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PRACTICE
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HSP
Grade 5
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1 2 3 4 5 6 7 8 9 10 073 16 15 14 13 12 11 10 09 08 07
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
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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
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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
© Harcourt • Grade 5
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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
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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.
.UMBEROF0ROBLEMS
-Y(OMEWORK0ROGRESS
.UMBEROF
0ROBLEMS!SSIGNED
.UMBEROF
0ROBLEMS#ORRECT
-ON
4UE
7ED
$AY
4HU
© Harcourt • Grade 5
Number of Problems
10
9
8
7
6
5
4
3
2
1
0
Mon
Wed
My Homework Progress
Tue
Day
Thu
Number of
Problems
Assigned
Number of
Problems
Correct
© Harcourt • Grade 5
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 ⫹ 20,000 ⫹ 1,000 ⫹ 80 ⫹ 5
What number makes the statement true?
16. 2,760,000 ⫽ 276 ⫻
15. 580,000 ⫽ 58 ⫻
Problem Solving and Test Prep
17. Fast Fact The diameter of Jupiter is
18. Clarrisa learns that the estimated
88,732 miles. How can Michael write the
diameter of Jupiter in expanded form?
19. What is the value of the underlined digit
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
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 ⫹ 70,000,000 ⫹ 8,000,000 ⫹ 300,000 ⫹ 8,000 ⫹ 200 ⫹ 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
© Harcourt • Grade 5
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Name
Lesson 1.3
Compare and Order Whole Numbers
Compare. Write ⬍, ⬎, or ⫽ 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 ⬍ 13,6
7 ⬍ 13,630
12. 529,781 ⬎ 529,78
⬎ 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
© Harcourt • Grade 5
MXENL08AWK5X_PH_C01_L3.indd PW3
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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
© Harcourt • Grade 5
Name
Lesson 1.5
Estimate Sums and Differences
Estimate by rounding.
1.
308,222
196,231
__
2.
925,461
173,509
__
3.
19,346
25,912
__
4.
125,689
236,817
__
5.
471,282
161,391
__
Estimate by using compatible numbers or other methods.
6.
123,636
78,239
__
7.
48,385
54,291
__
8.
$4,471
1,625
__
9.
69,371
73,253
__
10.
224,119
79,388
__
For 11–14, find the range the estimate will be within.
11.
$3,817
1,428
__
12.
28,204
53,185
__
13.
35,122
61,812
__
14.
482
512
__
Problem Solving and Test Prep
15. Brazil has a population of 186,112,794
16. What if the population of Brazil
increased by 4 hundred thousand
people, would that change your
estimate for problem 22? Explain.
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
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
© Harcourt • Grade 5
Name
Lesson 1.6
Add and Subtract Whole Numbers
Estimate. Then find the sum or difference.
1.
6,292
⫹ 7,318
__
2.
28,434
⫹ 49,617
__
3.
205,756
⫺ 201,765
___
4.
529,852
⫹ 476,196
___
5.
5,071,154
⫹ 483,913
___
6.
241,933
⫹ 51,209
__
7.
75,249
⫺ 41,326
__
8.
1,202,365
⫺ 278,495
___
9.
4,092,125
2,748,810
⫹
6,421,339
___
10.
11.
542,002
⫺ 319,428
___
12.
360,219
⫹ 815,364
___
4,687,184
⫺ 1,234,562
___
13. 32,109 ⫹ 6,234 ⫹ 4,827
14. 3,709,245 ⫺ 1,569,267
15. 200,408 ⫺ 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 ⫹ 683,681 ⫽
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
© Harcourt • Grade 5
Name
Lesson 2.1
Mental Math: Patterns in Multiples
Find the product.
1. 9 300
2. 3 100
3. 60 5
4. 5 7,000
6. 700 200
7. 20 9,000
8. 1,000 10
9. 5,000 30
11. 40 9,000
12. 7 200
13. 600 60
14. 100 600
5. 10 4,000
10. 6,000 80
15. 200 500
ALGEBRA Find the missing number.
16. 700 5,000 20 90,000 18. 600 17.
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
© Harcourt • Grade 5
Name
Lesson 2.2
Estimate Products
Estimate the product.
1. 65 22
2. 18 $34
3. 738 59
4. 195 23
5. 8,130 77
6. 91 49
7. 641 31
8. 555 470
9. 4,096 12
10. 42 1,912
11. 199 249
12. 467 124
13. 88 27
14. 4 96,725
15. 6,371 52
16. 33 180
17. 894 605
18. 5,720 79
19. 54 419
20. 76 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 54,090?
108 276?
A 40 50,000
A 100 200
B
40 60,000
B
100 300
C
50 50,000
C
200 200
D 50 60,000
D 200 300
PW9
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C02_L02.indd PW9
6/15/07 12:20:16 PM
Name
Lesson 2.3
Multiply by 1-Digit Numbers
Estimate. Then find the product.
1.
47
6
2.
26
6
3.
6.
339
7
7.
518
5
8.
207
3
4.
2,309
8
9.
783
9
8,014
3
5.
10.
428
5
9,237
6
11. 729 8
12. 6 802
13. 4 426
14. 339 5
15. 3,045 4
16. 9 1,218
17. 5,331 2
18. 61,372 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 (800 70 3)?
the total cost for 9 new windows?
A 8 (800,703)
A $3,725
B
64 56 24
B
$3,825
C
6,400 70 3
C
$4,725
D 6,400 560 24
D $4,825
PW10
Practice
© Harcourt • Grade 5
Name
Lesson 2.4
Multiply by Multi-Digit Numbers
Estimate. Then find the product.
342
28
_
2.
451
61
_
3.
709
53
_
4.
622
34
_
5.
6. $229
7.
907
83
_
8.
1,345
23
__
9.
172
91
_
10.
4,029
67
__
219
84
_
12.
727
33
_
13. $1,948
14.
1,220
42
__
15.
893
12
_
1.
77
11.
58
__
970
17
_
Problem Solving and Test Prep
16. Abby wants to cycle 25 miles each
17. Rachel participated in a Bike-a-Thon.
day for one full year, or 365 days. How
many miles is Abby planning to cycle
in all?
Twenty-three family members donated
$12 for each mile she rode. If Rachel rode
38 miles, how much did she collect?
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
MXENL08AWK5X_PHTE_C02_L04.indd PW11
6/15/07 12:22:23 PM
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?
3. An art-supply store sells sets of color
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
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?
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?
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
© Harcourt • Grade 5
Name
Lesson 2.6
Choose a Method
Find the product. Choose mental math, paper and pencil, or a calculator.
1.
820
⫻
10
_
2. 5,129
3.
⫻ 18
__
6. 500 ⫻ 12
7. 375 ⫻ 218
10. 400 ⫻ 320
11. 785 ⫻ 122
452
⫻
726
__
4.
304
⫻
21
_
8. 40 ⫻ 5,000
12. 93 ⫻ 11 ⫻ 34
5. 1,200
⫻ 12
__
9. 112 ⫻ 83
13. 40 ⫻ 10 ⫻ 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?
Animal
Time (hours per day)
Tiger
16
Pig
9
Cow
4
17. A typical giraffe may weigh about 145
16. A typical African elephant may weigh
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
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C02_L06.indd PW13
6/15/07 12:22:11 PM
Name
Lesson 3.1
Estimate with 1-Digit Divisors
Estimate the quotient.
1. 2
624
2. 6
534
3. 7
2,429
4. 8
3,008
5. 1,734 ⫼ 6
6. 224 ⫼ 7
7. 328 ⫼ 4
8. 2,331 ⫼ 9
9. 2,892 ⫼ 6
10. 4,168 ⫼ 8
11. 541 ⫼ 7
12. 263 ⫼ 5
Problem Solving and Test Prep
13. A shipment of motorcycles weighs
14. Another shipment of motorcycles weighs
2,776 pounds. The shipment included
8 identical motorcycles. About how
much did each motorcycle weigh?
2,079 pounds. This shipment included
7 mountain bikes. About how much did
each mountain bike 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
MXENL09AWK5X_PH_C03_L1.indd PW14
Practice
© Harcourt • Grade 5
7/2/07 2:20:28 PM
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.
4
348
3
837
2.
7.
7
952
8
3,672
3.
8.
4.
5
715
9.
7
8,043
6
414
9
5,342
5.
10.
9
2,874
3
7,458
Divide. Check by multiplying.
11. 2
736
12. 5
815
13. 7
662
14. 4
3,049
15. 8
5,431
16. 924 ⫼ 6
17. 261 ⫼ 3
18. 754 ⫼ 9
19. 5,765 ⫼ 7
20. 3,835 ⫼ 4
Problem Solving and Test Prep
21. There are 185 students going to a
22. There are 185 students at the museum.
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.
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?
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
© Harcourt • Grade 5
MXENL09AWK5X_PH_C03_L2.indd PW15
7/2/07 2:20:47 PM
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.
1. 6
912
2. 4
716
3. 8
829
4. 7
941
6. 5
634
7. 9
1,681
8. 4
871
9. 8
1,163
11. 764 ⫼ 2
12. 834 ⫼ 9
13. 2,251 ⫼ 4
14. 3,676 ⫼ 6
5. 3
1,373
10. 7
791
15. 5,794 ⫼ 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
© Hearcourt • Grade 5
MXENL09AWK5X_PH_C03_L4.indd PW17
6/15/07 12:27:06 PM
Name
Lesson 3.5
Algebra: Patterns in Division
Use basic facts and patterns to find the quotient.
1. 60 ⫼ 10
2. 140 ⫼ 7
3. $180 ⫼ 90
4. 480 ⫼ 6
5. 400 ⫼ 50
6. 160 ⫼ 40
7. 360 ⫼ 6
8. 560 ⫼ 80
9. 2,400 ⫼ 3
13. 81,000 ⫼ 90
10. $2,000 ⫼ 10
11. 6,300 ⫼ 70
12. 4,200 ⫼ 60
14. 80,000 ⫼ 2
15. 90,000 ⫼ 30
16. $35,000 ⫼ 50
Compare. Use ,, ., or ⴝ for each
17. 350 ⫼ 7
3,500 ⫼ 70
.
18. 240 ⫼ 8
24 ⫼ 8
19. 360 ⫼ 40
360 ⫼ 4
Problem Solving and Test Prep
20. A warehouse stored 10 crates of
21. An office bought 8 office chairs for a
paper. The paper weighed a total
of 7,000 pounds. How much did one
crate of paper weigh?
22. A clothing store spends $4,500 on
total of $720. Each chair came with
a $15 mail-in rebate. After the rebate,
how much money did each chair cost?
23. A business man spends $6,400 on
9 clothing racks. How much does
each clothing rack cost?
8 projectors for his company. How much
does each projector cost?
A $90
A $80
B
$500
B
$800
C
$540
C
$640
D $50
D $8
PW18
Practice
© Harcourt • Grade 5
Name
Lesson 3.6
Estimate with 2-Digit Divisors
Write two pairs of compatible numbers for each.
Then give two possible estimates.
1. 38
329
2. 54
386
3. 75
$384
4. 425 ⫼ 88
5. 5,234 ⫼ 91
6. $1,761 ⫼ 26
8. 31
$289
9. 72
6,102
Estimate the quotient.
7. 24
157
10. 181 ⫼ 35
11. 4,913 ⫼ 62
12. 55,208 ⫼ 87
Problem Solving and Test Prep
13. The distance from the bottom of the first 14. Maria ran one mile in 8 minutes after
school. Joshua ran one mile in 540
seconds after school. Who ran the mile
in less time?
floor of an office building to the top of
the 86th floor is 353 meters. About how
many meters tall is each floor?
16. Heather spent 480 minutes practicing
15. Joe built a tower out of blocks. It was
475 centimeters tall. The height of each
cube was 18 centimeters. About how
many cubes did Joe use?
basketball last month. How many hours
did Heather spend practicing basketball
last month?
A 10
A 60
B
24
B
4
C
18
C
10
D 48
D 8
PW19
Practice
© Harcourt • Grade 5
Name
Lesson 3.7
Divide by 2-Digit Divisors
Divide. Check your answer.
1. 23
713
2. 42
798
3. 64
832
4. 18
1,296
5. 56
792
6. 36
879
7. 26
936
8. 87
4,120
9. 785 34
10. 980 51
11. 1,939 74
12. 2,738 65
Problem Solving and Test Prep
13. The average person eats 53 pounds of
14. The average person in the U.S. uses
47 gallons of water each day. How many
days would it take for the average person
in the U.S. to use 846 gallons of water?
bread each year. How many years would
it take for the average person to eat 689
pounds of bread?
15. The school auditorium has 756 seats
16. A farmer planted a total of 768 corn
arranged in 27 equal rows. How many
seats are in each row?
seeds in 24 equal rows. How many
corn seeds are there in each row?
A 27
A 28
B
28
B
30
C
29
C
32
D 30
D 34
PW20
Practice
© Harcourt • Grade 5
MXENL09AWK5X_PH_C03_L7.indd PW20
6/15/07 12:28:35 PM
Name
Lesson 3.8
Correcting Quotients
Write low, high, or just right for each estimate.
1.
20
34
884
2.
100
18
1,224
3.
20
38
798
4.
30
24
624
5.
40
67
3,417
Divide.
6. 18
972
11. 2,312 ⫼ 49
7. 27
259
8. 32
6,730
9. 63
234
12. 734 ⫼ 56
13. 1,634 ⫼ 86
14. 6,324 ⫼ 62
10. 79
5,688
15. 846 ⫼ 94
Problem Solving and Test Prep
16. Robin needs to buy 250 coasters
17. A store orders 832 ounces of floor
for a graduation party. Each package
contains 18 coasters. How many
packages should Robin buy?
cleaner. Each bottle is 32 ounces and
costs $3. How much does the store
spend on the order?
18. The Comfortable Shoe Company can
19. A Disc Jockey has a collection of 816
fit 16 boxes of shoes in a crate. How
many crates will the company need
to pack 576 boxes of shoes?
CDs. The CD case that he likes holds
24 CDs. How many cases will the Disc
Jockey need to hold all his CDs?
A 36
A 43
B
40
B
30
C
35
C
34
D 30
D 40
PW21
Practice
© Harcourt • Grade 5
MXENL09AWK5X_PH_C03_L8.indd PW21
6/27/07 9:54:26 AM
Name
Lesson 3.9
Practice Division
Divide. Multiply to check your answer.
1. 7
371
2. 6
534
3. 4
547
4. 21
2,536
5. 57
3,672
6. 13
1,847
7. 36
2,643
8. 85
6,298
11. 1,516 ⫼ 47
12. 9,951 ⫼ 93
9. 582 ⫼ 6
10. 763 ⫼ 9
Problem Solving and Test Prep
13. Julia can make a paper crane in
14. Nathan spent 826 minutes making paper
8 minutes. She spent 992 minutes
making paper cranes for a party. How
many paper cranes did Julia make?
15. Sean has 6 piles of pennies. Each pile
origami boxes. He can make a paper
box in 7 minutes. How many origami
boxes did Nathan make?
16. A school cafeteria used 232 pieces of
has 37 pennies. How many pennies
does Sean have?
bread yesterday equaling 8 full loaves.
How many pieces of bread are in one
loaf?
A 42
A 26
B
45
B
27
C
216
C
28
D 222
D 29
PW22
Practice
© Harcourt • Grade 5
Name
Lesson 3.10
Problem Solving Workshop Skill: Relevant or
Irrelevant Information
Problem Solving Skill Practice
Solve.
1. A total of 47 fifth graders and 3 teachers
2. James receives $15 each week from his
went on a field trip to a play. The total
cost for the students’ tickets was $658.
The total cost for the teachers’ tickets
was $57. What was the price of each
student ticket?
3. Ryan’s collection of NFL cards is 5 times
parents as an allowance. His goal is to
save $1,196. If James saves $13 each
week, how many weeks will it take
James to reach his goal?
4. Melissa received 3 dozen roses and
1 dozen balloons on her birthday. How
many vases will she need if she wants to
put 9 roses in each vase?
more than Rickie’s card collection.
Rickie has 135 cards. It took Ryan
12 months to collect the cards. How
many NFL cards does Ryan have?
Mixed Applications
USE DATA For 3–6, use the table.
5. Jessica drove from Austin to Norland.
On average, she drove 60 miles per
hour. She used 40 gallons of gas.
How many hours did Jessica drive?
Distance Between Cities (in miles)
Denver,
CO
Austin,
TX
Boston,
MA
6. Joe drove from Boston to Fairfax at an
average rate of 56 miles per hour.
How many hours did Joe drive?
7. Julie drove from Austin to Redford. She
Fairfax,
CA
Norland,
FL
Redford,
MI
1,050
1,360
1,210
1,780
1,260
1,430
3,080
860
740
8. Sarah drove on average 50 miles per
traveled on average 65 miles per hour.
How many hours did Julie drive?
PW23
hour from Fairfax to Denver. Dan drove
on average 55 from Redford to Denver.
Who drove less time to reach Denver?
Practice
© Harcourt • Grade 5
Name
Lesson 4.1
Write Expressions
Write a numerical expression. Tell what the expression represents.
1. William shared 8 apples
equally among 4 friends.
2. Jillian bought 4 toys for
3. 35 more than 18
$7 each.
Write an algebraic expression. Tell what the variable represents.
4. Jasmine has three times
as many chores as her
younger brother does.
6. Neil spent 25 minutes on
5. Pedro swam some laps
in the pool and then
swam 2 more.
his math and some more
time on his history
homework.
Write an algebraic expression in words.
7. 3x 8
m
8. 17 __
4
9. n 9
Problem Solving and Test Prep
USE DATA For 10–11, use the table.
Aquarium Fish
10. Write an algebraic expression to
represent the total number of silver
dollars that could be in a 24-gallon tank.
Let d number of silver dollars.
11. Jason has 9 Bronze corys in a tank.
Type of Fish
Length (in inches)
Bronze Cory
3
Clown Barb
5
Silver Dollar
8
12. The temperature increased from a low
Write an algebraic expression to find the
minimum number of gallons of water in
the tank.
PW24
of 62 degrees. Which expression best
describes the new temperature?
A 62 t
B 62 t
C 62t
D t 62
Practice
© Harcourt • Grade 5
Name
Lesson 4.2
Evaluate Expressions
Evaluate each expression.
1. 27 ⫺ 15 ⫼ 3
2. 12 ⫻ 4 ⫼ 6
3. (17 ⫹ 8) ⫺ (2 ⫹ 8)
4. 60 ⫼ (10 ⫺ 4)
5. (3 ⫹ 12) ⫼ 3 ⫻ 4
6. 6 ⫻ 4 ⫺ 2 ⫻ 3
7. 30 ⫼ (2 + 3) ⫺ 1
8. 42 ⫺ 18 ⫼ 6 ⫹ 3
Evaluate the algebraic expression for the given value of the variable.
9. 31k if k ⫽ 4
10. 2r ⫺ 9 if r ⫽ 5.5
13. 3r ⫹ 4 ⫼ 2 ⫺ r
11. 21 ⫺ 3c if c ⫽ 7
14. 14 ⫺ (12 ⫼ y ⫺ 2) 15. 3(x ⫺ 1) ⫺ (3 ⫺ x)
if r ⫽ 7
if y ⫽ 3
12. 4p ⫹ 6 if p ⫽ 1 1_2
16. 18 ⫺ 1 ⫼ 5y ⫹ y
if x ⫽ 2
if y ⫽ 0.2
Use the expression to complete each table.
17.
h
0
2
5
10
n
18.
12h 3
1
2
5
7
14 2n
Problem Solving and Test Prep
USE DATA For 19–20, use the table.
Afternoon Games at Field Day
19. Write an expression to represent the
Game
number of students who run in the
50-meter dash and the 800-meter run.
Then evaluate the expression if there
are 41 students in the 800-meter run.
Number of Players
Long Jump
28
Softball Throw
s
50-Meter Dash
89
800-Meter Run
r
20. The softball participants were divided into 5 small groups. Write an expression to
represent this. Then find the number of participants in each group if 80 students
competed.
21. If k ⫽ 7, what is the value of
22. The expression 5w shows the cost of 5
books. If w ⫽ $7.45, what is the total
cost of the books?
2k ⫺ 3?
A 8
C
11
A $35.00
C
$37.25
9
D
24
B
$39.45
D
$12.45
B
PW25
Practice
© Harcourt • Grade 5
Name
Lesson 4.3
Properties
Name the property shown.
1.
28 19 19 28
2. 12 (8 30) (12 8) 30
3. 5 58 (5 50) (5 8)
4. (6 7) 4 (7 6) 4
Find the value of n. Identify the property used.
5. 46 n 0
6. 1 n 71
7. 12 85 n 12
8. 49 4 = n 49
9. 8 36 (8 n) (8 6) 10. 9 (n 5) (9 1) 5
Problem Solving and Test Prep
11. Show the Commutative Property of
Cari’s Rock Collection
Addition using Cari’s collection of flint
and garnet pieces.
12. Drake has 7 times the number of fluorite
and flint pieces than Cari has. Use the
Distributive Property to show the total
number of pieces Drake has.
Type of Rock
Fluorite
Amethyst
Flint
Garnet
0
2
4
6
8
10
12
Number of Pieces
13. The expression 30 (8 7) shows the
14. The expression (20 4) 12 shows the
amount of money Daniel earned. Which
expression represents the same amount
of money?
A
B
C
D
(30 8) 7
(30 8) (30 7)
(30 8) (30 7)
(30 8) (30 7)
amount of money Josie earned. Which
expression represents the same amount
of money?
A
B
C
D
PW26
(20 4) 12
(12 20) 4
20 (4 12)
(4 20) 12
Practice
© Harcourt • Grade 5
Name
Lesson 4.4
Mental Math: Use the Properties
Use properties and mental math to find the value.
1. 12 ⫹ 18 ⫹ 39
2. 53 ⫹ 64 ⫹ 37
3. 6 ⫻ 103
4. (20 ⫻ 4) ⫻ 3
5. 41 ⫹ 29 ⫹ 46
6. 26 ⫹ 43 ⫹ 34
7. 6 ⫻ 15 ⫻ 2
8. 4 ⫻ 180
9. 72 ⫹ 18 ⫹ 32
10. 7 ⫻ 4 ⫻ 15
11. 34 ⫻ 6
12. 33 ⫹ (37 ⫹ 32)
13. 42 ⫻ 7
14. 29 ⫹ 46 ⫹ 51
15. 5 ⫻ 6 ⫻ 12
16. 62 ⫻ 4
17. 36 ⫹ 18 ⫹ 24
18. 12 ⫻ 6 ⫻ 4
Problem Solving and Test Prep
19. FAST FACT A group of sea lions
20. Tell which property you would use to
mentally find the value of 5 ⫻ 4 ⫻ 45.
Then find the value.
together in the water are called a raft. In
a raft, sea lions can safely rest together.
During one afternoon, a research team
saw 4 rafts of sea lions. Each raft had 16
sea lions in it. How many sea lions did
the research team see?
21. There are 6 shelving units containing
22. Tickets for the movies cost $13 each.
5 shelves each. Each shelf holds
35 DVDs. Find the total number of
DVDs on the shelving unit.
James’ family buys 6 tickets. Explain
how to use mental math to find the total
cost of the movie tickets.
A 210
B
450
C
950
D 1,050
PW27
Practice
© Harcourt • Grade 5
Name
Lesson 4.5
Write Equations
Write an equation for each. Tell what the variable represents.
1. Paulina has a photo album with
2. Jarrod practiced the trumpet and piano
60 photos. Each page contains
5 photos. How many pages does
the album have?
for 45 minutes. He practiced piano for
15 minutes. How long did he practice
the trumpet?
Write a problem for each equation. Tell what the variable represents.
3. 7t ⫽ 63
4. 6 ⫹ b ⫽ 11
Problem Solving and Test Prep
5. Jaime has $130 in her savings account.
6. What if Jamie already bought the bike
and has $29 left in her account. How
much money did she have before
buying the bike? Write an equation with
a variable to represent the problem.
She wants to buy a bike for $225. How
much more money does Jaime need to
buy the bike? Write an equation with a
variable to represent the problem.
7. The Amsco building is 135 feet tall.
8. Tam had downloaded 25 songs for her
The Tyler building is 30 feet shorter than
the Amsco building. What is the Tyler
building’s height? Write an equation to
represent this problem.
MP3 player. She then downloaded some
more songs. She now has 31 songs for
her MP3 player. How many songs did
Tam download? Write an equation to
represent this problem.
A 135 ⫽ h ⫹ 30
A 25 ⫹ s ⫽ 31
B
h ⫽ 135 ⫺ 30
B
s ⫺ 31 ⫽ 25
C
135 ⫽ 30 ⫺ h
C
s ⫺ 25 ⫽ 31
D 56 ⫺ s ⫽ 31
D h ⫽ 135 ⫹ 30
PW28
Practice
© Harcourt • Grade 5
Name
Lesson 4.6
Solve Equations
Which of the numbers 5, 7, or 12 is the solution of the equation?
1. t 2 5
2. 30 e 6
3. 3 u 36
4. 18 p 30
Use mental math to solve each equation. Check your solution.
5. 56 8 t
6. 22 p 9
7. 25 n 13
9. d 4 8
10. 6 s 84
11. v 14 38
8. 72 y 12
12. $24 r $61
Problem Solving and Test Prep
13. Algebra A bear weighed 165 pounds
14. Algebra Sam took 42 pictures of
when it came out of hibernation. During
the summer it gained n pounds. At the
end of the summer the bear weighed
240 pounds. Write and solve an
equation to find out how much the bear
gained during the summer.
15. The equation $56 p $8 represents
animals on a nature hike. He placed the
same number of pictures on each page
of an album. He used 7 pages of his
album. Write and solve an equation to
find out how many pictures he placed
on each page of his album.
16. Jesse had a book of 14 crossword
puzzles. After solving some of the
puzzles, he has 3 puzzles left. Write and
solve an equation to find out how many
crossword puzzles Jesse solved.
the total cost of some books and the
cost per book. How many books were
bought?
A 7
B
8
C
9
D 12
PW29
Practice
© Harcourt • Grade 5
Name
Lesson 4.7
Functions
Write an equation to represent each function. Then complete the table.
1.
c
0
d
8
j
0
4.
1
k
7.
2
3
4
10
11
12
2
4
6
8
1
2
3
4
8
a
0
2
4
6
b
1
11
21
31
2.
5.
8.
m
0
1
p
0
4
2
3
4
12
16
v
12
15
18
w
3
6
9
y
3
6
z
9
21
9
21
3.
6.
9.
12
45
g
0
2
4
h
21
19
17
x
5
6
7
8
9
y
5
9
11
13
s
5
r
2
10
6
8
13
15
20
7
9.5
Use the rule and the equation to make a function table.
10. Rule: Multiply by 4
11. Rule: Add 8
m⫻4⫽r
a⫹8⫽b
m
a
r
b
Problem Solving and Test Prep
12. Dina pays $16 per week for piano lessons. How much will it cost for 6 weeks of
lessons if she takes one lesson per week? Make a function table to show the total cost
per week for 6 weeks.
13. Peg has ridden her bicycle a total of 200 miles this year. She rides 40 miles per week.
What will be her total miles after 8 more weeks? Make a function table to show her
expected total distance for the next 8 weeks.
14. The equation y ⫽ 12 x ⫹ 300 shows
15. The equation y ⫽ 280 ⫺ 30x shows the
the balance in Dale’s savings account
after x weeks. How much will be in the
account after 10 weeks?
number of pages Keiko has left to read
after x hours of reading. How much will
she have left to read after 4 hours?
A $180
C
$312
A 160 pages
C
310 pages
$288
D
$420
B
250 pages
D
400 pages
B
PW30
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C04_L7.indd PW30
6/15/07 12:22:33 PM
Name
Lesson 4.8
Inequalities
Which of the numbers 4, 6, 8, and 10 are solutions of each inequality?
1. x ⫹ 5 ⬎ 5
2. x ⫺ 6 ⬍ 2
3. x ⫺ 4 ⱕ 4
4. x ⫹ 9 ⱖ 15
5. x ⫹ 10 ⬍ 16
6. x ⫺ 10 ⱖ 0
7. x ⫹ 7 ⱕ 11
8. x ⫹ 12 ⬎ 20
Draw a number line from 0 to 8. Locate points to show the whole number
solutions from 0 to 8 for each inequality.
9. x ⫹ 2 ⬎ 4
10. x ⫹ 8 ⬎ 9
Write an inequality to match the words. Choose the variable for the unknown.
Tell what the variable represents.
11. Travel time to the park is at least
12. Magie, the cat, weighs less than
3 hours.
12 pounds.
Problem Solving and Test Prep
13. Let a ⫽ age. What ticket price does
Circus Admission
a ⬍ 5 represent?
Age
Under 5
14. Let n ⫽ age. What ticket price does
5–18/Child
n ⫺ 12 ⬎ 6 represent?
15. The inequality s ⫹ 4 ⱖ 6 represents
Over 18/Adult
Price
Free
$8
$15
16. The inequality s ⫺ 11 ⬍ 60 represents the
the least amount of money a snack
costs at the county fair. Which amount
is not a solution of the inequality?
greatest height in inches a person can be
to ride a rollercoaster. Which amount is a
solution of the inequality?
A 1
A 70
B
2
B
71
C
3
C
72
D 4
D 73
PW31
Practice
© Harcourt • Grade 5
Name
Lesson 4.9
Problem Solving Workshop Strategy: Predict and Test
Problem Solving Strategy Practice
Predict and test to solve the problem.
1. Andrea bought a total of 21 fish for her
2. Alec has two types of fish in his
aquarium. He has 22 fish in all.
The product of the numbers of each
type is 85. What are the two numbers?
aquarium. She bought 9 fewer angelfish
than guppies. How many angelfish and
guppies did she buy?
3. The sum of the ages of Michele and
4. Loni is thinking of two numbers. One
Clark’s ages is 27. Clark is twice as old
as Michele. How old are Clark and
Michele?
number is three times greater than
the second number. Their sum is 32.
What are the two numbers?
Mixed Strategy Practice
Aquarium Fish Price List
USE DATA For 5–7, use the table.
5. Denny spent $60 on Keyhole Cichlids
and Clown Loaches. He bought 10 fish.
How many of each did he buy?
6. Beth spent $210 on a fish tank and Tiger
$5
Clown Loach
$8
Black Skirt Tetra
$2
Tiger Barb
$3
Keyhole Cichlid
$4
7. Cora bought 3 Silver Dollars and
4 Clown Loaches for her fish tank.
She handed the cashier three $20 bills.
How much change did she receive?
Barbs. The tank cost $180. How many
Tiger Barbs did she buy?
8. A gallon of water weighs 10 pounds.
Silver Dollar
9. Open-Ended Bryce has $25 to spend
A fish tank weighs 35 pounds. How
much does it weigh if it holds 15
gallons?
on fish. He wants to purchase at least
three fish of two different kinds. Which
two kinds can he buy?
PW32
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C04_L9.indd PW32
7/2/07 2:15:40 PM
Name
Lesson 5.1
Decimal Place Value
Write the decimal shown by the shaded part of each model.
1.
2.
3.
4.
Find the value of the underlined digit in each number.
5. 6.029
7. 0.831
6. 8.172
9. 87.759
10. 74.038
11. 1.3496
8. 25.207
12. 0.9472
Write each number in two other forms.
13. ten and thirty-eight hundredths
14. two and one hundred two thousandths
15. 0.492
16. 5 ⫹ 0.3 ⫹ 0.06 ⫹ 0.009
Problem Solving and Test Prep
17. A robber fly’s greatest length in meters
18. A honey bee is 0.017 m. A carpenter
has 0 in the ones and tenths places and
5 in the hundredths place. What is this
length of a robber fly in meters?
19. What is the value of the underlined digit
bee is 0.008 m longer than a honey bee.
What is the length of a carpenter bee in
expanded form?
20. The decimal 0.9 is how many times
in 8.536?
greater than 0.009?
A 0.003
A 9
B
0.03
B
10
C
0.3
C
100
D 3.000
D 0.01
PW33
Practice
© Harcourt • Grade 5
Name
Lesson 5.2
Equivalent Decimals
Write equivalent or not equivalent to describe each pair of decimals.
1. 2.26 and 2.260
2. 8.05 and 8.50
3. 7.08 and 7.008
4. 9 and 9.00
Write an equivalent decimal for each number.
5. 0.9
9. 0.04
6. 1.800
7. 3.02
8. 8.640
10. 45.100
11. 4.60
12. 2.70
16. 3.0540
Write the two decimals that are equivalent.
13. 3.007
14. 0.930
15. 7.60
3.700
0.093
7.06
3.054
3.7000
0.93
7.600
3.504
Problem Solving and Test Prep
17. FAST FACT The calliope hummingbird
18. The calliope hummingbird is about
0.07 meter long, yet it can fly from
northern North America to Mexico for
the winter. Write an equivalent decimal
for the length of a calliope hummingbird.
is the smallest bird in North America.
It weighs about 2.5 grams and builds
a nest about the size of a quarter. Write
an equivalent decimal for 2.5.
19. The calliope hummingbird lives in the
20. A banded calliope hummingbird was
mountains. It has been seen as high as
335.23 meters above sea level. Write
an equivalent decimal for 335.23.
seen in Idaho and also in Virginia. It had
flown more than 2,440.95 miles. Which
decimal is equivalent to 2,440.95?
A 2,440.095
B
2,400.905
C
2,440.9500
D 2,440.9595
PW34
Practice
© Harcourt • Grade 5
Name
Lesson 5.3
Compare and Order Decimals
Compare. Write ,, ., or ⴝ for each
1. 0.37
0.370
5. 0.812
0.821
9. 5.202
5.220
2. 3.10
3.101
6. 9.810
10. 0.78
.
9.809
0.780
3. 0.579
0.576
4. 7.7
7. 0.955
0.95
8. 3.218
3.218
4.017
12. 0.897
0.987
11. 4.17
7.690
Order from least to greatest.
13. 0.301, 0.13, 0.139, 0.5
14. 7.203, 7.032, 7, 7.2
15. 0.761, 0.67, 0.776, 0.7
16. 0.987, 0.978, 0.97, 0.98
Problem Solving and Test Prep
USE DATA For 17–18, use the table.
17. Which beetle has the shortest length?
the longest length?
Sizes of Beetles
18. Another type of beetle is 1.281 cm long.
Which beetle has a length less than
1.281 cm?
Beetle
Size (in cm)
Japanese Beetle
1.295
June Bug
2.518
Firefly
1.063
19. Some types of beetles can jump as high 20. The depth the Japanese Beetle grub
as 15 cm. Suppose three beetles
jumped 14.03 cm, 14.029 cm, and
14.031 cm. What is the order of the
heights the beetles jumped from least to
greatest?
may hibernate underground is listed
below. Which is the highest number?
A 29.103
B
29.300
C
29.301
D 29.004
PW35
Practice
© Harcourt • Grade 5
Name
Lesson 5.4
Problem Solving Workshop Skill:
Draw Conclusions
Problem Solving Skill Practice
Draw a conclusion to solve the problem.
1. Mark planted 12 tomato plants. He
2. Kim plants 3 rows of corn. The first row
planted 4 in full sun, 4 in partial shade,
and 4 in full shade. Two weeks after all
the tomato plants were in the ground,
the plants in partial sun were the
healthiest, but a month later the plants in
full sun were the healthiest. What
conclusion can you draw about where to
plant tomatoes?
is fertilized with compost, the second
row with organic fertilizer, and the third
row was not fertilized. Each row receives
the same amount of water and sunshine.
The first row grew corn 1 day before the
second and third rows. The third row
grew 8 fewer ears of corn than the other
rows. What conclusion can you draw
about how the type of fertilizer affects
the growth of the corn?
Mixed Applications
USE DATA For 3–4, use the table.
3. Nan used fertilizer on 5 African violets.
Plant A had the most blooms. Plant E
had the fewest blooms. What conclusion
can she draw about how the number of
teaspoons of fertilizer relates to the
number of blooms?
Amount of Fertilizer Per Week
4. How much fertilizer will Nan give to all
Plant
Number of Teaspoons
A
1
B
2
C
3
D
4
E
5
her plants in a year?
5. Matt buys a plant for $1.35. He pays with
6. Tina has 25 plants on 5 shelves. Each shelf
8 coins. Which coins does Matt use?
has 2 more plants than the shelf above it.
How many plants are on each shelf?
PW36
Practice
© Harcourt • Grade 5
Name
Lesson 6.1
Round Decimals
Round each number to the place of the underlined digit.
1. 54.247
2. 0.109
3. 7.044
4. 12.581
5. 0.003
Round 1.613 to the place named.
6. tenths
7. ones
8. hundredths
Name the place to which each number was rounded.
9. 2.634 to 2.63
10. 6.075 to 6.1
11. 13.46 to 13.5
Round to the nearest tenth of a dollar and to the nearest dollar.
12. $0.78
13. $0.11
14. $25.54
Round each number to the nearest hundredth.
16. 50 ⫹ 9 ⫹ 0.8 ⫹ 0.005
15. six hundred thirty-five thousandths
Problem Solving and Test Prep
USE DATA For 21–22, use the graph.
17. Round the salt content of mozzarella
cheese to the nearest tenth of a gram.
18. Which cheese has a salt content of 0.17
when rounded to the nearest hundredth
of a gram?
19. Greta rounded 6.488 pounds to
20. Neil rounded 9.135 pounds to
6.49 pounds. To which place did she
round?
9.1 pounds. To which place did he
round?
A Ones
A Ones
B
Tenths
B
Tenths
C
Hundredths
C
Hundredths
D Thousandths
D Thousandths
PW37
Practice
© Harcourt • Grade 5
Name
Lesson 6.2
Add and Subtract Decimals
Find the sum or difference.
1.
5
0.9
_
2.
11.7
3.04
__
3.
12.67
18.5
__
4.
16.08
3.49
__
6.
$32.44
$4.78
__
7.
0.45
0.071
__
8.
0.868
0.23
__
9.
17.645
11.968
__
10.
9.46
0.5
__
5.
18.394
15.602
__
11.
$25.73
$15.48
__
12.
8
4.091
__
13.
0.12
1.095
__
14.
1.304
1.239
__
15.
0.49
0.561
2.7
16.
24.006
2.73
__
17.
8.18
0.517
1.304
18.
0.1
0.025
__
19.
0.775
5.31
3.016
20.
0.003
1
9.44
Problem Solving and Test Prep
21. Until the 2002 Olympics, the record
22. Beth and her grandmother paid $23.00
luge speed was 85.38 miles per hour.
Tony Benshoof broke that record with
a speed of 86.6 miles per hour. By how
many miles per hour did Tony Benshoof
exceed the record?
23. Lynne buys a meal and a milk at the
for tickets to a play. An adult ticket costs
$6.50 more than a child’s ticket. What
was the cost of Beth’s ticket?
24. Tim buys a daily planner and 1 pen at
school cafeteria. If Lynne pays with a
$5 bill, how much change should
she receive?
School Cafeteria
A $1.06
Item
Price
the school store. How much change
should Tim receive from a $20.00 bill?
School Store
A $9.76
B
$1.55
meal
$3.45
B
$9.86
C
$2.96
fruit
$0.80
C
$10.24
D $3.94
milk
$0.49
D $16.74
PW38
Item
Price
notebook
$4.55
12 pencils
$2.14
1 pen
$1.29
daily planner
$8.95
Practice
© Harcourt • Grade 5
Name
Lesson 6.3
Estimate Sums and Differences
Estimate by rounding.
1.
6.71
4.8
__
2.
10.238
7.842
__
3.
2.11
0.96
__
4.
7.
9.276
6.419
4.458
8.
0.63
0.31
__
9.
10.82
5.78
__
10.
$14.54
$7.35
__
1.53
0.15
__
5.
11.
9.786
8.914
__
6.
$3.28
$3.65
__
$5.34 12. 4.29
$5.34
$1.06
3.334
$1.06
__
2.68
$2.68
13. $6.14 $4.59
14. 12.3 2.85
15. 1.184 1.295
16. 8.72 5.43
17. 0.219 0.183
18. 3.64 0.58
19. 14.12 5.36
20. $15.41 $4.96
Problem Solving and Test Prep
USE DATA For 21–22, use the table.
21. About how long would it take to listen to
Top 3 Songs of 1956
the 3 songs in the chart?
Artist
Playing Time
(in minutes)
Hound Dog
Elvis Presley
2.25
Long Tall Sally
Little Richard
2.083
Blue Suede Shoes
Elvis Presley
1.983
Song
22. About how much longer is Elvis
Presley’s recording of Hound Dog than
his recording of Blue Suede Shoes?
23. Elise has $50. She buys notebooks for
24. Heather and her husband have $99.
$16.29 and pens for $9.54. About how
much money will she have left?
They buy glassware for $19.49 and
tablecloth for $22.53. About how much
money would they have left?
A $10
A $50
B
$25
B
$45
C
$35
C
$38
D $15
D $57
PW39
Practice
© Harcourt • Grade 5
Name
Lesson 6.4
Choose a Method
Choose a method. Find the sum or difference.
1.
8.24
⫹
0.673
__
2.
7.89
⫺
3.21
__
3.
41.621
⫺
38.94
__
4.
$12.56
⫹
$25.72
__
5.
6.
$14.27
⫹ $ 8.49
__
7.
4.803
⫺
2.77
__
8.
$21.40
⫺
$20.10
__
9.
$13.60
⫺
$11.32
__
10.
6.33
4.095
⫹ 1.708
11.
0.501
⫹
6.79
__
12.
14.
$57.19
⫹
$ 2.68
__
15.
1.005
⫺
0.07
__
16. 2.4 ⫹ 3.75 ⫹ 1.8
2.9
⫺
1.5
__
13.
3.37
⫹
6.73
__
17. 0.85 ⫺ 0.798
18. $1.95 ⫹ $7.65
3.1
4.75
⫹ 2.9
19. 5.4 ⫺ 0.54
Problem Solving and Test Prep
USE DATA For 20–21, use the table.
20. How much farther did Chistyakova
Women’s Long Jump Records
jump in 1988 than Joyner-Kersee in
1994?
Name
21. What is the difference in jump distances
from the earliest listed date to the latest
listed date?
22. Lydia has 3 dimes, a quarter, a dollar,
Year
Distance (in meters)
Galina Chistyakova
1988
7.52
Jackie Joyner-Kersee
1994
7.49
Heike Dreschler
1992
7.48
Anis oara Stanciu
1983
7.43
Tatyana Kotova
2002
7.42
Yelena Belevskaya
1987
7.39
23. Dylan has 2 dollars, 3 quarters, 4 dimes,
and 2 nickels. How much money does
Lydia have? Show your work.
PW40
and a nickel. How much money does
Dylan have? Show your work
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C06_L4.indd PW40
6/15/07 12:13:27 PM
Name
Lesson 6.5
Problem Solving Workshop Skill:
Estimate or Find Exact Answer
Problem Solving Skill Practice
Tell whether you need an estimate or an exact answer. Then solve.
1. Serena is purchasing workout clothes in
2. Alberto is purchasing a basketball for
a sports store. Including tax, she is
purchasing shoes for $41.66, socks for
$3.49, gym shorts for $9.62, and a T-shirt
for $7.84. Serena has only $10 bills in her
wallet. How many $10 bills should she
give to the cashier for all her purchases?
3. Jessa needs $140 to buy a bicycle. She
$32.24 and a backboard with rim for
$118.24. Both prices include tax. He
gives the cashier eight $20 bills. How
much change should Alberto receive?
4. The apples Carl wants to buy range in
weight from 0.8 pound to 1.2 pounds.
How many pounds will 12 apples weigh?
saves $10 each week. She has already
saved $60. How many weeks from
now can Jessa buy the bicycle?
Mixed Applications
5. Tom has 21 flowering plants in white,
6. At noon, the temperature was 58°F. In
the next hour, the temperature rose 2°.
The hour after that, it rose 4°. During the
following hour the temperature rose 6°,
and the hour after that, it rose 8°. What
was the temperature at 1:00 P.M.?
pink, and lavender flowers. He has
2 more pink flowering plants than he
has lavender flowering plants. What is
the greatest possible number of white
flowering plants that Tom has?
7. Each chicken has 2 legs, and each
8. Pose a Problem Look back at Exercise 6.
cow has 4 legs. How many legs do
9 chickens and 23 cows have?
Write a similar problem by changing the
beginning temperature.
PW41
Practice
© Harcourt • Grade 5
Name
Lesson 7.1
Model Multiplication by a Whole Number
Complete the multiplication expression for each model. Find the product.
1.
2.
0.34 4
Use decimal models to find the product.
3. 0.27 6 4. 4 0.33 Find the product.
5. 0.08 5
6. 0.29 4
7. 0.17 6
8. 0.41 3
9. 3 0.73
10. 5 0.57
11. 0.84 3
12. 0.26 8
13. 7 0.31
PW42
Practice
© Harcourt • Grade 5
Name
Lesson 7.2
Algebra: Patterns in Decimal
Factors and Products
Use patterns to find the product.
1. 2.67 ⫻ 10 ⫽
2. 1.789 ⫻ 10 ⫽
3. 0.409 ⫻ 10 ⫽
2.67 ⫻ 100 ⫽
1.789 ⫻ 100 ⫽
0.409 ⫻ 100 ⫽
2.67 ⫻ 1,000 ⫽
1.789 ⫻ 1,000 ⫽
0.409 ⫻ 1,000 ⫽
Multiply each number by 10, 100, 1,000, and 10,000.
4. 0.8
5. $3.99
6. 6.014
7. n ⫻ 10 ⫽ 15.81
8. 1,000 ⫻ 0.067 ⫽ n
9. 23.7 ⫻ n ⫽ 237
10. 100 ⫻ n ⫽ 25.4
11. n ⫻ 937 ⫽ 93,700
Find the value of n.
12. 0.004 ⫻ 1,000 ⫽ n
Length of Planet Year
Problem Solving and Test Prep
USE DATA For 13–14, use the graph.
13. How many Earth years is
10 years on Jupiter?
14. How many Earth years is 1,000 years on
Planet
Length of Year
Mercury
0.241 Earth years
Venus
0.615 Earth years
Jupiter
11.862 Earth years
Saturn
29.457 Earth years
15. A blank CD costs $0.36. How much will
100 blank CDs cost?
Mercury?
A 0.000241 Earth years
B 0.0241 Earth years
C 241 Earth years
D 2,410 Earth years
PW43
Practice
© Harcourt • Grade 5
Name
Lesson 7.3
Record Multiplication by a Whole Number
Find and record the product.
1.
3.74
5
__
6. 61.3 4
2.
6.81
7
__
7. 22.09 5
3.
3.13
25
__
8. 48.2 36
4.
4.92
16
__
5.
9. 27.14 20
17.07
3
__
10. 6.067 19
Find the value of n.
11. 4.3 6 n
12. 6 n 16.8
13. 52.45 3 n
14. 4.1 n 24.6
Problem Solving and Test Prep
15. It takes the planet Pluto 247.68 Earth
16. Pluto’s orbital speed (average speed as
it revolves around the sun) is 2.93 miles
per second. How fast does Pluto travel
in one minute?
years to revolve around the sun. How
many Earth years does it take for Pluto
to revolve around the sun five times?
17. Ms. Salera’s class rode 3.8 miles to the
18. It takes the moon 29.5 days to go
observatory. The next closest
observatory is 13 times as far. How many
miles is the second observatory?
through all of its phases. How many days
does it take the moon to go through all
of its phases 30 times?
A 13 miles
B 49.4 miles
C 494 miles
D 4,940 miles
PW44
Practice
© Harcourt • Grade 5
Name
Lesson 7.4
Model Multiplication by a Decimal
Use the model to find the product.
1.
3.
2.
0.5 ⫻ 0.7 ⫽
0.7 ⫻ 0.7 ⫽
0.3 ⫻ 0.6 ⫽
Make a model to find the product.
4. 0.1 ⫻ 0.4 ⫽
5. 0.8 ⫻ 0.2 ⫽
6. 1.3 ⫻ 0.9 ⫽
7. 0.7 ⫻ 0.3 ⫽
8. 0.6 ⫻ 0.6 ⫽
9. 1.7 ⫻ 0.4 ⫽
Find the value of n.
10. 0.6 ⫻ 0.7 ⫽ n
11. 0.5 ⫻ n ⫽ 0.45
12. n ⫻ 1.2 ⫽ 0.24
13. 0.3 ⫻ n ⫽ 0.39
14. 0.4 ⫻ n ⫽ 0.12
15. 0.9 ⫻ 0.3 ⫽ n
16. 1.3 ⫻ 0.5 ⫽ n
17. n ⫻ 0.5 ⫽ 0.55
Find the product.
18. 0.8 ⫻ 0.4 ⫽
19. 0.3 ⫻ 0.3 ⫽
20. 0.9 ⫻ 0.6 ⫽
21. 1.4 ⫻ 0.5 ⫽
22. 1.8 ⫻ 0.2 ⫽
23. 1.1 ⫻ 0.1 ⫽
PW45
Practice
© Harcourt • Grade 5
Name
Lesson 7.5
Estimate Products
Estimate the product.
1.
6.
34
2.1
__
7.1
7.1
__
11. 352.4 0.46
2.
0.3
0.8
__
3.
0.7
0.9
__
4.
4.4
0.6
__
5.
7.
26.3
5.4
__
8.
1.78
3.2
__
9.
44.7
2.5
__
10.
12. 0.129 22.3
13. 7.035 61
5.5
6.2
__
$9.06
0.63
__
14. $8.99 12
Problem Solving and Test Prep
15. FAST FACT The fastest marine mammal, 16. Brittany earns $6.25 an hour working at
the killer whale, can swim 35 miles per
hour. How many miles can the whale
swim in 10.25 hours?
17. A Ross seal at the aquarium weighs
the concession stand. How much does
she earn in 7.5 hours?
18. A bottlenose dolphin eats an average
430.92 pounds. A leopard seal weighs
2.3 times as much. Which expression
gives the closest estimate for the weight
of the leopard seal?
A 3 431
C
2 431
2 430
D
3 430
B
PW46
of 155.75 pounds of fish per week.
How much does the dolphin eat in
4.5 weeks?
Practice
© Harcourt • Grade 5
Name
Lesson 7.6
Practice Decimal Multiplication
Find the number of decimal places in each product.
1. 0.004 0.005
2. $9 0.02
3. 1.007 0.13
4. 0.08 2.08
5. 2.56 0.11
6. 0.012 1.2
7. 0.06 1.5
8. 0.01 0.01
Estimate. Then find the product.
9.
0.12
0.8
__
13. 6.6 0.05
10. $13.00
11.
0.007
__
14. $2 0.04
0.006
8.1
__
15. 0.07 0.3
12.
0.44
0.05
__
16. 0.07 0.09
Problem Solving and Test Prep
17. Dustin has 8 guitar picks that are each
18. FAST FACT The smallest fish recorded
0.009 of an inch thick. What is the total
height of the guitar picks if they are
stacked on top of each other?
is the stout infantfish at 0.25 inch long.
How long is 0.05 of the fish?
19. A Brussels sprout weighs 0.0025 of a
20. A light guitar string is 0.016 of an
kilogram. How many kilograms do
4 sprouts weigh?
inch thick. A heavy guitar string is
2.25 times as thick. How thick is the
heavy string?
A 0.001 kilogram
A 0.036 in.
B
0.01 kilogram
B
0.36 in.
C
0.1 kilogram
C
3.6 in.
D 36 in.
D 1 kilogram
PW47
Practice
© Harcourt • Grade 5
Name
Lesson 7.7
Problem Solving Workshop Skill:
Multistep Problems
Problem Solving Skill Practice
Describe the steps required to solve. Then solve the problem.
1. The crew of a fishing boat is paid
2. A lobster boat captain pays its crew
$0.50 per pound of king crab,
$0.30 per pound of blue crab and
$0.25 per pound of snow crab. If the
four-member crew caught 310 lb of
king crab, 140 lb of blue crab and
284 lb of snow crab, how much money
did each member make?
$0.85 per pound of lobster caught.
The lobster is then sold to the store for
$2.95 per pound. If 649 pounds of
lobster were caught, how much money
did the captain earn, after paying the
crew?
Mixed Applications
Captain Jack’s Fishing Adventure
3. USE DATA How much will it cost for
two children and three adults to take a
12-hour fishing trip?
4. USE DATA Mr. Chopra paid $180 for
Age
Length of Trip
Cost
Children
6 hours
$35
Children
12 hours
$65
Adult
6 hours
$55
Adult
12 hours
$95
5. FAST FACT The penny weighs
2.5 grams, the nickel weighs 5 grams
and the dime weighs 2.268 grams. If
you have eight pennies, four nickels
and six dimes in your pocket, how
much weight are you carrying?
a 6-hour fishing trip. Including himself,
how many adults and children did
Mr. Chopra pay for?
PW48
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C07_L7.indd PW48
6/15/07 12:14:57 PM
Name
Lesson 8.1
Decimal Division
Use decimal models or play money to model the quotient.
Record your answer.
1. 1.8 3 2. 1.2 4 3. $1.52 4 4. 0.24 4 5. 1.5 5 6. 0.63 9 7. 0.36 3 8. $1.25 5 PW49
Practice
© Harcourt • Grade 5
Name
Lesson 8.2
Estimate Quotients
Find two estimates for the quotient.
1. 1.38 ⫼ 6
2. 2.93 ⫼ 9
3. 458.2 ⫼ 7
4. 324.9 ⫼ 5
5. 30.4 ⫼ 39
6. 83.4 ⫼ 88
7. 6.271 ⫼ 71
8. 2.874 ⫼ 89
Use compatible numbers to estimate the quotient.
9. 47.8 ⫼ 7
10. 0.518 ⫼ 9
11. 275.8 ⫼ 5
12. 34.21 ⫼ 3
13. 0.726 ⫼ 8
14. 579.2 ⫼ 8
15. 53.19 ⫼ 92
16. 138.9 ⫼ 19
17. 8.23 ⫼ 43
18. 46.3 ⫼ 72
19. 297.4 ⫼ 33
20. 27.49 ⫼ 29
Problem Solving and Test Prep
21. During an 8-hour storm, it snowed
22. The greatest snowfall for one day was
4.2 inches. Estimate the average hourly
snowfall during this storm.
23. Which shows how you can best use
measured in Georgetown, Colorado
on December 4, 1913. It snowed
63.0 inches in 24 hours. Estimate the
hourly snowfall during this storm.
24. Which shows how you can best use
compatible numbers to estimate
35.4 ⫼ 8?
compatible numbers to estimate
58.3 ⫼ 6?
A 32 ⫼ 8
A 54 ⫼ 6
B
35 ⫼ 8
B
56 ⫼ 7
C
38 ⫼ 9
C
58 ⫼ 6
D 40 ⫼ 8
D 60 ⫼ 6
PW50
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C08_L2.indd PW50
6/15/07 12:13:57 PM
Name
Lesson 8.3
Divide Decimals by Whole Numbers
Copy the quotient and correctly place the decimal point.
0088
085
259
1. 3
77.7
2. 8
0.704
3. 7
5.95
$134
4. 69
$92.46
Divide. Check by multiplying.
5. 3
81.3
9. 7.83 ⫼ 9
6. 36
46.44
10. $158.22 ⫼ 54
7. 49
1.274
8. 21
77.28
11. 2.208 ⫼ 8
12. 656.6 ⫼ 67
Problem Solving and Test Prep
13. The fastest swimming record was set by 14. The mako shark can swim more than
Tom Jager in a 50-meter race on
March 24, 1990. He swam at a rate of
137.4 meters per minute. How far did
Jager swim per second at this speed?
0.09 miles per minute for short amounts
of time. About how far can it travel in
one second at this speed?
16. The Gibsons paid $50.00 for a summer
15. 529.2 ⫼ 18.
pass to Playland. If they went 20 times
during the summer, what was the cost
of each visit to Playland?
A 0.294
B
2.94
C
29.4
A $0.25
C
$25.00
D
294
B
$2.50
D
$250.00
PW51
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C08_L3.indd PW51
6/15/07 12:13:07 PM
Name
Lesson 8.4
Problem Solving Workshop Skill: Evaluate Answers
for Reasonableness
Problem Solving Skill Practice
1. Luis has 4 bottles of grape juice. Each
2. Angela bought 1.65 pounds of green
bottle contains 64.3 ounces of juice.
Luis says he has a total of 250 ounces of
grape juice. Ana says Luis has a total of
150 ounces of grape juice. Use
estimation to find whose answer is
reasonable. Explain.
peppers, 0.78 pounds of cucumbers, a
squash that weighs 4.32 pounds, and a
head of lettuce that weighs 0.33 pounds.
Angela says she bought 7.08 pounds of
vegetables. Tom says that Angela
bought 70.8 pounds of vegetables. Use
estimation to find whose answer is
reasonable. Explain.
Mixed Applications
USE DATA For 3–4, use the table.
3. Hideko says 1 U. S. dollar equals
Currency Exchange Rates
(April 2006)
27.73 Russian rubles. David says
1 U. S. dollar equals 2.773 Russian
rubles. Whose answer is reasonable?
U. S. Dollars
Currency
3
19.179 Australian Dollars
4
3.3 European Union (EU) Euros
6
706.8 Japanese Yen
14
388.22 Russian Ruble
18
139.662 Hong Kong Dollars
4. Suppose you exchange 200 U. S. dollars
5. John has 4.1 pizzas. He gave 2.7 pizzas
for EU euros. How many euros will you
receive? Which operation(s) did you use
to solve?
away. How many pizzas does John have
left? Is your solution an estimate or an
exact answer?
PW52
Practice
© Harcourt • Grade 5
Name
Lesson 9.1
Collect and Organize Data
A movie maker wants to find out what type of movies children ages 9–13 like to watch.
Tell whether each sample represents the population. If it does not, explain.
1. a random sample of
400 boys, ages 9–13
2. a random sample of
3. a random sample of
400 children, ages 9–13
400 teachers
Make a line plot. Find the range of hours.
4.
Volunter Hours Survey
Number of Hours
Frequency
2
4
4
10
5
6
7
2
Problem Solving and Test Prep
USE DATA For 5–6, use the tally table.
5. Tammy surveyed her classmates to find
out their favorite subjects. Which subject
has the greatest frequency?
Favorite Subjects
Spelling
Reading
6. What is the range of the data Tammy
Science
collected about her classmates’ favorite
subjects?
7. Which is the range for the following set
Math
Social Studies
8. Which set of data has a range
of data: 14, 9, 11, 21, 7?
of 15?
A 11
A 4, 9, 2, 15, 18
B
12
B
9, 5, 20, 3, 25
C
13
C
8, 2, 15, 13, 17
D 14
D 5, 20, 7, 14, 21
PW53
Practice
© Harcourt • Grade 5
Name
Lesson 9.2
Mean, Median, and Mode
Find the mean, median, and mode for each set of data.
1. 7, 9, 12, 9, 13
2. $18, $17, $22, $17
3. 1,024; 854; 720
4. 112, 130, 121, 109, 125
5. 9, 5, 10, 14, 7, 14, 11
6. 3.5, 5.4, 7, 6.4, 5.4, 3.8
7. 7, 12, 16, 7
8. $24, $17, $22
9. 45, 55, 25, 45, 75
10. 6.5, 3.4, 8.1, 9.4
ALGEBRA Use the given mean to find the missing number in each data set.
11. 14, 16, 18, 12,
; mean: 15
12. 36, 24,
, 16; mean: 24
Problem Solving and Test Prep
USE DATA For 13–14, use the table.
Moreau Little League Team
13. What is the mean number of runs for the
Moreau Little League team?
14. Reasoning How would the mean for
exercise 13 change if Game 3 had 8 runs?
15. What is the mode for the set of data?
C
28
1
5
2
2
3
4
4
5
for a set of data with an even number
of data values.
A 13
27
Number of Runs
16. Explain how you can find the median
31, 27, 26, 25, 31
B
Game
D 31
PW54
Practice
© Harcourt • Grade 5
Name
Lesson 9.3
Compare Data
Compare the mean, median, and range of the data sets.
1.
A: Number of stamps collected
B: Number of stamps collected
13
6
2.
25
19
32
66
22
19
Monday Homework Problems
2
3
6
2
6
3
4
5
4
13
21
20
15
13
24
Tuesday Homework Problems
5
10
4
2
5
3
4
6
9
6
1
Problem Solving and Test Prep
3. Reasoning Hannah and Tyler count the
4. Two data sets have different ranges
number of times the word what occurs.
Hannah’s data has a mean of 2.7 times.
What could Tyler’s mean be if his results
are similar?
and medians. Is the data in the data
sets similar or different? Explain.
5. Which shows how the median for the
6. Which shows how the mean for the
sets of data compare?
sets of data compare?
Baseball Cards Saved
111
101
Group A Pages Read
149
47
Football Cards Saved
124
87
A 111 ⫽ 111
B
111 ⬎ 98
98
33
52
36
Group B Pages Read
132
42
39
47
28
C
48 ⬎ 45
A 52 ⬎ 47
C
34.5 ⬍ 40.5
D
120.3 ⬎ 110.3
B
19 ⫺ 19
D
42 ⬎ 39
PW55
Practice
© Harcourt • Grade 5
Name
Lesson 9.4
Analyze Graphs
For 1–3, use the double-bar graph.
1. Which class period has the least number
Left-handed and Right-handed
Students
2. Which two class periods have the same
number of students?
Number of Students
of right-handed students?
18
16
14
12
10
8
6
4
2
0
3. What is the total number of left-handed
Left-handed
Right-handed
1
students in all four class periods?
2
3
Class Period
4
Problem Solving and Test Prep
4. Which sport has the greatest number
Favorite sport
of votes?
Soccer
Tennis
Key: Each
⫽ 3 votes.
5. How many total votes are there for
soccer and tennis?
6. A line graph shows a trend of less rain
7. Look at the double-bar graph at the top
this week than 2 weeks ago. Explain
what the line graph might look like.
of the page. Which statement about the
graph is NOT true?
A Class period 2 has the least students.
B
Class period 1 has 14 left-handed
students.
C
The median number of right-handed
students is 15.
D The median number of left-handed
students is 11.
PW56
Practice
© Harcourt • Grade 5
Name
Lesson 9.5
Problem Solving Workshop Strategy:
Draw a Diagram
Problem Solving Strategy Practice
Draw a Venn diagram to solve.
2. During a free period, 7 students used
1. Nine students wrote reports about
photosynthesis, 7 students wrote
reports about transport tissues in
plants, and 3 students wrote about
photosynthesis and transport tissues
in plants. How many students wrote
reports?
the computers, 8 students played board
games, and 4 students used the
computer and played board games.
How many students used the computer
and/or played board games during the
free period?
Mixed Strategy Practice
For 3–4, use the table.
3. Hank spent $26.06 on two supplies.
Which two supplies did he buy?
Science Supplies Sale
Science Supply
4. Madison bought the most expensive
item. Jerry bought safety goggles and a
ruler. How much more did Madison
spend than Jerry spent?
5. Twenty students each checked out a book
Price
Ruler
$2.39
Tongs
$11.50
Graduated Cylinder
$8.71
Hand Lens
$19.95
Safety Goggles
$14.56
6. Nora records the number of insects for
at the library. Eleven students checked out
history books. Five students checked out
biographies. The rest of the students
checked out novels. How many students
checked out novels? Show your work.
PW57
8 days. Day 1: 14 insects; Day 2: 28
insects; Day 3: 42 insects; Day 4: 56
insects. If the pattern continues to
increase this way, how many insects will
there be on day 8?
Practice
© Harcourt • Grade 5
Name
Lesson 10.1
Make Bar Graphs and Pictographs
For 1–2, use the graph at the right.
1. What scale and interval are used in the
bar graph?
2. How would the bars in the graph change
if the interval were changed to 10. Explain.
Number of Pets
Joe’s Pet Store
35
25
20
15
10
5
0
Rabbit
Cat
Dog
Hamster
Pets
Make a graph for the data set.
3.
Favorite Books
Book Type
Number of Votes
Mystery
35
Fantasy
15
Poetry
10
Sports
40
Problem Solving and Test Prep
USE DATA For 4–6, use the table.
4. Did the students have more CDs or
Number of CDs and Movies
more DVDs? How many more?
Name
5. What is a reasonable scale and interval
to graph the data?
Number of CDs Number of DVDs
Chuck
10
2
Emily
14
5
Tim
13
2
6. Make a double-bar graph for the data in
the space at the right.
7. Which interval would you use to make a
bar graph for the following data: 60, 55,
40, 35, and 65?
A 2
B
25
C
10
D
5
PW58
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C10_L1.indd PW58
6/15/07 1:01:08 PM
Name
Lesson 10.2
Make Histograms
For 1–2, use the table.
2. Make a histogram of the data.
Laps Swam In The Pool
12
24
32
31
22
10
17
25
14
21
19
20
9
14
8
17
15
21
40
30
19
16
30
23
21
1. What is a reasonable interval for the
laps swam in the pool?
For 3–4, decide whether a bar graph or a histogram would
better represent the data. Then make the graph.
3.
4.
Weight
(in pounds)
Number of Adult
Dogs
Red
16
43–45
3
Blue
23
46–48
8
Black
14
49–51
10
Color of Bicycle
Number of Bicycles
Problem Solving and Test Prep
USE DATA For 5–6, use the graph.
Ages of One-Mile Runners
Number of Runners
5. How many runners in all are in the age
groups 4–5 and 12–13?
6. How many people ran in the race?
7. How many runners are 10–11 years
8
6
4
2
0
4-5
6-7
8-9
Ages
10-11
12-13
8. How many runners are 6–7 years old?
old?
A 4
C
7
A 2
6
D
8
B
B
PW59
6
C
7
D 10
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C10_L2.indd PW59
6/15/07 12:50:00 PM
Name
Lesson 10.3
Algebra: Graph Ordered Pairs
Use the coordinate grid at the right. Write an ordered pair for each point.
1. A
y
2. B
10
3. C
4. D
A
9
D
B
8
7
Graph and label each point on the
coordinate grid at the right.
5.
E (4, 5)
6
5
4
6. F (2, 9)
3
2
7. G (8, 5)
8. H (3, 3)
1
C
0
1
9. I (0, 10)
2
4
3
5
x
6
7
8
9 10
10. J (7, 1)
y
N
10
Problem Solving and Test Prep
W
9
USE DATA For 11–14, use the map.
Each unit represents 1 city block.
E
8
S
7
11. What ordered pair gives the location for
the Playground?
Library School
6
5
F
4
D
3
12. What is the distance between Home and
the Theater?
Playground
2
Theater
Home
1
x
0
1
13. Use the map above. Suppose a museum
2
3
4
5
6
7
8
9 10
14. Use the map above. Suppose a gym is
is located at point D. What ordered pair
locates this point?
located at point F. What ordered pair
locates this point?
A (3, 2)
A (8, 4)
B
(2, 1)
B
(7, 4)
C
(1, 2)
C
(8, 3)
D (2, 3)
D (8, 5)
PW60
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C10_L3.indd PW60
6/15/07 12:49:46 PM
Name
Lesson 10.4
Make Line Graphs
USE DATA For 1–2, use the table.
1. What would be an appropriate scale and
Weights of 2 Kittens (Cutie and Magic)
interval to graph the data?
Month
0
1
2
3
Cutie
2
6
11
31
Magic
2.5
5
11.5
34
Weights of Cutie and Magic
2. Write the related pairs for the weights of
Cutie and Magic as ordered pairs.
3. In the box at the right, make a double-line
graph of the data.
Problem Solving and Test Prep
USE DATA For 4–7, use the table.
4. What is the range in the number of
inches in height for the first 7 years?
Tommy’s Height
5. Between which years in the table did
Tommy grow the most?
6. What would be an appropriate scale and
Age (years)
1
3
5
7
Height (in.)
29
34
37
43
7. Suppose you made a line graph of this
interval to graph this data?
data, which best describes the line from
age-1 to age-7?
A It goes up.
B
It goes down.
C
First it goes down, and then it goes up.
D First it goes up, and then it goes
down.
PW61
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C10_L4.indd PW61
6/28/07 1:11:01 PM
Name
Lesson 10.5
Make Circle Graphs
Use the data to make a circle graph.
1.
Fruit
50
Orange
20
Banana
20
Pear
10
Celine's Paycheck
Celine’s Paycheck
Item
4.
Number
Apple
2.
3.
Favorite Fruits
Students’ Favorite Fruits
Cost
Food
$35
Clothing
$20
Transportation
$15
Savings
$30
Ice Cream Orders
Ice Cream Flavors Ordered
Flavor
Number
Chocolate
4
Vanilla
3
Strawberry
1
Rocky Road
2
Pistachio
2
Art Club Earnings From Bake Sale
Item Sold
Earnings
Cupcakes
$50
Crumb Cake
$20
Muffins
$15
Juice
Cookies
Art Club Bake Sales
$5
$10
PW62
Practice
© Harcourt • Grade 5
Name
Lesson 10.6
Problem Solving Workshop
Strategy: Make a Graph
Problem Solving Strategy Practice
For 1–2, make and use a graph to solve.
1. Sarah’s bowling team recorded the scores
from their last tournament. Which group
of scores had the most scores:
70–79, 80–89, 90–99 or 100–109?
Sarah’s Team Bowling Scores
78
99
81
84
92
101 76
90
88
93
75
94
98
71
96
104 97
82
80
88
2. The high temperatures in May were
recorded for 20 years in San Jose, CA. What
is the mean, median, and mode of the data?
May High Temperatures in
San Jose(°F)
72
73
74
74
84
78
71
69
83
79
72
80
71
74
68
69
68
81
79
77
Mixed Strategy Practice
3. Paula has 1.5 times as many novels as
4. Pose a Problem Look back at
Problem 1. How would your graph
change if there were no scores above
93? Explain.
Carly. Carly has 12 novels. How many
novels does Paula have? Show
your work.
PW63
Practice
© Harcourt • Grade 5
Name
Lesson 10.7
Choose the Appropriate Graph
Choose the best type of graph or plot for the data. Explain your choice.
1. Hours Raul worked each
2. Number of library books
of the past 6 days
3. Water evaporated over
borrowed by 30 people
10 days
Draw the graph or plot that best displays each set of data.
Tell whether the data is categorical or numerical.
4.
5.
Paul’s Vacation Budget
Weather Service Almanac
Activity
Amount
Month
Rainfall (inches)
Food
$9
May
16
Rides
$7
June
22
Souvenirs
$5
July
18
Problem Solving and Test Prep
USE DATA For 6–7, use the table below.
Visitors To The Alamo By
The Minute
6. What graph would best represent this data?
7. Is the data in the table categorical or
numerical?
8. What type of graph would best display the
Test Scores
92
95
87
100
88
75
93
97
Visitors
1
14
2
30
3
45
4
65
9. What set of data is categorical?
data in table? Explain.
100
84
Minute
100
93
PW64
A Runs scored by the team in 5 games
B Items Ralph spent his allowance on
C High temperature each month for
6 months
D Votes given 10 congressman in
January
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C10_L7.indd PW64
6/15/07 12:50:28 PM
Name
Lesson 11.1
Multiples and the Least Common Multiple
List the first ten multiples of each number.
1. 5
2. 10
3. 7
4. 3
5. 9
Write the least common multiple of each set of numbers.
6. 2 and 4
7. 5 and 8
8. 8 and 6
9. 18, 3, 6
10. 3, 2, 7
Problem Solving and Test Prep
USE DATA For 11–12, use the table.
Packs of Marbles
11. What are the least numbers of packs of
Color of Marble
yellow marbles and blue marbles a person
would have to buy to have the same number
of each color of marble?
Number per Pack
Yellow
2
Green
4
Blue
3
Orange
6
12. What are the least numbers of packs of green marbles, blue marbles, and orange
marbles a person would have to buy to have the same number of each color of
marble?
13. Which set of numbers has an LCM
14. Which set of numbers has an LCM
of 36?
of 12?
A 5, 13, 18
A 2, 3, 5
B
4, 6, 18
B
4, 6, 8
C
6, 12, 18
C
1, 5, 12
D 6, 12, 16
D 2, 4, 6
PW65
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C11_L01.indd PW65
6/15/07 2:25:18 PM
Name
Lesson 11.2
Divisibility
Test each number to determine whether it is divisible by 2, 3, 5, 6, 9, or 10.
1. 571
2. 4,023
3. 43,104
4. 21,900
5. 6,305
6. 31,089
7. 83,292
8. 7,938
9. 15,846
10. 4,950
11. 956
12. 5,840
13. 8,846
14. 19,992
15. 15,804
Write true or false.
16. All odd numbers are divisible by 2.
17. All multiples of 7 are divisible by 7.
18. All even numbers are divisible by 4.
19. All numbers ending in 0 are
divisible by 10.
PW66
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C11_L02.indd PW66
6/15/07 2:25:09 PM
Name
Lesson 11.3
Factors and Greatest Common Factor
List the factors of each number.
1. 49
2. 19
3. 36
4. 56
5. 24
Write the common factors for each pair of numbers.
6. 11, 15
7. 16, 20
8. 13, 26
9. 5, 10
10. 22, 24
Write the greatest common factor for each pair of numbers.
11. 12, 36
12. 21, 56
13. 14, 21
14. 8, 24
15. 15, 25
Problem Solving and Test Prep
USE DATA For 16–17, use the table.
16. Sharon is dividing her green and blue
Sharon’s Rock Collection
rock collection into bags. Each bag
will contain the same number of each
color of rock. How many rocks of each
color will be in each bag?
Color
Number of Rocks
Red
12
Yellow
28
Green
16
Blue
24
17. Sharon also divides her red and yellow rocks into bags. Each bag will contain the same
number of each color of rock. How many bags will Sharon need?
18. The greatest common factor of 28
19. Which number is not a common factor
of 42 and 21?
and another number is 7. The second
number is between 60 and 70. What
is it?
A 7
C
21
6
D
3
B
PW67
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C11_L03.indd PW67
6/15/07 2:25:00 PM
Name
Lesson 11.4
Prime and Composite Numbers
Write prime or composite. You may use counters or draw arrays.
1. 12
2. 37
3. 44
4. 28
5. 35
6. 122
7. 61
8. 72
9. 89
10. 56
11. 49
12. 59
13. 101
14. 75
15. 88
16. 14
17. 83
18. 109
19. 36
20. 65
21. 111
PW68
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C11_L04.indd PW68
6/15/07 2:25:27 PM
Name
Lesson 11.5
Problem Solving Workshop Strategy:
Make an Organized List
Problem Solving Strategy Practice
Use an organized list to solve.
1. During the month of May, Jean has
2. Students are making picture frames.
photography class every third day and a
photography show every Saturday. On May 5
she has class and a show. During the month
of May, how many more times will she have
a class and a show on the same day? There
are 31 days in May.
They can choose from a brown or
black picture frame, and a red, yellow,
blue, or green matte. How many
different picture frame and matte
combinations can the students make?
Mixed Strategy Practice
3. USE DATA Complete the graph. Use the
clues below to find the missing data in the
graph.
Clue 1: The least favorite type of book is
fantasy.
Clue 2: Mystery books are favored by 10%
more students than western books.
Which Type Of Book Is
Your Favorite
Western,
20%
______ ,
10%
4. Carl spent $51.33 on three opera tickets.
How much did each ticket cost? Show your
work.
Adventure
24%
Humor,
16%
Mystery,
______
____
5. Robin has 7 red beads, 27 purple beads, and 24 yellow beads. She wants to make a
necklace with the pattern: 1 red bead; 3 purple beads; 2 yellow beads. How many
times can she repeat the pattern? Which color of beads will she run out of first?
PW69
Practice
© Harcourt • Grade 5
Name
Lesson 11.6
Introduction to Exponents
Write in exponent form.
1. 10,000,000
2. 1,000
3. 10
4. 100,000,000
5. 103
6. 108
7. 104
8. 106
9. 105
10. 102
11. 107
12. 101
Find the value.
ALGEBRA Find the value of n.
13. 102 n
14. 107 n
15. 105 n
Problem Solving and Test Prep
17. Kelly read the odometer on her
16. Aaron earned $10 each week for
10 weeks of picking up garbage. Kimberly
earned $10 each week for 10 weeks of
walking dogs. How much money did they
earn altogether?
18. Which number represents
parents’ car. She wrote down
105 miles. How many miles are shown
on the odometer?
19. Which number represents
10 10 10?
10 10 10 10 10 10?
A 10
A 103
0
B
101
B
106
C
102
C
104
D 103
D 107
PW70
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C11_L06.indd PW70
6/15/07 2:24:52 PM
Name
Lesson 11.7
Exponents and Square Numbers
Write in exponent form. Then find the value.
1. 5 5 5
2. 2 2
3. 8 8 8 8
4. 4 4 4 4 4
Find the value.
5. 122
10. 83
6. 55
7. 73
8. 18
11. 46
12. 32
13. 113
9. 115
14 57
Compare. Write ,, ., or ⴝ.
15. 53
23
16. 22
41
17. 54
78
18. 62
93
Problem Solving and Test Prep
USE DATA For 19–20, use the pattern in the table.
19. James earned 729 pennies. How many
plates did James wash in all?
Pennies Earned
20. What number in exponent form
represents the number of pennies James
would earn for washing 11 plates? How
many pennies would he earn for washing
11 plates?
21. Which is greater than 92?
Number of plates
washed
Pennies
Exponent
form
Start
1
30
1
3
31
2
9
32
3
27
33
22. What is the greatest square number
that is even and is less than 300? What
is the value of this square number?
A 2
7
43
C 52
D 41
B
PW71
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C11_L07.indd PW71
6/28/07 1:12:26 PM
Name
Lesson 11.8
Prime Factorization
1. Draw a factor tree to find the
prime factorization of 48. Write
the prime factorizaton.
Find the prime factorization. You may use a factor tree.
2. 4
3. 100
4. 155
5. 21
Rewrite the prime factorization by using exponents.
6. 2 ⫻ 5 ⫻ 7 ⫻ 2
7. 3 ⫻ 3 ⫻ 7 ⫻ 3 ⫻ 7
8. 19 ⫻ 19 ⫻ 19 ⫻ 19
Find the number for each prime factorization.
9. 3 ⫻ 73
13. 11 ⫻ 2 ⫻ 2
10. 5 ⫻ 5 ⫻ 5 ⫻ 3
11. 52 ⫻ 112
12. 2 ⫻ 2 ⫻ 19
14. 82 ⫻ 23
15. 32 ⫻ 63
16. 2 ⫻ 5 ⫻ 5 ⫻ 5
Problem Solving and Test Prep
17. The prime factors of a number are the
18. The prime factors of Patrick’s favorite
number are 2, 7, and 3. Two is repeated
once. What is Patrick’s favorite number?
first four prime numbers. No factor is
repeated. What is the number?
19. Which numbers are two of the prime
20. What is the least number that is the
factors of 36?
product of two different primes that are
squared?
A 2 and 3
B
11 and 3
C
5 and 2
D 4 and 13
PW72
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C11_L08.indd PW72
6/15/07 2:25:34 PM
Name
Lesson 12.1
Understand Fractions
Write a fraction for the shaded part. Write a fraction for the unshaded part.
1.
2.
3.
4.
Write a fraction to name the point on the number line.
5.
6.
7.
0
I
H
G
0
1
1
Write the fraction for each.
8. four fifths
9. five divided by ten
10. one sixth
0
1
11. two out of 9
Problem Solving and Test Prep
12. A basket of fruit has 3 apples, 2 pears,
13. A delivered pizza came cut in 6 equal
and 4 bananas. What fraction of the fruit
are bananas?
14. What fraction of the stars are gray?
slices. Mark ate 2 slices. Now 4 slices
remain. What fraction of the pizza did
Mark eat?
15. What fraction of the
triangles are gray?
1
A __
5
1
B __
4
C
D
1
A __
2
3
B __
5
3
__
4
4
__
5
PW73
C
D
3
__
8
5
__
8
Practice
© Harcourt • Grade 5
Name
Lesson 12.2
Equivalent Fractions
Write an equivalent fraction.
1
1. __
8
7
2. ___
10
4
3. __
5
6
4. __
8
3
5. __
4
1
6. __
3
3
7. __
6
8
8. ___
12
6
9. __
9
10
10. ___
15
10
11. ___
16
5
12. __
6
Tell which fraction is not equivalent to the others.
5 2 6
1 5 3
2 1 4
13. __, ___, __
14. __, __, ___
15. ___, __, ___
2 15 9
6 4 12
9 3 2
16. ___, __, __
12 4 5
10 3 12
Problem Solving and Test Prep
USE DATA For 17–18, use the table.
17. Natalie asked people which of the six
colors in the chart they preferred. What
four equivalent fractions show the
fraction of people who chose red?
Preferred Colors
18. Natalie asks 4 more people their
opinion, and they all say blue.
Now, what three equivalent fractions
show the fraction of people who
chose red?
19. Which fraction is equivalent to 2_5 ?
3
A ___
10
4
B ___
10
7
C ___
10
3
D __
5
Color
Number of People
Who Chose It
Orange
1
Red
4
Purple
2
Blue
3
Green
1
Yellow
1
__ ?
20. Which fraction is equivalent to 14
16
7
A __
8
7
B __
9
4
C __
6
2
D ___
16
PW74
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C12_L2.indd PW74
6/28/07 1:14:02 PM
Name
Lesson 12.3
Simplest Form
Name the GCF of the numerator and denominator.
3
2. __
4
___
1. 14
16
___
3. 12
36
9
4. ___
30
10
5. ___
25
16
9. ____
100
___
10. 24
30
Write each fraction in simplest form.
8
6. ___
22
___
7. 17
34
28
8. ___
77
10
11. ___
10
9
12. ___
16
20
13. ___
60
36
14. ___
45
___
15. 12
57
10
16. ___
24
15
17. ___
25
32
18. ___
40
70
19. ____
100
48
20. ___
60
Problem Solving and Test Prep
21. Fast Fact Eight states border one or
22. Twenty out of 75 salon clients made an
more of the five Great Lakes. Write a
fraction representing the part of the
50 states that border a Great Lake.
Write the fraction in simplest form.
21
23. Which fraction shows ___ in simplest
28
appointment for a haircut. What fraction
of the clients made a haircut
appointment? Write the fraction in
simplest form.
24. Twelve of 30 students rode the bus
form?
1
A __
B
C
D
today. What fraction of the students rode
the bus? Write the fraction in simplest
form.
8
1
__
7
3
__
7
3
__
4
PW75
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C12_L3.indd PW75
6/15/07 12:55:00 PM
Name
Lesson 12.4
Understand Mixed Numbers
Write each mixed number as a fraction. Write each fraction as a mixed number.
7
1. 1 __
8
10
2. ___
9
27
3. ___
4
4
4. 3 __
5
41
7. ___
10
41
8. ___
8
61
9. ___
3
9
10. 5 ___
10
1
11. 3 __
9
39
12. ___
5
3
13. 4 __
7
21
14. ___
4
57
15. ___
7
5
16. 8 __
6
4
17. 9 __
9
41
18. ___
6
2
19. 7 __
3
3
20. 6 ___
10
2
21. 4 ___
15
31
22. ___
4
16
23. ___
5
35
24. ___
6
11
5. 1 ___
15
1
6. 4 ___
12
Problem Solving and Test Prep
25. How many times will Gayle fill a 1_2 -cup
26. A recipe calls for 2 3_4 cups of milk.
27. Which fraction is the same as 2 4_5 ?
23
28. Which mixed number is the same as ___?
4
3
A 2 __
4
1
B 3 __
2
1
C 4 __
4
3
D 5 __
4
ladel to serve 8 1_2 cups of punch?
8
A __
5
9
B __
5
14
C ___
5
24
D ___
5
What is 2 3_4 written as a fraction?
PW76
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C12_L4.indd PW76
6/15/07 12:54:53 PM
Name
Lesson 12.5
Compare and Order Fractions and Mixed Numbers
Compare. Write ⬍, ⬎, or ⴝ for each
_5_
9
1. _4_
9
3
__
7
5
6. ___
12
6
7. ___
10
__
35
4
11. 3 __
5
6
8
3. ___
12
2
__
3
6
8. 1__
9
__
22
5
9. 4 __
8
__
43
4
2
10. 9 __
6
__
83
4
13. 4 __
6
__
33
1
14. 8 __
3
__
83
3
15. 6 __
8
__
61
_3_
5
3
2. __
4
2
12. 1___
10
4
__
5
1_1_
5
.
_4_
7
5
4. __
8
3
4
8
__
9
9
5. ___
11
5
9
4
Write in order from least to greatest.
3 3 1
16. __, __, __
8 4 4
5 3 5
18. 1__, 1__, 1__
8 4 6
2 __
__
17. __
, 1, 7
3 6 9
3 2
6
19. 7 __, 6 __, 6 ___
5 3 10
Problem Solving and Test Prep
USE DATA For 20–21, use the table.
20. Len paints and sells wooden flutes. List
the flutes in order from shortest to
longest.
Len’s Flutes
Flute Name
21. Len created a new flute that is
6 _23
inches
long. Which, if any, of his flutes are
longer?
22. Kayla practiced violin 2 1_4 hours on
3
Monday, 2 __
10 hours on Tuesday, and
1 4_9 hours on Wednesday. On which day
did she practice the longest?
A Tuesday
B
Friday
Length, in inches
Lily
6
3
4
Rose
6
5
8
Ivy
6 127
23. Dean practiced trombone 1 2_3 hours on
7
Monday, 1 __
12 hours on Tuesday, and
1 7_9 hours on Wednesday. On which day
did he practice the longest?
C
Monday
A Tuesday
D
Wednesday
B
PW77
Wednesday
C
Monday
D
Saturday
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C12_L5.indd PW77
6/15/07 12:55:09 PM
Name
Lesson 12.6
Problem Solving Workshop Strategy: Make a Model
Problem Solving Strategy Practice
Make a model to solve.
1. From home, Todd walked 3 blocks
2. Kayla is putting up a picket fence on
south and 2 blocks east to a friend’s
house. Then they walked 6 blocks west
to school. He cannot cut across blocks.
How many blocks from school does
Todd live?
one side of her garden. Each picket is
4 inches wide and 2 inches apart. She
has 12 pickets. How many inches long
will Kayla’s fence be?
Mixed Strategy Practice
Solve.
3. Lisa spent 10 minutes driving to the
4. Pose a Problem Look back at
grocery store and 50 minutes shopping
there. She spent 10 minutes driving
back home and 40 minutes making
sandwiches for a picnic. She drove
30 minutes from home and arrived at
the picnic at 3:30 P.M. What time did
Lisa leave to go to the grocery store?
Excercise 1. What if Todd and his friend
had only walked 5 blocks west to
school? How many blocks would Todd
live from school then?
5. A city garden is in the shape of a
rectangle. There is a walkway from
each corner of the rectangle to every
other corner of the rectangle. How
many walkways are there? Draw a
diagram in the space at the right
to solve.
PW78
Practice
© Harcourt • Grade 5
Name
Lesson 12.7
Relate Fractions and Decimals
Write each decimal as a fraction or mixed number in simplest form.
1. 0.33
2. 0.06
3. 0.625
4. 0.35
6. 1.05
7. 1.1
8. 1.12
9. 2.525
11. 3.700
12. 0.205
13. 0.025
5. 0.900
10. 4.08
14. 4.98
15. 8.25
Write each fraction or mixed number as a decimal.
7
16. _____
1000
8
17. ____
100
3
18. ___
10
9
19. ___
20
40
20. ___
50
6
21. 1 ___
25
27
22. 9 ___
45
6
23. 5 ___
15
13
24. 2 ___
50
36
25. 3 ___
40
Problem Solving and Test Prep
26. A player’s batting average is 0.425.
27. Kevin hit in 9 out of 40 at bats. What
What fraction is equivalent to 0.425?
28. Which fraction is NOT equivalent
to 0.8?
4
A __
5
8
B ___
10
is his batting average?
4
29. What decimal is equivalent to 1__?
5
12
C ___
15
3
D __
4
PW79
A 1.8
C 1.5
B 1.4
D 1.3
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C12_L7.indd PW79
6/15/07 12:55:19 PM
Name
Lesson 13.1
Add and Subtract Like Fractions
Find the sum or difference. Write it in simplest form.
1
1
1. __ ⫹ __
4
4
2
1
2. __ ⫹ __
7
7
3
1
3. __ ⫺ __
5
5
3
2
4. __ ⫹ __
7
7
5
7
5. __ ⫺ __
8
8
7
2
6. ___ ⫹ ___
10
10
3
4
7. __ ⫺ __
9
9
4
1
8. __ ⫺ __
6
6
3
3
9. __ ⫹ __
8
8
2
1
10. __ ⫹ __
5
5
8
5
11. ___ ⫺ ___
10
10
1
2
12. __ ⫹ __
6
6
9
3
13. ___ ⫺ ___
12
12
2
1
14. __ ⫺ __
4
4
3
5
15. ___ ⫹ ___
10
10
Problem Solving and Test Prep
_ of the world’s
16. Glaciers currently store 2
3
_1
3
17. When an iceberg floats in a body of
water, 1_7 of the mass can be seen above
water. How much of the iceberg
remains beneath the surface of the
water?
freshwater supply. If of those glaciers
melted, how much would be left in
glacier form?
18. Iceberg Alley is where bergs from the
19. Icebergs are usually white from millions
glaciers of Greenland drift down to
3
Newfoundland. If an iceberg floats __
10
5
mile in January, and __
10 mile in February,
how far should it travel in order for the
iceberg to have drifted 1 mile by March?
of tiny air bubbles trapped in the ice
with occasional blue streaks. If 5_8 of an
iceberg is white, how much of the
iceberg is streaked with blue?
A
2
__
10 mile
3
A __
8
B
_1
5
mile
B
2
__
8
C
1 mile
C
5
__
8
3
D 1__
8
D 1 1_2 miles
PW80
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C13_L1.indd PW80
6/15/07 12:50:12 PM
Name
Lesson 13.2
Model Addition of Unlike Fractions
Find the sum. Write it in simplest form.
1.
1
2
1
__
__ 5
2
8
1
8
1
8
1
8
1
8
1
8
2.
1
5
1
5
1
5
1
4
3
__
__ 1
5
4
3.
1
2
1
5
1
__
__ 1
5
2
Find the sum using fraction bars. Write it in simplest form.
1
4
4. __ ___ 5
10
3
1
5. __ ___ 2
10
5
2
6. __ __ 6
3
1
2
7. __ __ 3
4
1
1
8. __ __ 2
8
1
1
9. __ __ 3
2
5
2
10. __ __ 8
5
5
3
11. __ __ 8
4
3
2
12. __ __ 4
3
1
3
13. __ __ 5
2
3
2
14. __ __ 6
9
5
1
15. __ ___ 4
12
1
2
16. __ __ 2
6
6
1
17. ___ __ 10
3
3
1
18. ___ __ 12
4
PW81
Practice
© Harcourt • Grade 5
Name
Lesson 13.3
Model Subtraction of Unlike Fractions
Use fraction bars to find the difference. Write it in simplest form.
5
2
1. __ __ 6
3
1
6
1
6
1
3
3
1
2. __ __ 5
4
1
6
1
6
1
3
1
6
?
1
4
5
1
3. __ __ 8
4
1
4
1
5
1
8
1
4
1
8
1
8
1
4
?
1
8
1
8
?
Find the difference using fraction bars. Write it in simplest form.
2
2
4. __ ___ 5
10
1
1
5. __ ___ 2
12
7
1
6. __ __ 8
2
3
4
7. __ __ 4
6
2
1
8. __ __ 5
3
6
1
9. __ __ 7
2
3
4
10. __ ___ 5
10
7
1
11. ___ __ 12
3
1
1
12. __ ___ 4
10
3
7
13. __ __ 8
8
5
1
14. __ __ 7
2
8
1
15. __ __ 9
3
4
1
16. ___ __ 10
4
6
1
17. __ __ 7
3
3
1
18. __ __ 4
2
PW82
Practice
© Harcourt • Grade 5
Name
Lesson
Lesson13.4
8.3
Estimate Sums and Differences
Estimate each sum or difference.
5
1
1. __ __
7
4
3
1
2. __ __
7
6
8
2
3. __ __
5
9
10
6
4. ___ __
11
9
7
1
5. __ __
8
2
3
2
6. __ __
5
8
6
3
7. __ __
7
4
5
1
8. __ __
8
6
9
1
9. ___ __
12
9
5
4
10. __ __
5
8
Estimate to compare. Write , or . for each
6
1
11. __ __
5
7
1
3
7
12. ___ ___
11
10
.
4
1
__
__ 13. __
8
5
9
0
2
3
7
14. __ __
5
9
1
__
2
8
2
15. ___ ___
12
10
1
Problem Solving and Test Prep
16. Maria is making burritos for dinner. Her
_7
8
17. Jeremy rides his skateboard 2 miles
recipe calls for cup of ground beef
and 1_6 cup of shredded cheese. Estimate
the total amount of meat and cheese
Maria uses in her recipe.
19. Ling makes 1 gallon of fruit punch for
18. Gail is making a healthy snack for her
_3
5
from his home to school. After riding
3
_ mile, he realizes he left his lunch
8
money on the counter at home. About
how far does Jeremy have left to travel
when he realizes his mistake?
weekend hike. She adds cup of raisins
and 6_7 cup of peanuts. Estimate the total
amount that Gail adds.
1
A 1 __ cups
2
B
1 cup
C
2 cups
his sister’s graduation party using
orange juice and fresh fruit. If 5_9 gallons
of the punch is orange juice, about how
much is fresh fruit?
1
A __ gallon
4
1
B __ gallon
8
3
C __ gallon
4
1
D __ gallon
2
1
D __ cup
2
PW83
Practice
© Harcourt • Grade 5
Name
Lesson 13.5
Use Common Denominators
Find the sum or difference. Write it in simplest form.
4
1
1. __ ⫹ __
5
2
7
1
2. __ ⫹ __
8
4
1
1
3. ___ ⫹ __
5
10
7
1
4. ___ ⫹ __
4
12
2
1
5. __ ⫹ ___
9
10
6
3
6. __ ⫺ __
7
8
1
8
7. __ ⫺ __
9
2
3
1
8. __ ⫺ __
4
5
4
4
9. __ ⫺ ___
5
15
7
1
10. ___ ⫺ __
10
4
Problem Solving and Test Prep
11. The lroquois tribe lived in the
12. The lroquois tribe was skilled at tracking
Adirondack Mountains of New York
during the 1700s. The tribe members
were skilled deer hunters, utilizing all
parts of the animal to benefit the tribe.
If 1_2 of the deer was used for food and
1
_ was used for skins or clothing, how
4
much of the deer was utilized in all?
13. Which addition equation represents
animals through the Adirondack
Mountains. A favorite hunting trail was
7
_ mile long, but the hunters only
8
followed it for 1_6 mile before spotting the
first deer. How much more trail was
there to hunt after the first sighting?
14. Which addition equation represents
the fraction of beads that are black
or gray?
the fraction of beads that are white
or gray?
5
8
1
A ___ ⫹ __ ⫽ ___
12
4
12
5
9
1
B ___ ⫹ __ ⫽ ___
12
3
12
4
29
1
C __ ⫹ __ ⫽ ___
5
6
30
3
2
12
D __ ⫹ __ ⫽ ___
6
4
12
__ ⫹
A 1
2
3
B __ ⫹
8
__ ⫹
C 1
8
1
D __ ⫹
3
PW84
2
__
8
2
__
8
1
__
3
4
__
8
__
⫽6
8
__
⫽5
8
___
⫽ 11
24
__
⫽5
6
Practice
© Harcourt • Grade 5
Name
Lesson 13.6
Problem Solving Workshop Strategy:
Compare Strategies
Problem Solving Strategy Practice
1. Casey worked on memorizing her lines
2. What if Casey had worked on
memorizing lines for 5 7_8 hours. Then
how many hours did she spend working
on act three?
for the school’s three act play for
6 1_4 hours. She spent 2 3_4 hours working
on act one and 1 5_8 hours working on act
two. How many hours did Casey spend
working on act three?
Mixed Strategy Practice
USE DATA For 3–4, use the table.
3. Laurie wants to make 3 gowns. How
many yards of yellow silk will she need
for the gowns? Show your work.
Materials needed to
make 1 gown
Fabric
4. Tamera had 1 5_7 of gold trim left after
making 3 gowns. How many yards of
gold trim did Tamera have to start?
5. In the school musical, 1_4 of the actors
were playing lead roles and 1_5 of the
actors were playing supporting roles.
All of the other actors were chorus
members. What fraction of the actors
in the school musical were chorus
members? Predict and test to solve.
Amount in Yards
Blue Chiffon
1
32
Yellow Silk
3
25
Gold Trim
6
27
6. Heather bought 12 1_2 gallons of paint for
the scenery. If 8 1_3 gallons were red, 2 1_6
gallons were black, and the rest were
white, then how many gallons of the
paint were white?
PW85
Practice
© Harcourt • Grade 5
Name
Lesson 13.7
Choose a Method
Choose a method. Find the sum or difference. Write it in simplest form.
2
1
1. __ ⫹ __
7
6
2
1
2. __ ⫺ __
3
2
3
1
3. __ ⫹ __
4
4
6
1
4. ___ ⫺ ___
22
11
3
1
5. __ ⫹ __
5
5
6
1
6. ___ ⫺ __
11
6
3
1
7. __ ⫹ __
3
8
8
7
8. ___ ⫺ ___
10
15
5
4
9. ___ ⫹ ___
15
12
5
1
10. __ ⫺ __
6
6
3
1
11. __ ⫹ __
7
2
1
2
12. __ ⫹ __
8
5
4
1
13. __ ⫺ __
5
4
6
5
14. __ ⫹ __
7
7
4
1
15. __ ⫹ ___
7
21
Problem Solving and Test Prep
16. Mark lives near the Empire State Building 17. Mark took a taxi ride from the Empire
in New York City. On Sunday, Mark
spent 1_4 of his day visiting the Empire
5
State Building and __
12 of his day
rollerblading in Central Park. What
fraction of the day did Mark spend either
visiting the Empire State Building or
rollerblading?
18. Lillian is practicing shooting marbles for
State Building to Times Square. The
taxi ride is 7_9 mile but Mark made an
unexpected stop after 1_3 mile to buy a
hotdog from a vendor. How long is the
trip from the hot dog vendor to Times
Square?
19. Lillian is participating in the Holyoke
the competition. She hopes to shoot her
favorite red marble 3_4 foot. However, she
only makes 1_8 foot the first try, then 1_4 foot
on her second shot. How much further
must she shoot the red marble to reach
her goal?
PW86
Marble Championship in Massachusetts.
In her collection, 3_7 of her marbles are
agates and 2_5 are cat-eyes. How many of
Lillian’s marbles are agates and
cat-eyes? Show your work.
Practice
© Harcourt • Grade 5
Name
Lesson 14.1
Lesson
1.1
Model Addition of Mixed Numbers
Use fraction bars to find the sum. Write the answer in simplest form.
1
1
1. 3 __ 2 __
2
3
3
1
2. 1 __ 3 __
4
8
3
1
3. 3 __ 1 __
5
5
3
__
4. 5 ___
13
3
1
5. 2 __ 2 __
8
4
1
1
6. 5 __ 1 __
4
6
3
1
7. 4 __ 1 __
3
4
3
1
8. 2 __ 3 ___
5
10
5
1
9. 1 __ 2 ___
6
12
4
1
10. 4 ___ 1 __
10
2
11
2
11. 1 ___ 1 __
12
3
3
1
12. 2 ___ 2 __
10
2
13.
17.
21.
4
1 ___
14.
__
51
18.
__
21
22.
10
__
11
2
__
3
__
24
5
_
4
__
21
2
_
4
3 ___
15.
__
15
19.
1
3 __
23.
10
2
1 ___
10
__
6
___
4 5
12
_
3
___
3 7
12
_
PW87
10
__
11
16.
9
2 ___
20.
1
1__
24.
5
___
2 9
10
__
10
7
1 ___
10
__
4
__
51
2
_
5
__
32
5
__
31
2
_
__
43
8
__
31
4
_
__
31
2
__
42
5
_
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C14_L01.indd PW87
6/15/07 12:56:30 PM
Name
Lesson 14.2
Model Subtraction of Mixed Numbers
Use fraction bars, or draw a picture to find the difference. Write the answer in simplest form.
8
5
1. 3 ___ 2 ___
10
10
5
3
2. 5 __ 3 __
8
8
1
1
3. 6 __ 1 __
2
4
1
1
4. 4 __ __
3
4
3
3
5. 3 __ 2 __
4
8
3
1
6. 5 __ 3 __
5
2
5
1
7. 4 __ 1 ___
6
12
5
1
8. 5 __ 2 __
6
2
7
1
9. 3 ___ 1 __
12
2
2
1
10. 5 __ 4 __
3
4
11
1
11. 4 ___ 2 __
12
6
13.
17.
21.
__
47
14.
__
51
18.
__
53
22.
8
__
1 1
4
__
2
__
2 1
3
__
4
__
1 1
3
_
7
5___
10
__
5 1
5
__
15.
__
51
19.
___
6 11
23.
2
__
3 2
5
__
12
__
5 1
2
__
4
5 __
16.
__
22
20.
5
1
2 __
2
__
3
__
1 1
2
_
9
4___
10
__
4 1
5
__
PW88
1
1
12. 3 __ 1 __
5
2
24.
__
61
2
1
3 __
6
__
__
57
8
1
3 __
4
__
__
67
8
__
3 3
4
__
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C14_L02.indd PW88
6/15/07 12:56:04 PM
Name
Lesson 14.3
Record Addition and Subtraction
Find the sum or difference. Write the answer in simplest form.
1.
7
__ 9 ___
13
2.
__ 3 1
__ 82
3.
__ 5 2
__ 91
4.
__ 1 4
__ 61
5.
__ 6 1
__ 13
6.
__ 5 1
__ 10 3
7.
4
__ 2 ___
83
8.
___ 3 3
__ 12 11
9.
__ 9 3
__ 85
10
2
6
5
9
12
3
9
7
3
12
4
4
3
4
6
6
4
Problem Solving and Test Prep
USE DATA For 10–11, use the table.
10. How many miles did Sheryl run on
Monday and Tuesday in all?
Sheryl’s Training Record (In Miles)
Walking
1
3
1
2
4
Monday
11. How much farther did Sheryl walk on
4
Tuesday
Running
1
2
5
2
9
1
Monday than on Tuesday?
1 hours on
12. Dan played guitar for 2 _
2
Saturday and 1 _52 hours on Sunday.
How many hours total did Dan play
guitar in 2 days?
2 hours cleaning her room,
13. Ana spent 1 _
3
and Evelyn spent 1 8_9 hours cleaning her
room. How much longer did it take
Evelyn to clean her room?
7 hours
A 1 __
10
A 3 5_9 hours
B
3 3_7 hours
B
1 hour
C
3 1_2 hours
C
_2
3
hour
D
_2
9
hour
9
D 3 __
hours
10
PW89
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C14_L03.indd PW89
6/28/07 1:16:02 PM
Name
Lesson 14.4
Subtraction with Renaming
Use fraction bars to find the difference. Write the answer in simplest form.
1.
__ 1 5
__
53
5.
9
1
6 ___
2 ___
8
10
8
10
2.
__
721
6.
3
__
7 ___
13
4
10
5
3
1
3. 4 __ __
2
4
1
4
4. 4 __ 2 __
5
2
1
2
7. 7__ 6 __
2
3
1
7
8. 4 __ 3 ___
3
12
Problem Solving and Test Prep
Zack’s Large Fruit Smoothie
USE DATA For 9–10, use the table.
Ingredient
9. Zack decided to reduce the amount of
1 _78
banana by
ounces. How much banana
did Zack use?
Banana
Strawberry
Blueberry
Amount
3
ounces
4
1
2
6 ounces
1
3
ounces
2
4
5
10. Zack’s recipe makes a 10 __
-ounce smoothie. If blueberries were not included,
12
how many ounces would the smoothie be?
11. Stacey buys 4 1_4 yards of ribbon to make a 12. Jon used 5 1_4 ounces of cranberry juice
bow. She uses 2 5_8 yards. How much
ribbon is left?
and 3 2_3 ounces of orange juice to make
fruit punch. How much more cranberry
juice than orange juice did Jon use?
3
A 1 __ yards
8
5
B 1 __ yards
8
4
C 2 __ yards
8
5
__
D 2 yards
8
5
A 1 ___ ounces
12
7
B 1 ___ ounces
12
1
C 2 __ ounces
7
7
D 2 ___ ounces
12
PW90
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C14_L04.indd PW90
6/15/07 12:55:44 PM
Name
Lesson 14.5
Practice Addition and Subtraction
Estimate. Then write the sum or difference in simplest form.
1
91
1. 1 __ ⫹ 5 __
6
3
3
5
2. 14 __ ⫺ 9 __
4
6
3
11
3. 16 __ ⫹ 24 ___
4
12
5
5
4. 15 __ ⫺ 11 __
8
6
5
4
5. 11 __ ⫹ 25 __
5
8
5
6. 8 ⫺ 1 __
7
Use a calculator to find the sum or difference.
4
1
7. 39 __ ⫹ 17 __
5
2
3
1
8. 32 ___ ⫺ 19 __
5
10
3
7
9. 93 __ ⫹ 28 ___
4
10
Problem Solving and Test Prep
USE DATA For 10–11, use the table.
10. On which day did Cyndi spend the most
Cyndi’s Fielding Practice
time at fielding practice? The least?
Day
Monday
Wednesday
Friday
Time
1 3 hours
8
2 11 hours
12
1 5 hours
6
11. How much time in all did Cyndi spend
at fielding practice on Wednesday and Friday?
12. Amber’s speech has to be 8 1_2 minutes
long. If her speech is currently
7 7_8 minutes long, how much longer does
her speech need to be?
A
B
C
D
13. Mary sold 33 3_8 bushels of apples and
3
__
minute
8
5
__ minute
8
__ minutes
11
8
5
1 __
minute
8
21 2_3 bushels of pears. How many
bushels of fruit did she sell in all?
1
A 54 ___
24
5
B 54 ___
24
1
C 55 ___
24
5
D 55 ___
24
PW91
bushels
bushels
bushels
bushels
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C14_L05.indd PW91
6/15/07 12:56:21 PM
Name
Lesson 14.6
Problem Solving Workshop Strategy:
Use Logical Reasoning
Problem Solving Strategy Practice
Use logical reasoning to solve.
1. Sue had softball practice for 3 _32 hours. Sue’s mom came 3_4 hour after practice started,
and left 5_6 hour before practice ended. How many hours of practice did Sue’s mom
watch?
2. Mark, Dan, Brendan, and Alex sold popcorn for their baseball team. Dan sold twice as
many pounds as Brendan. Alex and Mark sold the same amount. Brendan sold 12 1_2
pounds, 5 more pounds than Mark. How many pounds did each boy sell?
Mixed Strategy Practice
USE DATA For 3–4, use the table.
3. The sum of the distances of the 3 homeruns
__ ft. What was the
hit in Game 1 is 278 11
18
distance of Nina’s homerun in Game 1?
Homerun Distance (Ft)
Carla
4. The sum of the distances of the 3 homeruns
hit in Game 2 is 9 1_2 ft less than the sum for
Game 1. What was the distance of Maria’s
homerun in Game 2?
Game 1
Game 2
88 2
3
90 7
9
85 1
2
Nina
Maria
93 1
6
5. Three pumpkins weigh 18 5_9 , 18 1_3 , and 18 5_6 pounds. Tim’s pumpkin weighs more than
Denny’s, but they weigh the same when rounded to the nearest whole number. Rich’s
pumpkin is lighter than Tim’s. How much does each boy’s pumpkin weigh?
6. The mailboxes are 41 1_2 , 40 1_4 , and 42 2_3 inches tall. Jill’s mailbox is 1 1_4 inches shorter than
Ali’s. Abby’s mailbox is the tallest. How tall is each girl’s mailbox?
PW92
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C14_L06.indd PW92
6/28/07 1:16:47 PM
Name
Lesson 15.1
Model Multiplication of Fractions
Use yellow and blue crayons to model the product.
4
1
1. __
__
5
2
1
__ 2. __
5
6
2
1
2
3. __
__
3
4
1
2
4. __
__
2
3
Find the product.
4
__
5. __
5
6
9
1
__
6. __
1
4
3
1
2
7. __ __
8
3
4
2
8. __ __
7
5
1
2
9. __ __
2
9
3
1
10. __ __
3
4
2
1
11. __ __
5
7
3
1
12. ___ __
10
2
1
__
13. __
2
3
9
1
5
14. __ __
4
7
PW93
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C15_L1.indd PW93
7/2/07 2:14:09 PM
Name
Lesson 15.2
Record Multiplication of Fractions
Find the product. Write the answer in simplest form.
9
2
1. __ ⫻ ___
3
10
6
1
2. __ ⫻ __
7
3
7
5
3. __ ⫻ ___
12
8
1
__
4. __
⫻3
7
4
2
__
5. __
⫻4
7
9
5
3
6. __ ⫻ ___
12
8
4
9
7. ___ ⫻ __
5
10
6
3
8. __ ⫻ __
9
7
4
__
9. ___
⫻7
8
10
1
5
10. __ ⫻ __
3
6
3
1
11. __
⫻ ___
10
9
3
2
12. __
⫻ ___
12
5
9
4
13. __
⫻ ___
10
7
3
10
14. ___ ⫻ __
5
12
4
__
15. __
⫻3
8
9
Problem Solving and Test Prep
16. Alexa uses 2_3 of her backyard for a dog
17. Charles uses 1_3 of his farm for a pumpkin
18. Jin picks 2_3 of 1_2 of his apple orchard to
19. Luisa planted 3_5 of the last 2_9 of her
make apple cider. What fraction of the
orchard did Jin pick?
flower garden with daffodils. What
fraction of her garden is daffodils?
1
A __
2
1
B __
6
1
C __
3
5
D __
9
5
A ___
20
1
B __
9
6
C __
7
2
D ___
15
run. She has 1_5 of the dog run fenced in.
What fraction of Alexa’s backyard is
fenced in?
patch. He uses 2_7 of the pumpkin patch
to grow white pumpkins. What fraction
of the farm grows white pumpkins?
PW94
Practice
© Harcourt • Grade 5
Name
Lesson 15.3
Multiply Fractions and Whole Numbers
Find the product.
9
1. 5 ___
10
3
2. __ 2
4
5
3. __ 3
6
1
4. 7 __
9
3
6. 10 __
5
9
7. ___ 4
10
5
8. __ 6
8
1
9. __
15
3
1
13. 11 __
9
8
14. __ 10
9
5
11. 8 __
9
6
12. 5 __
7
2
5. 12 __
7
4
10. 9 __
7
3
15. ___ 11
10
Problem Solving and Test Prep
16. Lloyd feeds his cats 2_9 of a 5 pound bag
17. Kyra uses 3_5 of a roll of yarn for each
of cat food each day. How many pounds
of food does Lloyd feed his cats daily?
18. Pedro used 2_3 of a 33 ounce bottle of
soap to wash his mother’s car. How
many ounces of soap did Pedro use?
A 22 ounces
C
28 ounces
20 ounces
D
30 ounces
B
scarf she makes. How many rolls of yarn
does she need to make 4 scarves?
6
19. Shyla used __ of the 5 gallons of paint for
7
her fence. How many gallons of paint
did Shyla use?
1
A 4 __ gallons
2
6
B 3 __ gallons
7
PW95
C
4 gallons
D
__ gallons
42
7
Practice
© Harcourt • Grade 5
Name
Lesson 15.4
Multiply with Mixed Numbers
Make a model to find the product.
1
1
1
1
1. 2 __ __ 2. __ 1 __ 2
3
4
2
__ 3. __
11
4
3
2
Find the product.
1
4. 5 4 __
2
__ 2 1
__
__ 1 1
9. 2
7
4
3
3
5. 2 1 __
5
1
6. 8 2 __
2
3
3
1
10. 1 __ 1 __ ___
5
3
10
__
__ 2
7. 2 1
7
6
5
3
1
11. 1 __ __ __
7
5
3
3
8. 1 __ 9
7
9
1
1
12. ___ 1 __ 2 __
10
4
2
Problem Solving and Test Prep
13. Alejandro has 7 1_3 pounds of flour. He
14. Isabel has 2 1_2 gallons of scarlet paint.
15. Kim hiked 5 2_3 miles on Saturday. She
16. Joshua danced 3 1_2 hours on Monday.
uses 3_4 of the flour to make bagels. How
many pounds of flour did he use?
used 2_5 of the time talking on the phone
while hiking. How many miles did Kim
talk on the phone while hiking?
She uses 2_3 of it to paint her dining
room. How many gallons of paint did
Isabel use?
1
A 3 __
9
3
B 2 __
4
5
C 2 __
8
9
D 1 ___
10
4
A 2 ___
15
B
3
C
___
2 11
D
Tess danced 3_4 time as long. How many
hours did Tess dance?
12
__
41
4
PW96
Practice
© Harcourt • Grade 5
Name
Lesson 15.5
Model Fraction Division
Write a division number sentence for each model.
1.
2.
3.
4.
Use fraction bars to find the quotient.
2
1
5. __ ⫼ __
9
6
1
1
9. __
⫼ ___
10
2
3
1
6. ___ ⫼ __
10
4
1
__
7. __
⫼1
8
4
3
1
8. ___ ⫼ __
11
4
4
__
10. __
⫼2
3
7
1
11. 1 ⫼ __
5
4
12. 6 ⫼ __
9
1
13. 5 ⫼ __
4
7
__
14. ___
⫼1
6
10
1
15. 4 ⫼ __
8
1
16. 2 ⫼ __
6
1
17. 8 ⫼ __
3
8
1
18. ___ ⫼ __
11
4
1
19. 2 ⫼ __
2
1
20. 4 ⫼ __
4
PW97
Practice
© Harcourt • Grade 5
Name
Lesson 15.6
Divide Whole Numbers by Fractions
Find the quotient. Write it in simplest form.
5
1. 1 ___
12
1
2. 2 __
2
2
3. 7 __
5
1
4. 9 __
3
3
5. 6 __
7
1
6. 4 __
6
7
7. 3 __
9
5
8. 8 ___
12
5
9. 7 __
6
3
10. 10 __
5
1
11. 5 __
4
1
12. 12 __
3
3
14. 9 __
4
3
15. 3 ___
10
1
13. 6 __
3
Problem Solving and Test Prep
16. Students are painting the set for the
17. Gerard is cleaning a sculpture garden.
He has 2 statues left to clean. It takes
him 2 hours to clean 1_3 of the first statue.
If he spends the same amount of time
cleaning each statue, how many hours
will it take Gerard to clean both statues?
community theater’s upcoming play. It
takes the students 3 hours to paint 2_5 of
the set. If they spend the same amount
of time painting each section, how many
hours will it take the students to paint
the whole set?
9
18. Henry cut a 10 foot log into __
10 foot
19. Melanie cut 5 feet of pretzel dough
pieces of firewood. How many pieces of
firewood did Henry cut the log into?
into 1_3 foot pieces. How many pieces did
Melanie cut the dough into?
A 10
A 12
B
C
D
__
11 1
9
__
12 1
3
5
__
9
9
B
15
C
18
D 20
PW98
Practice
© Harcourt • Grade 5
Name
Lesson 15.7
Divide Fractions
Write a division sentence for each model.
1.
2.
Divide. Write the answer in simplest form.
5
3
3. __ ___
8 12
5 1
4. __ __
7 3
1
5
8. 3__ __
9
2
1
1
9. 2__ 1__
4
5
2
6
5. __ __
5
9
3
5
10. ___
__
7
12
7
__
6. ___
3
8
10
1
2
7. 2__ __
5
4
4
3
11. __ __
9
8
2
1
12. 1__ __
3
5
Problem Solving and Test Prep
13. Bruce has 8 1_2 feet of lumber to make
14. Cory has 10 1_2 feet of paper to make
1 -cups of brown sugar.
15. A baker has 7 __
3
16. Lila can walk 2 3_4 miles in 4_5 of an hour.
banners. Each banner is 3_4 of a foot long.
How many banners can Cory make?
part of the set for a school play. Each
set part needs to be 1_4 feet tall. How
many set parts can Bruce build?
3
_
4
It takes -cup of brown sugar to make
a loaf of banana bread. How many
loaves of banana bread can the baker
make?
How fast can she walk in miles per hour?
1
A 2 __ miles per hour
5
1
B 3 __ miles per hour
3
C 2 miles per hour
3
D 1 __ miles per hour
4
PW99
Practice
© Harcourt • Grade 5
Name
Lesson 15.8
Problem Solving Workshop Skill: Choose
the Operation
Problem Solving Skill Practice
Tell which operation you would use to solve the problem. Then solve.
1. Jacinda works 2_5 of the days each month
_1
3
at the reference desk and of the days in
the children’s room at the library. How
often does Jacinda work at both places?
3. Padma cooks at the soup kitchen 3_5 of the
days each month and at the hospital 1_4
of the days each month. What fraction of
the days each month does Padma cook
at both places?
2. Harrison has blue, red, green, and tiger
eye marbles. Of the 15 marbles, 2_5 are
tiger eye marbles. How many of
Harrison’s marbles are tiger eye marbles?
4. Joaquin has 150 coins in his collection.
He has pennies, nickels, dimes, quarters,
and dollars. Of all the coins, 1_3 are
quarters. How many of Joaquin’s coins
are quarters?
Mixed Applications Practice
USE DATA For 5–6, use the table.
Softball Tournament Results
5. Garrett plays for the Buffalos, and Lucy
2
_
3
plays for the Bulldogs. They played of
their teams’ winning games. How many
more winning games did Lucy play than
Garrett?
6. The Bulldogs won the league title after
winning 90% of their games. How many
more games did the Bulldogs win than
the Lions?
Team
Wins
Losses
Bulldogs
9
1
Eagles
7
3
Buffalos
6
4
Lions
4
6
7. Ashley takes 1_2 of the days each month
PW100
for ballet lessons and 1_6 for tap dance
lessons. What fraction of the days each
month does Ashley take dance lessons?
Practice
© Harcourt • Grade 5
Name
Lesson 16.1
Understand and Express Ratios
Write each ratio three ways. Then name the type of ratio.
1. flags with stripes: flags
with stars
4. flags with stripes: total
number of flags
2. flags with a torch to flags
with stripes
3. total number of flags to
flags with a C
5. flags with a torch to flags
with a C
6. flags with stars to flags
with a torch
Problem Solving and Test Prep
7. The Arizona state flag has 7 red stripes
and 6 gold stripes. What is the ratio of
red stripes to gold stripes?
9. Sara has 5 books about dogs and
8. Fast Fact The state flag of Texas has
3 stripes. The blue stripe stands for
loyalty, the white stripe stands for
strength, and the red stripe stands for
bravery. The blue stripe has a white star
in its center. Write the ratio of blue stripes
to total number of stripes in three ways.
10. Cody used 4 paper towels to clean up a
3 books about horses. What is the
ratio of books about horses to books
about dogs?
mess. There are still 5 paper towels left
on the roll. What is the ratio of used
paper towels to total paper towels?
A 5:3
A 4:5
B
8:3
B
4:9
C
3:5
C
5:4
D 5:8
D 5:9
PW101
Practice
© Harcourt • Grade 5
Name
Lesson 16.2
Algebra: Equivalent Ratios and Proportions
Write two equivalent ratios for each ratio. Use multiplication or division.
1. 1:7
5
3. __
3
2. 28 to 4
4. 9:27
Tell whether the ratios form a proportion. Write yes or no.
3
1
5. __ and ___
4
12
13
52
7. ___ and ___
23
99
42
14
6. ___ and ___
9
3
8
4
8. ___ and __
49
9
Problem Solving and Test Prep
9. Mia makes purple paint. For 1 gallon
10. A flower bed has 7 red tulips and
of paint, she mixes 1 part red paint to
3 parts blue paint. Write a proportion
that shows how many parts of each
color Mia would need for 5 gallons of
purple paint.
9 yellow tulips. What is the ratio of red
tulips to yellow tulips?
11. In the library, the ratio of mysteries to
12. The ratio for making salad dressing is
westerns is 4 to 1. The library has
32 mystery books. How many western
books are there?
3 cups oil to 1 cup of vinegar. Which is
an equivalent ratio for 3 to 1?
A 3
A 3:1
B
5
B
5:15
C
8
C
6:1
D 28
D 9:6
PW102
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C16_L02.indd PW102
6/15/07 12:25:32 PM
Name
Lesson 16.3
Ratios and Rates
Write each ratio in fraction form. Then find the unit rate.
1. 243 seconds for 81
2. $3.52 for 4 pounds of
jumping jacks
3. 18 pages in 3 days
bananas
4. $4.98 for 2 gallons of milk
5. 48 ounces in 3 cans
6. 64 doors on 16 cars
7. 96 books on 8 shelves
8. 300 miles in 5 hours
9. $24 for 4 hours of work
10. 144 peaches in 3 cases
11. 104 boxes in 8 stacks
12. 455 miles in 7 hours
Problem Solving and Test Prep
13. A package of 12 juice boxes is $2.76.
14. Fast Fact There are 124 calories in two
A package of 16 juice boxes is $4.00.
Which package is the better buy?
cups of grapes. How many calories are
there in 1 cup of grapes?
15. Sara buys 3 pounds of chicken for
16. Alex spends $9.75 on 5 packages of
$17.97. What is the unit cost?
baseball cards. What is the unit cost?
A $2.98
A $1.95
B
$5.99
B
$3.25
C
$6.00
C
$4.75
D $17.97
D $14.75
PW103
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C16_L03.Indd PW103
6/15/07 12:25:49 PM
Name
Lesson 16.4
Understand Maps and Scales
Complete the ratio table.
1.
2.
Map Distance, in
1
2
6
Actual Distance, mi
60
120
300
Map Distance, cm
1
8
9
13
3.8
Actual Distance, km
480
49.4
57
The map distance is given. Find the actual distance.
For 3–6, the scale is 1 in. ⴝ 300 mi. For 7–10, the scale is 2 cm ⴝ 8.4 km.
3. 2.2 in.
4. 7 in.
5. 0.4 in.
7. 0.25 cm
8. 6 cm
9. 3.1 cm
6. 5.4 in.
10. 8 cm
Problem Solving and Test Prep
11. A map of Spain has a scale of
12. The scale on a map showing Fargo
4 cm ⫽ 220 km. Another map of Spain
is half the size. What is the scale of the
smaller map?
13. Amber draws a map of her town using
and Grand Forks is 0.5 in. ⫽ 20 mi.
The distance between these cities is
80 miles. What is the distance
on the map?
14. Nathan draws a map of his
a scale of 1 in. ⫽ 50 ft. The actual
distance between Amber’s house and
the library is 975 feet. What is the
distance on the map?
neighborhood using a scale of
1 cm ⫽ 4 km. The distance on the
map between Nathan’s house and
Mr. Smith’s house is 2.1 centimeters.
What is the actual distance?
A 7.5 in.
A 1.9 cm
B
7.5 ft
B
6.1 cm
C
19.5 in.
C
8.2 cm
D 19.5 ft
D 8.4 cm
PW104
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C16_L04 .indd PW104
6/15/07 12:28:04 PM
Name
Lesson 16.5
Problem Solving Workshop Strategy: Make a Table
Problem Solving Strategy Practice
Make a table to solve.
1. Tara and her extended family are going
to a theme park. Ticket prices are
divided by age groups: 0–2; 3–9; and
10⫹. The ages of the people are 1, 8, 7,
11, 39, 2, 3, 21, 13, 14, 4, 38, and 24.
How many people are in each group?
2. The prices for a single day theme park
ticket are free for ages 0–2, $23 for ages
3–9, and $33 for ages 10⫹. What will the
total cost of admission tickets be for
Tara and her extended family?
Mixed Strategy Practice
USE DATA For 3–5, use the information in the picture.
3. The height of the Petronas Towers 1 & 2
is 33 feet more than the height of the
Sears Tower. The Jin Mao Building is
290 feet shorter than the Taipei 101
building. Write the heights of the four
buildings in order from shortest to tallest.
Taipei 101
4. The height of the Empire State Building
_4
5
is 90 feet more than the height of the
Sears Tower. How tall is the Empire State
Building?
Petronas Towers 1 & 2
1,450 ft
Sears Tower
1,380 ft
Empire State Building
Jin Mao Building
5. How much taller is the Taipei 101
building than the Empire State Building?
PW105
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C16_L05.indd PW105
6/28/07 1:18:51 PM
Name
Lesson 16.6
Understand Percent
Write a ratio and a percent to represent the shaded part.
1.
2.
3.
4.
5.
6.
Write a decimal and a percent to represent the shaded part.
7.
8.
9.
10.
11.
12.
PW106
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C16_L06.indd PW106
7/2/07 2:16:05 PM
Name
Lesson 16.7
Fractions, Decimals, and Percents
Write each percent as a decimal and as a fraction in simplest form.
1. 10%
2. 45%
3. 30%
4. 26%
5. 18%
6. 59%
7. 82%
8. 67%
Write each fraction or decimal as a percent.
1
9. __
4
13. 0.178
10. 0.29
7
11. ___
10
12. 0.60
7
14. __
8
15. 0.058
3
16. ___
15
Problem Solving and Test Prep
17. California produces about 75% of the
strawberries in the United States.
What fraction of strawberries in the
United States does California produce?
19. Susan washed 3_5 of her clothes. What
18. If you eat about 10 medium strawberries
you will get 9% of the vitamin B6 you
should have every day. What fraction of
vitamin B6 do you still need for that day?
20. At the Corner Store, 85% of the
percent of her clothes did she wash?
100 shelves contain food. What is
the percent written as a decimal?
A 0.3
A 0.85
B
60%
B
8.05
C
0.35
C
8.5
D 53%
D 0.8
PW107
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C16_L07.indd PW107
6/15/07 12:27:18 PM
Name
Lesson 16.8
Find Percent of a Number
Complete the sentence. Then, find the percent of each number.
1. 30% of 40
2. 60% of 15 ⫽
10 counters represent 100%, or 40.
60
100
or ____ of 15
So, each counter represents 10%, or
30% of 40 ⫽
60% of 15 ⫽
Find the percent of each number.
3. 20% of 20
4. 75% of 24
5. 25% of 12
6. 50% of 14
7. 40% of 15
8. 30% of 50
9. 10% of 80
10. 80% of 90
11. 10% of 10
12. 90% of 20
13. 75% of 8
14. 40% of 25
15. 25% of 20
16. 30% of 10
17. 50% of 6
18. 20% of 30
19. 25% of 80
20. 75% of 32
21. 30% of 30
22. 60% of 70
PW108
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C16_L08.indd PW108
6/15/07 12:28:20 PM
Name
Lesson 17.1
Outcomes and Probability
Use the bag of marbles to write the probability of the event of pulling the
marble described.
1. striped
2. black
3. white
4. gray or black
5. gray or white
6. gray, white, or
black
Use a number cube labeled 1 through 6 to write the probability of the event
of tossing each number. Tell whether the event is likely, unlikely, certain,
or impossible.
7. 5
8. a number greater than 2
9. a number less than 8
Problem Solving and Test Prep
10. Genevieve has a bag of letter tiles that
11. Daniel has a number cube labeled 1-6.
spell out her name. What is the
probability of pulling a vowel tile?
What is the probability of rolling an odd
number?
12. What is the probability that the pointer
13. What is the probability of rolling a
will land on stripes?
number greater than 4 on a number
cube labeled 1 through 6?
1
A __
8
1
A. __
6
3
1
C. __ or __
2
6
2
1
B. __ or __
6
3
5
D. __
6
2
B __
4
1
C __
4
1
D __
3
PW109
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C17_L1.indd PW109
6/15/07 12:14:10 PM
Name
Lesson 17.2
Probability Experiments
For 1–4, use the table.
1. Rachel pulled a marble from a bag,
Rachel’s Marble Experiment
recorded its color, and put the marble
back in the bag. She did this 30 times
and recorded her results in the table.
What is the experimental probability of
Rachel pulling
Number of pulls
a red marble?
a green marble?
a blue marble?
Total
Red
Blue
6
7
Green
White
5
12
a white marble?
2. Predict how many times out of 80 pulls that Rachel would pull a red marble from the
bag.
3.
Based on experimental probabilities, would you predict that Rachel
would pull a red or a white marble more often if she pulled a marble from the bag
60 more times? Explain.
4. Predict the number of times out of 60 pulls that Rachel would pull a red or a green
marble from the bag.
5. Predict the probability out of 60 pulls that Rachel would not pull a blue or a green
marble from the bag.
PW110
Practice
© Harcourt • Grade 5
Name
Lesson 17.3
Probability and Predictions
Express the experimental probability as a fraction in simplest form. Then predict
the outcome of future trials. For 3–6, items are returned after each trial.
1. 8 heads in 20 coin tosses;
2. 5 wins in 10 games;
30 more tosses
6 more games
3. 3 pink buttons in 9 pulls;
4. 12 blue socks in 48 pulls
12 more pulls
16 more pulls
5. 24 bananas out of 30 pieces of fruit;
6. 2 yellow shirts in 12 pulls
45 more pieces of fruit
6 more pulls
Problem Solving and Test Prep
7. George won 8 of the 12 games of
8. Jojo rolled an even number on a number
cube 4 out of 10 rolls. How many odd
numbers could Jojo expect to roll in the
next 15 rolls?
checkers he played with Mon. If they
play once a day for the next
9 days, how many games could
George expect to win?
9. Bobby lost 3 out of 9 chess matches.
10. Perry’s soccer team won 4 out of 6
Predict how many times Bobby will lose
in 12 more matches?
games. Predict how many times Perry‘s
team will win in the next 15 games?
A
3 matches
A 10 games
B
4 matches
B 12 games
C
5 matches
C
8 games
D
6 matches
D
9 games
PW111
Practice
© Harcourt • Grade 5
Name
Lesson 17.4
Problem Solving Workshop Strategy:
Make an Organized List
Problem Solving Strategy Practice
USE DATA For 1–3, use the table.
Sal’s Pizza Parlor
1. Donita and her friends are trying to
decide what kind of 1-topping pizza to
order at Sal’s Pizza Parlor. How many
different combinations of pizza crust,
sauce, and topping are possible?
Crust
Sauce
Topping
Thick
Marinara
Sausages
Thin
Alfredo
Olives
Mushrooms
Peppers
2. Sal is experimenting with a new pesto
sauce. If he adds this to the menu, how
many diffrent combinations of pizza
crust, sauce, and topping would be
possible?
3. Sal uses 3 different types of cheese on
his pizza: parmesan, Romano, and
mozzarella. If this category were added
to the table, how many different
combinations of pizza crust, sauce,
topping, and cheese would be possible?
Mixed Strategy Practice
Menu
USE DATA for 4–7, use the menu.
Breakfast
Options
4. If Jess and his 4 friends each order one
breakfast option and one beverage,
how many different combinations of
breakfast options and beverage are
possible?
5. Bea ran out of quiche. Now how many
different combinations do Jess and his
friends have for breakfast?
Beverages
Pancakes
$4.80
Milk
$1.25
Omelet
$5.20
Juice
$1.75
French toast
$4.50
Sparkling
$1.55
Quiche
$5.10
Oatmeal or
cold cereal
$3.70
6. The total bill for breakfast is $30.85.
If Jess and his friends pay with two
$20 bills, how much change will they
get back?
7. Jess owes $6.05 for breakfast. What two combinations could he have ordered?
PW112
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C17_L4.indd PW112
6/18/07 10:21:10 AM
Name
Lesson 17.5
Tree Diagrams
For 1–3, use the tiles and the spinner. Draw a tree diagram to find the total number
of possible outcomes.
1. Draw a tile at random and spin the
pointer. How many possible outcomes?
A E I PQ R
3. Toss a number cube labeled 1 to 6 and
spin the pointer. How many possible
outcomes?
2. Toss coin and draw a tile at random.
How many possible outcomes?
Problem Solving and Test Prep
4. If Ian rolls a die labeled 1-12 and tosses
5. Liam Growser put his first name letter
tiles in one bag and his last name letter
tiles in another bag. How many
outcomes are possible if he randomly
removes one tile from each bag?
a coin, how many outcomes are
possible?
6. Imee can choose a gold, silver or string
7. Matt can choose a plain, poppy seed,
bracelet with red, green, blue, or yellow
beads. How many bracelet and bead
choices does Imee have?
A 7
garlic, or sesame bagel with plain or
herb cream cheese. How many bagel
sandwich choices does Matt have?
A 6
8
B
4
C 12
C
8
D 14
D 10
B
PW113
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C17_L5.indd PW113
6/15/07 12:14:41 PM
Name
Lesson 17.6
Combinations and Arrangements
Make a list or draw a tree diagram to find the total number of possibilities.
1. ice-cream combinations: mint, vanilla
2. summer-camp activity combinations:
hiking or horseback riding; 2-day, 3day, or 4-day outings
or chocolate ice cream; chocolate
chip, caramel syrup, or toffee topping
3. ways to arrange a penny, nickel, and
4. order in which Raymart, Nicole, Alissa,
dime in a line
and Marie line up to start a race
across the soccer field?
Problem Solving and Test Prep
5. Kim needs to groom her 4 cats Cutie,
6. Joy’s snack choices include 4 types of
Magic, Stitch, and Star. She grooms
Cutie first. In how many different orders
can Kim groom the remaining 3 cats?
7. Kathy has 3 shirts and 4 pairs of shorts
to choose from. How many possible
choices does Kathy have?
A 6
cookies and 2 types of drinks. If she
chooses one cookie and one drink, how
many possible combinations are there?
8. Leila has 4 pictures to hang on her wall
in a single line. In how many different
ways can she hang them?
A 3
B
7
B
24
C
9
C
9
D 12
D 12
PW114
Practice
© Harcourt • Grade 5
Name
Lesson 18.1
Points, Lines, and Angles
For 1–6, use the figure. Name an example of each.
1. point
2. line segment
J
3. line
M
K
L
4. plane
P
Q
5. vertex
6. vertical angles
N
R
O
S
For 7–14, use the figure above. Classify each angle. Write obtuse, acute, straight, or right.
7. ⬔MNO
11. ⬔JKS
8. ⬔KPS
9. ⬔SPR
10. ⬔JLQ
12. ⬔JLN
13. ⬔LPQ
14. ⬔QPR
Problem Solving and Test Prep
USE DATA For 15–16, use the map.
15. Name three streets that are parallel to
Historic Charles Street.
16. Chase Street forms a right angle with
which street?
17. Which of the following best describes
18. Which is the least whole number of
the figure?
degrees an obtuse angle can have?
A parallel lines
A 90⬚
B
right angles
B
91⬚
C
point
C
101⬚
D 45⬚
D intersecting lines
PW115
Practice
© Harcourt • Grade 5
Name
Lesson 18.2
Measure and Draw Angles
Estimate the measure of each angle.
Then use a protractor to find the measure.
1. ⬔YXZ
2. ⬔VXT
3. ⬔TXZ
4. ⬔UXZ
U
V
W
Y
T
X
Z
Use a protractor to draw each angle.
Classify each angle.
5. 25⬚
6. 90⬚
7. an angle whose measure
is greater than 135⬚
Problem Solving and Test Prep
USE DATA For 8–9, use the clocks.
8. Look at the angle shown by the hands
of the clock that shows 3:00. What is the
measure of this angle? Explain how you
know.
9. Estimate the measure of the angle formed by the hands of the clock that shows 4:00.
Then measure the angle.
10. Which angle measure names an acute
11. What is the approximate measure of the
angle?
angle below?
Z
A 82⬚
B
95⬚
C
105⬚
X
Y
D 90⬚
PW116
Practice
© Harcourt • Grade 5
Name
Lesson 18.3
Polygons
Name each polygon and tell whether it is regular or not regular.
1.
2.
3.
4.
Tell if the given angles could form a triangle.
5. 60⬚, 65⬚, 60⬚
6. 10⬚, 105⬚, 64⬚
7. 77⬚, 53⬚, 50⬚
Problem Solving and Test Prep
8. Amelia is trying to draw a triangle. She
wants to use the angle measures: 45⬚,
90⬚, and 45⬚. Can she draw a triangle
using these angles? Explain.
10. Which of the following angles could
9. Dante is going to try to draw a triangle.
He wants to use the angle measures:
47⬚, 84⬚, and 110⬚. Can he draw a triangle
using these angles? Explain.
11. Which polygon is not regular?
form a triangle?
A 85, 42⬚, 63⬚
A
B
20⬚, 70⬚, 10⬚
B
C
80⬚, 50⬚, 50⬚
C
D 45⬚, 45⬚, 70⬚
D
PW117
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C18_L03.indd PW117
6/15/07 12:52:11 PM
Name
Lesson 18.4
Problem Solving Workshop Skill:
Identify Relationships
Problem Solving Skill Practice
For 1–2, identify the relationship. Then solve.
1. What relationship can you find between
the length of a square’s sides and the
perimeter?
Length Of Square
Sides (In.)
3
4
5
6
Perimeter (In.)
12
16
20
24
2. Predict the perimeter, if the length of each side of a square is 14 inches?
Mixed Applications Practice
USE DATA For 3–4, use the table.
3. Identify the relationship displayed
in the table.
Number Of Sides On
A Prism Base
3
4
5
6
7
Number of Vertices
6
8
10
12
14
4. How many vertices would a base with 9 sides have?
5. Dennis, Carl, Paul, and Jeremy live in the first four houses on Park Street. Dennis lives in
the second house from the corner. Jeremy does not live next to Dennis. Paul lives on
the corner. In what place is Carl’s house on the street?
PW118
Practice
© Harcourt • Grade 5
Name
Lesson 18.5
Circles
For 1–6, use the circle at the right.
1. Name 5 radii.
2. Name a
3. Name a chord.
diameter.
B
C
___
4. Name the circle.
5. If AC is 7 inches,
___
___
D
6. If BD is 6.2
how long is BD?
inches,
___ how long
is AC ?
E
A
F
Complete 7–8. Then use a compass to draw each circle. Draw
and label the measurements.
7. radius ⫽
8. radius ⫽ 0.9 in.
diameter ⫽ 1.4 cm
diameter ⫽
Problem Solving and Test Prep
USE DATA For 9–10, use the circle.
9. What is the unknown measure in the circle?
99°
112°
82°
10. If 112˚ is changed to 95˚, what is the unknown
measure of the circle?
11. Which is the measure of ⬔AXC?
A 88⬚
A
B
88°
B
124⬚
C
148⬚
X
D 184⬚
C
12. Which is the measure of ⬔BXC?
124°
A 90⬚
B
99⬚
C
109⬚
D 171⬚
PW119
A
B
90°
X
171°
C
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C18_L05.indd PW119
6/15/07 12:51:26 PM
Name
Lesson 18.6
Congruent and Similar Figures
Write whether the two figures appear to be congruent, similar, or neither.
1.
2.
3.
4.
Identify the corresponding side or angle.
___
6. ⬔S
5. UT
9. ⬔U
___
10. SU
___
7. RS
8. ⬔T
11. ⬔R
12. TR
S
R
X
W
___
T
U
Z
Y
Problem Solving and Test Prep
USE DATA For 13–14, use the figures shown.
13. Do the figures appear to be congruent? Explain.
F
T
V
H
14. Do the figures appear to be similar? Explain.
15. Which best describes the two figures
below?
A congruent
B
similar
C
regular polygons
U
G
16. Quadrilaterals ABCD and EFGH
are congruent. The measure of ⬔C is
150⬚. What is the measure of the
corresponding angle, ⬔G ?
D neither congruent nor similar
PW120
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C18_L06.indd PW120
6/15/07 12:50:58 PM
Name
Lesson 18.7
Symmetry
Draw all lines of symmetry. Then tell whether each figure has
rotational symmetry by writing yes or no.
1.
2.
3.
4.
5.
6.
7.
8.
Each figure has rotational symmetry. Tell the fraction and the
angle measure of each turn.
10.
9.
11.
12.
Problem Solving and Test Prep
13. Does a right triangle have lines of
symmetry? rotational symmetry?
14. Brandon makes a design that has
1
rotational symmetry every __-turn.
2
What angle measure describes the
design’s symmetry?
15. Which figure has rotational
symmetry?
16. Which figure has rotational
symmetry?
A
C
A
C
B
D
B
D
PW121
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C18_L07.indd PW121
6/27/07 9:57:05 AM
Name
Lesson 19.1
Classify Triangles
Classify each triangle. Write isosceles, scalene, or equilateral.
1.
2.
8 ft
4 ft
3.
7 cm
7 ft
9m
5m
7 cm
9m
7 cm
Classify each triangle. Write acute, right, or obtuse.
4.
5.
6.
Problem Solving and Test Prep
For 7–9, use the models of the sails.
21 in.
7. What type of triangle is school A’s flag?
6 in.
School A
17 in.
8. What type of triangle is school B’s flag?
18 in.
10 in.
9. Two of the angles in school A’s flag
measure 75⬚ and 20⬚. What is the
measure of the third angle?
10. A triangle has two equal sides. What
School B
18 in.
11. James draws a triangle with angles that
type of triangle is it?
measure 45⬚ and 60⬚. What is the
measure of the third angle?
A scalene
A 105⬚
B
obtuse
B
90⬚
C
acute
C
75⬚
D isosceles
D 45⬚
PW122
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C19_L1.indd PW122
6/15/07 12:18:10 PM
Name
Lesson 19.2
Classify Quadrilaterals
Classify each figure in as many ways as possible.
Write quadrilateral, parallelogram, square, rectangle, rhombus, or trapezoid.
1.
2.
3.
4.
For each quadrilateral name the parallel, perpendicular, and congruent sides.
B
5.
A
C
C
6.
D
D
A
B
Problem Solving and Test Prep
7. Draw and name a quadrilateral with
8. Algebra One pair of congruent angles
4 right angles and 4 pairs of
congruent sides.
in a parallelogram each measure 54⬚.
What is the measure of each of the
missing angles?
9. A quadrilateral has 4 congruent angles
10. The sum of the measures of three
and 2 pairs of congruent sides. What
type of quadrilateral is it?
angles in a quadrilateral is 280⬚. What
is the measure of the fourth angle?
A rectangle
A 180⬚
B
trapezoid
B
120⬚
C
rhombus
C
90⬚
D parallelogram
D 80⬚
PW123
Practice
© Harcourt • Grade 5
Name
Lesson 19.3
Draw Plane Figures
Use a protractor and a ruler to draw each figure on a coordinate
plane. Classify each figure by writing the name that best describes it.
1. 2 congruent sides each measuring
2. angles measuring 30⬚, 70⬚, 80⬚;
3 inches; 2 congruent angles each
measuring 45⬚
no congruent sides
Use a protractor and a ruler to draw each quadrilateral. Classify
each quadrilateral by writing the name that best describes it.
3. 4 right angles; 1 pair of congruent sides
4. 2 pairs of congruent angles, 1 pair
measuring 2 inches and 1 pair of
congruent sides measuring 4 inches
measures 75⬚; 4 congruent sides each
measuring 3 inches
PW124
Practice
© Harcourt • Grade 5
Name
Lesson 19.4
Solid Figures
Classify each solid figure. Write prism, pyramid, cone, cylinder, or sphere.
1.
2.
3.
4.
Write the number of faces, edges, and vertices. Then classify each solid figure.
5.
6.
Problem Solving and Test Prep
USE DATA For 7–9, use the solid figure to the right.
7. What is the shape of the base of the figure?
8. What is the shape of the sides of the figure?
9. How many faces, edges, and vertices does the figure have?
10. Which solid figure has a triangle as a
11. Which solid figure has 0 faces, 0 edges
base and 3 rectangular faces?
and 0 vertices?
A pyramid
A sphere
B
rectangular prism
B
triangular prism
C
triangular prism
C
pyramid
D cube
D pentagonal prism
PW125
Practice
© Harcourt • Grade 5
Name
Lesson 19.5
Problem Solving Workshop Strategy:
Compare Strategies
Problem Solving Strategy Practice
1. Sara is building prisms by using pieces
2. Bill is building a triangular pyramid by
of clay for the vertices and straws for
the edges. How many pieces of clay
and how many straws will Sara need to
build a pentagonal prism?
3. Sara also makes a pentagonal pyramid
using pieces of clay for the vertices and
straws for the edges. How many pieces
of clay and how many straws will Bill
need to build a triangular pyramid?
4. Larissa made a model of a polyhedron
using 8 pieces of clay for the vertices
and 18 straws for the edges. What type
of polyhedron did Larissa make?
by using pieces of clay for the vertices
and straws for the edges. How many
pieces of clay and how many straws
will Sara need to make the pentagonal
pyramid?
Mixed Strategy Practice
USE DATA For 5–6, use the data in the diagram.
15 m
5. The diagram is of a new monument that
15 m
will be installed in the town square of
Duncan’s hometown. What type of
polyhedron is it?
10 m
6. Duncan saw a model that was 1_5 the
10 m
7. Duncan lives 1.3 miles from the town
size of the actual monument. Write an
equation to find the length of each side
of the base in the model. Then solve it.
square. If he rode his bike to and from
the town square twice in one day, how
many miles did he ride in all?
PW126
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C19_L5.indd PW126
6/15/07 12:17:27 PM
Name
Lesson 19.6
Nets for Solid Figures
Match each solid figure with its net.
1.
2.
3.
4.
a.
b.
c.
d.
Problem Solving and Test Prep
5. Draw a net for a rectangular prism and
6. Draw a net for a pyramid and for a
for a triangular prism. Compare the nets
by describing the shapes and number of
bases and faces.
7. How many rectangles will the net for a
triangular pyramid. Compare the nets
by describing the shapes and number of
bases and faces.
8. How many triangles will the net for a
triangular prism contain?
pentagonal pyramid contain?
A 2
C
4
A 3
C
5
3
D
5
B
4
D
7
B
PW127
Practice
© Harcourt • Grade 5
Name
18.7
Lesson 19.7
Draw Solid Figures from Different Views
Identify the solid figure that has the given views.
1.
2.
Top
Front
Side
3.
Top
Front
Side
Top
Front
Side
On the grids below, draw each figure from the top, the front, and the side.
4.
5.
6.
top view
top view
top view
front view
front view
front view
side view
side view
side view
7. Write Math Explain which solid figures have a top view that is the same as
the bottom view.
PW128
Practice
© Harcourt • Grade 5
Name
Lesson 20.1
Transformations
Name each transformation.
1.
2.
3.
Draw figures to show a translation, a rotation, and a reflection of each.
4.
5.
Problem Solving and Test Prep
6. Draw a translation of the figure.
7. Draw a rotation of the figure.
8. Which is a transformation?
9. Which kind of transformation flips a figure
over a line?
A quadrilateral
B
translation
C
triangle
D circle
PW129
Practice
© Harcourt • Grade 5
Name
Lesson 20.2
Tessellations
Predict whether the figure or figures will tessellate. Trace and cut out several copies
of each figure and then test your predictions. Write yes or no.
1.
2.
3.
4.
5.
6.
7.
8.
PW130
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C20_L2.indd PW130
7/2/07 2:14:40 PM
Name
Lesson 20.3
Create a Geometric Pattern
Tell how each pattern might have been created.
1.
2.
3.
4.
Trace each figure. Then transform it to create a pattern.
Sketch your design.
5. Translate the figure horizontally four
times.
6. Draw a point of rotation. Rotate the
figure clockwise 1_4 turn five times.
PW131
Practice
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MXENL08AWK5X_PH_C20_L3.indd PW131
6/15/07 12:19:17 PM
Name
Lesson 20.4
Numeric Patterns
Identify the rule for each pattern.
1. 8, 10, 12, 14, 16 ...
2. 5, 25, 125, 625, 3125 ...
3. 200, 100, 50, 25, 12.5 ...
Find the missing number in each pattern.
4. 74, 69, ? , 59, 54
5. 3, ? , 23, 68, 203
6. 12, 14, 18, 24, ?
Find the mistake in each pattern. Write the correct number.
7. 7, 10, 13, 14, 19
8. 1000, 500, 10, 1, 0.1
9. 56, 53, 50, 47, 45
Write the first four terms in each pattern.
10. rule: add 6
first term: 43
11. rule: divide by 2
12. rule: multiply by 3, add
first term: 88
1 first term: 2
Problem Solving and Test Prep
13. Em buys beads every month. By the
14. Henry is arranging his pennies into piles.
end of 1 month she has 24 beads, by
the end of the second month she has
48, and by the end of the third month
she has 72. How many beads does she
have at the end of the fifth month ?
15. 30, 29, 27, 24, 20, 15, ...
A 10
The first pile has 1 penny, the second
has 2 pennies, the third has 5 pennies,
the fourth has 13 pennies, and the fifth
has 34 pennies. How many pennies are
in the sixth pile ?
16. 3, 9, 27, __, 243, 729
A 81
B
12
B
30
C
9
C
108
D 7
D 45
PW132
Practice
© Harcourt • Grade 5
Name
Lesson 20.5
Problem Solving Workshop Strategy:
Find a Pattern
Problem Solving Strategy Practice
1. When Ari’s figure has 1 side, Brenda’s
2. Tonya makes a bracelet out of beads.
figure has 4 sides. When Ari’s figure
has 2 sides, Brenda’s figure has 6 sides.
When Ari’s figure has 7 sides, how
many sides does Brenda’s figure have?
3. Julia builds a model using 105 blocks in
Her design is shown below. What are
the shapes of the next two beads in
the design?
4. Hector is painting a design around the
the first row, 90 blocks in the second
row, and 105 blocks in the third row. If
Julia continues this pattern, how many
blocks will she use in the fourth row?
floor of his tree house. If he continues
the pattern below, what will be the
next four figures in Hector’s design?
Mixed Strategy Practice
5. Pose a Problem If in exercise 1 above,
6. Rose made a border around a
Brenda had a figure with 22 sides, how
many sides does Ari’s figure have?
painting. She used 40 figures in all,
and used her pattern unit 8 times.
How many figures are in Rose’s
pattern unit?
7. Each student is given 36 yellow beads and 32 green beads. They need to put the
beads into equal sized groups, each having the same number of yellow beads and
green beads. What is the greatest number of yellow and green beads that can be
in each group?
PW133
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C20_L5.indd PW133
6/15/07 12:17:09 PM
Name
Lesson 21.1
Algebra: Graph Relationships
Write the ordered pairs. Then graph them.
1.
y
Number of rectangle faces, x
6
9
12
15
Number of triangular prisms, y
2
3
4
5
6
5
4
3
2
1
0
2.
Number of cylinders, x
1
5
8
9
Number of square bases, y
0
0
0
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
x
y
5
4
3
2
1
0
x
1 2 3 4 5 6 7 8 9 10
Problem Solving and Test Prep
USE DATA For 3–4, use the table.
3. Mathew wrote the ordered pair (8,2)
for 2 quadrilaterals with 8 interior
angles of 90⬚. What is his error?
What should he have written?
Number of quadrilaterals, x
1
2
3
4
Number of Interior Angles of 90°, y
4
8
12
16
4. Rick wrote the ordered pair (4,4) for 4 quadrilaterals with 16 interior
angles of 90⬚. What is his error? What should he have written?
5. What is the number 5 in the ordered
pair (5,7)?
A x-axis
6. What is the number 8 in the ordered
pair (7,8)?
A x-axis
B
y-axis
B
y-axis
C
x-coordinate
C
x-coordinate
D y-coordinate
D y-coordinate
PW134
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C21_L1.indd PW134
6/15/07 2:54:56 PM
Name
Lesson 21.2
Algebra: Equations and Functions
Find the rule to complete the function table. Then write an equation.
1.
2.
x
27
y
9
8
21
18
7
6
15
4
y
24
3
2
1
12
6
0
y
Use the equation to make a function table with
at least 4 ordered pairs. Then graph the ordered
pairs on the grid.
3.
x
10
9
8
7
6
5
4
3
2
1
y⫽x⫹4
x
y
0
1 2 3 4 5 6 7 8 9 10
x
Problem Solving and Test Prep
Brice makes 3 more potholders an hour than Katie does.
Use this information for 5 and 6.
4. Write an equation to show the relationship between how many potholders Brice and
Katie make.
5. Choose four values for x in the equation
you wrote. Create a function table in the
box to the right.
6. If you graph the equation y ⫽ x ⫹ 3,
7. If you graph the equation y ⫽ 3x ⫹ 2,
which of the following pairs would you
graph?
which of the following pairs would
you graph?
A (2,5)
A (2,7)
B
(5,2)
B
(7,4)
C
(7,3)
C
(4,14)
D (3,7)
D (14,4)
PW135
Practice
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6/15/07 12:51:46 PM
Name
Lesson 21.3
Problem Solving Workshop Strategy:
Write an Equation
Write an equation to solve.
1. Carson spends $2.50 each weekday on
2. Gesa parks her car at the subway stop at
a muffin and juice on his way to school.
How much does Carson spend in 3
weeks?
$4 per day. Then she takes the subway
to the amusement park. The price of a
one-way ticket to the amusement park is
$2. What is her total transportation cost
for the day?
Mixed Strategy Practice
minutes, x
USE DATA For 3–4, use the function table.
3. The table shows the amount of money
a cab fare costs for rides of different
lengths. How much is a 25-minute cab
fare?
fare, y
5
10
15
20
25
$2.50 $5.00 $7.50 $10.00
30
$15.00
4. If each cab ride starts with a $4 flat fee,
what equation can you write to
determine what a 35-minute cab fare
would be?
USE DATA For 5–7, use the ferry schedule.
Seattle – Bainbridge Island
Ferry Schedule
5. Ms. Mallory lives in Seattle and works
on Bainbridge Island. It takes her 15
minutes to drive to work from the
Bainbridge Island terminal. If she needs
to be at work at 7:00 A.M., which ferry
does she need to take?
6
Ms. Mallory lives 10 minutes from the
Seattle ferry terminal. If she stops for an
additional 10 minutes to get a bagel
sandwich and juice on her way to the
ferry terminal, how long is her trip from
home to work.
Depart Seattle
Arrive Bainbridge
5:30 A.M.
6:35 A.M.
6:10 A.M.
6:45 A.M.
7:05 A.M.
7:40 A.M.
7:55 A.M.
8:30 A.M.
7. Each round-trip ferry ride costs $11.25.
If Ms. Mallory takes the ferry an
average of 15 times each month, how
much does she spend on ferry fares in
one year?
PW136
Practice
© Harcourt • Grade 5
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6/15/07 2:55:56 PM
Name
Lesson 21.4
Understand Integers
Identify the integers graphed on the number line.
1.
2.
$(' $/ $- $+ $) ' ") "+ "- "/ "('
$(' $/ $- $+ $) ' ") "+ "- "/ "('
Write an integer to represent each situation.
3. grow 5 inches
4. lost 2 pounds
5. break even
Write the opposite of each integer.
6.
32
7.
41
8.
749
9.
802
10.
5,426
Write the absolute value of the integer.
11. | 1|
12. | 1|
14. |508|
13. | 19|
15. | 29|
Problem Solving and Test Prep
16. FAST FACT The coldest temperature
17. FAST FACT The warmest temperature
recorded in California happened in
Boca. The temperature reached
45 degrees Fahrenheit below zero on
January 20, 1937. Write the temperature
as an integer.
18. Which integer is the opposite
of 513?
A
B
C
D
513
recorded in Alaska happened in Fort
Yukon. The temperature reached
100 degrees Fahrenheit on June 27, 1915.
Write the temperature as an integer.
19. Which integer represents 4 years from
now?
A
315
B
315
C
513
D
PW137
4,000
4
4
4,000
Practice
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6/18/07 10:21:38 AM
Name
Lesson 21.5
Compare and Order Integers
Compare. Write ,, ., or ⴝ for each
1.
5.
9.
⫹
⫹
7
6
2.
⫹
⫺
7
6.
⫹
⫺
0
10.
7
3
.
⫺
⫺
⫺
⫺
90
56
⫺
14
41
3.
60
7.
0
11.
⫺
⫹
12
9
⫺
⫹
⫺
⫺
19
4
26
4.
8.
26
12.
5, ⫺2, ⫹1, ⫺6
16.
⫹
⫹
18
22
⫹
⫹
54
54
⫺
⫺
865
864
Order each set of integers from greatest to least.
13.
17.
⫺
1, ⫹1, ⫺5
⫺
4, 4, 3, ⫺2
14.
⫺
3, 0, ⫺7, ⫹10
15.
18. 6, ⫺9, 1, ⫺2
⫹
19. 5, ⫺5, ⫺6, 7
20.
⫹
7, ⫺9, ⫺4, 0
⫺
8, 6, 0, ⫺3
Problem Solving and Test Prep
USE DATA For 21–22, use the table.
21. The Brotulid family of fish live around
⫺
7000 meters. In what zone does this
fish live?
Zones of the Oceans
Zone Name
Sunlight
⫺
22. A viper fish thrives 80 meters to
⫺
1600 meters. Name the zones this fish
lives in.
⫺
23. Which integer is less than 27?
A
B
C
D
Range of depth (in meters)
0 to –200
Twilight
–200 to –1,000
Midnight
Abyssal
–1,000 to –4,000
–4,000 to –6,000
Hadal
–6,000 to –11,000
⫹
24. Which integer is greater than 8?
⫺
28
A
⫺
27
B
⫹
27
C
⫹
28
D
PW138
⫺
8
⫺
7
⫹
8
⫹
9
Practice
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6/15/07 12:55:54 PM
Name
Lesson 21.6
Algebra: Graph Integers on the Coordinate Plane
For 1–6, identify the ordered pair for each point.
1. point A
2. point E
3. point C
y-axis
+5
+4
4. point F
5. point B
6. point D
F
10. P (3, 3)
8. N (⫺1, 1)
11. Q (0, 2)
B
+2
+1
C
A
-5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5
-1
-2
E
-3
D 4
For 7–12, graph and label the ordered pairs
on the coordinate plane at the right.
7. M (5, ⫺2)
+3
9. O (⫺3, 0)
x-axis
-5
12. R (⫺5, ⫺5)
Name the ordered pair that is described.
13. Start at the origin. Move 3 units to the
14. Start at the origin. Move 11 units to the
left and 2 units up.
left.
Problem Solving and Test Prep
15. Allen was walking on a giant coordinate
grid. He started at the origin and took
2 steps to the right. Then he took 5 steps
up. What ordered pair did he walk to?
17. Start at the origin. Go to the left 1 unit.
16. Alexis was walking on a giant coordinate
grid. She started at the origin and took
1 step to the left. Then she took 3 steps
down. What ordered pair did she
walk to?
18. Start at the origin. Move 3 units up.
Go down 1 unit. What is the ordered
pair?
What is the ordered pair?
A (1, 1)
A (0, 3)
⫺
B
( 1, 1)
B
(3, 0)
C
(1, ⫺1)
C
(0, ⫺3)
D (⫺1, ⫺1)
D (⫺3, 0)
PW139
Practice
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6/15/07 12:51:56 PM
Name
Lesson 22.1
Customary Length
Estimate the length of the stapler in inches. Then measure the length.
1. to the nearest inch:
1
2. to the nearest __ inch:
2
1
3. to the nearest __ inch:
8
4. In Exercises 5⫺7, which measurement is
most precise? Explain.
Tell which measurement is more precise.
1
1
1
5. 4 __ inches or 4 __ inches
6. 1 foot or 11 __ inches
8
4
3
7
7. __ inches or __ inches
8
4
2
1
8
Estimate the length in inches. Then measure to the nearest __ inch.
8.
9.
Estimate:
Estimate:
Measurement:
Measurement:
PW140
Practice
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6/15/07 2:56:06 PM
Name
Lesson 22.2
Metric Length
Estimate the length of the pen in centimeters. Then measure the length.
1. to the nearest centimeter.
2. to the nearest millimeter.
Write the appropriate metric unit for measuring each.
3. distance from Phoenix to
4. width of a dictionary
5. height of the ceiling in
New York
6. length of an apple stem
your classroom
7. distance from Reno to
8. width of a key on a
Minneapolis
computer keyboard
Estimate and measure each.
9.
10.
Estimate:
Estimate:
Measurement:
Measurement:
11.
12.
Estimate:
Estimate:
Measurement:
Measurement:
PW141
Practice
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6/15/07 2:55:20 PM
Name
Lesson 22.3
Change Linear Units
Change the unit.
1. 10 yd ft
2. 1,500 m 4. 23 cm mm
5. 3.5 mi yd
6. 160 mm 7. 112 yd ft
8. 19 km m
9. 23 cm km
3. 93 ft in.
m
m
Find the sum or difference.
10.
7 ft 6 in.
4 ft 10 in.
___
11.
10 yd 1 ft
2 yd 2 ft
__
12.
13 ft 7 in.
12 ft 6 in.
___
13.
1 yd 2 ft
1 yd 1 ft
__
14.
9 ft 4 in.
3
ft 8 in.
__
15.
3 yd 6 in.
4 yd 2 in.
___
16.
14 ft 0 in.
0 ft 8 in.
__
17.
4 ft 1 in.
2
ft 10 in.
___
18. 12 mm 12 cm 19. 7 km 0.6 km 20. 20 cm 0.2 m 21. 12 km 1,100 m ALGEBRA Find the missing measurement.
22. 1 ft 2 yd
24. 23 cm 23. 1,000 m 1.24 m
25. 16 mm 1.5 km
2 cm
Problem Solving and Test Prep
26. Junie is 61.5 inches tall; Aaron is 5 feet,
3 inches tall. Who is taller, and what is
the difference in their heights?
28. McKenna swam 1,250 meters. How
27. There are 5 yards left of the fabric Bryce
needs for a project. How many feet of
fabric are left?
29. Chris cut 40 cm off a 1.5-m long string.
many kilometers did she swim?
How long is the string now?
A 125 km
A 1.46 m
B
12.5 km
B
1.4 m
C
1.25 km
C
1.1 m
D 0.125 km
D 0.9 m
PW142
Practice
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6/15/07 2:55:36 PM
Name
Lesson 22.4
Customary Capacity and Weight
Change the unit.
1. 5 lb 4. 4,500 lb 7. 16 qt 2. 16 c oz
5. 72 oz T
lb
8. 10 c gal
3. 8 gal qt
qt
6. 12 fl oz c
9. 4.5 lb qt
oz
Find the sum or difference.
10.
7 lb 6 oz
4
lb 10 oz
___
11.
11 gal 2 c
2 gal 1 c
___
12.
14.
2 c 2 fl oz
4 c 6 fl oz
___
15.
3 qt 3 c
4
qt 2 c
__
16.
4 pt 1 c
1 pt 1 c
__
2 T 200 lb
1 T 20 lb
___
13.
17.
23 lb 2 oz
20
lb 14 oz
___
4 pt 2 fl oz
2
pt 6 fl oz
___
ALGEBRA Find the missing measurement.
18. 1 c 20. 33 oz 22. 2 c 24. 2 fl oz 2 qt
19. 12 fl oz 4 lb
21. 4 pt 1 gal
23. 1,500 lb 1 pt
25. 8 oz 2c
4 gal
1T
3.5 lb
Problem Solving and Test Prep
26. Mrs. Moore handed out 4 ounces of
27. Camryn made 3 gallons of iced tea for a
almonds to each of her 22 students.
How many pounds of almonds did
Mrs. Moore hand out?
party. How many cups of iced tea did
Camryn make?
28. Tommy uses 4 ounces of cheese in
29. Riley drank 8 cups of water during a
each pizza he makes. How many
pounds of cheese does Tommy need to
make 28 pizzas? Explain.
soccer tournament. How many fluid
ounces did he drink?
A 64 fl oz
B
32 fl oz
C
16 fl oz
D 64 qt
PW143
Practice
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6/15/07 2:56:27 PM
Name
Lesson 22.5
Metric Capacity and Mass
Change the unit.
1. 80 L ⫽
2. 900 mg ⫽
kL
4. 18,000 mL ⫽
7. 336 g ⫽
L
mg
5. 5 kg ⫽
3. 7,500 mL ⫽
g
6. 130 mL ⫽
g
8. 8.25 L ⫽
9. 1,200 mg ⫽
mL
L
L
g
Find the sum or difference.
10. 12 mg ⫹ 12 mg ⫽
11. 0.7 kL ⫺ 0.6 kL ⫽
12. 20 mL ⫺ 0.2 mL ⫽
13. 12 g ⫹ 1,100 g ⫽
14. 13 kL ⫹ 121 kL ⫽
15. 1,200 g ⫺ 729 g ⫽
ALGEBRA Find the missing measurement.
16. 4 g ⫺
⫽ 250 mg
17. 1 L ⫺
⫽ 2 mL
Problem Solving and Test Prep
18. Jenna and Annie are making applesauce 19. Cal drank 800 milliliters of water at
and need 5 kilograms of apples. How
many grams are in 5 kilograms?
school today and 500 milliliters at home.
How many liters did Cal drink in all?
20. Kennedy’s dog weighs 34,000 g. How
21. How many milliliters are in a
many kilograms does Kennedy’s dog
weigh?
6.6 liter jug?
A 3,400 kg
A 6,605 mL
B
340 kg
B
606 mL
C
34 kg
C
6,060 mL
D 3.4 kg
D 6,600 mL
PW144
Practice
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6/15/07 2:56:52 PM
Name
Lesson 22.6
Problem Solving Workshop Skill:
Estimate or Actual Measurement
Problem Solving Skill Practice
Tell whether you need an estimate or an actual measurement. Then solve.
1. Janet is making pendant necklaces
2. Dominic is making a birdhouse and
for 5 of her friends. She has a spool
that has 2.2 m of leather string. If Janet
needs 42 cm of leather string for each
necklace, how much excess string will
remain?
needs to cut 3 pieces of trim that are
14, 31, and 44 cm long. Dominic has
one 1-meter-long piece of trim. Is it long
enough? Explain.
.
Mixed Applications
USE DATA For 3–5, use the table.
3. Leslie is shopping for beading materials.
She wants to make 51 20-cm bracelets
with silver wire. How many 10-meter
silver wire spools will Leslie need to
buy?
.
4. Mrs. Bisogno wants to make four 45-cm
necklaces. If the store will let her buy
her stringing material by the meter
instead of by the spool, how many
meters should Mrs. Bisogno ask for?
Stringing Materials
Material
Cost
10-meter Satin cord spool
$2.89
10-meter Elastic thread spool
$2.31
10-meter Silver wire spool
$2.50
10-meter Silk thread spool
$8.63
5. Jeff and Mia buy 2 spools of silver wire
and 4 spools of elastic thread. They pay
with two $10 bills. How much change
should they receive?
PW145
Practice
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6/15/07 2:56:35 PM
Name
Lesson 22.7
Elapsed Time
Write the time for each.
1. Start: 7:14 A.M.
2. Start:
Elapsed time: 12 hr 3 min
End: 6:57 P.M.
Elapsed time: 2 hr 50 min
End:
3. Start: 4:12 P.M.
4. Start: January 1, 3:00 A.M.
Elapsed time: 4 days 3 hr 30 min
End:
Elapsed time:
End: 6:43 P.M.
6. Start: Monday, 2 P.M.
5. Start:
Elapsed time: 22 hr 12 min
End: 11:12 P.M.
Elapsed time:
End: Tuesday, 6 A.M.
Add or subtract.
7.
11.
3 days 2 hr
1 day 10 hr
___
8.
12 min 22 sec
2 min 32 sec
___
32 min 9 sec 12.
6 hr 6 min
4 hr 19 min
40 min 10 sec
___
____
9.
2 hr 12 min
1 hr 49 min
___
10.
13.
1 day 12 hr
2 days 14 hr
___
14.
6 wk 6 days
4 wk 5 days
___
5 wk 3 days
4 wk 6 days
___
Problem Solving and Test Prep
15. Christian checked out a book from the
16. Mr. Lee requests that Ava and her
classmates read for 25 minutes at home
each weekday. How much time will they
spend reading at home over 3 weeks?
library that is due
in 2 weeks. If he
checked it out on
April 3, what is the
due date?
17. Josh swam every Monday and Friday in
18. The movie started at 7:10 P.M. and lasted
June. How many days did he swim?
for 1 hour 54 minutes. What time did the
movie end?
A 4 days
A 11:58 A.M.
B
6 days
B
9:04 P.M.
C
8 days
C
10:00 P.M.
D 10 days
D 9:40 P.M.
PW146
Practice
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6/15/07 12:15:34 PM
Name
Lesson 22.8
Temperature
Find the change in temperature.
1. 56ºC to 20ºC
4.
7.
⫺
16ºC to 30ºC
⫺
16ºC to 20ºC
2. 7ºF to ⫺17ºF
5.
3. 88ºF to 101ºF
⫺
6ºC to 2ºC
6. 100ºF to 0ºF
8. 7ºF to 17ºF
9. 18ºC to 49ºC
⫺
10. 1ºF to 26ºF
11.
16ºF to 9ºF
13. 50ºC to 50ºC
14. 7ºC to ⫺1ºC
16. 77ºF to 0ºF
17.
12. 0ºC to 0ºC
15. 50ºF to 100ºF
⫺
30ºC to ⫺10ºC
18.
⫺
14ºC to 22ºC
Problem Solving and Test Prep
19. In Madrid, the temperature is 12°C, and
20. If the refrigerator is 38°F and the freezer
in New York City, it is 48°C. What is the
temperature difference in degrees C?
is ⫺1°F, what is the difference in
temperature in degrees F?
21. What is the change in temperature from 22. What is the change in temperature from
41ºF to 23ºF?
12ºC to 20ºC?
A 62°F
A 5°C
B
32°F
B
7°C
C
24°F
C
8°C
D 18°F
D 10°C
PW147
Practice
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7/2/07 2:15:22 PM
Name
Lesson 23.1
Estimate and Measure Perimeter
Estimate perimeter.
1. Trace around the outline of a pen in the space below. Then use
string and a ruler to estimate the perimeter in centimeters.
2. Using string and a ruler, estimate the perimeter of your desk or table top.
Find the perimeter of each polygon in centimeters.
3.
4.
5.
6.
PW148
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6/15/07 2:24:09 PM
Name
Lesson 23.2
Find Perimeter
Find the perimeter of each polygon.
1.
2.
24 in.
29 in.
1.8 m
1.5 m
29 in.
3.
7 ft
2.3 m
7 ft
7 yd
9 ft
24 in.
5.
4.
11 ft
6.
5.7 m
7.
8.
3m
1.3 m
2.6 cm
3m
3m
5.9 m
2.4 cm
3.1 m
1m
30 in.
4.3 m
3.5 m
Problem Solving and Test Prep
9. Cecil drew a diagram of a beehive
10. Algebra Candace wants to build a
in the shape of a regular hexagon.
The length of each side of the hexagon
is 4.5 inches. What is the perimeter
of Cecil’s model drawing?
11. The polygon below is a regular triangle.
model of the Pentagon. She has
enough balsa wood for a perimeter
of 100 centimeters. Write an equation
she could use to find the length of each
side of the model. Then solve the
equation.
12. The flower is inside the square frame.
What is the length of the frame that
encloses the flower?
5 cm
2.6 cm
What is the perimeter?
A 5 cm
B
15 cm
C
150 cm
D 1,500 cm
What is the perimeter?
A 1.4 cm
B
PW149
4.6 cm
C
10.4 cm
D 14 cm
Practice
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6/15/07 2:23:26 PM
Name
Lesson 23.3
Algebra: Perimeter Formulas
Find the length of each regular polygon by using a formula.
1.
2.
9 mi
27 in.
3.
4.
10 yd
10 yd
7.2 mi
19.1 mi
18.5 in.
4.2 mi
6 yd
5.
6.
7.
15 m
8.
121 yd
1.75 in.
17 cm
Problem Solving and Test Prep
9. ALGEBRA The perimeter of a regular
hexagon is 42 yards. What is the length
of each side?
11. For which polygon could you use the
10. Each of the side chambers of the Lincoln
Memorial are 38 feet wide and 63 feet
long. What is the perimeter of one of the
side chambers?
12. For which regular polygon could you use
formula P ⫽ 2l ⫹ 2w to find its
perimeter?
the formula P ⫽ 5x to find its perimeter?
A triangle
A triangle
B
parallelogram
B
square
C
trapezoid
C
pentagon
D pentagon
D hexagon
PW150
Practice
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6/15/07 2:22:15 PM
Name
Lesson 23.4
13.4
Problem Solving Workshop Skill:
Make Generalizations
Problem Solving Skill Practice
Make generalizations to solve.
1. A rectangular shaped kitchen has
2. The top of a table has a perimeter of
measurements of 12 feet by 16 feet.
The perimeter of the kitchen is half the
perimeter of the family room. What is
the perimeter of the family room?
3. Two boxes of cereal are the same
204 inches. A leaf extends the length
of the top by 8 inches. What is the
perimeter of the table top with
the leaf?
4. The Pyramid of Khafre is the second
shape. The corn cereal box is 2 inches
wide and 10 inches long. The perimeter
of the wheat cereal box is 5 inches more
than the corn cereal box. What is the
perimeter of the wheat cereal box?
largest pyramid in Giza. It is the same
shape as the Great Pyramid. The
perimeter of its base is 2,816 feet.
How long is each side of its base?
Mixed Applications
5. The length of the longest leg bone in a
6. Kerri has a tree house that is 5 feet by
human, the femur, is 19.88 inches. The
length of the longest arm bone in a
human, the humerus, is 14.35 inches.
What is the difference in length between
the femur and the humerus?
7 feet. His circular table has a diameter
of 6 feet. Will the table fit in his tree
house? Explain.
.
7. Brett and Bart are identical twins. Carly
8. Todd is cutting a rectangular piece of
and Carl are also identical twins. Can
you find the ages of Brett and Bart?
Explain.
cloth into smaller pieces. It measures
12 inches by 6 inches. If each smaller
piece is 3 inches square, how many
smaller pieces can he cut?
PW151
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C23_L4.indd PW151
6/15/07 2:23:14 PM
Name
Lesson 23.5
Circumference
For 1–3, complete the table.
C⫼d
Object
C
d
1.
plate
25.12 in.
8 in.
2.
wheel
81.64 in.
3.
pizza
3.14
14 in.
3.14
4. Becca has a circular pillow. She wants to add a ribbon trim around its edge.
If the diameter of the pillow is 20 centimeters, how many centimeters of
ribbon does Becca need?
To the nearest hundredth, find the circumference of a circle that has
5. a diameter of 16 yd
6. a radius of 2 m
7. a diameter of 2.5 km
8. a radius of 4 ft
9. a diameter of 14 in.
10. a radius of 22 cm
11. a diameter of 9 mi
12. a radius of 9 m
13. a diameter of 5.9 ft
14. a radius of 12.6 km
15. Reasoning If you double the diameter, what happens to the circumference?
PW152
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C23_L5.indd PW152
6/15/07 2:22:45 PM
Name
Lesson 24.1
Estimate Area
Estimate the area of the shaded figure. Each square on the grid is 1 cm2.
1.
2.
3.
Problem Solving and Test Prep
4. The jigsaw puzzle of a train at the right
Train Puzzle (each square is 1 inch)
has 100 pieces. Estimate the area of the
puzzle.
5. Estimate the area of the train in the
jigsaw puzzle at the right.
6. Which is a reasonable estimate for the
7. Which of the following is a reasonable
area of the figure?
estimate for the area of the banner?
A 15 in.2
F
4 cm2
B
9 in.2
G 8 cm2
C
4 in.2
H 12 cm2
D 2 in.2
1 in.2
J
PW153
15 cm2
1 cm.2
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C24_L1.indd PW153
7/31/07 9:08:51 AM
Name
Lesson 24.2
Algebra: Area of Squares and Rectangles
Find the area of each figure.
1.
2.
8 ft
3.
6 1 in.
4
5 ft
6 ft
16 cm
3.5 ft
2 3 in.
5
16 cm
For each square or rectangle, find each missing measurement.
S = 7.5 m
4.
5.
A=
S = 5 in.
S = 2 1_4 ft
6.
A=
7.
S = 8.5 m
W = 3 ft
W = 11 m
A=
A=
Problem Solving and Test Prep
For 6–7, use the table.
8. Cassie plans to paint the hickory wood
panel. What is its area?
9. Which panel has an area of about
2,500 in. ?
2
10. How many 1 in.2 tiles are needed to
cover an 18 in. ⫻ 30 in. countertop?
A 324 tiles
Wood
Panel
Height
Length
Hickory
68 in.
40 in.
Pine
54 in.
36 in.
Oak
52 in.
48 in.
11. What is the area of a 12 ft ⫻ 21 1_2 ft
driveway?
A 258 ft2
B
540 tiles
B
144 ft2
C
900 tiles
C
462 1_2 ft2
D 630 tiles
D 326 1_2 ft2
PW154
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C24_L2.indd PW154
6/15/07 12:16:00 PM
Name
Lesson 24.3
Algebra: Relate Perimeter and Area
For the given perimeter, find the length and width of the rectangle with the greatest
area. Use whole numbers only.
1. 80 ft
2. 36 yd
3. 6 mi
4. 200 cm
5. 76 m
For the given area, find the length and width of the rectangle with the least perimeter.
Use whole numbers only.
6. 50 mm2
7. 16 in.2
8. 48 yd2
9. 65 mi2
10. 144 ft2
Problem Solving and Test Prep
11. Complete the table to find
the areas of rectangles with a
perimeter of 20 m. Describe the
patterns you see.
Width (m)
Length (m)
Area (m2)
2
3
4
5
6
12. Using 200 feet of fencing, what is the greatest area that can be fenced? The least
area? Use whole numbers.
13. What is the greatest possible area for a
14. What is the least possible perimeter for
rectangle with a perimeter of 30 cm?
a rectangle with an area of 169 ft2?
A 30 cm2
A 13 ft
B
49 cm2
B
52 ft
C
56 cm
C
26 ft
2
D 64 cm2
D 152 ft
PW155
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C24_L3.indd PW155
7/16/07 5:27:22 PM
Name
Lesson 24.4
Algebra: Area of Triangles
Find the area of each triangle in square units.
1.
9 in.
2.
3 cm
3.
7 ft
11 cm
18 in.
12 ft
Find the area of each triangle.
4. base (b) = 5 m
5. base (b) = 10 ft
height (h) = 9 m
Area (A) =
6. base (b) = 7 in.
height (h) = 6 ft
Area (A) =
height (h) = 12 in.
Area (A) =
Problem Solving and Test Prep
USE DATA For 7–8, use the pattern.
7. Kate bought blue tiles to fill the middle of the
pattern. How many blue tiles did she buy?
8. Reasoning The tiles in the pattern are right
isosceles triangles. The two shorter sides of
each triangle are each 1 inch long. Estimate
the area of the shaded part of the pattern.
9. What is the area of the triangle?
A 120 m
B
50 m2
C
55 m
D 60 m
2
10. What is the area of the triangular figure?
A 45.5 in.2
height = 12 m
2
2
base = 10 m
B
91 in.2
C
55.5 in.
D 20 in.2
PW156
7 in.
2
13 in.
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PH_C24_L4.indd PW156
6/15/07 12:16:26 PM
Name
Lesson 24.5
Algebra: Area of Parallelograms
Find the area of each parallelogram.
1.
2.
3.
9 cm
6m
7 ft
5m
5 cm
3 ft
4.
5.
6.
13 ft
1
5 2 in.
10.4 yd
8 in.
13 ft
13.6 yd
Problem Solving and Test Prep
7. A yard is shaped like a parallelogram
8. A parallelogram has a length of 15 cm
with a base of 27 m and a height of
30 m. What is the area of the yard?
9. What is the area of the
and a height of 20 cm. It is divided into
two congruent triangles. What is the
area of each triangle?
10. A playground is divided into two equal
parallelogram?
parallelograms. What is the area of the
entire playground? Show your work.
14 ft
A 300 ft2
B
70 ft2
C
294 ft2
12 m
21 ft
20 m
D 147 ft2
PW157
Practice
© Harcourt • Grade 5
Name
Lesson 24.6
Problem Solving Workshop Strategy:
Solve a Simpler Problem
Problem Solving Strategy Practice
Solve.
1. Jane designed the figure below as a sun
catcher. What is the area of the figure?
4 in.
2. Luke made his sun catcher into a rocket.
What is the area of the rocket?
6 cm
14 in.
6 in.
5 cm
5 cm
18 cm
6 in.
5 cm
8 in.
5 cm
6 cm
Mixed Strategy Practice
4 cm
11 cm
USE DATA For 3–4, use the diagram.
5 cm
3. Chris designed his sun catcher to the
1 cm
right into an airplane. What is the area
of Chris’ airplane?
7 cm
5 cm
20 cm
4 cm
4. Chris bought the materials for the sun
catcher. He paid $1.50 each for each
rectangle, $2.25 for each triangle, $1.75
for each parallelogram, $3.00 for stain
and 3 feet of chain for $4.50 a foot.
How much did Chris spend in all?
5. Joy made a sun catcher with alternating
blue and red squares. She began with a
blue square. The sun catcher has 9 rows
of 5 squares each. How many squares of
each color are there?
PW158
Practice
© Harcourt • Grade 5
Name
Lesson 24.7
Surface Area
Use the net to find the surface area of each figure in square units.
1. Which faces on the net are congruent?
C
What is the area of the congruent faces?
E
B
A
F
D
What is the surface area of the prism?
2.
B
D
A
E
C
Find the surface area in ft2.
3.
4.
.
5.
.
.
6. WRITE Math Explain the difference between area and surface area.
PW159
Practice
© Harcourt • Grade 5
Name
Lesson 24.8
Algebra: Estimate and Find Volume
Find the volume of each rectangular prism.
1.
2.
3.
8 yd
8 cm
13 cm
5 yd
12 yd
2 cm
Problem Solving and Test Prep
USE DATA For 4–5, use the table.
4. Which of the three pools has the
Swimming Pool Dimensions
(in feet)
greatest volume?
Pool
5. In the winter, Pool A is filled to a depth
of only 2 feet. What is the volume of the
Pool A?
6. What is the volume of the prism
Length
Width
Depth
Pool A
20
17
9
Pool B
25
15
8
Pool C
30
15
7
7. Compare the volumes of the treasure
below?
chests. Which can hold more gold?
Explain your answer.
2 21 ft
3 ft
2 ft
3 21 ft
2 21 ft
3 ft
A 15 units3
B
60 units3
C
20 units3
D 12 units3
PW160
Practice
© Harcourt • Grade 5
Name
Lesson 24.9
Relate Perimeter, Area, and Volume
Tell the unit you would use for measuring each. Write linear, square, or cubic.
2. a door frame
1. how much tile
3. the amount of
water in a lake
needed to cover
a floor
4. how much wall
paper needed to
cover a wall
Write the units you would use for measuring each.
5. surface area of this
6. perimeter of this triangle
7. volume of this prism
prism
5 cm
5m
9 ft
6 ft
4m
8 cm
6 ft
12 cm
4.5 m
Problem Solving and Test Prep
USE DATA for 8–9, use the picture of the aquarium.
8. What is the aquarium’s volume?
15 in.
9. What is the area of the water’s surface
that is exposed to the air?
18 in.
24 in.
10. Joe wraps a 9 in. ⫻ 6 in. ⫻ 4 in. gift.
11. Mary bought a 6 in. ⫻ 8 in. ⫻ 1 in.
What unit should Joe use to decide how
much wrapping paper he needs?
picture frame. What unit should she use
to decide the width that is needed on a
shelf for the picture frame?
A inches
A inches
B
square feet
B
square feet
C
square inches
C
square inches
D cubic inches
D cubic inches
PW161
Practice
© Harcourt • Grade 5
Name
Lesson 24.10
Problem Solving Workshop Strategy:
Compare Strategies
Problem Solving Strategy Practice
Draw a conclusion to solve the problem.
1. Joyce is replacing the hardwood flooring
in her rectangular shaped dining room.
The area of the floor is 238 ft2. The
length of the floor is 17 ft. What is the
width of the floor?
2. Anthony’s plans to mow his lawn that is
in the shape of a rectangle. He knows
that the lawn is 15 m wide and has an
area of 345 m2. What is the length of
Anthony’s lawn?
Mixed Strategy Practice
USE DATA For 3–4, use the table.
3. Reasoning The height of the tool chest
that John bought is more than 8 in.
The width is less than 22 in. What is the
volume of his toolbox? How much did
John pay for it?
Tool Chests
Length
(in.)
Width
(in.)
Heigth
(in.)
Price
12
20
8
$54.99
10
22
9
$49.99
14
21
10
$74.99
14
20
8
$59.99
4. The sales clerk gave Carrie $5.26 back
5. Samantha is having her driveway paved.
in change when he bought the toolbox
that has a volume of 1,920 in.3. How
much money did Carrie give the clerk?
She wants the driveway to be the same
width as her garage and have an area of
748 ft2. If the length of her driveway is
34 ft, how wide is her driveway?
PW162
Practice
© Harcourt · Grade 5
SPIRAL
REVIEW
Week 1
Name
Spiral Review
For 1–4, round each number
to the place of the underlined
digit.
For 12, make an organized list to
solve.
12. Ken is making tickets for the fair.
1. 124,516
Each type of ticket will be a different
color. There will be adult and child
tickets. There will be 1-day, 2-day,
and weekly tickets. How many
different ticket colors will there be?
2. 6,732
3. 25,019
4. 3,723,801
For 5–6, name the place to which each
number was rounded.
5. 76,812 to 80,000
6. 251,006,475 to 251,006,480
For 7–9, find the elapsed time.
7. start: 11:15 A.M.
end: 2:00 P.M.
8. start: 3:30 P.M.
For 13–14, tell whether the
two figures are congruent
and similar, similar, or neither.
13.
end: 6:45 P.M.
9. start: 9:30 P.M.
end: 4:15 A.M.
For 10–11, find the ending time.
10. start: 4:00 P.M.
elapsed time: 5 hr 15 min
14.
11. start: 10:30 P.M.
elapsed time: 2 hr 20 min
SR1
Spiral Review
© Harcourt • Grade 5
Week 2
Name
Spiral Review
For 1–8, estimate. Then
find the product.
1.
26
⫻ 7
2.
672
⫻ 4
For 11, use the frequency table.
Tell whether the statement
is true or false. Explain.
Favorite Type of Music
Type of Music
3.
429
⫻ 6
4.
5. 842 ⫻ 5
783
⫻ 3
6. 239 ⫻ 7
Votes
Country
43
Rock
37
Rap
34
11. More people chose rap than rock as
7. 3 ⫻ 462
their favorite.
8. 1,364 ⫻ 6
For 9–10, use the thermometer
to find the temperature in °F.
9.
&
For 12–13, find a rule. Write
the rule as an equation. Find
the missing numbers.
12.
10.
Input, x
9
15
18
Output, y
3
5
6
Input, a
2
3
5
Output, b
16
24
40
21
27
6
8
-15
-20
13.
-25
°F
SR2
Spiral Review
© Harcourt • Grade 5
Week 3
Name
Spiral Review
For 1–6, divide.
1. 8
512
2. 4
385
3. 5
247
4. 3
844
For 9–10, for each
experiment, tell whether
events A and B are equally likely or
not equally likely. If they are not equally
likely, name the event that is more likely.
9. Experiment: Spin the pointer.
Event A: gray
Event B: white
5. 821 ⫼ 6 ⫽
6. 198 ⫼ 2 ⫽
10. Experiment: Toss a number cube
numbered 1–6.
Event A: even number
Event B: odd number
For 7–8, find the perimeter.
7.
For 11–12, classify each
figure in as many ways as possible.
Write quadrilateral, parallelogram,
rhombus, rectangle, square, or
trapezoid.
11.
8.
12.
SR3
Spiral Review
© Harcourt • Grade 5
Week 4
Name
Spiral Review
For 1–4, use basic facts and
patterns to find the missing
quotient.
For 17–18, place the
numbers where they belong
in the Venn diagram.
17. 2, 6, 3, 9, 12, 4, 15, 18, 21
1. 30 10
Multiples of 2
Multiples of 3
2. 540 90
3. 4,200 6
4. $15,0000 30
For 5–6, divide. Check your answer.
18. 23, 18, 6, 25, 8, 16, 37, 9, 11
Numbers
less than 20
5. 32
426
Numbers
greater than 10
6. 47
529
For 7–16, change each unit.
For 19–29, use properties and
mental math to find the value.
7. 24 in. ft
8. 4 c pt
9. 24 ft yd
21. 4 370
10. 2 T lb
22. (46 + 58) + 4
11. 2 c fl oz
23. 10 6 2
12. 2 gal qt
24. 6 7 5
13. 6 yd ft
14. 5,280 ft mi
15. 4 ft in.
28. 87 + 61 + 3
16. 3 lb oz
29. 7 410
19. 43 + (16 + 24)
20. 29 + 28 + 21
25. 26 + 43 + 34
26. 4 8 5
27. 6 34
SR4
Spiral Review
© Harcourt • Grade 5
Week 5
Name
Spiral Review
For 1–4, write the value of the
underlined digit.
For 10–11, use the doublebar graph.
1. 2.65
Careers
90
80
70
60
50
40
30
20
10
0
2. 12.81
3. 5.97
4. 3.49
Men
Women
Engineer
Teacher
Chemist
Doctor
Career
Write the number in two other forms.
10. What two sets of data are compared in
5. 6.35
the graph?
11. Which careers have more men than
women?
For 6–9, find the perimeter of
each figure.
6.
7.
For 12–13, name any line
relationships you see in each
figure. Write intersecting, parallel, or
perpendicular.
12.
8.
9.
13.
SR5
Spiral Review
© Harcourt • Grade 5
Week 6
Name
Spiral Review
For 1–6, find the sum or difference.
1.
91.47
⫹ 23.76
2.
105.308
⫺ 61.487
3.
8.759
⫹ 5.413
4.
2.704
⫺ 0.285
For 8–10, use the picture.
List all possible outcomes
of each experiment.
8. tossing a penny
9. spinning the pointer
5.
0.42
0.309
⫹ 2.695
6.
18.751
6.049
⫹ 12.201
Find the perimeter and area
of the figure. Then draw
another figure that has the same
perimeter but a different area.
10. tossing the penny and spinning
the pointer
For 11–12, write an algebraic
expression.
11. Caroline had 37 songs in
her MP3 player. She deleted some
of them.
7.
3 cm
5 cm
12. Forty-three increased by some
number.
For 13–14, find the value for each
expression.
13. 17 – n for n = 4
14. p + 7 for p = 12
SR6
Spiral Review
© Harcourt • Grade 5
Week 7
Name
Spiral Review
For 1–6 estimate. Then find the
product.
For 9–10, find the median
and mode.
9. 1, 2, 3, 4, 5, 2, 1, 4, 1, 6
1.
0.6
⫻ 0.7
2.
2.4
⫻ 0.8
3.
25.9
⫻ 0.3
4.
7.40
⫻ 2.7
10. 6, 8, 1, 7, 3, 6, 9
5. 0.47 ⫻ 0.62 =
6. 0.452 ⫻ 3.6 =
For 7–8, find the area.
7.
14 ft
6 ft
For 11–12, tell whether the figure
appears to have line symmetry,
rotational symmetry, both,
or neither.
11.
8.
12.
7 cm
7 cm
For 13–14, draw all lines of symmetry.
13.
SR7
14.
Spiral Review
© Harcourt • Grade 5
MXENL08AWK5X_SR_WK07.indd SR7
6/15/07 2:26:37 PM
Week 8
Name
Spiral Review
For 1–4, find the quotient.
1. 6
20.4
2. 4
9.66
For 7–10, choose 5, 10, or
100 as the most reasonable
interval for each set of data.
7. 90, 350, 260, 185, 415
8. 7, 23, 25, 18, 11
3. 23
59.11
9. 52, 76, 24, 54, 61
4. 53
75.26
10. 218, 371, 882, 119, 505
For 5-6, find the volume.
5.
For 11-14, write an algebraic
expression for each phrase.
11. 15 books on each of b shelves
12. 22 more than m DVDs
13. $36 shared equally among y friends
6.
14. 18 less than r
For 15–18, evaluate each expression
for a = 6.
15. a + 27
16. 24 ⫼ a
17. 14 ⫻ a
18. 19 – a
SR8
Spiral Review
© Harcourt • Grade 5
MXENL08AWK5X_SR_WK08.indd SR8
6/19/07 10:41:18 AM
Week 9
Name
Spiral Review
For 1–4, complete to
find the sum or difference.
1.
3.
738,521
⫹ 601,994
54,639
⫺ 37,840
2.
1B,7B9
1,34B,B1B
4,193
⫹ 5,570
4.
B,7B3
65,574
⫺ 7,321
5B,2B3
For 5–6, estimate. Then find the sum or
difference.
5.
84,679
⫹ 39,213
6.
5,807,436
⫹ 2,789,015
For 7–9, find the elapsed time.
7. start: 10:45 a.m.
end: 1:00 p.m.
For 12–15, find the mean
for each set of data.
12. 13, 8, 11, 9, 14
13. 68, 73, 86, 61
14. 234, 186, 213
15. 78, 63, 98, 27, 44
For 16–18, use the given mean to find
the missing value in each set of data.
16. 17, 12, 18,
; mean: 13
17. 69, 84, 73,
; mean: 81
18. 78, 93, 86,
; mean: 82
For 19–21, name a solid
figure that is described.
19. one circular face
8. start: 4:30 p.m.
end: 7:15 p.m.
9. start: 8:30 p.m.
20. six rectangular faces
end: 11:00 p.m.
21. four vertices
For 10–11, find the ending time.
10. start: 3:00 p.m.
elapsed time: 4 hr 20 mi
11. start: 8:30 p.m.
For 22–23, would the net make a cube.
Write yes or no.
22.
23.
elapsed time: 5 hr 45 mi
SR9
Spiral Review
© Harcourt • Grade 5
Week 10
Name
Spiral Review
For 1–12, estimate the product.
2. 61 ⫻ 28
3. 57 ⫻ 214
4. 46 ⫻ 697
5. 425 ⫻ 19
6. 768 ⫻ 86
T-Shirt Sales
Number Sold
1. 23 ⫻ 44
For 23–25, use the graph.
60
50
40
30
20
10
0
Aug
Sept
Oct
Month
Nov
Dec
23. During which month were 30 T-shirts
7. 61 ⫻ 926
sold?
8. 584 ⫻ 73
24. How many T-shirts were sold in
9. 836 ⫻ 5,927
10. 2,483 ⫻ 369
September?
25. Describe the change in T-shirt sales
between October and November.
11. 82 ⫻ 9,371
12. 46 ⫻ 34,672
For 13–22, change each unit.
For 26–28, write an
algebraic expression.
13. 500 cm =
m
14. 30 mm =
cm
15. 8 cm =
mm
16. 10 m =
cm
17. 700 mm =
cm
18. 20 cm =
m
19. 5 m =
mm
20. 2,000 =
m
For 29–31, find the value for each
expression.
21. 400 mm =
m
29. 14 + n for n = 6
22. 60 m =
cm
26. James had $34 in his wallet.
He spent some of the money.
27. Twenty-six decreased by some
number.
28. Anna had 14 DVDs. She bought
some more DVDs
30. 9p for p = 11
31. 15 – b for b = 7
SR10
Spiral Review
© Harcourt • Grade 5
Week 11
Name
Spiral Review
For 1–11, find all the factors for
each product.
1. 24
For 13–16, use the picture to
find the probability of each
event.
2. 16
3. 27
4. 30
13. pulling a 1
5. 42
6.
8
14. pulling a 2 or 3
7. 14
8. 21
9.
5
15. pulling a 1 or 4
10. 12
11. 10
16. pulling a tile that is not 3
Find the perimeter and area
of the figure below. Then draw
another figure that has the same area
but a different perimeter.
For 17–19, draw circle A with
a 3-centimeter radius. Label
each of the following.
12.
8 cm
6 cm
17. radius BA
18. chord CD
19. diameter FG
SR11
Spiral Review
© Harcourt • Grade 5
Week 12
Name
Spiral Review
For 1–6, compare.
Write <, >, or = for each
1
1. __
3
5
2. __
7
1
__
2
3
__
3. 4 7
7
___
5. 2 12
Make a bar graph to show
the data below.
__
42
5
__
25
8
__3
13.
5
1
__
4. 3 3
4
3 ___
12
__
22
8
1 ___
6.
3
Joe’s Marbles
Red
Green
Blue
Brown
21
16
10
23
15
For 7–8, write in order
from least to greatest.
5
1
__ , 5
__ , 1
__
__ 2
__ 4
__
7.
8. 2 , 3 , 2
3 6 6
6
For 9–10, find the volume.
9.
3
9
For 12–17, use counters to
show all arrays for each
number. Write prime or composite.
12. 35
13. 9
14. 29
10.
15. 101
16. 75
17. 55
SR12
Spiral Review
© Harcourt • Grade 5
Week 13
Name
Spiral Review
For 1–6, add or subtract. Then
write the answer in simplest
form.
1.
__
41
2.
8
5
+ 3__
8
_
For 9–11, use the tally table.
Length of Family Vacations
3
8 ___
12
1
⫺3___
12
_
Days
Tally
Total
5
10
15
20
__ ⫹ 7 2
__ ⫽
3. 5 1
3
3
__ ⫺ 2 2
__ ⫽
4. 9 5
9
9. Complete the total column
9
in the tally table.
10. How many family vacations last 10
6
7
5. 6 ___
⫺ 1 ___
⫽
10
10
__ ⫹ 6 2
__ ⫽
6. 3 1
4
4
days?
11. Which number of family vacation days
has the greatest total?
For 7–8, use the thermometer to
find the temperature in °C.
7.
For 12–15, write parallel,
intersecting, or
perpendicular for each.
60
12.
55
13.
W
Y
X
L
P
O
M
A
B
D
C
Z
50
°C
Q
14.
8.
15.
0
R
S
-5
-10
°C
SR13
Spiral Review
© Harcourt • Grade 5
MXENL08AWK5X_SR_WK13.indd SR13
7/2/07 2:17:09 PM
Week 14
Name
Spiral Review
For 12–13, for each experiment,
tell whether events A and B are
equally likely or not equally likely. If
they are not equally likely, name the
event that is more likely.
For 1–6, write each fraction as
a decimal.
1.
3
5
2.
5
25
3.
4
10
4.
37
100
28
5.
50
12. Experiment: Flip a coin
Event A: heads
Event B: tails
2
6.
100
For 7–9, write each decimal
as a fraction in simplest form.
7. 0.35
8. 0.45
13. Experiment: Pick a marble
9. 0.26
Event A: gray
Event B: black
For 10–11, find the area.
10.
For 14–15, write an equation.
Tell what the variable
represents.
3m
14. Brad has 28 oranges. He gives some
away. He now has 11 oranges. How
many oranges does Brad give away?
7m
11.
13 in.
15. Gina divides some crackers among
13 in.
her 4 friends. She gives each friend
6 crackers. How many crackers did
Gina have?
SR14
Spiral Review
© Harcourt • Grade 5
Week 15
Name
Spiral Review
For 1–4, solve each problem.
For 7–9, use the bar graph.
1. What is the value of the underlined
.UMBEROF-OONS
digit in 4,239,561?
2. Write 2,345,587 in expanded form.
3. Write the standard form of three
hundred three million, five hundred
twenty-six thousand, ninety-one.
.EPTUNE 3ATURN 5RANUS
0LANET
-ARS
%ARTH
7. Which planet has the greatest number
of moons?
8. Which planet has 1 more moon than
4. Write 9,641,508 in word form.
Earth?
9. How many moons does Neptune
have?
For 10–13, classify each triangle.
Write isosceles, scalene, or
equilateral. Then write right, acute,
or obtuse.
For 5–6, find the perimeter.
5.
)+`e%
10.
,Zd
11.
,`e%
*`e%
,Zd
+`e%
,Zd
*.`e%
6.
12.
0d
(,d
0d
(0d
(+d
13.
/]k
/]k
,]k
()d
SR15
Spiral Review
© Harcourt • Grade 5
Week 16
Name
Spiral Review
For 1–8, find the sum or
difference in simplest form.
1.
2
2
⫺
⫽
5 10
2.
3 1
⫹ ⫽
4 3
3.
1 1
⫹ ⫽
2 6
4.
2 1
⫺ ⫽
3 6
For 12–15, use the picture to find
the probability of each event.
12. pulling a gray marble
5.
7.
3 1
⫺ ⫽
4 2
6.
3
1
⫹ ⫽
10 5
8.
1 3
⫹ ⫽
4 8
5 1
⫺ ⫽
8 4
13. pulling a gray or black marble
14. pulling a white or gray marble
15. pulling a blue marble
For 9–11, use a calendar to solve.
9. The zoo will be offering discount
tickets from January 3 to January 29.
How many days will tickets be
discounted?
For 16–21, graph and label
the following points on the
coordinate grid.
16. A (4,3)
17. B (2,5)
18.
C (0,7)
19. D (3,4)
20.
E (6,4)
21.
F (5,1)
10. The pet store is having a sale on dog
p
and cat food from February 1 to
February 16. How many days will the
food be on sale?
/
.
,
+
*
)
(
11. Delia paid for her newspaper delivery
on July 1. She last paid for it three
weeks and four days ago. When did
she last pay for her newspaper
delivery?
'
SR16
( ) * + , - . /
o
Spiral Review
© Harcourt • Grade 5
MXENL08AWK5X_SR_WK16.indd SR16
7/31/07 9:37:59 AM
Week 17
Name
Spiral Review
For 1–10, estimate the product.
1. 23 ⫻ 44
2. 61 ⫻ 28
For 18–21, use the stem-andleaf plot.
Grades on a Science Test
Stem
3. 57 ⫻ 214
4. 46 ⫻ 697
5. 425 ⫻ 19
6. 768 ⫻ 86
6
7
8
9
Leaf
7 9
0 3 4 6 6 9
2 4 4 6 7 8 8 9
1 3 5 5 5 8
6 | 7 represents 67
18. How many students earned a grade
of 76?
7. 61 ⫻ 926
8. 584 ⫻ 73
19. How many students earned a grade
between 85 and 90?
20. Which grade occurred most often?
9. 86 ⫻ 597
10. 243 ⫻ 36
21. What is the difference between the
highest grade and the lowest grade?
For 11–17, change the unit.
11. 5,000 m ⫽
12. 8 kL ⫽
13. 16 m ⫽
14. 36 cm ⫽
15. 200 cm ⫽
16. 6,000 L ⫽
17. 71 km ⫽
km
L
For 22–25, classify each solid
figure. Write prism, pyramid,
cylinder, cone, or sphere.
22.
23.
24.
25.
cm
mm
m
kL
m
SR17
Spiral Review
© Harcourt • Grade 5
Week 18
Name
Spiral Review
For 1–4, write an equivalent
fraction.
1.
3.
1
2
2.
4
10
4.
3
9
Make a tree diagram to find the
number of possible combinations.
12. Activity choices
activity: zoo, park, museum
time: morning, afternoon, evening
3
15
For 5–8, tell which fraction is not
equivalent to the others.
2 4 3
5 4 2
5.
, ,
6.
, ,
5 10 8
12 8 4
7.
1 5 2
, ,
3 9 6
8.
6 4 9
, ,
8 6 12
For 9–10, find the perimeter of
each polygon.
9.
23 cm
For 13–14, find the rule to
complete the function table. Then
write the rule as an equation.
13.
11 cm
11 cm
input, x
24
output, y
8
4
2
input, x
2
6
8
output, y
4
18
12
16 cm
10.
9 in.
14.
SR18
10
16
Spiral Review
© Harcourt • Grade 5
Week 19
Name
Spiral Review
For 1–4, multiply.
1.
3.
308
⫻ 52
_
2.
582
⫻
41
_
4.
Use the data to make a
circle graph.
649
⫻ 37
_
6.
825
⫻
24
_
Name
Number of Votes
Sarah
30
Ty
50
Mike
20
Class President Election
Find the perimeter and area
of the figure. Then draw
another figure that has the same
perimeter but a different area.
5.
Class President Election
For 7–9, tell if the net would
make a cube. Write yes or no.
8 in.
7.
2 in.
8.
9.
SR19
Spiral Review
© Harcourt • Grade 5
MXENL08AWK5X_SR_WK19.indd SR19
7/2/07 2:18:41 PM
Week 20
Name
Spiral Review
For 1–6, find the sum or
difference.
1.
3.
85.19
37.48
__
2.
7.081
6.254
__
4.
For 9–11, use the doublebar graph.
Activities
251.895
75.362
__
Boys
Girls
25
20
15
10
5
0
3.582
0.763
__
Drama
Club
Science
Club
Poetry
Club
Soccer
Activity
9. How many sets of data does the graph
5.
0.85
0.063
3.572
6.
11.804
6.137
15.749
For 7–8, find the volume of each
rectangular prism.
show?
10. Which activity has the greatest number
of girls?
11. How many more girls than boys are
signed up for drama club?
For 12–19, solve each equation.
12. 39 15 r
13. 3 n 75
14. a 8 8
15. 36 w 20
16. 4 y 20
17. 80 h 4
7.
*p[
*p[
(,p[
8.
7 ft
7 ft
18. y 3 49 13 19. 25 17 48 b
7 ft
SR20
Spiral Review
© Harcourt • Grade 5
Week 21
Name
Spiral Review
For 11–13, tell whether each
sample represents the
population. If it does not, explain.
A food company wants to know if people
ages 18–40 like their new pasta.
For 1–4, use basic facts
and patterns to solve.
1. 60 ⫼ 10
2. 630 ⫼ 70
11. a random sample of 500 women,
ages 18–40
3. 7,200 ⫼ 8
4. 48,000 ⫼ 60
12. a random sample of 500 people,
ages 18–40
For 5–6, divide.
5. 24
318
6. 72
609
For 7–10, write the time shown
on the analog clock.
7.
9.
11 12 1
2
10
9
3
4
8
7 6 5
5 6
11 12 1
2
10
9
3
4
8
7 6 5
8.
10.
13. a random sample of 500 adults
For 14–19, use the figure.
Name an example of each.
11 12 1
2
10
9
3
4
8
7 66 55
6
11 12 51
2
10
9
3
4
8
7 6 5
<
A
9
;
?
8
=
>
:
14. ray
15. point
16. line
17. vertex
18. line segment
19. vertical
angles
For 20–21, use the figure above. Classify
each angle. Write acute, obtuse, straight,
or right.
20. ⬔DAB
21. ⬔BAC
SR21
Spiral Review
© Harcourt • Grade 5
Week 22
Name
Spiral Review
For 1–6, compare.
Write ⬍, ⬎, or ⴝ for each
1.
5
7
2
3
2.
Make a list or tree diagram to
find all possible combinations.
.
4
5
13. Sandwich choices
6
7
3. 3
1
5
3
1
3
4. 1
4
6
1
2
3
5. 3
3
4
3
7
12
6. 2
1
2
2
5
6
meat: ham, turkey, roast beef
cheese: American, cheddar
bread: wheat, white
For 7–8, write in order from least to
greatest.
7.
5 7 2
, ,
6 12 5
3
4
5
9
8. 3 , 3 , 3
For 9–12, write the time for
each.
9. Start: 7:38 A.M.
Elapsed time: 3 hr 52 min
1
3
For 14–16, find the rule to
complete the function table.
Then write an equation.
14.
End:
x
0
1
y
0
6
x
12
10
y
6
x
13
y
9
2
4
18
24
6
4
10. Start:
Elapsed time: 2 hr 31 min
End: 10:25 P.M.
15.
8
4
2
11. Start: 11:16 A.M.
Elapsed time: 1 hr 19 min
End:
16.
12. Start: 2:37 P.M.
11
9
7
5
3
5
Elapsed time:
End: 4:19 P.M.
SR22
Spiral Review
© Harcourt • Grade 5
Week 23
Name
Spiral Review
For 12–14, use the table. The
table shows the results of
a marble experiment.
For 1–3, compare. Write ⬍, ⬎,
or ⫽ for each
1. 0.754
2. 1.09
3. 10
.
0.734
Marble Experiment
1.10
0.909
Red
Blue
Green
8
3
9
Number of Pulls
Total
For 4–6, order from greatest to least.
12. What is the experimental probability of
4. 1.345; 1.305; 1.354
pulling a red marble?
5. 0.101; 0.110; 0.100
13. What is the experimental probability of
pulling a blue marble?
6. 73.806; 7.386; 73.860
14. What is the experimental probability of
pulling a green marble?
For 7–11, use the thermometer
to find the change in temperature.
7. 12°F to 31°F
8. 0°F to 35°F
9.
10°F to 7°F
–
10. 74°F to 88°F
11. 0°F to –6°F
100
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
–10
For 15–16, classify each figure in
as many ways as possible. Write
quadrilateral, parallelogram, square,
rectangle, rhombus, or trapezoid.
15.
–10
16.
°F
SR23
Spiral Review
© Harcourt • Grade 5
Week 24
Name
Spiral Review
For 1–8, find the sum or difference.
Write it in simplest form.
2
2
1. __
__ 5
5
3
1
2. __
__ 8
8
For 11–12, use the table to find
the experimental probability. Then
predict the outcome of future trials.
11. number of green tiles in 40 more pulls
Tile Pulls
__ __ 1
3. 4
9
9
2
5
4. __ __ 7
7
6
4
5. ___
___
12
12
1
3
6. __ __ 4
4
Green
Red
Orange
12. number of wins in 36 more games
Games
2
6
7. ___ ___ 10
10
Wins
2
8
8. __ __ 9
9
For 9–10, estimate the area of the
shaded figure. Each square on the
grid is 1 cm2.
Losses
For 13–20, solve each equation.
13. 49 h 17
14. 24 a 8
15. 9 n 54
16. $42 w $35
17. 3 y 42
18. h 7 4
19. d 9 21 3
20. 34 8 n 10
9.
10.
SR24
Spiral Review
© Harcourt • Grade 5
Week 25
Name
Spiral Review
For 1–6, write two equivalent
ratios for each ratio. Use
multiplication and division.
Make a bar graph of the data.
19.
__
1. 2
3
Stock X Price
Month
Jan
Feb
Mar
Apr
Price
$46
$65
$52
$48
2. 4 to 10
3. 3:5
15
4. ___
18
5. 1 to 7
6. 15:5
For 7–18, change the unit.
7. 36 in. ft
8. 28 qt gal
9. 5 lb oz
10. 24 ft yd
11. 4 pt fl oz
12. 3 T lb
13. 3 mi ft
14. 36 qt gal
15. 48 c qt
16. 2.5 T lb
17. 2 ft 4 in. in.
18. 6 yd 3 ft in.
For 20–23, draw lines of
symmetry. Tell whether each
figure has rotational symmetry.
Write yes or no.
20.
21.
22.
23.
SR25
Spiral Review
© Harcourt • Grade 5
MXENL08AWK5X_SR_WK25.indd SR25
6/15/07 2:28:02 PM
Week 26
Name
Spiral Review
Make a list or draw a tree
diagram to find the total
number of arrangements.
For 1–4, solve each problem.
1. Write 690,303,520,002 in
expanded form.
10. ways to pull green, yellow, and blue
tiles from a bag without looking
2. What is the value of the underlined digit
in 32,405,922,287?
3. Write the standard form of five billion,
six hundred ninety-six million, three
hundred seventy-five thousand, twelve.
4. What digit is in the ten billions place in
670,050,213,604?
For 5–9, use the thermometer
to find the change in
temperature.
30
5. 0°C to 18°C
20°C to ⫺5°C
6.
⫺
7.
⫺
Write the ordered pairs.
Then graph them.
30
20
20
10
10
0
0
11.
x
0
1
2
3
4
y
0
3
6
9
12
8. 75°C to 10°C
9. 0°C to
16°C
–10
–10
–20
–20
–30
–30
y-axis
15°C to 10°C
⫺
°C
12
11
10
9
8
7
6
5
4
3
2
1
0
SR26
1 2 3 4 5 6 7 8 9 10 11 12
x-axis
Spiral Review
© Harcourt • Grade 5
Week 27
Name
Spiral Review
For 1–4, find the product. Write
it in simplest form.
3
1
1. __ ⫻ __ ⫽
7
3
For 16–18, use the tally table.
Books Students Read
Books
2
1
2. __ ⫻ __ ⫽
5
3
Students
Frequency
2
3
3
2
3. __ ⫻ __ ⫽
5
4
5
3
4. __ ⫻ ___ ⫽
6
10
For 5–8, use a reciprocal to write a
multiplication problem for the division
problem.
1
5. 1__ ⫼ 2 ⫽
2
7
1
6. ___ ⫼ __ ⫽
2
3
7. 3__ ⫼ __ ⫽
3
4
5
1
8. __ ⫼ __ ⫽
8
4
12
4
5
16. Complete the frequency column in the
table.
17. How many books read have the
greatest frequency?
4
For 9–15, write the appropriate
metric unit to measure each.
18. What is the range of the data?
For 19–25, write acute, right,
or obtuse for each angle.
9. length of your hand
:
;
9
10. height of a house
11. length of an insect
8
=
<
19. ⬔ AFD
20. ⬔ BFA
12. distance from New York to Michigan
13. length of a soccer field
21. ⬔ CFD
22. ⬔ BFE
23. ⬔ DFE
14. length of a classroom
24. ⬔ CFA
25. ⬔ EFC
15. length of a crayon
SR27
Spiral Review
© Harcourt • Grade 5
Week 28
Name
Spiral Review
For 1–3, write each percent as a
decimal and as a fraction in
simplest form.
For 9–11, use the
Fundamental Counting
Principle to find the total number
of outcomes.
1. 36%
9. choosing an outfit with blue or tan
2. 74%
pants and a green or red shirt
3. 40%
For 4–6, write each fraction or decimal as
a percent.
___
4. 12
25
10. tossing a cube labeled 1 to 6 and
flipping a penny
11. using two spinners, both with four
5. 0.06
equal sections of red, blue, green,
and yellow
9
6. ___
20
For 7–8, find the area of each
figure.
7.
)-]k
(*]k
8.
For 12–17, graph and label
the ordered pairs on the
coordinate plane.
12. A (3,1)
13. B (0,5)
14. C (4,2)
15. D (4,1)
16. E (5,2)
17. F (3,2)
y-axis
(,Zd
(,Zd
7
6
5
4
3
2
1
0
SR28
1 2 3 4 5 6 7
x-axis
Spiral Review
© Harcourt • Grade 5
MXENL08AWK5X_SR_WK28.indd SR28
6/15/07 2:26:10 PM
Week 29
Name
Spiral Review
For 1–8, estimate by rounding.
1.
29.63
⫹ 18.05
2.
87.905
⫺ 38.714
For 13–16, choose the best type
of graph or plot for the data.
13. number of students in 7 classrooms
3.
4.139
⫹ 7.652
4.
2.763
⫺ 0.509
14. hours people spend fishing
5. 93.47 ⫺ 62.13
6. 11.042 ⫹ 8.765
15. different seating sections of a stadium
7. 43.869 ⫺ 10.062
8. 0.654 ⫺ 0.398
For 9–12, write the missing time
for each.
9. Start: 9:45 A.M.
Elapsed time: 2 hr 45 min
End:
16. deer population over a 6-year period
For 17–18, classify each figure
in as many ways as possible.
Write quadrilateral, parallelogram,
square, rectangle, rhombus, or trapezoid.
17.
10. Start:
Elapsed time: 3 hr 25 min
End: 8:15 P.M.
11. Start: 10:29 A.M.
Elapsed time: 2 hr 19 min
End:
18.
12. Start: 3:15 P.M.
Elapsed time:
End: 4:57 P.M.
SR29
Spiral Review
© Harcourt • Grade 5
Week 30
Name
Spiral Review
For 1–4, find the product.
1.
3.
315
57
_
2.
493
62
_
4.
Draw a tree diagram to find
the total number of outcomes.
642
38
_
9. tossing a number cube labeled
1 to 6 and tossing a coin
510
26
_
For 10–15, use prime or
composite.
For 5–8, find the perimeter of
each regular polygon.
5.
()Zd
6. /d
10. 7
11. 27
12. 16
7.
8.
13. 81
)(*p[
14. 19
/%)]k
15. 12
SR30
Spiral Review
© Harcourt • Grade 5
Week 31
Name
Spiral Review
For 1–3, name the GCF of the
numerator and denominator.
1.
8
14
2.
12
32
3.
For 18–20, use the line plot.
✗
✗
✗
✗ ✗ ✗ ✗
✗ ✗ ✗ ✗ ✗
12
36
For 4–6, write each fraction in simplest
form.
6
4.
15
16
5.
28
1
2
3
4
5
✗
✗ ✗ ✗
✗ ✗ ✗ ✗
6
7
8
9 10
Number of Miles Run
25
6.
40
18. What is the median?
For 7–9, complete.
19. What is the mode?
7.
2
8
=
3
8.
30
=
1
6
9.
4
=
12
21
20. What is the mean?
For 10–17, find the sum or
difference.
For 21–23, match each solid figure
with its net.
10. 3.50 cm ⫹ 2.7 m ⫽
21.
a.
22.
b
23.
c
11. 15 m ⫹ 25 cm ⫽
12. 54 mm ⫺ 5.4 cm ⫽
13. 2.036 m ⫺ 36 mm ⫽
14.
6 ft 5 in.
⫹ 3 ft 6 in.
15.
12 yd 2 ft
⫹ 5 yd 1 ft
16.
9 ft 3 in.
⫺ 7 ft 4 in.
27.
12 yd
⫺ 3 yd 2 ft
SR31
Spiral Review
© Harcourt • Grade 5
MXENL08AWK5X_SR_WK31.indd SR31
6/15/07 2:28:21 PM
Week 32
Name
Spiral Review
For 1–11, write the common
factors for each pair of numbers.
1. 10, 35
For 14–16, express the
experimental probability as
a fraction in simplest form.
14. 3 green sections in 18 spins.
2. 8, 32
How many green sections in 24
more spins?
3. 7, 42
4. 15, 45
5. 12, 30
15. 6 red marbles out of 15 pulls.
How many red marbles in 35
more pulls?
6. 9, 27
7. 13, 26
8. 16, 40
16. 10 losses in 16 games.
9. 21, 63
How many losses in 40 more
games?
10. 4, 20
11. 18, 24
For 12–13, find the volume of each
rectangular prism.
Write the ordered pairs.
Then graph them.
12.
17.
-Zd
x
0
1
2
3
4
y
0
3
6
9
12
,Zd
(/Zd
.`e%
13.
.`e%
y-axis
(*`e%
()
((
('
0
/
.
-
,
+
*
)
(
' ( ) * + , - . / 0 (' (( ()
x-axis
SR32
Spiral Review
© Harcourt • Grade 5
Week 33
Name
Spiral Review
For 11–12, use the graph.
For 1–4, write each mixed
number as a fraction.
Average Monthly Temperature (°F)
100
3. 1
Temperature (°F)
2
4
1. 1 5
2. 2 3
2
7
4. 3
8.
8
20
June
July
Aug
Sept
Month
11. What scale and interval are used in
the line graph?
12. How would you change the graph if
13
7. 17
40
May
6. 15
5
60
0
3
8
For 5– 8, write each fraction
as a mixed number.
5. 8
80
the temperature for August were
80° Fahrenheit?
37
12
For 9–10, write whether you need
to find perimeter, area, or volume
to solve the problem. Then solve
using the appropriate formula.
For 13–14, name each
transformation. Write
translation, reflection, or rotation.
13.
9. tile for this floor
12 ft
15 ft
14.
10. wrapping paper for this box
8 in.
20 in.
8 in.
SR33
Spiral Review
© Harcourt • Grade 5
Week 34
Name
Spiral Review
For 1–7, compare. Write ⬍, ⬎,
or ⫽ for each
.
For 10–14, write a fraction
to show the probability of
tossing a number cube labeled 1 to 6.
1. 0.643
0.629
2. 1.517
1.538
3. 3.249
2.221
11. an odd number
4. 7.440
7.442
12. a prime number
5. 0.820
0.82
6. 0.137
0.13
7. 2.228
3.282
For 8–9, find the area.
8.
10. a 3
13. a number greater than 4
14. a number less than 8
For 15-16, write a numerical
expression. Tell what the
expression represents.
15. Kate had $30. She spent $8 to
()]k
see a movie and $15 to buy a shirt.
(/]k
9.
16. Tyler scored 12 points in the first half
/`e%
of the game and 17 points in the
second half of the game.
(+`e%
SR34
Spiral Review
© Harcourt • Grade 5
MXENL08AWK5X_SR_WK34.indd SR34
7/2/07 2:19:07 PM
Week 35
Name
Spiral Review
For 1–8, estimate the product.
1. 68 ⫻ 24
2. 83 ⫻ 49
For 11–13, name the most
appropriate graph.
11. Which type of graph would be most
3. 35 ⫻ 853
appropriate to record the growth of a
plant over 5 weeks?
4. 73 ⫻ 985
12. Which type of graph would be most
5. 568 ⫻ 31
6. 828 ⫻ 76
7. 34 ⫻ 964
8. 672 ⫻ 95
appropriate to show the attendance for
a week at the state fair?
13. Which type of graph would be most
appropriate to show how a person’s
income is spent each month?
For 9–10, find the perimeter.
9.
For 14–15, classify each triangle.
Write isosceles, scalene, or
equilateral.
14 in.
14.
8 cm
5 cm
37 in.
15.
14 ft
14 ft
11 cm
9 ft
10.
15 m
9m
12 m
Classify each triangle. Write acute, right or
obtuse.
16.
SR35
Spiral Review
© Harcourt • Grade 5
Week 36
Name
Spiral Review
For 1–6, write each fraction as
a decimal.
__
1. 4
5
7
2. ___
20
3
3. ___
10
84
4. ____
100
35
5. ___
50
78
6. ____
100
For 18–21, use the spinner.
Write the probability of each
event. Tell whether the event is certain,
likely, unlikely, or impossible.
18. spinning black
19. spinning gray
For 7–12, write each decimal as a fraction
in simplest form.
7. 0.2
8. 0.38
9. 0.57
10. 0.46
11. 0.65
12. 0.44
20. spinning white or gray
21. spinning green
For 13–17, tell the units you
would use for measuring each.
Write linear, square, or cubic.
For 22–24, find the rule to
complete the function table.
Then write the rule as an
equation.
13. the amount of carpet needed to cover
22.
a floor
input, x
24
output, y
6
4
3
input, x
15
19
21
output, y
17
input, x
5
output, y
35
20
16
14. the amount of water in a bathtub
23.
15. the amount of wrapping paper needed
19
23
to cover a box
16. the height of a picture frame
24.
9
49
11
77
17. the width of a door
SR36
Spiral Review
© Harcourt • Grade 5
MXENL08AWK5X_SR_WK36.indd SR36
6/19/07 10:41:55 AM