PRACTICE
Workbook
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HSP
Grade 5
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UNIT 1: USE WHOLE NUMBERS
Chapter 1: Place Value, Addition, and Subtraction
1.1
1.2
1.3
1.4
1.5
1.6
1.7
Place Value Through Millions ............PW1
Understand Billions ............................PW2
Compare and Order
Whole Numbers .................................PW3
Round Whole Numbers .....................PW4
Estimate Sums and Differences .........PW5
Add and Subtract Whole Numbers ...PW6
Problem Solving Workshop
Strategy: Work Backward ..................PW7
4.7
4.8
4.9
UNIT 2: USE DECIMALS
Chapter 5: Understand Decimals
5.1
5.2
5.3
5.4
Chapter 2: Multiply Whole Numbers
2.1
2.2
2.3
2.4
2.5
2.6
Mental Math: Patterns in
Multiples .............................................PW8
Estimate Products ...............................PW9
Multiply by 1-Digit Numbers ...........PW10
Multiply by Multi-Digit Numbers ....PW11
Problem Solving Workshop
Strategy: Find a Pattern ...................PW12
Choose a Method .............................PW13
Chapter 3: Divide by 1- and 2-Digit Divisors
3.1
3.2
3.3
Estimate with 1-Digit Divisors .........PW14
Divide by 1-Digit Divisors ................PW15
Problem Solving Workshop Skill:
Interpret the Remainder..................PW16
3.4 Zeros in Division ...............................PW17
3.5 Algebra: Patterns in Division ...........PW18
3.6 Estimate with 2-Digit Divisors .........PW19
3.7 Divide by 2-Digit Divisors ................PW20
3.8 Correcting Quotients .......................PW21
3.9 Practice Division ...............................PW22
3.10 Problem Solving Workshop Skill:
Relevant or Irrelevant
Information ......................................PW23
Chapter 4: Expressions and Equations
4.1
4.2
4.3
4.4
4.5
4.6
Write Expressions .............................PW24
Evaluate Expressions ........................PW25
Properties..........................................PW26
Mental Math: Use the Properties....PW27
Write Equations................................PW28
Solve Equations ................................PW29
Functions...........................................PW30
Inequalities .......................................PW31
Problem Solving Workshop
Strategy: Predict and Test ................PW32
Decimal Place Value .........................PW33
Equivalent Decimals .........................PW34
Compare and Order Decimals .........PW35
Problem Solving Workshop Skill:
Draw Conclusions .............................PW36
Chapter 6: Add and Subtract Decimals
6.1
6.2
6.3
6.4
6.5
Round Decimals ................................PW37
Add and Subtract Decimals .............PW38
Estimate Sums and Decimals ...........PW39
Choose a Method .............................PW40
Problem Solving Workshop Skill:
Estimate or Find Exact Answer........PW41
Chapter 7: Multiply Decimals
7.1
7.2
7.3
7.4
7.5
7.6
7.7
Model Multiplication by
a Whole Number ..............................PW42
Algebra: Patterns in Decimal
Factors and Products ........................PW43
Record Multiplication by
a Whole Number ..............................PW44
Model Multiplication by
a Decimal ..........................................PW45
Estimate Products .............................PW46
Practice Decimal Multiplication ......PW47
Problem Solving Workshop Skill:
Multistep Problems .........................PW48
Chapter 8: Divide Decimals by Whole Numbers
8.1
8.2
8.3
8.4
Decimal Division ...............................PW49
Estimate Quotients ..........................PW50
Divide Decimals by Whole
Numbers............................................PW51
Problem Solving Workshop Skill:
Evaluate Answers for
Reasonableness ................................PW52
â Harcourt ã Grade 5
UNIT 3: DATA AND GRAPHING
UNIT 5: FRACTION OPERATIONS
Chapter 9: Data and Statistics
Chapter 13: Add and Subtract Fractions
9.1
9.2
9.3
9.4
9.5
Collect and Organize Data ..............PW53
Mean, Median, and Mode ...............PW54
Compare Data ..................................PW55
Analyze Graphs ................................PW56
Problem Solving Workshop
Strategy: Draw a Diagram ..............PW57
Chapter 10: Make Graphs
10.1 Make Bar Graphs and
Pictographs .......................................PW58
10.2 Make Histograms .............................PW59
10.3 Algebra: Graph Ordered Pairs .........PW60
10.4 Make Line Graphs ............................PW61
10.5 Make Circle Graphs ..........................PW62
10.6 Problem Solving Workshop
Strategy: Make a Graph .................PW63
10.7 Choose the Appropriate Graph ......PW64
UNIT 4: NUMBER THEORY AND FRACTION
CONCEPTS
Chapter 11: Number Theory
11.1 Multiples and the Least Common
Multiple ............................................PW65
11.2 Divisibility .........................................PW66
11.3 Factors and Greatest Common
Factor ................................................PW67
11.4 Prime and Composite Numbers ......PW68
11.5 Problem Solving Workshop
Strategy: Make an Organized List ..PW69
11.6 Introduction to Exponents ..............PW70
11.7 Exponents and Square Numbers .....PW71
11.8 Prime Factorization ..........................PW72
Chapter 12: Fraction Concepts
12.1
12.2
12.3
12.4
12.5
Understand Fractions .......................PW73
Equivalent Fractions .........................PW74
Simplest Form ...................................PW75
Understand Mixed Numbers ...........PW76
Compare and Order Fractions
and Mixed Numbers.........................PW77
12.6 Problem Solving Workshop
Strategy: Make a Model .................PW78
12.7 Relate Fractions and Decimals ........PW79
13.1 Add and Subtract Like Fractions .....PW80
13.2 Model Addition of Unlike
Fractions............................................PW81
13.3 Model Subtraction of Unlike
Fractions............................................PW82
13.4 Estimate Sums and Differences .......PW83
13.5 Use Common Denominators ...........PW84
13.6 Problem Solving Workshop
Strategy: Compare Strategies ........PW85
13.7 Choose a Method .............................PW86
Chapter 14: Add and Subtract Mixed Numbers
14.1 Model Addition of Mixed
Numbers............................................PW87
14.2 Model Subtraction of Mixed
Numbers............................................PW88
14.3 Record Addition and Subtraction ...PW89
14.4 Subtraction with Renaming ............PW90
14.5 Practice Addition and
Subtraction .......................................PW91
14.6 Problem Solving Workshop
Strategy: Use Logical Reasoning .....PW92
Chapter 15: Multiply and Divide Fractions
15.1 Model Multiplication of
Fractions............................................PW93
15.2 Record Multiplication of
Fractions............................................PW94
15.3 Multiply Fractions and Whole
Numbers............................................PW95
15.4 Multiply with Mixed Numbers ........PW96
15.5 Model Fraction Division ...................PW97
15.6 Divide Whole Numbers by
Fractions............................................PW98
15.7 Divide Fractions ................................PW99
15.8 Problem Solving Workshop Skill:
Choose the Operation ...................PW100
UNIT 6: RATIO, PERCENT, AND
PROBABILITY
Chapter 16: Ratios and Percents
16.1 Understand and Express Ratios .....PW101
16.2 Algebra: Equivalent Ratios and
Proportions .....................................PW102
© Harcourt • Grade 5
16.3 Ratios and Rates .............................PW103
16.4 Understand Maps and Scales ........PW104
16.5 Problem Solving Workshop
Strategy: Make a Table ..................PW105
16.6 Understand Percent .......................PW106
16.7 Fractions, Decimals, and
Percents...........................................PW107
16.8 Find Percent of
a Number ........................................PW108
Chapter 17: Probability
17.1
17.2
17.3
17.4
Outcomes and Probability .............PW109
Probability Experiments .................PW110
Probability and Predictions ...........PW111
Problem Solving Workshop
Strategy: Make an
Organized List ................................PW112
17.5 Tree Diagrams.................................PW113
17.6 Combinations and Arrangements .PW114
UNIT 7: GEOMETRY AND ALGEBRA
Chapter 18: Geometric Figures
18.1
18.2
18.3
18.4
Points, Lines, and Angles ...............PW115
Measure and Draw Angles ............PW116
Polygons..........................................PW117
Problem Solving Workshop Skill:
Identify Relationships ....................PW118
18.5 Circles ..............................................PW119
18.6 Congruent and Similar Figures .....PW120
18.7 Symmetry ........................................PW121
Chapter 19: Plane and Solid Figures
19.1
19.2
19.3
19.4
19.5
Classify Triangles ............................PW122
Classify Quadrilaterals ...................PW123
Draw Plane Figures ........................PW124
Solid Figures ...................................PW125
Problem Solving Workshop
Strategy: Compare Strategies ......PW126
19.6 Nets for Solid Figures .....................PW127
19.7 Draw Solid Figures from
Different Views ..............................PW128
Chapter 20: Patterns
20.1 Transformations .............................PW129
20.2 Tessellations ....................................PW130
20.3 Create a Geometric Pattern ..........PW131
20.4 Numeric Patterns ............................PW132
20.5 Problem Solving Workshop
Strategy: Find a Pattern................PW133
Chapter 21: Integers and the Coordinate Plane
21.1 Algebra: Graph Relationships .......PW134
21.2 Algebra: Equations and
Functions.........................................PW135
21.3 Problem Solving Workshop
Strategy: Write an Equation ........PW136
21.4 Understand Integers ......................PW137
21.5 Compare and Order Integers ........PW138
21.6 Algebra: Graph Integers on the
Coordinate Plane ...........................PW139
UNIT 8: MEASUREMENT
Chapter 22: Customary and Metric Measurements
22.1
22.2
22.3
22.4
22.5
22.6
Customary Length ..........................PW140
Metric Length .................................PW141
Change Linear Units.......................PW142
Customary Capacity and Weight...PW143
Metric Capacity and Mass ..............PW144
Problem Solving Workshop Skill:
Estimate or Actual
Measurement .................................PW145
22.7 Elapsed Time...................................PW146
22.8 Temperature ...................................PW147
Chapter 23: Perimeter
23.1 Estimate and Measure
Perimeter ........................................PW148
23.2 Find Perimeter ................................PW149
23.3 Algebra: Perimeter Formulas ........PW150
23.4 Problem Solving Workshop Skill:
Make Generalizations ....................PW151
23.5 Circumference ................................PW152
Chapter 24: Area and Volume
24.1 Estimate Area .................................PW153
24.2 Algebra: Area of Squares and
Rectangles.......................................PW154
24.3 Algebra: Relate Perimeter and
Area.................................................PW155
24.4 Algebra: Area of Triangles ............PW156
24.5 Algebra: Area of Parallelograms ..PW157
â Harcourt ã Grade 5
24.6 Problem Solving Workshop
Strategy: Solve a Simpler
Problem...........................................PW158
24.7 Surface Area ...................................PW159
24.8 Algebra: Estimate and Find
Volume ............................................PW160
24.9 Relate Perimeter, Area, and
Volume ............................................PW161
24.10 Problem Solving Workshop
Strategy: Compare Strategies........PW162
Spiral Review
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
Week
1.......................................................... SR1
2.......................................................... SR2
3.......................................................... SR3
4.......................................................... SR4
5.......................................................... SR5
6.......................................................... SR6
7.......................................................... SR7
8.......................................................... SR8
9.......................................................... SR9
10...................................................... SR10
11...................................................... SR11
12...................................................... SR12
13...................................................... SR13
14...................................................... SR14
15...................................................... SR15
16...................................................... SR16
17...................................................... SR17
18...................................................... SR18
19...................................................... SR19
20...................................................... SR20
21...................................................... SR21
22...................................................... SR22
23...................................................... SR23
24...................................................... SR24
25...................................................... SR25
26...................................................... SR26
27...................................................... SR27
28...................................................... SR28
29...................................................... SR29
30...................................................... SR30
31...................................................... SR31
32...................................................... SR32
33...................................................... SR33
34...................................................... SR34
35...................................................... SR35
36...................................................... SR36
â Harcourt ã Grade 5
Homework Management
A good homework management plan can streamline the process, maximize usefulness, and
encourage student involvement. The plan offered here focuses on:
• Student Ownership
• Teacher led discussion
• Quality, not quantity
• Balanced-concepts, skills, and problem solving
• Daily Feedback
• Analysis, not just checked
• Progress Graphs
HSP Math offers the following resources for homework management:
■ Suggested Homework Problems, recommended problems circled in the
Teacher’s Edition
■ Rationale Card in the Teacher’s Edition for easy reference and rationale to
suggested homework problems
■ Progress Graphs for students to chart progress throughout the week
Suggested Homework Problems are on each worksheet. The suggested problems have
been carefully selected because they are a good representation of the problems in the day’s
lesson. No more than 10 problems are suggested for each lesson.
A Rationale Card provides the rationale behind the suggested problem chosen. You can
review the rationale to evaluate which problems best suit your students’ needs before you
assign homework.
Progress Graphs are provided for students as a template to use with the suggested
homework problems that may be assigned. Students shade the double-bar graph each day
to demonstrate the progress they make on their suggested homework assignments
throughout the week. The left bar reflects the total number of problems that are assigned.
The right bar reflects the total number of problems the student got correct. After you write
the answers on the chalkboard, students check their own homework during the morning
routine while you circulate the room to review their papers. Homework is assigned Monday
through Thursday only, so at the end of the week students can analyze their own work by
writing two sentences about their progress. The graphs can also be placed in student
portfolios for parent/teacher conferences. A sample graph is shown below. The template is
provided on the next page.
© Harcourt • Grade 5
© Harcourt • Grade 5
My Homework Progress
10
9
Number of Problems
8
7
Number of
Problems
Assigned
6
5
Number of
Problems
Correct
4
3
2
1
0
Mon
Tue
Wed
Day
Thu
Name
Lesson 1.1
Place Value Through Millions
Write the value of the underlined digit.
1. 189,612,357
2. 512,897,934
3.
83,705
4. 37,115,296
5. 254,678,128
6. 631,189
7.
72,334,105
8. 345,132
9. 57,912
10. 12,465,983
11.
256,245,371
12. 15,279,328
Write the number in two other forms.
13. 647,200
14. 40,000,000 ϩ 20,000 ϩ 1,000 ϩ 80 ϩ 5
What number makes the statement true?
16. 2,760,000 ϭ 276 ϫ
15. 580,000 ϭ 58 ϫ
Problem Solving and Test Prep
18. Clarrisa learns that the estimated
17. Fast Fact The diameter of Jupiter is
distance between the Sun and Venus is
sixty-seven million miles. How can she
write this number in standard form for a
poster she is making
88,732 miles. How can Michael write the
diameter of Jupiter in expanded form?
19. What is the value of the underlined digit
20. In 358,247,061, which digit is in the
in 729,340,233?
hundred thousands place?
A 20,000
A 0
20,000
C 2,000,000
D 20,000,000
B
2
C
3
B
D 5
PW1
Practice
© Harcourt • Grade 5
Name
Lesson 1.2
Understand Billions
Write the value of the underlined digit.
1. 855,283,612,681
2. 752,801,874,345
3. 25,908,167,238
4. 358,354,678,540
5. 902,851,638,411
6. 93,668,334,312
Write the number in two other forms.
7. 50,000,000,000 ϩ 70,000,000 ϩ 8,000,000 ϩ 300,000 ϩ 8,000 ϩ 200 ϩ 5
8. seventy billion, two hundred seventeen million, five hundred thirty-one
9. 35,089,207,450
Problem Solving and Test Prep
10. How many dimes equal the same total
11. During a year-long penny drive, a
amount as 1,000,000,000 pennies?
12. What is the standard form of fifty-two
volunteer group collected 10,000,000
pennies. How many stacks of 100
pennies could they make with all of
their pennies?
13. In 538,479,247,061, which digit is in
million, six hundred eight thousand,
thirty-nine?
the ten billions place?
A 52,680,390
C 52,608,039
A 5
C 2
B 52,608,390
D 52,068,039
B 3
D 0
PW2
Practice
â Harcourt ã Grade 5
Name
Lesson 1.3
Compare and Order Whole Numbers
Compare. Write Ͻ, Ͼ, or ϭ for each
1. 6,574
6,547
4. 3,541,320
3,541,230
.
2. 270,908
270,908
3. 8,306,722
5. 670,980
680,790
6. 12,453,671
8,360,272
12,543,671
Order from least to greatest.
7. 1,345,919; 1,299,184; 1,134,845
8. 417,689,200; 417,698,200; 417,698,100
Order from greatest to least.
9. 63,574; 63,547; 63,745
10. 5,807,334; 5,708,434; 5,807,433
ALGEBRA Find the missing digit to make each statement true.
11. 13,625 Ͻ 13,6
7 Ͻ 13,630
12. 529,781 Ͼ 529,78
Ͼ 529,778
Problem Solving and Test Prep
Quarters Minted in 2005
USE DATA For 13–14, use the table.
State
13. What state quarter was minted in the
greatest number in 2005?
14. Order California, Minnesota, and Oregon
from least to greatest according to their
number of quarters minted in 2005.
15. Which number is less than 61,534?
Number of Quarters Minted
California
520,400,000
Minnesota
488,000,000
Oregon
720,200,000
Kansas
563,400,000
West Virginia
721,600,000
16. Which shows the numbers in order
from greatest to least?
A 61,354
A 722,319; 722,913; 722,139
B 61,543
B 722,139; 722,319; 722,913
C 63,154
C 722,913; 722,139; 722,319
D 63,145
D 722,913; 722,319; 722,139
PW3
Practice
â Harcourt ã Grade 5
Name
Lesson 1.4
Round Whole Numbers
Round each number to the place of the underlined digit.
1. 325,689,029
2. 45,673
3. 91,341,281
4. 621,732,193
5. 8,067
6. 42,991,335
7. 182,351,413
8. 539,605,281
10. 76,805,439
11. 518,812,051
12. 657,388,369
9. 999,887,423
Name the place to which each number was rounded.
13. 25,398 to 30,000
14. 828,828 to 830,000
15. 7,234,851 to 7,234,900
16. 612,623 to 600,000
17. 435,299 to 435,000
18. 8,523,194 to 9,000,000
Round 34,251,622 to the place named.
19. millions
20. hundred thousands
21. thousand
Problem Solving and Test Prep
22. Fast Fact Wrigley Field in Chicago,
Illinois has a seating capacity of
41,118 people. In a newspaper article,
that number is rounded to the nearest
ten thousand. What number is written
in the newspaper article?
23. Reasoning The number of seats in
Shea Stadium can be rounded to
56,000 when rounded to the nearest
thousand. What could be the exact
number of seats in Shea Stadium?
24. Name the place to which the number
25. Name the place to which the number
was rounded.
was rounded.
43,771,012 to 40,000,000
622,192,013 to 622,200,000
A hundred thousands
C tens
A ten thousands
C hundred thousands
B ten millions
D millions
B hundreds
D ten millions
PW4
Practice
â Harcourt ã Grade 5
Name
Lesson 1.5
Estimate Sums and Differences
Estimate by rounding.
1.
308,222
Ϫ
196,231
__
2.
925,461
Ϫ
173,509
__
3.
19,346
ϩ
25,912
__
4.
125,689
ϩ
236,817
__
5.
471,282
Ϫ
161,391
__
Estimate by using compatible numbers or other methods.
6.
123,636
ϩ
78,239
__
7.
48,385
ϩ
54,291
__
8.
$4,471
Ϫ
1,625
__
9.
69,371
ϩ
73,253
__
10.
224,119
Ϫ
79,388
__
For 11–14, find the range the estimate will be within.
11.
$3,817
ϩ
1,428
__
12.
28,204
ϩ
53,185
__
13.
35,122
ϩ
61,812
__
14.
482
ϩ
512
__
Problem Solving and Test Prep
15. Brazil has a population of 186,112,794
16. What if the population of Brazil
people. Argentina has a population of
39,537,943 people. About how many
people live in Brazil and Argentina in all?
17. Sarah rode her bike 5 days. The longest
increased by 4 hundred thousand
people, would that change your
estimate for problem 22? Explain.
18. Estimate. Round to the nearest
distance she rode in one day was
6 miles, and the shortest distance she
rode was 5 miles. What is a reasonable
total number of miles Sarah biked
during the 5 days?
ten-thousand.
A Less than 12 mi
A 700,000
B Between 4 mi and 6 mi
B 640,000
C Between 15 mi and 20 mi
C 630,000
D More than 20 mi
D 65,000
249,118
394,417
__
PW5
Practice
â Harcourt ã Grade 5
Name
Lesson 1.6
Add and Subtract Whole Numbers
Estimate. Then find the sum or difference.
1.
6,292
ϩ 7,318
__
2.
28,434
ϩ 49,617
__
3.
205,756
Ϫ 201,765
___
4.
529,852
ϩ 476,196
___
5.
5,071,154
ϩ 483,913
___
6.
241,933
ϩ 51,209
__
7.
75,249
Ϫ 41,326
__
8.
1,202,365
Ϫ 278,495
___
9.
4,092,125
2,748,810
ϩ
6,421,339
___
10.
11.
542,002
Ϫ 319,428
___
12.
360,219
ϩ 815,364
___
4,687,184
Ϫ 1,234,562
___
13. 32,109 ϩ 6,234 ϩ 4,827
14. 3,709,245 Ϫ 1,569,267
15. 200,408 Ϫ 64,159
Problem Solving and Test Prep
USE DATA For 16–17, use the table.
16. How many more square miles of
Great Lakes Facts
surface area does Lake Michigan have
than Lake Ontario has?
17. What is the total surface area of the
two lakes with the greatest water
surface area?
Lake
Water Surface Area
(in sq mi)
Superior
31,700
Michigan
22,300
Ontario
7,340
Erie
9,910
Huron
18. 328,954 ϩ 683,681 ϭ
19. Over the first weekend in July, a movie
theater sold 78,234 tickets. Over the
second weekend in July, the movie theater
sold 62,784 tickets. How many more
tickets were sold over the first weekend
than the second weekend in July?
A 901,535
B
23,000
1,001,535
C 1,012,635
D 1,012,645
PW6
Practice
© Harcourt • Grade 5
Name
Lesson 1.7
Problem Solving Workshop Strategy: Work Backward
Problem Solving Strategy Practice
Work backward to solve.
1. In the 1980s, the Northern white
rhinoceros population decreased by
485 from what it was in the 1970s. By
the 1990s the population increased to
2 more than twice the population in the
1970s. By the 2000s, the population
dropped 25 rhinoceroses to about 7
Northern white rhinoceroses today.
What was the Northern white
rhinoceros population in the 1970s?
2. The bus is scheduled to stop at
7:20 A.M. Cal wants to be at the stop
5 minutes before that. If he needs
7 minutes to walk to the stop,
12 minutes to eat breakfast, 4 minutes
to dress, and 10 minutes to shower,
then what time should Cal get up in the
morning?
Mixed Application
USE DATA For 3–5, use the table.
3. The latest Minke whale population is
Whale Population Estimates
55 times the latest gray whale
population. What is the latest Minke
whale population?
Whale
7,800
548,000
110,000
20,000
18,000
Humpback
115,000
10,000
Minke
490,000
-
Right
100,000
3,200
Sei
256,000
54,000
Fin
Gray
decrease in the number of right whales
from their original count.
Latest Count
30,000
Bowhead
4. Write and solve an equation to find the
Original Count
6. Pose a Problem Look back at
5. Which type of whale had the greatest
Problem 4. Write a similar problem by
changing the type of whale.
decrease in population? Explain how
you know.
PW7
Practice
â Harcourt ã Grade 5
Name
Lesson 2.1
Mental Math: Patterns in Multiples
Find the product.
1. 9 ϫ 300
2. 3 ϫ 100
3. 60 ϫ 5
4. 5 ϫ 7,000
6. 700 ϫ 200
7. 20 ϫ 9,000
8. 1,000 ϫ 10
9. 5,000 ϫ 30
11. 40 ϫ 9,000
12. 7 ϫ 200
13. 600 ϫ 60
14. 100 ϫ 600
5. 10 ϫ 4,000
10. 6,000 ϫ 80
15. 200 ϫ 500
ALGEBRA Find the missing number.
16. 700 ϫ 5,000 ϭ
ϫ 20 ϭ 90,000 18. 600 ϫ
17.
ϭ 1,200
Problem Solving and Test Prep
20. Each pair of macaroni penguins lays
19. One colony of macaroni penguins has
2 eggs. How many eggs do 12,000,000
pairs of penguins lay?
about 8,000 nests. If three penguins
occupy each nest, how many penguins
are there in all?
22. A sedan at a car dealership sells for
21. Tickets to a baseball game cost $90
each. How much money will be made in
ticket sales if 5,000 tickets are sold?
A $45,000
B $450,000
C $4,500,000
D $45,000,000
PW8
$20,000. How much money will be made
from the sale of 200 sedans?
A $40,000
B $400,000
C $4,000,000
D $40,000,000
Practice
â Harcourt ã Grade 5
Name
Lesson 2.2
Estimate Products
Estimate the product.
1. 65 ϫ 22
2. 18 ϫ $34
3. 738 ϫ 59
4. 195 ϫ 23
5. 8,130 ϫ 77
6. 91 ϫ 49
7. 641 ϫ 31
8. 555 ϫ 470
9. 4,096 ϫ 12
10. 42 ϫ 1,912
11. 199 ϫ 249
12. 467 ϫ 124
13. 88 ϫ 27
14. 4 ϫ 96,725
15. 6,371 ϫ 52
16. 33 ϫ 180
17. 894 ϫ 605
18. 5,720 ϫ 79
19. 54 ϫ 419
20. 76 ϫ 5,118
.
Problem Solving and Test Prep
USE DATA For 21–22, use the table.
21. The Municipal Park Committee has
Green Park Expenses
budgeted $500 for 32 Japanese red
maple trees for Green Park. Did the
committee budget enough money?
Estimate to solve.
Tree
Cost
Silver Maple
$11
Red Maple
Japanese Red Maple
$9
$18
22. The park committee also wants to purchase 24 silver maples using a budget of $300.
Did the committee budget enough money? Estimate to solve.
23. Which would give the best estimate for
24. Which would give the best estimate for
48 ϫ 54,090?
108 ϫ 276?
A 40 ϫ 50,000
A 100 ϫ 200
B
40 ϫ 60,000
B
100 ϫ 300
C
50 ϫ 50,000
C
200 ϫ 200
D 50 ϫ 60,000
D 200 300
PW9
Practice
â Harcourt ã Grade 5
Name
Lesson 2.3
Multiply by 1-Digit Numbers
Estimate. Then find the product.
1.
47
ϫ 6
2.
26
ϫ 6
3.
6.
339
ϫ 7
7.
518
ϫ 5
8.
207
ϫ 3
4.
2,309
ϫ
8
9.
783
ϫ 9
8,014
ϫ
3
5.
10.
428
ϫ 5
9,237
ϫ 6
11. 729 ϫ 8
12. 6 ϫ 802
13. 4 ϫ 426
14. 339 ϫ 5
15. 3,045 ϫ 4
16. 9 ϫ 1,218
17. 5,331 ϫ 2
18. 61,372 ϫ 8
Problem Solving and Test Prep
USE DATA For 23–24, use the table.
19. How much would it cost a family of 6 to
Round Trip Airfares
from Chicago, IL
fly roundtrip from Chicago to
Vancouver?
Destination
20. How much more would it cost for 2 people
to fly roundtrip from Chicago to Honolulu
than to fly from Chicago to London?
21. Which expression has the same value as
Cost in Dollars
Honolulu, HI
$619
London, England
$548
Vancouver, WA
$282
22. New windows cost $425 each. What is
8 ϫ (800 ϩ 70 ϩ 3)?
the total cost for 9 new windows?
A 8 ϫ (800,703)
A $3,725
B
64 ϩ 56 ϩ 24
B
$3,825
C
6,400 ϩ 70 ϩ 3
C
$4,725
D $4,825
D 6,400 ϩ 560 ϩ 24
PW10
Practice
© Harcourt • Grade 5
Name
Lesson 2.4
Multiply by Multi-Digit Numbers
Estimate. Then find the product.
342
ϫ
28
_
2.
451
ϫ 61
_
3.
709
ϫ 53
_
4.
622
ϫ
34
_
5.
6. $229
7.
907
ϫ
83
_
8.
1,345
ϫ
23
__
9.
172
ϫ
91
_
10.
4,029
ϫ
67
__
12.
727
ϫ
33
_
13. $1,948
14.
1,220
ϫ
42
__
15.
893
ϫ
12
_
1.
ϫ 77
11.
219
ϫ
84
_
ϫ
58
__
970
ϫ
17
_
Problem Solving and Test Prep
17. Rachel participated in a Bike-a-Thon.
16. Abby wants to cycle 25 miles each
Twenty-three family members donated
$12 for each mile she rode. If Rachel rode
38 miles, how much did she collect?
day for one full year, or 365 days. How
many miles is Abby planning to cycle
in all?
18. Viola is training for a swimming
19. Mon is training for a track and field
competition on a pool in which one
lap is 20 yards. Viola has swam
8 laps. What distance has Viola swam?
event on a track where one lap is
400 meters. So far Mon has finished
2 laps. What distance has Mon ran?
A 160 yards
A 220 meters
B 180 yards
B 440 meters
C 1,600 yards
C 800 meters
D 1,800 yards
D 202 meters
PW11
Practice
© Harcourt • Grade 5
Name
Lesson 2.5
Problem Solving Workshop Strategy:
Find a Pattern
Problem Solving Strategy Practice
Find a pattern to solve.
1. An art gallery has been open for a
2. Prices for framing artwork in a framing
month. The first week, there were
19 visitors. The second week, there
were 38 visitors. The third week, there
were 76 visitors. If the pattern
continues, how many people will visit
the museum on the fourth week?
store are calculated using the length of
the frame. If a 40-49” frame costs $60, a
30-39” frame costs $45, and a 20-29”
frame costs $30, how much does a
10-19” frame cost?
4. A group of six statues made by a famous
3. An art-supply store sells sets of color
artist will be sold for $39,375. If each
successive statue sells for twice as much
as the previous one and the first statue
sells for $625, then how much will the
6th statue sell for?
pencils. If a 10-pencil set costs $12, a
15-pencil set costs $15, and a 20-pencil
set costs $18, what rule can you use to
determine how much a 25-pencil set
costs?
Mixed Strategy Practice
USE DATA For 5–6, use the data in the diagram.
5. Elsi made a model of the wooden frame
she will make for a watercolor painting.
Write an equation you would use to find
the amount of wood she will need to
make one frame.
20
inches
32 inches
6
Pose a Problem Look back at Problem
5. Write a similar problem by changing
the number of frames Elsi will make.
7. Tom’s brother is 5 inches shorter than
.
PW12
Tom, and Tom’s mom is 26 inches
shorter than their heights combined.
How tall is Tom’s mom if Tom is 4 ft., 2 in.
tall?
Practice
â Harcourt ã Grade 5
Name
Lesson 2.6
Choose a Method
Find the product. Choose mental math, paper and pencil, or a calculator.
1.
820
ϫ
10
_
2. 5,129
3.
ϫ 18
__
6. 500 ϫ 12
7. 375 ϫ 218
10. 400 ϫ 320
11. 785 ϫ 122
452
ϫ
726
__
4.
304
ϫ
21
_
8. 40 ϫ 5,000
12. 93 ϫ 11 ϫ 34
5. 1,200
ϫ 12
__
9. 112 ϫ 83
13. 40 ϫ 10 ϫ 200
Problem Solving and Test Prep
USE DATA For 14–15, use the table.
14. How many hours does a tiger sleep in
one year?
Animal Sleep
15. In one year, how many more hours
does a pig sleep more than a cow
sleeps?
16. A typical African elephant may weigh
Animal
Time (hours per day)
Tiger
16
Pig
9
Cow
4
17. A typical giraffe may weigh about 145
about 185 pounds at birth. At maturity
its weight is 32 times as great. What
does a typical African elephant weigh at
maturity?
A 1,075 pounds
A 3,710 pounds
B
1,305 pounds
B
4,920 pounds
C
2,380 pounds
C
5,920 pounds
D 2,610 pounds
pounds at birth. At maturity its weight is
18 times as great. What does a typical
giraffe weigh at maturity?
D 6,910 pounds
PW13
Practice
â Harcourt ã Grade 5
Name
Lesson 3.1
Estimate with 1-Digit Divisors
Estimate the quotient.
1. 2ͤෆ
624
2. 6ͤෆ
534
3. 7ͤෆ
2,429
4. 8ͤෆ
3,008
5. 1,734 Ϭ 6
6. 224 Ϭ 7
7. 328 Ϭ 4
8. 2,331 Ϭ 9
9. 2,892 Ϭ 6
10. 4,168 Ϭ 8
11. 541 Ϭ 7
12. 263 Ϭ 5
Problem Solving and Test Prep
14. Another shipment of motorcycles weighs
13. A shipment of motorcycles weighs
2,079 pounds. This shipment included
7 mountain bikes. About how much did
each mountain bike weigh?
2,776 pounds. The shipment included
8 identical motorcycles. About how
much did each motorcycle weigh?
15. Mr Jones drove 571 miles in 4 days. If he 16. John traveled 885 miles in 3 days. If he
drove the same number of miles each
day, what is the best estimate of how far
Mr. Jones drove on the first day?
traveled the same number of miles each
day, what is the best estimate of how far
John drove on the first day?
A 162 mi
C
115 mi
A 190 mi
C
300 mi
140 mi
D
96 mi
B
268 mi
D
250 mi
B
PW14
Practice
â Harcourt ã Grade 5
Name
Lesson 3.2
Divide by 1-Digit Divisors
Name the position of the first digit of the quotient. Then find the first digit.
1.
6.
4ͤෆ
348
3ͤෆ
837
2.
7.
7ͤෆ
952
8ͤෆ
3,672
3.
8.
4.
5ͤෆ
715
9.
7ͤෆ
8,043
6ͤෆ
414
9ͤෆ
5,342
5.
10.
9ͤෆ
2,874
3ͤෆ
7,458
Divide. Check by multiplying.
736
11. 2ͤෆ
12. 5ͤෆ
815
13. 7ͤෆ
662
14. 4ͤෆ
3,049
15. 8ͤෆ
5,431
16. 924 Ϭ 6
17. 261 Ϭ 3
18. 754 Ϭ 9
19. 5,765 Ϭ 7
20. 3,835 Ϭ 4
Problem Solving and Test Prep
22. There are 185 students at the museum.
21. There are 185 students going to a
Each adult has 8 students in their group.
How many adults will have a group of
8 students? How many students will not
be in a group of 8 students?
museum. Each van can hold 9 students.
How many vans of 9 students are
needed? How many students are riding
in a van that is not full?
23. One case can hold 9 boxes of cereal.
24. A fifth-grade class made 436 cookies.
How many cases are needed to hold
144 boxes of cereal?
The class put 6 cookies in each bag.
How many cookies remained?
A 1,296
A 72 r4
B
16
B
2,616
C
17
C
4
D 9
D 72
PW15
Practice
â Harcourt ã Grade 5
Name
Lesson 3.3
Problem Solving Workshop Skill:
Interpret the Remainder
Tell how you would interpret the remainder. Then give the answer.
1. A total of 110 fifth graders are going on
2. The Bradt family is planning a hiking trip
in the mountains. The Bradt’s want to
hike 9 miles each day. How many days
will it take for the Bradt family to hike
114 miles? How many miles will they
hike on the last day?
a field trip to a museum. Vans will be
used for transportation. Each van holds
8 students. How many vans will be
needed for the trip?
3. A total of 124 players are riding a
4. There are 230 books in the storeroom.
car to the soccer game. If 5 players can
ride in each car, how many cars are
needed?
Each box holds 7 books. How many
boxes are needed to store all of the
books?
Mixed Applications
USE DATA For 3–4, use the table.
5. Pete biked through the Appalachian
Mountains on his vacation. He rode his
bike for 9 miles each day until he
finished his trip. How many miles did
Pete bike on his last day?
Miles Biked on Vacation
Biker
Miles
Sue
114
Pete
124
Brenda
137
Charlie
109
6. If all bikers rode for 9 miles each day,
who had to bike the least on the last
day to finish their trip?
PW16
Practice
© Harcourt • Grade 5
Name
Lesson 3.4
Zeros in Division
Divide.
912
1. 6ͤෆ
2. 4ͤෆ
716
3. 8ͤෆ
829
4. 7ͤෆ
941
6. 5ͤෆ
634
7. 9ͤෆ
1,681
8. 4ͤෆ
871
9. 8ͤෆ
1,163
11. 764 Ϭ 2
12. 834 Ϭ 9
13. 2,251 Ϭ 4
14. 3,676 Ϭ 6
5. 3ͤෆ
1,373
10. 7ͤෆ
791
15. 5,794 Ϭ 8
Problem Solving and Test Prep
16. Each pack of marigold flowers can hold
17. Each pack of tulips can hold 9 tulips.
6 marigolds. There are 458 marigolds.
How many full packs of marigolds are
there? How many more marigolds are
needed to fill a 6-pack of marigolds?
There are 956 tulips to be packed.
How many tulips will be left? How
many more tulips are needed to fill a
9-pack container of tulips?
18. The population of the world in July 2006 19. A pet store sells dog bones in packages
of 6. How many packages can they
make from 762 dog bones?
was about 6,628,506,453. What is the
value of the digit 2 in that number?
A 127
B
4,572
C
6
D 172
PW17
Practice
â Hearcourt ã Grade 5
