Trent’s
drawing?
A.
D.
B.
2.
What is the name of this figure?
C.
A.
octagon
B.
rectangle
C.
square
D.
hexagon
D.
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Lesson 22: Two-Dimensional Figures
5.
Jenna needs to know the different types of two-dimensional figures.
Part A.
Draw a rectangle. Then draw a figure with fewer sides than a
rectangle. Label both figures.
Part B.
Use what you know about two-dimensional figures to tell why
your drawings are correct.
Geometry
Math
Words
Label each figure with a word from the box.
hexagon
circle
pentagon
octagon
rectangle
square
6.
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Three-Dimensional
23 Figures
LESSON
When you work with three-dimensional figures,
remember these figures:
cube
cylinder
sphere
pyramid
cone
Geometry
rectangular prism
What three-dimensional figure does the building look like?
THINK The
Step 1
Compare the shape of the building to the
figures at the top of the page.
So, the building is a
building has flat
faces. There
are no curved
surfaces.
.
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Lesson 23: Three-Dimensional Figures
Name the three-dimensional figure.
1.
2.
1.
Which figure
has triangle
faces?
A cube or a
pyramid?
3.
4.
3.
Does the
baseball have any
flat surfaces?
Yes or no?
Geometry
5.
6.
Solve.
7.
8.
Jamie drank a juice box with her lunch. What
three-dimensional figure does a juice box look like?
Taro ate an ice cream cone with one scoop of ice
cream for a treat. What two three-dimensional
figures does his treat look like?
7.
What does a
juice box look
like?
or ?
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Circle the answer for each question.
1.
Which shape is a cylinder?
3.
A.
B.
B.
C.
Geometry
C.
D.
2.
Julie needed to bring in a cone
for her math class. Which of
these is a cone?
A.
D.
Oatmeal
Which best describes the shape
of these objects?
4.
Which of the following is a
sphere?
A.
a tissue box
A.
pyramid
B.
a party hat
B.
cone
C.
a paint can
C.
cube
D.
a golf ball
D.
rectangular prism
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Lesson 23: Three-Dimensional Figures
5.
Mrs. Roberts had a list for grocery shopping. Name the three-dimensional
figure each item on her list looks like.
can of tomato soup
orange
box of cereal
box of tissues
party hats
Math
Words
Label each figure with a word from the box.
cube
sphere
pyramid
Geometry
cone
cylinder
6.
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LESSON
24 Symmetry
When you find symmetry, remember this word:
line of symmetry a line that divides a
figure in half
line of
symmetry
Geometry
Find how many lines of symmetry the figure has.
Step 1
Step 2
H
H
Imagine folding the figure in half vertically.
REMEMBER If the two
halves match exactly, the
fold is a line of symmetry.
Imagine other ways you could fold the figure in half.
Draw any other lines of symmetry you find.
THINK Try folding
the figure horizontally
or diagonally.
So, the figure has
lines of symmetry.
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Lesson 24: Symmetry
Tell if the dashed line is a line of
symmetry. Write yes or no.
1.
1.
Do both sides
of the hexagon
match?
Yes or no?
2.
3.
P
➡
Geometry
4.
4.
Would both
sides match if
you folded P in
half?
Yes or no?
Draw the line(s) of symmetry for each figure.
5.
7.
6.
8.
X
5.
How many lines
of symmetry are
there?
1 or 2?
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Circle the answer for each question.
Geometry
1.
2.
Which of these shows a line of
symmetry?
3.
Which figure has exactly two
lines of symmetry?
A.
A.
B.
B.
C.
C.
D.
D.
How many lines of symmetry
does the trapezoid have?
A.
3
B.
2
C.
1
D.
0
4.
Which letter has a line of
symmetry?
A.
I
B.
N
C.
S
D.
Z
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Lesson 24: Symmetry
5.
Jill says that a square has more lines of symmetry than a circle. Is she
correct? Explain why or why not.
6.
Draw all the lines of symmetry the figure has.
Match the description to the figures.
7.
line of symmetry
8.
cube
9.
hexagon
10.
cone
Geometry
Math
Words
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LESSON
25 Patterns with Numbers
When you use patterns, remember this word:
pattern a set of numbers or objects that follows a rule
Find the next number in the pattern.
2, 5, 8, 11,
Step 1
Find how the numbers change in the pattern.
5 is greater than 2. Try addition first.
Algebraic Concepts
2
5
THINK 2 plus what
number equals 5?
Step 2
Check to see if the same rule works with the rest of the pattern.
538
83
Step 3
Use the rule to find the next number in the pattern.
11 So, the next number in the pattern is
.
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Lesson 25: Patterns with Numbers
Find the next number in each
pattern.
1.
22, 19, 16, 13,
2.
20, 25, 30, 35,
3.
2, 6, 10, 14,
4.
34, 29, 24, 19,
5.
10, 30, 50, 70,
6.
8, 16, 24, 32,
7.
64, 57, 50, 43,
8.
41, 47, 53, 59,
1.
Will you
subtract 3 or
add 3?
Find the missing number in each pattern.
9.
14, 17,
11.
80,
13.
95, 75,
15.
63,
, 23, 26
10.
64, 60, 56,
, 48
, 64, 56, 48
12.
3, 10, 17,
, 31
, 35, 15
14.
35, 38, 41,
, 47
, 53, 48, 43
16.
77, 83, 89,
, 101
9.
Do the numbers
in the pattern
get larger or
smaller?
17.
18.
Aidan saved $9 the first week, $18 the second
week, and $27 the third week. If this pattern
continues, how much money will Aidan have saved
the fourth week?
Algebraic Concepts
Solve.
17.
What number
plus 9 equals 18?
2, 6, or 9?
Jess made a tower with 10 blocks in the first row, 7
blocks in the second row, and 4 blocks in the third
row. If this pattern continues, how many blocks will
be in the fourth row?
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Circle the answer for each question.
1.
Which number is missing from
the pattern?
47, 45,
2.
4.
What is the next number in the
pattern?
, 41, 39
33, 39, 45, 51,
A.
44
A.
57
B.
43
B.
55
C.
42
C.
52
D.
38
D.
50
What is the next number in the
pattern?
5.
Which number is missing from
the pattern?
Algebraic Concepts
49, 58, 67, 76,
3.
68,
, 44, 32, 20
A.
77
A.
80
C.
56
B.
80
B.
60
D.
8
C.
85
D.
94
Colleen wrote this pattern of
numbers.
62, 57, 52, 47, 42
What rule did Colleen use?
6.
Piper drew a pattern of circles. In
the first, row she used 18 circles.
In the second row, she used 24
circles. In the third row, she used
30 circles. If she continues to use
this pattern, how many circles
will there be in the fourth row?
A.
subtract 7
A.
36 circles
B.
add 7
B.
31 circles
C.
add 5
C.
28 circles
D.
subtract 5
D.
26 circles
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Lesson 25: Patterns with Numbers
7.
Write the missing number in the pattern.
43, 47,
8.
, 55, 59
Look at the pattern shown below.
58, 52, 46, 40, 34,
Part A.
Write the next number in the pattern.
Part B.
Explain how you found the next number in the pattern.
Math
Words
9.
Write the meaning using your own words.
pattern
Algebraic Concepts
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LESSON
26 Patterns with Shapes
Remember, a pattern changes or repeats using a
rule.
Find the next shape in the pattern.
Step 1
Look at each figure and the ones near it.
How are the figures alike?
How are the figures different?
Step 2
Decide how one figure is changed to get to the next figure.
Algebraic Concepts
THINK The second figure
has 1 more square.
Step 3
Check to see if the same rule works with the rest of the figures.
The rule add 1 square (works / does not work) with the rest of the
pattern.
Step 4
Use the rule to draw the next figure in the pattern.
So, the next figure in the pattern has
squares.
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Lesson 26: Patterns with Shapes
Draw the next figure in the pattern.
1.
2.
1.
How many
more parts does
the second circle
have than the
first circle?
1 or 2?
3.
4.
Draw the missing figure in the pattern.
5.
6.
What shape
comes right after
the circle?
Square or
triangle?
Algebraic Concepts
5.
7.
8.
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Circle the answer for each question.
1.
Which of the following shapes
comes next in the pattern?
3.
Which of the following shapes
comes next in the pattern?
A.
A.
C.
B.
D.
B.
C.
D.
Algebraic Concepts
2.
What is the missing figure in
the pattern?
4.
What is the missing figure in
the pattern?
A.
A.
B.
B.
C.
C.
D.
D.
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Lesson 26: Patterns with Shapes
5.
Noel drew this pattern.
Part A.
Draw the figure that is missing from Noel’s pattern.
Part B.
Use what you know about patterns to explain why your
drawing is correct.
Algebraic Concepts
Math
Words
Circle the correct word.
6.
Will started with one square and added one square to each figure. Will
made a (pattern / product).
7.
Add 1 square is the (rule / law) for Will’s pattern.
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Completing Number
27 Sentences
LESSON
When you use number sentences, remember this
word:
number sentence a statement
written with numbers and symbols
4 8 12 12 is a number sentence
Write , , or to make the sentence true.
Algebraic Concepts
17 9
74
Step 1
Solve each side of the sentence.
17 9 8
7 4 11
Step 2
Compare the two sides. Choose the symbol.
17 9
74
8
11
So, 17 9
THINK You need to solve
each problem to decide
which symbol to use.
THINK Which symbol
means is less than?
7 4.
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Lesson 27: Completing Number Sentences
Find the missing number for each.
1.
7
3
3.
5.
7.
9.
2.
8 11
4.
8
6.
12 6
14
5 8
4
20
15 6
4 28
28
8.
10.
12 12.
36
1.
What number
plus 3 equals 7?
4 or 5?
6.
How many
groups of 4 are
in 28?
6, 7, or 8?
20
Write , , or .
38
13.
11 9
15.
52
17.
29
12 3
15 7
92
14.
42
12 3
13 6
16.
55
46
25 9
18.
23 6
14 5
11.
Algebraic Concepts
11.
Which symbol
means greater
than?
or ?
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Circle the answer for each question.
1.
Which number makes this
number sentence true?
10 2.
Algebraic Concepts
What number makes this
number sentence true?
6
13 A.
3
A.
9
B.
4
B.
8
C.
5
C.
7
D.
16
D.
6
Which number makes this
number sentence true?
4
3.
4.
5.
Which symbol makes this
number sentence true?
28
64
A.
9
A.
B.
8
B.
C.
7
C.
D.
6
D.
Which symbol makes this
number sentence true?
83
6.
22
15 7
Which symbol makes this
number sentence true?
64
17 4
A.
A.
B.
B.
C.
C.
D.
D.
74
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Lesson 27: Completing Number Sentences
7.
Paloma wrote this number sentence:
64
28
Part A.
Write , , or to make the number sentence true.
Part B.
Explain how you decided what symbol completed the number
sentence.
Math
Words
Fill in the blanks.
8.
The symbol means is
to.
9.
The symbol means is
than.
10.
The symbol means is
than.
Algebraic Concepts
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Solving Problems with
28 Number Sentences
LESSON
When writing a number sentence, first choose
the operation, next find the numbers to use, and
then write the number sentence.
There are 8 teams in a hockey event. Each team has 15 players.
Write a number sentence to find the total number of players in the
hockey event.
Step 1
Choose an operation.
Should you add, subtract, or multiply?
Step 2
Find the numbers you need to use.
There are 8 teams.
Each team has
Algebraic Concepts
Step 3
THINK You want to find the total
for 8 equal groups. What is the
easiest way to solve this problem?
players.
Write a number sentence using the numbers and operation.
number of teams
operation
number of players
equals
total
8
REMEMBER You can leave
the total blank because the
question only asks you to
write a number sentence.
So, the number sentence for the problem is
.
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Lesson 28: Solving Problems with Number Sentences
Write a number sentence for each
problem.
1.
Callie bought 4 puzzles for $6 each. Write a number
sentence to find the total cost of the puzzles.
2.
Chris had $20. He spent $14 on a board game.
Write a number sentence to find the amount of
money Chris has left.
3.
Oscar spent 18 minutes on his math homework
and 13 minutes on his spelling homework. Write
a number sentence to find the total number of
minutes he spent studying.
1.
Will you
multiply or add?
3.
Which
operation symbol
will you use?
or ?
Write a sentence using , , or for each
problem.
5.
During a bowling game, Trinisha scored 123 points
and Alberto scored 126 points. Write a sentence
comparing their scores.
Algebraic Concepts
4.
4.
Which symbol
means is less
than?
or ?
The mass of one mineral was 145 grams and the
mass of another mineral was 145 grams. Write a
sentence comparing the masses.
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Circle the answer for each question.
1.
Algebraic Concepts
2.
3.
Jess is 3 years younger than her
brother. Her brother is 11 years
old. Which number sentence
can be used to find Jess’ age?
A.
11 3 B.
11 3 C.
11 3 D.
11 3 Jin wants to give 6 balloons to
each of his 4 friends. Which
number sentence can he use to
find how many total balloons he
will give to his friends?
A.
64
B.
64
C.
64
D.
64
Krista has 47¢. Her sister
Misty has 53¢. Which sentence
compares the amounts of money
Krista and Misty have?
A.
47¢ 53¢
B.
47¢ 53¢
C.
53¢ 47¢
D.
47¢ 53¢
4.
5.
Gavin scored 24 points in his
first basketball game and 16
points in his second basketball
game. Which number sentence
can be used to find the total
number of points he scored?
A.
24 16 B.
24 16 C.
24 16 D.
24 16 Mrs. Bell bought 9 boxes of
crayons. Each box cost $3.
Which number sentence can be
used to find the total amount
Mrs. Bell spent on the crayons?
A.
93
B.
93
C.
93
D.
93
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Lesson 28: Solving Problems with Number Sentences
6.
At the carnival, rides cost $2 each.
Part A.
Write a number sentence to show how much it would cost to
go on 7 rides.
Part B.
Use what you know about number sentences to explain why
your answer is correct.
-ATH
7ORDS
Draw a line to match the operation to its symbol.
addition
8.
subtraction
9.
multiplication
Algebraic Concepts
7.
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LESSON
29 Bar Graphs
When you use a bar graph, remember these
words:
bar graph a graph that uses bars
scale the numbers on a line that tell
you the number for each bar
Number of Students
Find how many students chose science as their favorite class.
Favorite Class
10
THINK The bar for
8
science is halfway
between two lines.
6
4
2
0
Math
Reading Social Studies Science
Class
Step 1
Find the bar for science.
Step 2
With your finger, trace a line from the top of the bar for science to the
left side of the graph.
Step 3
Read the scale.
Statistics and Probability
The line for science is halfway between
So,
and
.
students picked science as their favorite class.
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Lesson 29: Bar Graphs
Use the graph to answer
Questions 1-6.
Animal Speeds
Miles per Hour
60
50
40
30
20
10
0
1.
Lion
Turkey
Elk
Zebra
Animal
Cat
Which animal has the fastest speed?
2.
Which animal has a speed of 45 miles per hour?
3.
What is the speed of a turkey?
1.
Which bar
shows the fastest
speed?
Shortest bar or
tallest bar?
3.
4.
Which animal is faster than a zebra but slower
than a lion?
5.
What is the difference in speed between an elk
and a cat?
6.
An elephant can have a speed of 25 miles per hour.
Show this on the graph.
What number
is halfway
between 10 and
20?
12, 15, or 18?
6.
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Statistics and Probability
What lines
will the bar end
between?
10 and 20 or 0
and 30?
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Circle the answer for each question.
Use the graph to answer
Questions 1 and 2.
Calories Burned
Favorite Movies
8
Scary
6
4
2
0
Skiing
Jogging
Swimming
Activity
1.
2.
Jumping
Rope
Type of Movie
Calories per Minute
10
Statistics and Probability
Use the graph to answer
Questions 3 and 4.
Cartoon
Drama
Comedy
How many calories do you burn
each minute jumping rope?
0
5
10
15
20
Number of Votes
25
A.
7 calories
B.
8 calories
Which type of movie did the
fewest people vote for?
C.
9 calories
A.
comedy
D.
10 calories
B.
drama
C.
cartoon
D.
scary
3.
Which activity do you burn 8
calories per minute?
A.
skiing
B.
jogging
How many students voted for
comedy or cartoon?
C.
swimming
A.
5 students
D.
jumping rope
B.
50 students
C.
55 students
D.
75 students
4.
30
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Lesson 29: Bar Graphs
Number of Books Read
Use the graph to answer Questions 5 and 6.
Book-A-Thon
50
40
30
20
10
0
Mr. Rios
Miss Morgan Mrs. Clarke Mrs. Trong
Classroom Teacher
5.
How many books did the students in Mrs. Clarke’s class read?
6.
Look at the graph.
Part A.
Draw a bar to show 20 books were read in Mr. Ely’s class.
Part B.
Use what you know about bar graphs to explain why your
answer is correct.
Math
Words
Fill in the blanks.
7.
A
shows information using bars.
8.
Numbers that help you read a graph are the
.
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Statistics and Probability
121
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LESSON
30 Tables
When you use tables, remember these words:
table a chart that uses tallies and
numbers to show information
tally a way of counting by making a
mark for each item
shows 7
How many third graders visited Scranton?
Cities Visited in Pennsylvania
City
Tally
Number
Statistics and Probability
Scranton
So,
Lebanon
12
Harrisburg
21
Reading
4
Step 1
Find Scranton on the table.
The first row shows the number of third graders who visited Scranton.
Step 2
Count the tallies.
5, 10, 15, 16,
,
REMEMBER
5
1
third graders visited Scranton.
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Lesson 30: Tables
Use the table to answer
Questions 1–5.
Plants in Mr. Rowe’s Garden
Plant
Tally
Number
Tomato
Cucumber
Pepper
Carrots
1.
How many tomato plants are in Mr. Rowe’s
garden?
2.
Which plant does Mr. Rowe have the fewest of in
his garden?
3.
How many plants in all are in Mr. Rowe’s garden?
4.
How many more carrot plants than pepper plants
does Mr. Rowe have?
5.
Mr. Rowe decides to plant 17 bean plants. Draw
the tally marks you would make to show this on
the table.
Bean
Tally
Number
How many does
each
stand
for?
1 or 5?
3.
How can you
find the total
number?
Add or subtract?
5.
How many
do you need to
show 15?
3, 5, or 15?
17
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Statistics and Probability
Plant
1.
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Circle the answer for each question.
Use the table to answer Questions
1 and 2.
Use the table to answer Questions
3 and 4.
Favorite Games of Third Graders
Favorite Places to Visit
Game
Number
Place
Go Fish
Mountains
Chess
Zoo
Dominos
Museum
Checkers
Park
1.
2.
Statistics and Probability
Tally
How many third graders chose
chess?
3.
Tally
Which place did 29 students
choose?
A.
22 third graders
A.
mountains
B.
27 third graders
B.
zoo
C.
52 third graders
C.
museum
D.
62 third graders
D.
park
What is the least popular game?
4.
Number
How many more students chose
the zoo than the museum?
A.
go fish
B.
chess
A.
7 students
C.
dominos
B.
8 students
D.
checkers
C.
9 students
D.
11 students
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Lesson 30: Tables
Use the table to answer Questions 5 and 6.
Favorite Season
Season
Tally
Number
Winter
Spring
Summer
Fall
5.
Which season did 22 students choose?
6.
19 students chose fall as their favorite season.
Part A.
Draw tally marks on the table to show how many students
chose fall.
Part B.
Explain how you knew how many
Math
Words
and to draw.
Fill in the blanks.
7.
A
uses tallies and numbers to show information.
8.
A mark for each item counted is called a
.
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Statistics and Probability
125
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Math Words
to find the total
number when you join
groups of different sizes
add
A
bottom
number of a fraction; it tells the
number of equal parts (Lesson 4)
D
(Lesson 8)
addend
a graph that uses
bars (Lesson 29)
capacity
C
the answer to a
subtraction problem (Lesson 10)
difference
a number added (Lesson 9)
bar graph
B
denominator the
E
the amount of
time that passes between two
events (Lesson 21)
elapsed time
a symbol used
to show two numbers have the same
value (Lesson 3)
is equal to (⫽)
how much a container
can hold (Lesson 17)
to find a number that is
close to the exact number (Lesson 13)
centimeter
a metric unit used to
measure length (Lesson 15)
estimate
a round two-dimensional
figure with all points the same
distance from the center (Lesson 22)
even numbers
circle
or 8 (Lesson 2)
end in 0, 2, 4, 6,
expanded form writing
numbers
by adding the values of the digits
a three-dimensional figure
whose only face is a circle (Lesson 23)
cone
(Lesson 1)
a rectangular prism with six
congruent square faces (Lesson 23)
cube
a three-dimensional figure
with two same-size circular bases
and a curved surface that connects
the bases (Lesson 23)
cylinder
F
names part of a whole
or part of a set (Lesson 4)
fraction
a set of related
addition and subtraction number
sentences (Lesson 6)
fact family
a customary unit used to
measure length (Lesson 15)
foot
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G
is greater than (⬎) a
symbol used to compare two
numbers when the larger number is
fi rst (Lesson 3)
M
a metric unit used to
measure length (Lesson 15)
meter
a customary unit used to
measure length (Lesson 15)
mile
a metric unit used to
measure length (Lesson 15)
millimeter
H
I
K
L
hexagon a
two-dimensional
figure with 6 sides and 6
corners (Lesson 22)
a customary unit used to
measure length (Lesson 15)
inch
to find the total when
given equal groups (Lesson 8)
multiply
statement
written with numbers and
symbols (Lesson 27)
N
numerator
the distance of an object
from end to end (Lesson 18)
a symbol used
to compare two numbers when the
lesser number is first (Lesson 3)
is less than (⬍)
line of symmetry
the top number of a
fraction (Lesson 4)
a metric unit used to
measure length (Lesson 15)
kilometer
length
number sentence a
O
octagon a
two-dimensional
figure with 8 sides and 8 corners
(Lesson 22)
odd numbers
or 9 (Lesson 2)
end in 1, 3, 5, 7,
a line that
divides a figure in half (Lesson 24)
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a set of numbers or
objects that follows a rule
pattern
P
S
the numbers on a line
that tell you the number for each
scale
(Lesson 25)
bar (Lesson 29)
a two-dimensional figure
with 5 sides and 5 corners (Lesson 22)
sphere a
three-dimensional
figure shaped like a round, smooth
ball (Lesson 23)
pentagon
place value
the value of a position
a rectangle with sides that
are the same length (Lesson 22)
in a number (Lesson 1)
square
pyramid a
three-dimensional figure
with a bottom face with straight sides
and the other faces are all triangles
standard form writing
with digits (Lesson 1)
(Lesson 23)
subtract
numbers
to compare or find a
difference (Lesson 8)
R
the answer to an addition
problem (Lesson 9)
sum
rectangle a
two-dimensional
figure with 4 sides and 4 square
corners; its opposite sides are the
same length (Lesson 22)
rectangular prism a
threedimensional figure with 6 faces that
are rectangles (Lesson 23)
to estimate a number to the
nearest 10 or 100 (Lesson 12)
round
ruler
a tool used to measure
length (Lesson 18)
T
a chart that uses
tallies and numbers to show
information (Lesson 30)
table
a way of counting by making
a mark for each item (Lesson 30)
tally
triangle a
two-dimensional figure
with 3 sides and 3 corners (Lesson 22)
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Math Words
W
weight
how heavy something
is (Lesson 16)
Y
a customary unit used to
measure length (Lesson 15)
yard
My Math Words
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