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PRACTICE Workbook
Visit The Learning Site! www.harcourtschool.com
HSP
Grade 5
Copyright © by Harcourt, Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission is hereby granted to individuals using the corresponding student’s textbook or kit as the major vehicle for regular classroom instruction to photocopy entire pages from this publication in classroom quantities for instructional use and not for resale. Requests for information on other matters regarding duplication of this work should be addressed to School Permissions and Copyrights, Harcourt, Inc., 6277 Sea Harbor Drive, Orlando, Florida 32887-6777. Fax: 407-345-2418. HARCOURT and the Harcourt Logo are trademarks of Harcourt, Inc., registered in the United States of America and/or other jurisdictions. Printed in the United States of America ISBN 13: 978-0-15-356762-9 ISBN 10: 0-15-356762-7 If you have received these materials as examination copies free of charge, Harcourt School Publishers retains title to the materials and they may not be resold. Resale of examination copies is strictly prohibited and is illegal.
Possession of this publication in print format does not entitle users to convert this publication, or any portion of it, into electronic format. 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 © Harcourt • Grade 5
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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
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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.
.UMBER OF 0ROBLEMS
-Y (OMEWORK 0ROGRESS .UMBER OF 0ROBLEMS !SSIGNED
.UMBER OF 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
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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
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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
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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
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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
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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
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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
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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?
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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
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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
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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
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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
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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.
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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
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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
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6
C
7
D 10
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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
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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.
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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.
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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)
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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?
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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
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4,000
4
4
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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
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⫺
8
⫺
7
⫹
8
⫹
9
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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)
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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:
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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:
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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
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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
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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
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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?
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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.
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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
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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.
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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
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4.6 cm
C
10.4 cm
D 14 cm
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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
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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?
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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?
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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
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15 cm2
1 cm.2
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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
.UMBER OF -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
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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
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UNIT 1: USE WHOLE NUMBERS Chapter 1: Place Value, Addition, and Subtraction 1.1 1.2 1.3 1.4 1.5 1.6 1.7
Place Value Through Millions ............PW1 Understand Billions ............................PW2 Compare and Order Whole Numbers .................................PW3 Round Whole Numbers .....................PW4 Estimate Sums and Differences .........PW5 Add and Subtract Whole Numbers ...PW6 Problem Solving Workshop Strategy: Work Backward ..................PW7
4.7 4.8 4.9
UNIT 2: USE DECIMALS Chapter 5: Understand Decimals 5.1 5.2 5.3 5.4
Chapter 2: Multiply Whole Numbers 2.1 2.2 2.3 2.4 2.5 2.6
Mental Math: Patterns in Multiples .............................................PW8 Estimate Products ...............................PW9 Multiply by 1-Digit Numbers ...........PW10 Multiply by Multi-Digit Numbers ....PW11 Problem Solving Workshop Strategy: Find a Pattern ...................PW12 Choose a Method .............................PW13
Chapter 3: Divide by 1- and 2-Digit Divisors 3.1 3.2 3.3
Estimate with 1-Digit Divisors .........PW14 Divide by 1-Digit Divisors ................PW15 Problem Solving Workshop Skill: Interpret the Remainder..................PW16 3.4 Zeros in Division ...............................PW17 3.5 Algebra: Patterns in Division ...........PW18 3.6 Estimate with 2-Digit Divisors .........PW19 3.7 Divide by 2-Digit Divisors ................PW20 3.8 Correcting Quotients .......................PW21 3.9 Practice Division ...............................PW22 3.10 Problem Solving Workshop Skill: Relevant or Irrelevant Information ......................................PW23
Chapter 4: Expressions and Equations 4.1 4.2 4.3 4.4 4.5 4.6
Write Expressions .............................PW24 Evaluate Expressions ........................PW25 Properties..........................................PW26 Mental Math: Use the Properties....PW27 Write Equations................................PW28 Solve Equations ................................PW29
Functions...........................................PW30 Inequalities .......................................PW31 Problem Solving Workshop Strategy: Predict and Test ................PW32
Decimal Place Value .........................PW33 Equivalent Decimals .........................PW34 Compare and Order Decimals .........PW35 Problem Solving Workshop Skill: Draw Conclusions .............................PW36
Chapter 6: Add and Subtract Decimals 6.1 6.2 6.3 6.4 6.5
Round Decimals ................................PW37 Add and Subtract Decimals .............PW38 Estimate Sums and Decimals ...........PW39 Choose a Method .............................PW40 Problem Solving Workshop Skill: Estimate or Find Exact Answer........PW41
Chapter 7: Multiply Decimals 7.1 7.2 7.3 7.4 7.5 7.6 7.7
Model Multiplication by a Whole Number ..............................PW42 Algebra: Patterns in Decimal Factors and Products ........................PW43 Record Multiplication by a Whole Number ..............................PW44 Model Multiplication by a Decimal ..........................................PW45 Estimate Products .............................PW46 Practice Decimal Multiplication ......PW47 Problem Solving Workshop Skill: Multistep Problems .........................PW48
Chapter 8: Divide Decimals by Whole Numbers 8.1 8.2 8.3 8.4
Decimal Division ...............................PW49 Estimate Quotients ..........................PW50 Divide Decimals by Whole Numbers............................................PW51 Problem Solving Workshop Skill: Evaluate Answers for Reasonableness ................................PW52
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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 © Harcourt • Grade 5
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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
© Harcourt • Grade 5
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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.
.UMBER OF 0ROBLEMS
-Y (OMEWORK 0ROGRESS .UMBER OF 0ROBLEMS !SSIGNED
.UMBER OF 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
MXENL08AWK5X_PH_C01_L2.indd PW2
6/27/07 9:53:13 AM
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
6/15/07 12:12:35 PM
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
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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
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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
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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
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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?
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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
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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
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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
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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?
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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
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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
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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
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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.
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and a nickel. How much money does Dylan have? Show your work
Practice © Harcourt • Grade 5
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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.
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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
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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
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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
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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
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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
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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
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Practice © Harcourt • Grade 5
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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
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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
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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?
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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
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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
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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
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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.
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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.
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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
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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
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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
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6
C
7
D 10
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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)
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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.
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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
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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.
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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
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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
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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
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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.
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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
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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
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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?
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Practice © Harcourt • Grade 5
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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?
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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
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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
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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
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Practice © Harcourt • Grade 5
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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
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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
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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
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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
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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
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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
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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?
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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.
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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
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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
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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
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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?
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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
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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
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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
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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⬚
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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
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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
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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
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B
90° X
171° C
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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
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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
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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⬚
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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⬚
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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
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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
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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?
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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
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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.
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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
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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.
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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.
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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
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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?
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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
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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)
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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?
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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
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4,000
4
4
4,000
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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
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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)
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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:
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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:
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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
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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
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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
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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?
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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.
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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
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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.
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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
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4.6 cm
C
10.4 cm
D 14 cm
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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
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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?
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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?
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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
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15 cm2
1 cm.2
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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
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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
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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
.UMBER OF -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
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