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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 © Harcourt • Grade 5 MXENL08AWK5X_PH_TEFM.indd iii 6/28/07 1:07:08 PM 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 MXENL08AWK5X_PH_TEFM.indd iv 7/2/07 2:53:43 PM 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 MXENL08AWK5X_PH_TEFM.indd v 7/2/07 2:53:50 PM 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 MXENL08AWK5X_PH_TEFM.indd vi 6/28/07 1:07:31 PM Homework Management A good homework management plan can streamline the process, maximize usefulness, and encourage student involvement. The plan offered here focuses on: • Student Ownership • Teacher led discussion • Quality, not quantity • Balanced-concepts, skills, and problem solving • Daily Feedback • Analysis, not just checked • Progress Graphs HSP Math offers the following resources for homework management: ■ Suggested Homework Problems, recommended problems circled in the Teacher’s Edition ■ Rationale Card in the Teacher’s Edition for easy reference and rationale to suggested homework problems ■ Progress Graphs for students to chart progress throughout the week Suggested Homework Problems are on each worksheet. The suggested problems have been carefully selected because they are a good representation of the problems in the day’s lesson. No more than 10 problems are suggested for each lesson. A Rationale Card provides the rationale behind the suggested problem chosen. You can review the rationale to evaluate which problems best suit your students’ needs before you assign homework. Progress Graphs are provided for students as a template to use with the suggested homework problems that may be assigned. Students shade the double-bar graph each day to demonstrate the progress they make on their suggested homework assignments throughout the week. The left bar reflects the total number of problems that are assigned. The right bar reflects the total number of problems the student got correct. After you write the answers on the chalkboard, students check their own homework during the morning routine while you circulate the room to review their papers. Homework is assigned Monday through Thursday only, so at the end of the week students can analyze their own work by writing two sentences about their progress. The graphs can also be placed in student portfolios for parent/teacher conferences. A sample graph is shown below. The template is provided on the next page. .UMBEROF0ROBLEMS -Y(OMEWORK0ROGRESS .UMBEROF 0ROBLEMS!SSIGNED .UMBEROF 0ROBLEMS#ORRECT -ON 4UE 7ED $AY 4HU © Harcourt • Grade 5 Number of Problems 10 9 8 7 6 5 4 3 2 1 0 Mon Wed My Homework Progress Tue Day Thu Number of Problems Assigned Number of Problems Correct © Harcourt • Grade 5 Name Lesson 1.1 Place Value Through Millions Write the value of the underlined digit. 1. 189,612,357 2. 512,897,934 3. 83,705 4. 37,115,296 5. 254,678,128 6. 631,189 7. 72,334,105 8. 345,132 9. 57,912 10. 12,465,983 11. 256,245,371 12. 15,279,328 Write the number in two other forms. 13. 647,200 14. 40,000,000 ⫹ 20,000 ⫹ 1,000 ⫹ 80 ⫹ 5 What number makes the statement true? 16. 2,760,000 ⫽ 276 ⫻ 15. 580,000 ⫽ 58 ⫻ Problem Solving and Test Prep 17. Fast Fact The diameter of Jupiter is 18. Clarrisa learns that the estimated 88,732 miles. How can Michael write the diameter of Jupiter in expanded form? 19. What is the value of the underlined digit distance between the Sun and Venus is sixty-seven million miles. How can she write this number in standard form for a poster she is making 20. In 358,247,061, which digit is in the in 729,340,233? hundred thousands place? A 20,000 A 0 20,000 C 2,000,000 D 20,000,000 B 2 C 3 B D 5 PW1 Practice © Harcourt • Grade 5 Name Lesson 1.2 Understand Billions Write the value of the underlined digit. 1. 855,283,612,681 2. 752,801,874,345 3. 25,908,167,238 4. 358,354,678,540 5. 902,851,638,411 6. 93,668,334,312 Write the number in two other forms. 7. 50,000,000,000 ⫹ 70,000,000 ⫹ 8,000,000 ⫹ 300,000 ⫹ 8,000 ⫹ 200 ⫹ 5 8. seventy billion, two hundred seventeen million, five hundred thirty-one 9. 35,089,207,450 Problem Solving and Test Prep 10. How many dimes equal the same total 11. During a year-long penny drive, a amount as 1,000,000,000 pennies? 12. What is the standard form of fifty-two volunteer group collected 10,000,000 pennies. How many stacks of 100 pennies could they make with all of their pennies? 13. In 538,479,247,061, which digit is in million, six hundred eight thousand, thirty-nine? the ten billions place? A 52,680,390 C 52,608,039 A 5 C 2 B 52,608,390 D 52,068,039 B 3 D 0 PW2 Practice © Harcourt • Grade 5 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 MXENL09AWK5X_PH_C03_L2.indd PW15 7/2/07 2:20:47 PM Name Lesson 3.3 Problem Solving Workshop Skill: Interpret the Remainder Tell how you would interpret the remainder. Then give the answer. 1. A total of 110 fifth graders are going on 2. The Bradt family is planning a hiking trip in the mountains. The Bradt’s want to hike 9 miles each day. How many days will it take for the Bradt family to hike 114 miles? How many miles will they hike on the last day? a field trip to a museum. Vans will be used for transportation. Each van holds 8 students. How many vans will be needed for the trip? 3. A total of 124 players are riding a 4. There are 230 books in the storeroom. car to the soccer game. If 5 players can ride in each car, how many cars are needed? Each box holds 7 books. How many boxes are needed to store all of the books? Mixed Applications USE DATA For 3–4, use the table. 5. Pete biked through the Appalachian Mountains on his vacation. He rode his bike for 9 miles each day until he finished his trip. How many miles did Pete bike on his last day? Miles Biked on Vacation Biker Miles Sue 114 Pete 124 Brenda 137 Charlie 109 6. If all bikers rode for 9 miles each day, who had to bike the least on the last day to finish their trip? PW16 Practice © Harcourt • Grade 5 Name Lesson 3.4 Zeros in Division Divide. 1. 6 912 2. 4 716 3. 8 829 4. 7 941 6. 5 634 7. 9 1,681 8. 4 871 9. 8 1,163 11. 764 ⫼ 2 12. 834 ⫼ 9 13. 2,251 ⫼ 4 14. 3,676 ⫼ 6 5. 3 1,373 10. 7 791 15. 5,794 ⫼ 8 Problem Solving and Test Prep 16. Each pack of marigold flowers can hold 17. Each pack of tulips can hold 9 tulips. 6 marigolds. There are 458 marigolds. How many full packs of marigolds are there? How many more marigolds are needed to fill a 6-pack of marigolds? There are 956 tulips to be packed. How many tulips will be left? How many more tulips are needed to fill a 9-pack container of tulips? 18. The population of the world in July 2006 19. A pet store sells dog bones in packages of 6. How many packages can they make from 762 dog bones? was about 6,628,506,453. What is the value of the digit 2 in that number? A 127 B 4,572 C 6 D 172 PW17 Practice © Hearcourt • Grade 5 MXENL09AWK5X_PH_C03_L4.indd PW17 6/15/07 12:27:06 PM Name Lesson 3.5 Algebra: Patterns in Division Use basic facts and patterns to find the quotient. 1. 60 ⫼ 10 2. 140 ⫼ 7 3. $180 ⫼ 90 4. 480 ⫼ 6 5. 400 ⫼ 50 6. 160 ⫼ 40 7. 360 ⫼ 6 8. 560 ⫼ 80 9. 2,400 ⫼ 3 13. 81,000 ⫼ 90 10. $2,000 ⫼ 10 11. 6,300 ⫼ 70 12. 4,200 ⫼ 60 14. 80,000 ⫼ 2 15. 90,000 ⫼ 30 16. $35,000 ⫼ 50 Compare. Use ,, ., or ⴝ for each 17. 350 ⫼ 7 3,500 ⫼ 70 . 18. 240 ⫼ 8 24 ⫼ 8 19. 360 ⫼ 40 360 ⫼ 4 Problem Solving and Test Prep 20. A warehouse stored 10 crates of 21. An office bought 8 office chairs for a paper. The paper weighed a total of 7,000 pounds. How much did one crate of paper weigh? 22. A clothing store spends $4,500 on total of $720. Each chair came with a $15 mail-in rebate. After the rebate, how much money did each chair cost? 23. A business man spends $6,400 on 9 clothing racks. How much does each clothing rack cost? 8 projectors for his company. How much does each projector cost? A $90 A $80 B $500 B $800 C $540 C $640 D $50 D $8 PW18 Practice © Harcourt • Grade 5 Name Lesson 3.6 Estimate with 2-Digit Divisors Write two pairs of compatible numbers for each. Then give two possible estimates. 1. 38 329 2. 54 386 3. 75 $384 4. 425 ⫼ 88 5. 5,234 ⫼ 91 6. $1,761 ⫼ 26 8. 31 $289 9. 72 6,102 Estimate the quotient. 7. 24 157 10. 181 ⫼ 35 11. 4,913 ⫼ 62 12. 55,208 ⫼ 87 Problem Solving and Test Prep 13. The distance from the bottom of the first 14. Maria ran one mile in 8 minutes after school. Joshua ran one mile in 540 seconds after school. Who ran the mile in less time? floor of an office building to the top of the 86th floor is 353 meters. About how many meters tall is each floor? 16. Heather spent 480 minutes practicing 15. Joe built a tower out of blocks. It was 475 centimeters tall. The height of each cube was 18 centimeters. About how many cubes did Joe use? basketball last month. How many hours did Heather spend practicing basketball last month? A 10 A 60 B 24 B 4 C 18 C 10 D 48 D 8 PW19 Practice © Harcourt • Grade 5 Name Lesson 3.7 Divide by 2-Digit Divisors Divide. Check your answer. 1. 23 713 2. 42 798 3. 64 832 4. 18 1,296 5. 56 792 6. 36 879 7. 26 936 8. 87 4,120 9. 785 34 10. 980 51 11. 1,939 74 12. 2,738 65 Problem Solving and Test Prep 13. The average person eats 53 pounds of 14. The average person in the U.S. uses 47 gallons of water each day. How many days would it take for the average person in the U.S. to use 846 gallons of water? bread each year. How many years would it take for the average person to eat 689 pounds of bread? 15. The school auditorium has 756 seats 16. A farmer planted a total of 768 corn arranged in 27 equal rows. How many seats are in each row? seeds in 24 equal rows. How many corn seeds are there in each row? A 27 A 28 B 28 B 30 C 29 C 32 D 30 D 34 PW20 Practice © Harcourt • Grade 5 MXENL09AWK5X_PH_C03_L7.indd PW20 6/15/07 12:28:35 PM Name Lesson 3.8 Correcting Quotients Write low, high, or just right for each estimate. 1. 20 34 884 2. 100 18 1,224 3. 20 38 798 4. 30 24 624 5. 40 67 3,417 Divide. 6. 18 972 11. 2,312 ⫼ 49 7. 27 259 8. 32 6,730 9. 63 234 12. 734 ⫼ 56 13. 1,634 ⫼ 86 14. 6,324 ⫼ 62 10. 79 5,688 15. 846 ⫼ 94 Problem Solving and Test Prep 16. Robin needs to buy 250 coasters 17. A store orders 832 ounces of floor for a graduation party. Each package contains 18 coasters. How many packages should Robin buy? cleaner. Each bottle is 32 ounces and costs $3. How much does the store spend on the order? 18. The Comfortable Shoe Company can 19. A Disc Jockey has a collection of 816 fit 16 boxes of shoes in a crate. How many crates will the company need to pack 576 boxes of shoes? CDs. The CD case that he likes holds 24 CDs. How many cases will the Disc Jockey need to hold all his CDs? A 36 A 43 B 40 B 30 C 35 C 34 D 30 D 40 PW21 Practice © Harcourt • Grade 5 MXENL09AWK5X_PH_C03_L8.indd PW21 6/27/07 9:54:26 AM Name Lesson 3.9 Practice Division Divide. Multiply to check your answer. 1. 7 371 2. 6 534 3. 4 547 4. 21 2,536 5. 57 3,672 6. 13 1,847 7. 36 2,643 8. 85 6,298 11. 1,516 ⫼ 47 12. 9,951 ⫼ 93 9. 582 ⫼ 6 10. 763 ⫼ 9 Problem Solving and Test Prep 13. Julia can make a paper crane in 14. Nathan spent 826 minutes making paper 8 minutes. She spent 992 minutes making paper cranes for a party. How many paper cranes did Julia make? 15. Sean has 6 piles of pennies. Each pile origami boxes. He can make a paper box in 7 minutes. How many origami boxes did Nathan make? 16. A school cafeteria used 232 pieces of has 37 pennies. How many pennies does Sean have? bread yesterday equaling 8 full loaves. How many pieces of bread are in one loaf? A 42 A 26 B 45 B 27 C 216 C 28 D 222 D 29 PW22 Practice © Harcourt • Grade 5 Name Lesson 3.10 Problem Solving Workshop Skill: Relevant or Irrelevant Information Problem Solving Skill Practice Solve. 1. A total of 47 fifth graders and 3 teachers 2. James receives $15 each week from his went on a field trip to a play. The total cost for the students’ tickets was $658. The total cost for the teachers’ tickets was $57. What was the price of each student ticket? 3. Ryan’s collection of NFL cards is 5 times parents as an allowance. His goal is to save $1,196. If James saves $13 each week, how many weeks will it take James to reach his goal? 4. Melissa received 3 dozen roses and 1 dozen balloons on her birthday. How many vases will she need if she wants to put 9 roses in each vase? more than Rickie’s card collection. Rickie has 135 cards. It took Ryan 12 months to collect the cards. How many NFL cards does Ryan have? Mixed Applications USE DATA For 3–6, use the table. 5. Jessica drove from Austin to Norland. On average, she drove 60 miles per hour. She used 40 gallons of gas. How many hours did Jessica drive? Distance Between Cities (in miles) Denver, CO Austin, TX Boston, MA 6. Joe drove from Boston to Fairfax at an average rate of 56 miles per hour. How many hours did Joe drive? 7. Julie drove from Austin to Redford. She Fairfax, CA Norland, FL Redford, MI 1,050 1,360 1,210 1,780 1,260 1,430 3,080 860 740 8. Sarah drove on average 50 miles per traveled on average 65 miles per hour. How many hours did Julie drive? PW23 hour from Fairfax to Denver. Dan drove on average 55 from Redford to Denver. Who drove less time to reach Denver? Practice © Harcourt • Grade 5 Name Lesson 4.1 Write Expressions Write a numerical expression. Tell what the expression represents. 1. William shared 8 apples equally among 4 friends. 2. Jillian bought 4 toys for 3. 35 more than 18 $7 each. Write an algebraic expression. Tell what the variable represents. 4. Jasmine has three times as many chores as her younger brother does. 6. Neil spent 25 minutes on 5. Pedro swam some laps in the pool and then swam 2 more. his math and some more time on his history homework. Write an algebraic expression in words. 7. 3x 8 m 8. 17 __ 4 9. n 9 Problem Solving and Test Prep USE DATA For 10–11, use the table. Aquarium Fish 10. Write an algebraic expression to represent the total number of silver dollars that could be in a 24-gallon tank. Let d number of silver dollars. 11. Jason has 9 Bronze corys in a tank. Type of Fish Length (in inches) Bronze Cory 3 Clown Barb 5 Silver Dollar 8 12. The temperature increased from a low Write an algebraic expression to find the minimum number of gallons of water in the tank. PW24 of 62 degrees. Which expression best describes the new temperature? A 62 t B 62 t C 62t D t 62 Practice © Harcourt • Grade 5 Name Lesson 4.2 Evaluate Expressions Evaluate each expression. 1. 27 ⫺ 15 ⫼ 3 2. 12 ⫻ 4 ⫼ 6 3. (17 ⫹ 8) ⫺ (2 ⫹ 8) 4. 60 ⫼ (10 ⫺ 4) 5. (3 ⫹ 12) ⫼ 3 ⫻ 4 6. 6 ⫻ 4 ⫺ 2 ⫻ 3 7. 30 ⫼ (2 + 3) ⫺ 1 8. 42 ⫺ 18 ⫼ 6 ⫹ 3 Evaluate the algebraic expression for the given value of the variable. 9. 31k if k ⫽ 4 10. 2r ⫺ 9 if r ⫽ 5.5 13. 3r ⫹ 4 ⫼ 2 ⫺ r 11. 21 ⫺ 3c if c ⫽ 7 14. 14 ⫺ (12 ⫼ y ⫺ 2) 15. 3(x ⫺ 1) ⫺ (3 ⫺ x) if r ⫽ 7 if y ⫽ 3 12. 4p ⫹ 6 if p ⫽ 1 1_2 16. 18 ⫺ 1 ⫼ 5y ⫹ y if x ⫽ 2 if y ⫽ 0.2 Use the expression to complete each table. 17. h 0 2 5 10 n 18. 12h 3 1 2 5 7 14 2n Problem Solving and Test Prep USE DATA For 19–20, use the table. Afternoon Games at Field Day 19. Write an expression to represent the Game number of students who run in the 50-meter dash and the 800-meter run. Then evaluate the expression if there are 41 students in the 800-meter run. Number of Players Long Jump 28 Softball Throw s 50-Meter Dash 89 800-Meter Run r 20. The softball participants were divided into 5 small groups. Write an expression to represent this. Then find the number of participants in each group if 80 students competed. 21. If k ⫽ 7, what is the value of 22. The expression 5w shows the cost of 5 books. If w ⫽ $7.45, what is the total cost of the books? 2k ⫺ 3? A 8 C 11 A $35.00 C $37.25 9 D 24 B $39.45 D $12.45 B PW25 Practice © Harcourt • Grade 5 Name Lesson 4.3 Properties Name the property shown. 1. 28 19 19 28 2. 12 (8 30) (12 8) 30 3. 5 58 (5 50) (5 8) 4. (6 7) 4 (7 6) 4 Find the value of n. Identify the property used. 5. 46 n 0 6. 1 n 71 7. 12 85 n 12 8. 49 4 = n 49 9. 8 36 (8 n) (8 6) 10. 9 (n 5) (9 1) 5 Problem Solving and Test Prep 11. Show the Commutative Property of Cari’s Rock Collection Addition using Cari’s collection of flint and garnet pieces. 12. Drake has 7 times the number of fluorite and flint pieces than Cari has. Use the Distributive Property to show the total number of pieces Drake has. Type of Rock Fluorite Amethyst Flint Garnet 0 2 4 6 8 10 12 Number of Pieces 13. The expression 30 (8 7) shows the 14. The expression (20 4) 12 shows the amount of money Daniel earned. Which expression represents the same amount of money? A B C D (30 8) 7 (30 8) (30 7) (30 8) (30 7) (30 8) (30 7) amount of money Josie earned. Which expression represents the same amount of money? A B C D PW26 (20 4) 12 (12 20) 4 20 (4 12) (4 20) 12 Practice © Harcourt • Grade 5 Name Lesson 4.4 Mental Math: Use the Properties Use properties and mental math to find the value. 1. 12 ⫹ 18 ⫹ 39 2. 53 ⫹ 64 ⫹ 37 3. 6 ⫻ 103 4. (20 ⫻ 4) ⫻ 3 5. 41 ⫹ 29 ⫹ 46 6. 26 ⫹ 43 ⫹ 34 7. 6 ⫻ 15 ⫻ 2 8. 4 ⫻ 180 9. 72 ⫹ 18 ⫹ 32 10. 7 ⫻ 4 ⫻ 15 11. 34 ⫻ 6 12. 33 ⫹ (37 ⫹ 32) 13. 42 ⫻ 7 14. 29 ⫹ 46 ⫹ 51 15. 5 ⫻ 6 ⫻ 12 16. 62 ⫻ 4 17. 36 ⫹ 18 ⫹ 24 18. 12 ⫻ 6 ⫻ 4 Problem Solving and Test Prep 19. FAST FACT A group of sea lions 20. Tell which property you would use to mentally find the value of 5 ⫻ 4 ⫻ 45. Then find the value. together in the water are called a raft. In a raft, sea lions can safely rest together. During one afternoon, a research team saw 4 rafts of sea lions. Each raft had 16 sea lions in it. How many sea lions did the research team see? 21. There are 6 shelving units containing 22. Tickets for the movies cost $13 each. 5 shelves each. Each shelf holds 35 DVDs. Find the total number of DVDs on the shelving unit. James’ family buys 6 tickets. Explain how to use mental math to find the total cost of the movie tickets. A 210 B 450 C 950 D 1,050 PW27 Practice © Harcourt • Grade 5 Name Lesson 4.5 Write Equations Write an equation for each. Tell what the variable represents. 1. Paulina has a photo album with 2. Jarrod practiced the trumpet and piano 60 photos. Each page contains 5 photos. How many pages does the album have? for 45 minutes. He practiced piano for 15 minutes. How long did he practice the trumpet? Write a problem for each equation. Tell what the variable represents. 3. 7t ⫽ 63 4. 6 ⫹ b ⫽ 11 Problem Solving and Test Prep 5. Jaime has $130 in her savings account. 6. What if Jamie already bought the bike and has $29 left in her account. How much money did she have before buying the bike? Write an equation with a variable to represent the problem. She wants to buy a bike for $225. How much more money does Jaime need to buy the bike? Write an equation with a variable to represent the problem. 7. The Amsco building is 135 feet tall. 8. Tam had downloaded 25 songs for her The Tyler building is 30 feet shorter than the Amsco building. What is the Tyler building’s height? Write an equation to represent this problem. MP3 player. She then downloaded some more songs. She now has 31 songs for her MP3 player. How many songs did Tam download? Write an equation to represent this problem. A 135 ⫽ h ⫹ 30 A 25 ⫹ s ⫽ 31 B h ⫽ 135 ⫺ 30 B s ⫺ 31 ⫽ 25 C 135 ⫽ 30 ⫺ h C s ⫺ 25 ⫽ 31 D 56 ⫺ s ⫽ 31 D h ⫽ 135 ⫹ 30 PW28 Practice © Harcourt • Grade 5 Name Lesson 4.6 Solve Equations Which of the numbers 5, 7, or 12 is the solution of the equation? 1. t 2 5 2. 30 e 6 3. 3 u 36 4. 18 p 30 Use mental math to solve each equation. Check your solution. 5. 56 8 t 6. 22 p 9 7. 25 n 13 9. d 4 8 10. 6 s 84 11. v 14 38 8. 72 y 12 12. $24 r $61 Problem Solving and Test Prep 13. Algebra A bear weighed 165 pounds 14. Algebra Sam took 42 pictures of when it came out of hibernation. During the summer it gained n pounds. At the end of the summer the bear weighed 240 pounds. Write and solve an equation to find out how much the bear gained during the summer. 15. The equation $56 p $8 represents animals on a nature hike. He placed the same number of pictures on each page of an album. He used 7 pages of his album. Write and solve an equation to find out how many pictures he placed on each page of his album. 16. Jesse had a book of 14 crossword puzzles. After solving some of the puzzles, he has 3 puzzles left. Write and solve an equation to find out how many crossword puzzles Jesse solved. the total cost of some books and the cost per book. How many books were bought? A 7 B 8 C 9 D 12 PW29 Practice © Harcourt • Grade 5 Name Lesson 4.7 Functions Write an equation to represent each function. Then complete the table. 1. c 0 d 8 j 0 4. 1 k 7. 2 3 4 10 11 12 2 4 6 8 1 2 3 4 8 a 0 2 4 6 b 1 11 21 31 2. 5. 8. m 0 1 p 0 4 2 3 4 12 16 v 12 15 18 w 3 6 9 y 3 6 z 9 21 9 21 3. 6. 9. 12 45 g 0 2 4 h 21 19 17 x 5 6 7 8 9 y 5 9 11 13 s 5 r 2 10 6 8 13 15 20 7 9.5 Use the rule and the equation to make a function table. 10. Rule: Multiply by 4 11. Rule: Add 8 m⫻4⫽r a⫹8⫽b m a r b Problem Solving and Test Prep 12. Dina pays $16 per week for piano lessons. How much will it cost for 6 weeks of lessons if she takes one lesson per week? Make a function table to show the total cost per week for 6 weeks. 13. Peg has ridden her bicycle a total of 200 miles this year. She rides 40 miles per week. What will be her total miles after 8 more weeks? Make a function table to show her expected total distance for the next 8 weeks. 14. The equation y ⫽ 12 x ⫹ 300 shows 15. The equation y ⫽ 280 ⫺ 30x shows the the balance in Dale’s savings account after x weeks. How much will be in the account after 10 weeks? number of pages Keiko has left to read after x hours of reading. How much will she have left to read after 4 hours? A $180 C $312 A 160 pages C 310 pages $288 D $420 B 250 pages D 400 pages B PW30 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C04_L7.indd PW30 6/15/07 12:22:33 PM Name Lesson 4.8 Inequalities Which of the numbers 4, 6, 8, and 10 are solutions of each inequality? 1. x ⫹ 5 ⬎ 5 2. x ⫺ 6 ⬍ 2 3. x ⫺ 4 ⱕ 4 4. x ⫹ 9 ⱖ 15 5. x ⫹ 10 ⬍ 16 6. x ⫺ 10 ⱖ 0 7. x ⫹ 7 ⱕ 11 8. x ⫹ 12 ⬎ 20 Draw a number line from 0 to 8. Locate points to show the whole number solutions from 0 to 8 for each inequality. 9. x ⫹ 2 ⬎ 4 10. x ⫹ 8 ⬎ 9 Write an inequality to match the words. Choose the variable for the unknown. Tell what the variable represents. 11. Travel time to the park is at least 12. Magie, the cat, weighs less than 3 hours. 12 pounds. Problem Solving and Test Prep 13. Let a ⫽ age. What ticket price does Circus Admission a ⬍ 5 represent? Age Under 5 14. Let n ⫽ age. What ticket price does 5–18/Child n ⫺ 12 ⬎ 6 represent? 15. The inequality s ⫹ 4 ⱖ 6 represents Over 18/Adult Price Free $8 $15 16. The inequality s ⫺ 11 ⬍ 60 represents the the least amount of money a snack costs at the county fair. Which amount is not a solution of the inequality? greatest height in inches a person can be to ride a rollercoaster. Which amount is a solution of the inequality? A 1 A 70 B 2 B 71 C 3 C 72 D 4 D 73 PW31 Practice © Harcourt • Grade 5 Name Lesson 4.9 Problem Solving Workshop Strategy: Predict and Test Problem Solving Strategy Practice Predict and test to solve the problem. 1. Andrea bought a total of 21 fish for her 2. Alec has two types of fish in his aquarium. He has 22 fish in all. The product of the numbers of each type is 85. What are the two numbers? aquarium. She bought 9 fewer angelfish than guppies. How many angelfish and guppies did she buy? 3. The sum of the ages of Michele and 4. Loni is thinking of two numbers. One Clark’s ages is 27. Clark is twice as old as Michele. How old are Clark and Michele? number is three times greater than the second number. Their sum is 32. What are the two numbers? Mixed Strategy Practice Aquarium Fish Price List USE DATA For 5–7, use the table. 5. Denny spent $60 on Keyhole Cichlids and Clown Loaches. He bought 10 fish. How many of each did he buy? 6. Beth spent $210 on a fish tank and Tiger $5 Clown Loach $8 Black Skirt Tetra $2 Tiger Barb $3 Keyhole Cichlid $4 7. Cora bought 3 Silver Dollars and 4 Clown Loaches for her fish tank. She handed the cashier three $20 bills. How much change did she receive? Barbs. The tank cost $180. How many Tiger Barbs did she buy? 8. A gallon of water weighs 10 pounds. Silver Dollar 9. Open-Ended Bryce has $25 to spend A fish tank weighs 35 pounds. How much does it weigh if it holds 15 gallons? on fish. He wants to purchase at least three fish of two different kinds. Which two kinds can he buy? PW32 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C04_L9.indd PW32 7/2/07 2:15:40 PM Name Lesson 5.1 Decimal Place Value Write the decimal shown by the shaded part of each model. 1. 2. 3. 4. Find the value of the underlined digit in each number. 5. 6.029 7. 0.831 6. 8.172 9. 87.759 10. 74.038 11. 1.3496 8. 25.207 12. 0.9472 Write each number in two other forms. 13. ten and thirty-eight hundredths 14. two and one hundred two thousandths 15. 0.492 16. 5 ⫹ 0.3 ⫹ 0.06 ⫹ 0.009 Problem Solving and Test Prep 17. A robber fly’s greatest length in meters 18. A honey bee is 0.017 m. A carpenter has 0 in the ones and tenths places and 5 in the hundredths place. What is this length of a robber fly in meters? 19. What is the value of the underlined digit bee is 0.008 m longer than a honey bee. What is the length of a carpenter bee in expanded form? 20. The decimal 0.9 is how many times in 8.536? greater than 0.009? A 0.003 A 9 B 0.03 B 10 C 0.3 C 100 D 3.000 D 0.01 PW33 Practice © Harcourt • Grade 5 Name Lesson 5.2 Equivalent Decimals Write equivalent or not equivalent to describe each pair of decimals. 1. 2.26 and 2.260 2. 8.05 and 8.50 3. 7.08 and 7.008 4. 9 and 9.00 Write an equivalent decimal for each number. 5. 0.9 9. 0.04 6. 1.800 7. 3.02 8. 8.640 10. 45.100 11. 4.60 12. 2.70 16. 3.0540 Write the two decimals that are equivalent. 13. 3.007 14. 0.930 15. 7.60 3.700 0.093 7.06 3.054 3.7000 0.93 7.600 3.504 Problem Solving and Test Prep 17. FAST FACT The calliope hummingbird 18. The calliope hummingbird is about 0.07 meter long, yet it can fly from northern North America to Mexico for the winter. Write an equivalent decimal for the length of a calliope hummingbird. is the smallest bird in North America. It weighs about 2.5 grams and builds a nest about the size of a quarter. Write an equivalent decimal for 2.5. 19. The calliope hummingbird lives in the 20. A banded calliope hummingbird was mountains. It has been seen as high as 335.23 meters above sea level. Write an equivalent decimal for 335.23. seen in Idaho and also in Virginia. It had flown more than 2,440.95 miles. Which decimal is equivalent to 2,440.95? A 2,440.095 B 2,400.905 C 2,440.9500 D 2,440.9595 PW34 Practice © Harcourt • Grade 5 Name Lesson 5.3 Compare and Order Decimals Compare. Write ,, ., or ⴝ for each 1. 0.37 0.370 5. 0.812 0.821 9. 5.202 5.220 2. 3.10 3.101 6. 9.810 10. 0.78 . 9.809 0.780 3. 0.579 0.576 4. 7.7 7. 0.955 0.95 8. 3.218 3.218 4.017 12. 0.897 0.987 11. 4.17 7.690 Order from least to greatest. 13. 0.301, 0.13, 0.139, 0.5 14. 7.203, 7.032, 7, 7.2 15. 0.761, 0.67, 0.776, 0.7 16. 0.987, 0.978, 0.97, 0.98 Problem Solving and Test Prep USE DATA For 17–18, use the table. 17. Which beetle has the shortest length? the longest length? Sizes of Beetles 18. Another type of beetle is 1.281 cm long. Which beetle has a length less than 1.281 cm? Beetle Size (in cm) Japanese Beetle 1.295 June Bug 2.518 Firefly 1.063 19. Some types of beetles can jump as high 20. The depth the Japanese Beetle grub as 15 cm. Suppose three beetles jumped 14.03 cm, 14.029 cm, and 14.031 cm. What is the order of the heights the beetles jumped from least to greatest? may hibernate underground is listed below. Which is the highest number? A 29.103 B 29.300 C 29.301 D 29.004 PW35 Practice © Harcourt • Grade 5 Name Lesson 5.4 Problem Solving Workshop Skill: Draw Conclusions Problem Solving Skill Practice Draw a conclusion to solve the problem. 1. Mark planted 12 tomato plants. He 2. Kim plants 3 rows of corn. The first row planted 4 in full sun, 4 in partial shade, and 4 in full shade. Two weeks after all the tomato plants were in the ground, the plants in partial sun were the healthiest, but a month later the plants in full sun were the healthiest. What conclusion can you draw about where to plant tomatoes? is fertilized with compost, the second row with organic fertilizer, and the third row was not fertilized. Each row receives the same amount of water and sunshine. The first row grew corn 1 day before the second and third rows. The third row grew 8 fewer ears of corn than the other rows. What conclusion can you draw about how the type of fertilizer affects the growth of the corn? Mixed Applications USE DATA For 3–4, use the table. 3. Nan used fertilizer on 5 African violets. Plant A had the most blooms. Plant E had the fewest blooms. What conclusion can she draw about how the number of teaspoons of fertilizer relates to the number of blooms? Amount of Fertilizer Per Week 4. How much fertilizer will Nan give to all Plant Number of Teaspoons A 1 B 2 C 3 D 4 E 5 her plants in a year? 5. Matt buys a plant for $1.35. He pays with 6. Tina has 25 plants on 5 shelves. Each shelf 8 coins. Which coins does Matt use? has 2 more plants than the shelf above it. How many plants are on each shelf? PW36 Practice © Harcourt • Grade 5 Name Lesson 6.1 Round Decimals Round each number to the place of the underlined digit. 1. 54.247 2. 0.109 3. 7.044 4. 12.581 5. 0.003 Round 1.613 to the place named. 6. tenths 7. ones 8. hundredths Name the place to which each number was rounded. 9. 2.634 to 2.63 10. 6.075 to 6.1 11. 13.46 to 13.5 Round to the nearest tenth of a dollar and to the nearest dollar. 12. $0.78 13. $0.11 14. $25.54 Round each number to the nearest hundredth. 16. 50 ⫹ 9 ⫹ 0.8 ⫹ 0.005 15. six hundred thirty-five thousandths Problem Solving and Test Prep USE DATA For 21–22, use the graph. 17. Round the salt content of mozzarella cheese to the nearest tenth of a gram. 18. Which cheese has a salt content of 0.17 when rounded to the nearest hundredth of a gram? 19. Greta rounded 6.488 pounds to 20. Neil rounded 9.135 pounds to 6.49 pounds. To which place did she round? 9.1 pounds. To which place did he round? A Ones A Ones B Tenths B Tenths C Hundredths C Hundredths D Thousandths D Thousandths PW37 Practice © Harcourt • Grade 5 Name Lesson 6.2 Add and Subtract Decimals Find the sum or difference. 1. 5 0.9 _ 2. 11.7 3.04 __ 3. 12.67 18.5 __ 4. 16.08 3.49 __ 6. $32.44 $4.78 __ 7. 0.45 0.071 __ 8. 0.868 0.23 __ 9. 17.645 11.968 __ 10. 9.46 0.5 __ 5. 18.394 15.602 __ 11. $25.73 $15.48 __ 12. 8 4.091 __ 13. 0.12 1.095 __ 14. 1.304 1.239 __ 15. 0.49 0.561 2.7 16. 24.006 2.73 __ 17. 8.18 0.517 1.304 18. 0.1 0.025 __ 19. 0.775 5.31 3.016 20. 0.003 1 9.44 Problem Solving and Test Prep 21. Until the 2002 Olympics, the record 22. Beth and her grandmother paid $23.00 luge speed was 85.38 miles per hour. Tony Benshoof broke that record with a speed of 86.6 miles per hour. By how many miles per hour did Tony Benshoof exceed the record? 23. Lynne buys a meal and a milk at the for tickets to a play. An adult ticket costs $6.50 more than a child’s ticket. What was the cost of Beth’s ticket? 24. Tim buys a daily planner and 1 pen at school cafeteria. If Lynne pays with a $5 bill, how much change should she receive? School Cafeteria A $1.06 Item Price the school store. How much change should Tim receive from a $20.00 bill? School Store A $9.76 B $1.55 meal $3.45 B $9.86 C $2.96 fruit $0.80 C $10.24 D $3.94 milk $0.49 D $16.74 PW38 Item Price notebook $4.55 12 pencils $2.14 1 pen $1.29 daily planner $8.95 Practice © Harcourt • Grade 5 Name Lesson 6.3 Estimate Sums and Differences Estimate by rounding. 1. 6.71 4.8 __ 2. 10.238 7.842 __ 3. 2.11 0.96 __ 4. 7. 9.276 6.419 4.458 8. 0.63 0.31 __ 9. 10.82 5.78 __ 10. $14.54 $7.35 __ 1.53 0.15 __ 5. 11. 9.786 8.914 __ 6. $3.28 $3.65 __ $5.34 12. 4.29 $5.34 $1.06 3.334 $1.06 __ 2.68 $2.68 13. $6.14 $4.59 14. 12.3 2.85 15. 1.184 1.295 16. 8.72 5.43 17. 0.219 0.183 18. 3.64 0.58 19. 14.12 5.36 20. $15.41 $4.96 Problem Solving and Test Prep USE DATA For 21–22, use the table. 21. About how long would it take to listen to Top 3 Songs of 1956 the 3 songs in the chart? Artist Playing Time (in minutes) Hound Dog Elvis Presley 2.25 Long Tall Sally Little Richard 2.083 Blue Suede Shoes Elvis Presley 1.983 Song 22. About how much longer is Elvis Presley’s recording of Hound Dog than his recording of Blue Suede Shoes? 23. Elise has $50. She buys notebooks for 24. Heather and her husband have $99. $16.29 and pens for $9.54. About how much money will she have left? They buy glassware for $19.49 and tablecloth for $22.53. About how much money would they have left? A $10 A $50 B $25 B $45 C $35 C $38 D $15 D $57 PW39 Practice © Harcourt • Grade 5 Name Lesson 6.4 Choose a Method Choose a method. Find the sum or difference. 1. 8.24 ⫹ 0.673 __ 2. 7.89 ⫺ 3.21 __ 3. 41.621 ⫺ 38.94 __ 4. $12.56 ⫹ $25.72 __ 5. 6. $14.27 ⫹ $ 8.49 __ 7. 4.803 ⫺ 2.77 __ 8. $21.40 ⫺ $20.10 __ 9. $13.60 ⫺ $11.32 __ 10. 6.33 4.095 ⫹ 1.708 11. 0.501 ⫹ 6.79 __ 12. 14. $57.19 ⫹ $ 2.68 __ 15. 1.005 ⫺ 0.07 __ 16. 2.4 ⫹ 3.75 ⫹ 1.8 2.9 ⫺ 1.5 __ 13. 3.37 ⫹ 6.73 __ 17. 0.85 ⫺ 0.798 18. $1.95 ⫹ $7.65 3.1 4.75 ⫹ 2.9 19. 5.4 ⫺ 0.54 Problem Solving and Test Prep USE DATA For 20–21, use the table. 20. How much farther did Chistyakova Women’s Long Jump Records jump in 1988 than Joyner-Kersee in 1994? Name 21. What is the difference in jump distances from the earliest listed date to the latest listed date? 22. Lydia has 3 dimes, a quarter, a dollar, Year Distance (in meters) Galina Chistyakova 1988 7.52 Jackie Joyner-Kersee 1994 7.49 Heike Dreschler 1992 7.48 Anis oara Stanciu 1983 7.43 Tatyana Kotova 2002 7.42 Yelena Belevskaya 1987 7.39 23. Dylan has 2 dollars, 3 quarters, 4 dimes, and 2 nickels. How much money does Lydia have? Show your work. PW40 and a nickel. How much money does Dylan have? Show your work Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C06_L4.indd PW40 6/15/07 12:13:27 PM Name Lesson 6.5 Problem Solving Workshop Skill: Estimate or Find Exact Answer Problem Solving Skill Practice Tell whether you need an estimate or an exact answer. Then solve. 1. Serena is purchasing workout clothes in 2. Alberto is purchasing a basketball for a sports store. Including tax, she is purchasing shoes for $41.66, socks for $3.49, gym shorts for $9.62, and a T-shirt for $7.84. Serena has only $10 bills in her wallet. How many $10 bills should she give to the cashier for all her purchases? 3. Jessa needs $140 to buy a bicycle. She $32.24 and a backboard with rim for $118.24. Both prices include tax. He gives the cashier eight $20 bills. How much change should Alberto receive? 4. The apples Carl wants to buy range in weight from 0.8 pound to 1.2 pounds. How many pounds will 12 apples weigh? saves $10 each week. She has already saved $60. How many weeks from now can Jessa buy the bicycle? Mixed Applications 5. Tom has 21 flowering plants in white, 6. At noon, the temperature was 58°F. In the next hour, the temperature rose 2°. The hour after that, it rose 4°. During the following hour the temperature rose 6°, and the hour after that, it rose 8°. What was the temperature at 1:00 P.M.? pink, and lavender flowers. He has 2 more pink flowering plants than he has lavender flowering plants. What is the greatest possible number of white flowering plants that Tom has? 7. Each chicken has 2 legs, and each 8. Pose a Problem Look back at Exercise 6. cow has 4 legs. How many legs do 9 chickens and 23 cows have? Write a similar problem by changing the beginning temperature. PW41 Practice © Harcourt • Grade 5 Name Lesson 7.1 Model Multiplication by a Whole Number Complete the multiplication expression for each model. Find the product. 1. 2. 0.34 4 Use decimal models to find the product. 3. 0.27 6 4. 4 0.33 Find the product. 5. 0.08 5 6. 0.29 4 7. 0.17 6 8. 0.41 3 9. 3 0.73 10. 5 0.57 11. 0.84 3 12. 0.26 8 13. 7 0.31 PW42 Practice © Harcourt • Grade 5 Name Lesson 7.2 Algebra: Patterns in Decimal Factors and Products Use patterns to find the product. 1. 2.67 ⫻ 10 ⫽ 2. 1.789 ⫻ 10 ⫽ 3. 0.409 ⫻ 10 ⫽ 2.67 ⫻ 100 ⫽ 1.789 ⫻ 100 ⫽ 0.409 ⫻ 100 ⫽ 2.67 ⫻ 1,000 ⫽ 1.789 ⫻ 1,000 ⫽ 0.409 ⫻ 1,000 ⫽ Multiply each number by 10, 100, 1,000, and 10,000. 4. 0.8 5. $3.99 6. 6.014 7. n ⫻ 10 ⫽ 15.81 8. 1,000 ⫻ 0.067 ⫽ n 9. 23.7 ⫻ n ⫽ 237 10. 100 ⫻ n ⫽ 25.4 11. n ⫻ 937 ⫽ 93,700 Find the value of n. 12. 0.004 ⫻ 1,000 ⫽ n Length of Planet Year Problem Solving and Test Prep USE DATA For 13–14, use the graph. 13. How many Earth years is 10 years on Jupiter? 14. How many Earth years is 1,000 years on Planet Length of Year Mercury 0.241 Earth years Venus 0.615 Earth years Jupiter 11.862 Earth years Saturn 29.457 Earth years 15. A blank CD costs $0.36. How much will 100 blank CDs cost? Mercury? A 0.000241 Earth years B 0.0241 Earth years C 241 Earth years D 2,410 Earth years PW43 Practice © Harcourt • Grade 5 Name Lesson 7.3 Record Multiplication by a Whole Number Find and record the product. 1. 3.74 5 __ 6. 61.3 4 2. 6.81 7 __ 7. 22.09 5 3. 3.13 25 __ 8. 48.2 36 4. 4.92 16 __ 5. 9. 27.14 20 17.07 3 __ 10. 6.067 19 Find the value of n. 11. 4.3 6 n 12. 6 n 16.8 13. 52.45 3 n 14. 4.1 n 24.6 Problem Solving and Test Prep 15. It takes the planet Pluto 247.68 Earth 16. Pluto’s orbital speed (average speed as it revolves around the sun) is 2.93 miles per second. How fast does Pluto travel in one minute? years to revolve around the sun. How many Earth years does it take for Pluto to revolve around the sun five times? 17. Ms. Salera’s class rode 3.8 miles to the 18. It takes the moon 29.5 days to go observatory. The next closest observatory is 13 times as far. How many miles is the second observatory? through all of its phases. How many days does it take the moon to go through all of its phases 30 times? A 13 miles B 49.4 miles C 494 miles D 4,940 miles PW44 Practice © Harcourt • Grade 5 Name Lesson 7.4 Model Multiplication by a Decimal Use the model to find the product. 1. 3. 2. 0.5 ⫻ 0.7 ⫽ 0.7 ⫻ 0.7 ⫽ 0.3 ⫻ 0.6 ⫽ Make a model to find the product. 4. 0.1 ⫻ 0.4 ⫽ 5. 0.8 ⫻ 0.2 ⫽ 6. 1.3 ⫻ 0.9 ⫽ 7. 0.7 ⫻ 0.3 ⫽ 8. 0.6 ⫻ 0.6 ⫽ 9. 1.7 ⫻ 0.4 ⫽ Find the value of n. 10. 0.6 ⫻ 0.7 ⫽ n 11. 0.5 ⫻ n ⫽ 0.45 12. n ⫻ 1.2 ⫽ 0.24 13. 0.3 ⫻ n ⫽ 0.39 14. 0.4 ⫻ n ⫽ 0.12 15. 0.9 ⫻ 0.3 ⫽ n 16. 1.3 ⫻ 0.5 ⫽ n 17. n ⫻ 0.5 ⫽ 0.55 Find the product. 18. 0.8 ⫻ 0.4 ⫽ 19. 0.3 ⫻ 0.3 ⫽ 20. 0.9 ⫻ 0.6 ⫽ 21. 1.4 ⫻ 0.5 ⫽ 22. 1.8 ⫻ 0.2 ⫽ 23. 1.1 ⫻ 0.1 ⫽ PW45 Practice © Harcourt • Grade 5 Name Lesson 7.5 Estimate Products Estimate the product. 1. 6. 34 2.1 __ 7.1 7.1 __ 11. 352.4 0.46 2. 0.3 0.8 __ 3. 0.7 0.9 __ 4. 4.4 0.6 __ 5. 7. 26.3 5.4 __ 8. 1.78 3.2 __ 9. 44.7 2.5 __ 10. 12. 0.129 22.3 13. 7.035 61 5.5 6.2 __ $9.06 0.63 __ 14. $8.99 12 Problem Solving and Test Prep 15. FAST FACT The fastest marine mammal, 16. Brittany earns $6.25 an hour working at the killer whale, can swim 35 miles per hour. How many miles can the whale swim in 10.25 hours? 17. A Ross seal at the aquarium weighs the concession stand. How much does she earn in 7.5 hours? 18. A bottlenose dolphin eats an average 430.92 pounds. A leopard seal weighs 2.3 times as much. Which expression gives the closest estimate for the weight of the leopard seal? A 3 431 C 2 431 2 430 D 3 430 B PW46 of 155.75 pounds of fish per week. How much does the dolphin eat in 4.5 weeks? Practice © Harcourt • Grade 5 Name Lesson 7.6 Practice Decimal Multiplication Find the number of decimal places in each product. 1. 0.004 0.005 2. $9 0.02 3. 1.007 0.13 4. 0.08 2.08 5. 2.56 0.11 6. 0.012 1.2 7. 0.06 1.5 8. 0.01 0.01 Estimate. Then find the product. 9. 0.12 0.8 __ 13. 6.6 0.05 10. $13.00 11. 0.007 __ 14. $2 0.04 0.006 8.1 __ 15. 0.07 0.3 12. 0.44 0.05 __ 16. 0.07 0.09 Problem Solving and Test Prep 17. Dustin has 8 guitar picks that are each 18. FAST FACT The smallest fish recorded 0.009 of an inch thick. What is the total height of the guitar picks if they are stacked on top of each other? is the stout infantfish at 0.25 inch long. How long is 0.05 of the fish? 19. A Brussels sprout weighs 0.0025 of a 20. A light guitar string is 0.016 of an kilogram. How many kilograms do 4 sprouts weigh? inch thick. A heavy guitar string is 2.25 times as thick. How thick is the heavy string? A 0.001 kilogram A 0.036 in. B 0.01 kilogram B 0.36 in. C 0.1 kilogram C 3.6 in. D 36 in. D 1 kilogram PW47 Practice © Harcourt • Grade 5 Name Lesson 7.7 Problem Solving Workshop Skill: Multistep Problems Problem Solving Skill Practice Describe the steps required to solve. Then solve the problem. 1. The crew of a fishing boat is paid 2. A lobster boat captain pays its crew $0.50 per pound of king crab, $0.30 per pound of blue crab and $0.25 per pound of snow crab. If the four-member crew caught 310 lb of king crab, 140 lb of blue crab and 284 lb of snow crab, how much money did each member make? $0.85 per pound of lobster caught. The lobster is then sold to the store for $2.95 per pound. If 649 pounds of lobster were caught, how much money did the captain earn, after paying the crew? Mixed Applications Captain Jack’s Fishing Adventure 3. USE DATA How much will it cost for two children and three adults to take a 12-hour fishing trip? 4. USE DATA Mr. Chopra paid $180 for Age Length of Trip Cost Children 6 hours $35 Children 12 hours $65 Adult 6 hours $55 Adult 12 hours $95 5. FAST FACT The penny weighs 2.5 grams, the nickel weighs 5 grams and the dime weighs 2.268 grams. If you have eight pennies, four nickels and six dimes in your pocket, how much weight are you carrying? a 6-hour fishing trip. Including himself, how many adults and children did Mr. Chopra pay for? PW48 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C07_L7.indd PW48 6/15/07 12:14:57 PM Name Lesson 8.1 Decimal Division Use decimal models or play money to model the quotient. Record your answer. 1. 1.8 3 2. 1.2 4 3. $1.52 4 4. 0.24 4 5. 1.5 5 6. 0.63 9 7. 0.36 3 8. $1.25 5 PW49 Practice © Harcourt • Grade 5 Name Lesson 8.2 Estimate Quotients Find two estimates for the quotient. 1. 1.38 ⫼ 6 2. 2.93 ⫼ 9 3. 458.2 ⫼ 7 4. 324.9 ⫼ 5 5. 30.4 ⫼ 39 6. 83.4 ⫼ 88 7. 6.271 ⫼ 71 8. 2.874 ⫼ 89 Use compatible numbers to estimate the quotient. 9. 47.8 ⫼ 7 10. 0.518 ⫼ 9 11. 275.8 ⫼ 5 12. 34.21 ⫼ 3 13. 0.726 ⫼ 8 14. 579.2 ⫼ 8 15. 53.19 ⫼ 92 16. 138.9 ⫼ 19 17. 8.23 ⫼ 43 18. 46.3 ⫼ 72 19. 297.4 ⫼ 33 20. 27.49 ⫼ 29 Problem Solving and Test Prep 21. During an 8-hour storm, it snowed 22. The greatest snowfall for one day was 4.2 inches. Estimate the average hourly snowfall during this storm. 23. Which shows how you can best use measured in Georgetown, Colorado on December 4, 1913. It snowed 63.0 inches in 24 hours. Estimate the hourly snowfall during this storm. 24. Which shows how you can best use compatible numbers to estimate 35.4 ⫼ 8? compatible numbers to estimate 58.3 ⫼ 6? A 32 ⫼ 8 A 54 ⫼ 6 B 35 ⫼ 8 B 56 ⫼ 7 C 38 ⫼ 9 C 58 ⫼ 6 D 40 ⫼ 8 D 60 ⫼ 6 PW50 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C08_L2.indd PW50 6/15/07 12:13:57 PM Name Lesson 8.3 Divide Decimals by Whole Numbers Copy the quotient and correctly place the decimal point. 0088 085 259 1. 3 77.7 2. 8 0.704 3. 7 5.95 $134 4. 69 $92.46 Divide. Check by multiplying. 5. 3 81.3 9. 7.83 ⫼ 9 6. 36 46.44 10. $158.22 ⫼ 54 7. 49 1.274 8. 21 77.28 11. 2.208 ⫼ 8 12. 656.6 ⫼ 67 Problem Solving and Test Prep 13. The fastest swimming record was set by 14. The mako shark can swim more than Tom Jager in a 50-meter race on March 24, 1990. He swam at a rate of 137.4 meters per minute. How far did Jager swim per second at this speed? 0.09 miles per minute for short amounts of time. About how far can it travel in one second at this speed? 16. The Gibsons paid $50.00 for a summer 15. 529.2 ⫼ 18. pass to Playland. If they went 20 times during the summer, what was the cost of each visit to Playland? A 0.294 B 2.94 C 29.4 A $0.25 C $25.00 D 294 B $2.50 D $250.00 PW51 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C08_L3.indd PW51 6/15/07 12:13:07 PM Name Lesson 8.4 Problem Solving Workshop Skill: Evaluate Answers for Reasonableness Problem Solving Skill Practice 1. Luis has 4 bottles of grape juice. Each 2. Angela bought 1.65 pounds of green bottle contains 64.3 ounces of juice. Luis says he has a total of 250 ounces of grape juice. Ana says Luis has a total of 150 ounces of grape juice. Use estimation to find whose answer is reasonable. Explain. peppers, 0.78 pounds of cucumbers, a squash that weighs 4.32 pounds, and a head of lettuce that weighs 0.33 pounds. Angela says she bought 7.08 pounds of vegetables. Tom says that Angela bought 70.8 pounds of vegetables. Use estimation to find whose answer is reasonable. Explain. Mixed Applications USE DATA For 3–4, use the table. 3. Hideko says 1 U. S. dollar equals Currency Exchange Rates (April 2006) 27.73 Russian rubles. David says 1 U. S. dollar equals 2.773 Russian rubles. Whose answer is reasonable? U. S. Dollars Currency 3 19.179 Australian Dollars 4 3.3 European Union (EU) Euros 6 706.8 Japanese Yen 14 388.22 Russian Ruble 18 139.662 Hong Kong Dollars 4. Suppose you exchange 200 U. S. dollars 5. John has 4.1 pizzas. He gave 2.7 pizzas for EU euros. How many euros will you receive? Which operation(s) did you use to solve? away. How many pizzas does John have left? Is your solution an estimate or an exact answer? PW52 Practice © Harcourt • Grade 5 Name Lesson 9.1 Collect and Organize Data A movie maker wants to find out what type of movies children ages 9–13 like to watch. Tell whether each sample represents the population. If it does not, explain. 1. a random sample of 400 boys, ages 9–13 2. a random sample of 3. a random sample of 400 children, ages 9–13 400 teachers Make a line plot. Find the range of hours. 4. Volunter Hours Survey Number of Hours Frequency 2 4 4 10 5 6 7 2 Problem Solving and Test Prep USE DATA For 5–6, use the tally table. 5. Tammy surveyed her classmates to find out their favorite subjects. Which subject has the greatest frequency? Favorite Subjects Spelling Reading 6. What is the range of the data Tammy Science collected about her classmates’ favorite subjects? 7. Which is the range for the following set Math Social Studies 8. Which set of data has a range of data: 14, 9, 11, 21, 7? of 15? A 11 A 4, 9, 2, 15, 18 B 12 B 9, 5, 20, 3, 25 C 13 C 8, 2, 15, 13, 17 D 14 D 5, 20, 7, 14, 21 PW53 Practice © Harcourt • Grade 5 Name Lesson 9.2 Mean, Median, and Mode Find the mean, median, and mode for each set of data. 1. 7, 9, 12, 9, 13 2. $18, $17, $22, $17 3. 1,024; 854; 720 4. 112, 130, 121, 109, 125 5. 9, 5, 10, 14, 7, 14, 11 6. 3.5, 5.4, 7, 6.4, 5.4, 3.8 7. 7, 12, 16, 7 8. $24, $17, $22 9. 45, 55, 25, 45, 75 10. 6.5, 3.4, 8.1, 9.4 ALGEBRA Use the given mean to find the missing number in each data set. 11. 14, 16, 18, 12, ; mean: 15 12. 36, 24, , 16; mean: 24 Problem Solving and Test Prep USE DATA For 13–14, use the table. Moreau Little League Team 13. What is the mean number of runs for the Moreau Little League team? 14. Reasoning How would the mean for exercise 13 change if Game 3 had 8 runs? 15. What is the mode for the set of data? C 28 1 5 2 2 3 4 4 5 for a set of data with an even number of data values. A 13 27 Number of Runs 16. Explain how you can find the median 31, 27, 26, 25, 31 B Game D 31 PW54 Practice © Harcourt • Grade 5 Name Lesson 9.3 Compare Data Compare the mean, median, and range of the data sets. 1. A: Number of stamps collected B: Number of stamps collected 13 6 2. 25 19 32 66 22 19 Monday Homework Problems 2 3 6 2 6 3 4 5 4 13 21 20 15 13 24 Tuesday Homework Problems 5 10 4 2 5 3 4 6 9 6 1 Problem Solving and Test Prep 3. Reasoning Hannah and Tyler count the 4. Two data sets have different ranges number of times the word what occurs. Hannah’s data has a mean of 2.7 times. What could Tyler’s mean be if his results are similar? and medians. Is the data in the data sets similar or different? Explain. 5. Which shows how the median for the 6. Which shows how the mean for the sets of data compare? sets of data compare? Baseball Cards Saved 111 101 Group A Pages Read 149 47 Football Cards Saved 124 87 A 111 ⫽ 111 B 111 ⬎ 98 98 33 52 36 Group B Pages Read 132 42 39 47 28 C 48 ⬎ 45 A 52 ⬎ 47 C 34.5 ⬍ 40.5 D 120.3 ⬎ 110.3 B 19 ⫺ 19 D 42 ⬎ 39 PW55 Practice © Harcourt • Grade 5 Name Lesson 9.4 Analyze Graphs For 1–3, use the double-bar graph. 1. Which class period has the least number Left-handed and Right-handed Students 2. Which two class periods have the same number of students? Number of Students of right-handed students? 18 16 14 12 10 8 6 4 2 0 3. What is the total number of left-handed Left-handed Right-handed 1 students in all four class periods? 2 3 Class Period 4 Problem Solving and Test Prep 4. Which sport has the greatest number Favorite sport of votes? Soccer Tennis Key: Each ⫽ 3 votes. 5. How many total votes are there for soccer and tennis? 6. A line graph shows a trend of less rain 7. Look at the double-bar graph at the top this week than 2 weeks ago. Explain what the line graph might look like. of the page. Which statement about the graph is NOT true? A Class period 2 has the least students. B Class period 1 has 14 left-handed students. C The median number of right-handed students is 15. D The median number of left-handed students is 11. PW56 Practice © Harcourt • Grade 5 Name Lesson 9.5 Problem Solving Workshop Strategy: Draw a Diagram Problem Solving Strategy Practice Draw a Venn diagram to solve. 2. During a free period, 7 students used 1. Nine students wrote reports about photosynthesis, 7 students wrote reports about transport tissues in plants, and 3 students wrote about photosynthesis and transport tissues in plants. How many students wrote reports? the computers, 8 students played board games, and 4 students used the computer and played board games. How many students used the computer and/or played board games during the free period? Mixed Strategy Practice For 3–4, use the table. 3. Hank spent $26.06 on two supplies. Which two supplies did he buy? Science Supplies Sale Science Supply 4. Madison bought the most expensive item. Jerry bought safety goggles and a ruler. How much more did Madison spend than Jerry spent? 5. Twenty students each checked out a book Price Ruler $2.39 Tongs $11.50 Graduated Cylinder $8.71 Hand Lens $19.95 Safety Goggles $14.56 6. Nora records the number of insects for at the library. Eleven students checked out history books. Five students checked out biographies. The rest of the students checked out novels. How many students checked out novels? Show your work. PW57 8 days. Day 1: 14 insects; Day 2: 28 insects; Day 3: 42 insects; Day 4: 56 insects. If the pattern continues to increase this way, how many insects will there be on day 8? Practice © Harcourt • Grade 5 Name Lesson 10.1 Make Bar Graphs and Pictographs For 1–2, use the graph at the right. 1. What scale and interval are used in the bar graph? 2. How would the bars in the graph change if the interval were changed to 10. Explain. Number of Pets Joe’s Pet Store 35 25 20 15 10 5 0 Rabbit Cat Dog Hamster Pets Make a graph for the data set. 3. Favorite Books Book Type Number of Votes Mystery 35 Fantasy 15 Poetry 10 Sports 40 Problem Solving and Test Prep USE DATA For 4–6, use the table. 4. Did the students have more CDs or Number of CDs and Movies more DVDs? How many more? Name 5. What is a reasonable scale and interval to graph the data? Number of CDs Number of DVDs Chuck 10 2 Emily 14 5 Tim 13 2 6. Make a double-bar graph for the data in the space at the right. 7. Which interval would you use to make a bar graph for the following data: 60, 55, 40, 35, and 65? A 2 B 25 C 10 D 5 PW58 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C10_L1.indd PW58 6/15/07 1:01:08 PM Name Lesson 10.2 Make Histograms For 1–2, use the table. 2. Make a histogram of the data. Laps Swam In The Pool 12 24 32 31 22 10 17 25 14 21 19 20 9 14 8 17 15 21 40 30 19 16 30 23 21 1. What is a reasonable interval for the laps swam in the pool? For 3–4, decide whether a bar graph or a histogram would better represent the data. Then make the graph. 3. 4. Weight (in pounds) Number of Adult Dogs Red 16 43–45 3 Blue 23 46–48 8 Black 14 49–51 10 Color of Bicycle Number of Bicycles Problem Solving and Test Prep USE DATA For 5–6, use the graph. Ages of One-Mile Runners Number of Runners 5. How many runners in all are in the age groups 4–5 and 12–13? 6. How many people ran in the race? 7. How many runners are 10–11 years 8 6 4 2 0 4-5 6-7 8-9 Ages 10-11 12-13 8. How many runners are 6–7 years old? old? A 4 C 7 A 2 6 D 8 B B PW59 6 C 7 D 10 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C10_L2.indd PW59 6/15/07 12:50:00 PM Name Lesson 10.3 Algebra: Graph Ordered Pairs Use the coordinate grid at the right. Write an ordered pair for each point. 1. A y 2. B 10 3. C 4. D A 9 D B 8 7 Graph and label each point on the coordinate grid at the right. 5. E (4, 5) 6 5 4 6. F (2, 9) 3 2 7. G (8, 5) 8. H (3, 3) 1 C 0 1 9. I (0, 10) 2 4 3 5 x 6 7 8 9 10 10. J (7, 1) y N 10 Problem Solving and Test Prep W 9 USE DATA For 11–14, use the map. Each unit represents 1 city block. E 8 S 7 11. What ordered pair gives the location for the Playground? Library School 6 5 F 4 D 3 12. What is the distance between Home and the Theater? Playground 2 Theater Home 1 x 0 1 13. Use the map above. Suppose a museum 2 3 4 5 6 7 8 9 10 14. Use the map above. Suppose a gym is is located at point D. What ordered pair locates this point? located at point F. What ordered pair locates this point? A (3, 2) A (8, 4) B (2, 1) B (7, 4) C (1, 2) C (8, 3) D (2, 3) D (8, 5) PW60 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C10_L3.indd PW60 6/15/07 12:49:46 PM Name Lesson 10.4 Make Line Graphs USE DATA For 1–2, use the table. 1. What would be an appropriate scale and Weights of 2 Kittens (Cutie and Magic) interval to graph the data? Month 0 1 2 3 Cutie 2 6 11 31 Magic 2.5 5 11.5 34 Weights of Cutie and Magic 2. Write the related pairs for the weights of Cutie and Magic as ordered pairs. 3. In the box at the right, make a double-line graph of the data. Problem Solving and Test Prep USE DATA For 4–7, use the table. 4. What is the range in the number of inches in height for the first 7 years? Tommy’s Height 5. Between which years in the table did Tommy grow the most? 6. What would be an appropriate scale and Age (years) 1 3 5 7 Height (in.) 29 34 37 43 7. Suppose you made a line graph of this interval to graph this data? data, which best describes the line from age-1 to age-7? A It goes up. B It goes down. C First it goes down, and then it goes up. D First it goes up, and then it goes down. PW61 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C10_L4.indd PW61 6/28/07 1:11:01 PM Name Lesson 10.5 Make Circle Graphs Use the data to make a circle graph. 1. Fruit 50 Orange 20 Banana 20 Pear 10 Celine's Paycheck Celine’s Paycheck Item 4. Number Apple 2. 3. Favorite Fruits Students’ Favorite Fruits Cost Food $35 Clothing $20 Transportation $15 Savings $30 Ice Cream Orders Ice Cream Flavors Ordered Flavor Number Chocolate 4 Vanilla 3 Strawberry 1 Rocky Road 2 Pistachio 2 Art Club Earnings From Bake Sale Item Sold Earnings Cupcakes $50 Crumb Cake $20 Muffins $15 Juice Cookies Art Club Bake Sales $5 $10 PW62 Practice © Harcourt • Grade 5 Name Lesson 10.6 Problem Solving Workshop Strategy: Make a Graph Problem Solving Strategy Practice For 1–2, make and use a graph to solve. 1. Sarah’s bowling team recorded the scores from their last tournament. Which group of scores had the most scores: 70–79, 80–89, 90–99 or 100–109? Sarah’s Team Bowling Scores 78 99 81 84 92 101 76 90 88 93 75 94 98 71 96 104 97 82 80 88 2. The high temperatures in May were recorded for 20 years in San Jose, CA. What is the mean, median, and mode of the data? May High Temperatures in San Jose(°F) 72 73 74 74 84 78 71 69 83 79 72 80 71 74 68 69 68 81 79 77 Mixed Strategy Practice 3. Paula has 1.5 times as many novels as 4. Pose a Problem Look back at Problem 1. How would your graph change if there were no scores above 93? Explain. Carly. Carly has 12 novels. How many novels does Paula have? Show your work. PW63 Practice © Harcourt • Grade 5 Name Lesson 10.7 Choose the Appropriate Graph Choose the best type of graph or plot for the data. Explain your choice. 1. Hours Raul worked each 2. Number of library books of the past 6 days 3. Water evaporated over borrowed by 30 people 10 days Draw the graph or plot that best displays each set of data. Tell whether the data is categorical or numerical. 4. 5. Paul’s Vacation Budget Weather Service Almanac Activity Amount Month Rainfall (inches) Food $9 May 16 Rides $7 June 22 Souvenirs $5 July 18 Problem Solving and Test Prep USE DATA For 6–7, use the table below. Visitors To The Alamo By The Minute 6. What graph would best represent this data? 7. Is the data in the table categorical or numerical? 8. What type of graph would best display the Test Scores 92 95 87 100 88 75 93 97 Visitors 1 14 2 30 3 45 4 65 9. What set of data is categorical? data in table? Explain. 100 84 Minute 100 93 PW64 A Runs scored by the team in 5 games B Items Ralph spent his allowance on C High temperature each month for 6 months D Votes given 10 congressman in January Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C10_L7.indd PW64 6/15/07 12:50:28 PM Name Lesson 11.1 Multiples and the Least Common Multiple List the first ten multiples of each number. 1. 5 2. 10 3. 7 4. 3 5. 9 Write the least common multiple of each set of numbers. 6. 2 and 4 7. 5 and 8 8. 8 and 6 9. 18, 3, 6 10. 3, 2, 7 Problem Solving and Test Prep USE DATA For 11–12, use the table. Packs of Marbles 11. What are the least numbers of packs of Color of Marble yellow marbles and blue marbles a person would have to buy to have the same number of each color of marble? Number per Pack Yellow 2 Green 4 Blue 3 Orange 6 12. What are the least numbers of packs of green marbles, blue marbles, and orange marbles a person would have to buy to have the same number of each color of marble? 13. Which set of numbers has an LCM 14. Which set of numbers has an LCM of 36? of 12? A 5, 13, 18 A 2, 3, 5 B 4, 6, 18 B 4, 6, 8 C 6, 12, 18 C 1, 5, 12 D 6, 12, 16 D 2, 4, 6 PW65 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C11_L01.indd PW65 6/15/07 2:25:18 PM Name Lesson 11.2 Divisibility Test each number to determine whether it is divisible by 2, 3, 5, 6, 9, or 10. 1. 571 2. 4,023 3. 43,104 4. 21,900 5. 6,305 6. 31,089 7. 83,292 8. 7,938 9. 15,846 10. 4,950 11. 956 12. 5,840 13. 8,846 14. 19,992 15. 15,804 Write true or false. 16. All odd numbers are divisible by 2. 17. All multiples of 7 are divisible by 7. 18. All even numbers are divisible by 4. 19. All numbers ending in 0 are divisible by 10. PW66 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C11_L02.indd PW66 6/15/07 2:25:09 PM Name Lesson 11.3 Factors and Greatest Common Factor List the factors of each number. 1. 49 2. 19 3. 36 4. 56 5. 24 Write the common factors for each pair of numbers. 6. 11, 15 7. 16, 20 8. 13, 26 9. 5, 10 10. 22, 24 Write the greatest common factor for each pair of numbers. 11. 12, 36 12. 21, 56 13. 14, 21 14. 8, 24 15. 15, 25 Problem Solving and Test Prep USE DATA For 16–17, use the table. 16. Sharon is dividing her green and blue Sharon’s Rock Collection rock collection into bags. Each bag will contain the same number of each color of rock. How many rocks of each color will be in each bag? Color Number of Rocks Red 12 Yellow 28 Green 16 Blue 24 17. Sharon also divides her red and yellow rocks into bags. Each bag will contain the same number of each color of rock. How many bags will Sharon need? 18. The greatest common factor of 28 19. Which number is not a common factor of 42 and 21? and another number is 7. The second number is between 60 and 70. What is it? A 7 C 21 6 D 3 B PW67 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C11_L03.indd PW67 6/15/07 2:25:00 PM Name Lesson 11.4 Prime and Composite Numbers Write prime or composite. You may use counters or draw arrays. 1. 12 2. 37 3. 44 4. 28 5. 35 6. 122 7. 61 8. 72 9. 89 10. 56 11. 49 12. 59 13. 101 14. 75 15. 88 16. 14 17. 83 18. 109 19. 36 20. 65 21. 111 PW68 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C11_L04.indd PW68 6/15/07 2:25:27 PM Name Lesson 11.5 Problem Solving Workshop Strategy: Make an Organized List Problem Solving Strategy Practice Use an organized list to solve. 1. During the month of May, Jean has 2. Students are making picture frames. photography class every third day and a photography show every Saturday. On May 5 she has class and a show. During the month of May, how many more times will she have a class and a show on the same day? There are 31 days in May. They can choose from a brown or black picture frame, and a red, yellow, blue, or green matte. How many different picture frame and matte combinations can the students make? Mixed Strategy Practice 3. USE DATA Complete the graph. Use the clues below to find the missing data in the graph. Clue 1: The least favorite type of book is fantasy. Clue 2: Mystery books are favored by 10% more students than western books. Which Type Of Book Is Your Favorite Western, 20% ______ , 10% 4. Carl spent $51.33 on three opera tickets. How much did each ticket cost? Show your work. Adventure 24% Humor, 16% Mystery, ______ ____ 5. Robin has 7 red beads, 27 purple beads, and 24 yellow beads. She wants to make a necklace with the pattern: 1 red bead; 3 purple beads; 2 yellow beads. How many times can she repeat the pattern? Which color of beads will she run out of first? PW69 Practice © Harcourt • Grade 5 Name Lesson 11.6 Introduction to Exponents Write in exponent form. 1. 10,000,000 2. 1,000 3. 10 4. 100,000,000 5. 103 6. 108 7. 104 8. 106 9. 105 10. 102 11. 107 12. 101 Find the value. ALGEBRA Find the value of n. 13. 102 n 14. 107 n 15. 105 n Problem Solving and Test Prep 17. Kelly read the odometer on her 16. Aaron earned $10 each week for 10 weeks of picking up garbage. Kimberly earned $10 each week for 10 weeks of walking dogs. How much money did they earn altogether? 18. Which number represents parents’ car. She wrote down 105 miles. How many miles are shown on the odometer? 19. Which number represents 10 10 10? 10 10 10 10 10 10? A 10 A 103 0 B 101 B 106 C 102 C 104 D 103 D 107 PW70 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C11_L06.indd PW70 6/15/07 2:24:52 PM Name Lesson 11.7 Exponents and Square Numbers Write in exponent form. Then find the value. 1. 5 5 5 2. 2 2 3. 8 8 8 8 4. 4 4 4 4 4 Find the value. 5. 122 10. 83 6. 55 7. 73 8. 18 11. 46 12. 32 13. 113 9. 115 14 57 Compare. Write ,, ., or ⴝ. 15. 53 23 16. 22 41 17. 54 78 18. 62 93 Problem Solving and Test Prep USE DATA For 19–20, use the pattern in the table. 19. James earned 729 pennies. How many plates did James wash in all? Pennies Earned 20. What number in exponent form represents the number of pennies James would earn for washing 11 plates? How many pennies would he earn for washing 11 plates? 21. Which is greater than 92? Number of plates washed Pennies Exponent form Start 1 30 1 3 31 2 9 32 3 27 33 22. What is the greatest square number that is even and is less than 300? What is the value of this square number? A 2 7 43 C 52 D 41 B PW71 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C11_L07.indd PW71 6/28/07 1:12:26 PM Name Lesson 11.8 Prime Factorization 1. Draw a factor tree to find the prime factorization of 48. Write the prime factorizaton. Find the prime factorization. You may use a factor tree. 2. 4 3. 100 4. 155 5. 21 Rewrite the prime factorization by using exponents. 6. 2 ⫻ 5 ⫻ 7 ⫻ 2 7. 3 ⫻ 3 ⫻ 7 ⫻ 3 ⫻ 7 8. 19 ⫻ 19 ⫻ 19 ⫻ 19 Find the number for each prime factorization. 9. 3 ⫻ 73 13. 11 ⫻ 2 ⫻ 2 10. 5 ⫻ 5 ⫻ 5 ⫻ 3 11. 52 ⫻ 112 12. 2 ⫻ 2 ⫻ 19 14. 82 ⫻ 23 15. 32 ⫻ 63 16. 2 ⫻ 5 ⫻ 5 ⫻ 5 Problem Solving and Test Prep 17. The prime factors of a number are the 18. The prime factors of Patrick’s favorite number are 2, 7, and 3. Two is repeated once. What is Patrick’s favorite number? first four prime numbers. No factor is repeated. What is the number? 19. Which numbers are two of the prime 20. What is the least number that is the factors of 36? product of two different primes that are squared? A 2 and 3 B 11 and 3 C 5 and 2 D 4 and 13 PW72 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C11_L08.indd PW72 6/15/07 2:25:34 PM Name Lesson 12.1 Understand Fractions Write a fraction for the shaded part. Write a fraction for the unshaded part. 1. 2. 3. 4. Write a fraction to name the point on the number line. 5. 6. 7. 0 I H G 0 1 1 Write the fraction for each. 8. four fifths 9. five divided by ten 10. one sixth 0 1 11. two out of 9 Problem Solving and Test Prep 12. A basket of fruit has 3 apples, 2 pears, 13. A delivered pizza came cut in 6 equal and 4 bananas. What fraction of the fruit are bananas? 14. What fraction of the stars are gray? slices. Mark ate 2 slices. Now 4 slices remain. What fraction of the pizza did Mark eat? 15. What fraction of the triangles are gray? 1 A __ 5 1 B __ 4 C D 1 A __ 2 3 B __ 5 3 __ 4 4 __ 5 PW73 C D 3 __ 8 5 __ 8 Practice © Harcourt • Grade 5 Name Lesson 12.2 Equivalent Fractions Write an equivalent fraction. 1 1. __ 8 7 2. ___ 10 4 3. __ 5 6 4. __ 8 3 5. __ 4 1 6. __ 3 3 7. __ 6 8 8. ___ 12 6 9. __ 9 10 10. ___ 15 10 11. ___ 16 5 12. __ 6 Tell which fraction is not equivalent to the others. 5 2 6 1 5 3 2 1 4 13. __, ___, __ 14. __, __, ___ 15. ___, __, ___ 2 15 9 6 4 12 9 3 2 16. ___, __, __ 12 4 5 10 3 12 Problem Solving and Test Prep USE DATA For 17–18, use the table. 17. Natalie asked people which of the six colors in the chart they preferred. What four equivalent fractions show the fraction of people who chose red? Preferred Colors 18. Natalie asks 4 more people their opinion, and they all say blue. Now, what three equivalent fractions show the fraction of people who chose red? 19. Which fraction is equivalent to 2_5 ? 3 A ___ 10 4 B ___ 10 7 C ___ 10 3 D __ 5 Color Number of People Who Chose It Orange 1 Red 4 Purple 2 Blue 3 Green 1 Yellow 1 __ ? 20. Which fraction is equivalent to 14 16 7 A __ 8 7 B __ 9 4 C __ 6 2 D ___ 16 PW74 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C12_L2.indd PW74 6/28/07 1:14:02 PM Name Lesson 12.3 Simplest Form Name the GCF of the numerator and denominator. 3 2. __ 4 ___ 1. 14 16 ___ 3. 12 36 9 4. ___ 30 10 5. ___ 25 16 9. ____ 100 ___ 10. 24 30 Write each fraction in simplest form. 8 6. ___ 22 ___ 7. 17 34 28 8. ___ 77 10 11. ___ 10 9 12. ___ 16 20 13. ___ 60 36 14. ___ 45 ___ 15. 12 57 10 16. ___ 24 15 17. ___ 25 32 18. ___ 40 70 19. ____ 100 48 20. ___ 60 Problem Solving and Test Prep 21. Fast Fact Eight states border one or 22. Twenty out of 75 salon clients made an more of the five Great Lakes. Write a fraction representing the part of the 50 states that border a Great Lake. Write the fraction in simplest form. 21 23. Which fraction shows ___ in simplest 28 appointment for a haircut. What fraction of the clients made a haircut appointment? Write the fraction in simplest form. 24. Twelve of 30 students rode the bus form? 1 A __ B C D today. What fraction of the students rode the bus? Write the fraction in simplest form. 8 1 __ 7 3 __ 7 3 __ 4 PW75 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C12_L3.indd PW75 6/15/07 12:55:00 PM Name Lesson 12.4 Understand Mixed Numbers Write each mixed number as a fraction. Write each fraction as a mixed number. 7 1. 1 __ 8 10 2. ___ 9 27 3. ___ 4 4 4. 3 __ 5 41 7. ___ 10 41 8. ___ 8 61 9. ___ 3 9 10. 5 ___ 10 1 11. 3 __ 9 39 12. ___ 5 3 13. 4 __ 7 21 14. ___ 4 57 15. ___ 7 5 16. 8 __ 6 4 17. 9 __ 9 41 18. ___ 6 2 19. 7 __ 3 3 20. 6 ___ 10 2 21. 4 ___ 15 31 22. ___ 4 16 23. ___ 5 35 24. ___ 6 11 5. 1 ___ 15 1 6. 4 ___ 12 Problem Solving and Test Prep 25. How many times will Gayle fill a 1_2 -cup 26. A recipe calls for 2 3_4 cups of milk. 27. Which fraction is the same as 2 4_5 ? 23 28. Which mixed number is the same as ___? 4 3 A 2 __ 4 1 B 3 __ 2 1 C 4 __ 4 3 D 5 __ 4 ladel to serve 8 1_2 cups of punch? 8 A __ 5 9 B __ 5 14 C ___ 5 24 D ___ 5 What is 2 3_4 written as a fraction? PW76 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C12_L4.indd PW76 6/15/07 12:54:53 PM Name Lesson 12.5 Compare and Order Fractions and Mixed Numbers Compare. Write ⬍, ⬎, or ⴝ for each _5_ 9 1. _4_ 9 3 __ 7 5 6. ___ 12 6 7. ___ 10 __ 35 4 11. 3 __ 5 6 8 3. ___ 12 2 __ 3 6 8. 1__ 9 __ 22 5 9. 4 __ 8 __ 43 4 2 10. 9 __ 6 __ 83 4 13. 4 __ 6 __ 33 1 14. 8 __ 3 __ 83 3 15. 6 __ 8 __ 61 _3_ 5 3 2. __ 4 2 12. 1___ 10 4 __ 5 1_1_ 5 . _4_ 7 5 4. __ 8 3 4 8 __ 9 9 5. ___ 11 5 9 4 Write in order from least to greatest. 3 3 1 16. __, __, __ 8 4 4 5 3 5 18. 1__, 1__, 1__ 8 4 6 2 __ __ 17. __ , 1, 7 3 6 9 3 2 6 19. 7 __, 6 __, 6 ___ 5 3 10 Problem Solving and Test Prep USE DATA For 20–21, use the table. 20. Len paints and sells wooden flutes. List the flutes in order from shortest to longest. Len’s Flutes Flute Name 21. Len created a new flute that is 6 _23 inches long. Which, if any, of his flutes are longer? 22. Kayla practiced violin 2 1_4 hours on 3 Monday, 2 __ 10 hours on Tuesday, and 1 4_9 hours on Wednesday. On which day did she practice the longest? A Tuesday B Friday Length, in inches Lily 6 3 4 Rose 6 5 8 Ivy 6 127 23. Dean practiced trombone 1 2_3 hours on 7 Monday, 1 __ 12 hours on Tuesday, and 1 7_9 hours on Wednesday. On which day did he practice the longest? C Monday A Tuesday D Wednesday B PW77 Wednesday C Monday D Saturday Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C12_L5.indd PW77 6/15/07 12:55:09 PM Name Lesson 12.6 Problem Solving Workshop Strategy: Make a Model Problem Solving Strategy Practice Make a model to solve. 1. From home, Todd walked 3 blocks 2. Kayla is putting up a picket fence on south and 2 blocks east to a friend’s house. Then they walked 6 blocks west to school. He cannot cut across blocks. How many blocks from school does Todd live? one side of her garden. Each picket is 4 inches wide and 2 inches apart. She has 12 pickets. How many inches long will Kayla’s fence be? Mixed Strategy Practice Solve. 3. Lisa spent 10 minutes driving to the 4. Pose a Problem Look back at grocery store and 50 minutes shopping there. She spent 10 minutes driving back home and 40 minutes making sandwiches for a picnic. She drove 30 minutes from home and arrived at the picnic at 3:30 P.M. What time did Lisa leave to go to the grocery store? Excercise 1. What if Todd and his friend had only walked 5 blocks west to school? How many blocks would Todd live from school then? 5. A city garden is in the shape of a rectangle. There is a walkway from each corner of the rectangle to every other corner of the rectangle. How many walkways are there? Draw a diagram in the space at the right to solve. PW78 Practice © Harcourt • Grade 5 Name Lesson 12.7 Relate Fractions and Decimals Write each decimal as a fraction or mixed number in simplest form. 1. 0.33 2. 0.06 3. 0.625 4. 0.35 6. 1.05 7. 1.1 8. 1.12 9. 2.525 11. 3.700 12. 0.205 13. 0.025 5. 0.900 10. 4.08 14. 4.98 15. 8.25 Write each fraction or mixed number as a decimal. 7 16. _____ 1000 8 17. ____ 100 3 18. ___ 10 9 19. ___ 20 40 20. ___ 50 6 21. 1 ___ 25 27 22. 9 ___ 45 6 23. 5 ___ 15 13 24. 2 ___ 50 36 25. 3 ___ 40 Problem Solving and Test Prep 26. A player’s batting average is 0.425. 27. Kevin hit in 9 out of 40 at bats. What What fraction is equivalent to 0.425? 28. Which fraction is NOT equivalent to 0.8? 4 A __ 5 8 B ___ 10 is his batting average? 4 29. What decimal is equivalent to 1__? 5 12 C ___ 15 3 D __ 4 PW79 A 1.8 C 1.5 B 1.4 D 1.3 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C12_L7.indd PW79 6/15/07 12:55:19 PM Name Lesson 13.1 Add and Subtract Like Fractions Find the sum or difference. Write it in simplest form. 1 1 1. __ ⫹ __ 4 4 2 1 2. __ ⫹ __ 7 7 3 1 3. __ ⫺ __ 5 5 3 2 4. __ ⫹ __ 7 7 5 7 5. __ ⫺ __ 8 8 7 2 6. ___ ⫹ ___ 10 10 3 4 7. __ ⫺ __ 9 9 4 1 8. __ ⫺ __ 6 6 3 3 9. __ ⫹ __ 8 8 2 1 10. __ ⫹ __ 5 5 8 5 11. ___ ⫺ ___ 10 10 1 2 12. __ ⫹ __ 6 6 9 3 13. ___ ⫺ ___ 12 12 2 1 14. __ ⫺ __ 4 4 3 5 15. ___ ⫹ ___ 10 10 Problem Solving and Test Prep _ of the world’s 16. Glaciers currently store 2 3 _1 3 17. When an iceberg floats in a body of water, 1_7 of the mass can be seen above water. How much of the iceberg remains beneath the surface of the water? freshwater supply. If of those glaciers melted, how much would be left in glacier form? 18. Iceberg Alley is where bergs from the 19. Icebergs are usually white from millions glaciers of Greenland drift down to 3 Newfoundland. If an iceberg floats __ 10 5 mile in January, and __ 10 mile in February, how far should it travel in order for the iceberg to have drifted 1 mile by March? of tiny air bubbles trapped in the ice with occasional blue streaks. If 5_8 of an iceberg is white, how much of the iceberg is streaked with blue? A 2 __ 10 mile 3 A __ 8 B _1 5 mile B 2 __ 8 C 1 mile C 5 __ 8 3 D 1__ 8 D 1 1_2 miles PW80 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C13_L1.indd PW80 6/15/07 12:50:12 PM Name Lesson 13.2 Model Addition of Unlike Fractions Find the sum. Write it in simplest form. 1. 1 2 1 __ __ 5 2 8 1 8 1 8 1 8 1 8 1 8 2. 1 5 1 5 1 5 1 4 3 __ __ 1 5 4 3. 1 2 1 5 1 __ __ 1 5 2 Find the sum using fraction bars. Write it in simplest form. 1 4 4. __ ___ 5 10 3 1 5. __ ___ 2 10 5 2 6. __ __ 6 3 1 2 7. __ __ 3 4 1 1 8. __ __ 2 8 1 1 9. __ __ 3 2 5 2 10. __ __ 8 5 5 3 11. __ __ 8 4 3 2 12. __ __ 4 3 1 3 13. __ __ 5 2 3 2 14. __ __ 6 9 5 1 15. __ ___ 4 12 1 2 16. __ __ 2 6 6 1 17. ___ __ 10 3 3 1 18. ___ __ 12 4 PW81 Practice © Harcourt • Grade 5 Name Lesson 13.3 Model Subtraction of Unlike Fractions Use fraction bars to find the difference. Write it in simplest form. 5 2 1. __ __ 6 3 1 6 1 6 1 3 3 1 2. __ __ 5 4 1 6 1 6 1 3 1 6 ? 1 4 5 1 3. __ __ 8 4 1 4 1 5 1 8 1 4 1 8 1 8 1 4 ? 1 8 1 8 ? Find the difference using fraction bars. Write it in simplest form. 2 2 4. __ ___ 5 10 1 1 5. __ ___ 2 12 7 1 6. __ __ 8 2 3 4 7. __ __ 4 6 2 1 8. __ __ 5 3 6 1 9. __ __ 7 2 3 4 10. __ ___ 5 10 7 1 11. ___ __ 12 3 1 1 12. __ ___ 4 10 3 7 13. __ __ 8 8 5 1 14. __ __ 7 2 8 1 15. __ __ 9 3 4 1 16. ___ __ 10 4 6 1 17. __ __ 7 3 3 1 18. __ __ 4 2 PW82 Practice © Harcourt • Grade 5 Name Lesson Lesson13.4 8.3 Estimate Sums and Differences Estimate each sum or difference. 5 1 1. __ __ 7 4 3 1 2. __ __ 7 6 8 2 3. __ __ 5 9 10 6 4. ___ __ 11 9 7 1 5. __ __ 8 2 3 2 6. __ __ 5 8 6 3 7. __ __ 7 4 5 1 8. __ __ 8 6 9 1 9. ___ __ 12 9 5 4 10. __ __ 5 8 Estimate to compare. Write , or . for each 6 1 11. __ __ 5 7 1 3 7 12. ___ ___ 11 10 . 4 1 __ __ 13. __ 8 5 9 0 2 3 7 14. __ __ 5 9 1 __ 2 8 2 15. ___ ___ 12 10 1 Problem Solving and Test Prep 16. Maria is making burritos for dinner. Her _7 8 17. Jeremy rides his skateboard 2 miles recipe calls for cup of ground beef and 1_6 cup of shredded cheese. Estimate the total amount of meat and cheese Maria uses in her recipe. 19. Ling makes 1 gallon of fruit punch for 18. Gail is making a healthy snack for her _3 5 from his home to school. After riding 3 _ mile, he realizes he left his lunch 8 money on the counter at home. About how far does Jeremy have left to travel when he realizes his mistake? weekend hike. She adds cup of raisins and 6_7 cup of peanuts. Estimate the total amount that Gail adds. 1 A 1 __ cups 2 B 1 cup C 2 cups his sister’s graduation party using orange juice and fresh fruit. If 5_9 gallons of the punch is orange juice, about how much is fresh fruit? 1 A __ gallon 4 1 B __ gallon 8 3 C __ gallon 4 1 D __ gallon 2 1 D __ cup 2 PW83 Practice © Harcourt • Grade 5 Name Lesson 13.5 Use Common Denominators Find the sum or difference. Write it in simplest form. 4 1 1. __ ⫹ __ 5 2 7 1 2. __ ⫹ __ 8 4 1 1 3. ___ ⫹ __ 5 10 7 1 4. ___ ⫹ __ 4 12 2 1 5. __ ⫹ ___ 9 10 6 3 6. __ ⫺ __ 7 8 1 8 7. __ ⫺ __ 9 2 3 1 8. __ ⫺ __ 4 5 4 4 9. __ ⫺ ___ 5 15 7 1 10. ___ ⫺ __ 10 4 Problem Solving and Test Prep 11. The lroquois tribe lived in the 12. The lroquois tribe was skilled at tracking Adirondack Mountains of New York during the 1700s. The tribe members were skilled deer hunters, utilizing all parts of the animal to benefit the tribe. If 1_2 of the deer was used for food and 1 _ was used for skins or clothing, how 4 much of the deer was utilized in all? 13. Which addition equation represents animals through the Adirondack Mountains. A favorite hunting trail was 7 _ mile long, but the hunters only 8 followed it for 1_6 mile before spotting the first deer. How much more trail was there to hunt after the first sighting? 14. Which addition equation represents the fraction of beads that are black or gray? the fraction of beads that are white or gray? 5 8 1 A ___ ⫹ __ ⫽ ___ 12 4 12 5 9 1 B ___ ⫹ __ ⫽ ___ 12 3 12 4 29 1 C __ ⫹ __ ⫽ ___ 5 6 30 3 2 12 D __ ⫹ __ ⫽ ___ 6 4 12 __ ⫹ A 1 2 3 B __ ⫹ 8 __ ⫹ C 1 8 1 D __ ⫹ 3 PW84 2 __ 8 2 __ 8 1 __ 3 4 __ 8 __ ⫽6 8 __ ⫽5 8 ___ ⫽ 11 24 __ ⫽5 6 Practice © Harcourt • Grade 5 Name Lesson 13.6 Problem Solving Workshop Strategy: Compare Strategies Problem Solving Strategy Practice 1. Casey worked on memorizing her lines 2. What if Casey had worked on memorizing lines for 5 7_8 hours. Then how many hours did she spend working on act three? for the school’s three act play for 6 1_4 hours. She spent 2 3_4 hours working on act one and 1 5_8 hours working on act two. How many hours did Casey spend working on act three? Mixed Strategy Practice USE DATA For 3–4, use the table. 3. Laurie wants to make 3 gowns. How many yards of yellow silk will she need for the gowns? Show your work. Materials needed to make 1 gown Fabric 4. Tamera had 1 5_7 of gold trim left after making 3 gowns. How many yards of gold trim did Tamera have to start? 5. In the school musical, 1_4 of the actors were playing lead roles and 1_5 of the actors were playing supporting roles. All of the other actors were chorus members. What fraction of the actors in the school musical were chorus members? Predict and test to solve. Amount in Yards Blue Chiffon 1 32 Yellow Silk 3 25 Gold Trim 6 27 6. Heather bought 12 1_2 gallons of paint for the scenery. If 8 1_3 gallons were red, 2 1_6 gallons were black, and the rest were white, then how many gallons of the paint were white? PW85 Practice © Harcourt • Grade 5 Name Lesson 13.7 Choose a Method Choose a method. Find the sum or difference. Write it in simplest form. 2 1 1. __ ⫹ __ 7 6 2 1 2. __ ⫺ __ 3 2 3 1 3. __ ⫹ __ 4 4 6 1 4. ___ ⫺ ___ 22 11 3 1 5. __ ⫹ __ 5 5 6 1 6. ___ ⫺ __ 11 6 3 1 7. __ ⫹ __ 3 8 8 7 8. ___ ⫺ ___ 10 15 5 4 9. ___ ⫹ ___ 15 12 5 1 10. __ ⫺ __ 6 6 3 1 11. __ ⫹ __ 7 2 1 2 12. __ ⫹ __ 8 5 4 1 13. __ ⫺ __ 5 4 6 5 14. __ ⫹ __ 7 7 4 1 15. __ ⫹ ___ 7 21 Problem Solving and Test Prep 16. Mark lives near the Empire State Building 17. Mark took a taxi ride from the Empire in New York City. On Sunday, Mark spent 1_4 of his day visiting the Empire 5 State Building and __ 12 of his day rollerblading in Central Park. What fraction of the day did Mark spend either visiting the Empire State Building or rollerblading? 18. Lillian is practicing shooting marbles for State Building to Times Square. The taxi ride is 7_9 mile but Mark made an unexpected stop after 1_3 mile to buy a hotdog from a vendor. How long is the trip from the hot dog vendor to Times Square? 19. Lillian is participating in the Holyoke the competition. She hopes to shoot her favorite red marble 3_4 foot. However, she only makes 1_8 foot the first try, then 1_4 foot on her second shot. How much further must she shoot the red marble to reach her goal? PW86 Marble Championship in Massachusetts. In her collection, 3_7 of her marbles are agates and 2_5 are cat-eyes. How many of Lillian’s marbles are agates and cat-eyes? Show your work. Practice © Harcourt • Grade 5 Name Lesson 14.1 Lesson 1.1 Model Addition of Mixed Numbers Use fraction bars to find the sum. Write the answer in simplest form. 1 1 1. 3 __ 2 __ 2 3 3 1 2. 1 __ 3 __ 4 8 3 1 3. 3 __ 1 __ 5 5 3 __ 4. 5 ___ 13 3 1 5. 2 __ 2 __ 8 4 1 1 6. 5 __ 1 __ 4 6 3 1 7. 4 __ 1 __ 3 4 3 1 8. 2 __ 3 ___ 5 10 5 1 9. 1 __ 2 ___ 6 12 4 1 10. 4 ___ 1 __ 10 2 11 2 11. 1 ___ 1 __ 12 3 3 1 12. 2 ___ 2 __ 10 2 13. 17. 21. 4 1 ___ 14. __ 51 18. __ 21 22. 10 __ 11 2 __ 3 __ 24 5 _ 4 __ 21 2 _ 4 3 ___ 15. __ 15 19. 1 3 __ 23. 10 2 1 ___ 10 __ 6 ___ 4 5 12 _ 3 ___ 3 7 12 _ PW87 10 __ 11 16. 9 2 ___ 20. 1 1__ 24. 5 ___ 2 9 10 __ 10 7 1 ___ 10 __ 4 __ 51 2 _ 5 __ 32 5 __ 31 2 _ __ 43 8 __ 31 4 _ __ 31 2 __ 42 5 _ Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C14_L01.indd PW87 6/15/07 12:56:30 PM Name Lesson 14.2 Model Subtraction of Mixed Numbers Use fraction bars, or draw a picture to find the difference. Write the answer in simplest form. 8 5 1. 3 ___ 2 ___ 10 10 5 3 2. 5 __ 3 __ 8 8 1 1 3. 6 __ 1 __ 2 4 1 1 4. 4 __ __ 3 4 3 3 5. 3 __ 2 __ 4 8 3 1 6. 5 __ 3 __ 5 2 5 1 7. 4 __ 1 ___ 6 12 5 1 8. 5 __ 2 __ 6 2 7 1 9. 3 ___ 1 __ 12 2 2 1 10. 5 __ 4 __ 3 4 11 1 11. 4 ___ 2 __ 12 6 13. 17. 21. __ 47 14. __ 51 18. __ 53 22. 8 __ 1 1 4 __ 2 __ 2 1 3 __ 4 __ 1 1 3 _ 7 5___ 10 __ 5 1 5 __ 15. __ 51 19. ___ 6 11 23. 2 __ 3 2 5 __ 12 __ 5 1 2 __ 4 5 __ 16. __ 22 20. 5 1 2 __ 2 __ 3 __ 1 1 2 _ 9 4___ 10 __ 4 1 5 __ PW88 1 1 12. 3 __ 1 __ 5 2 24. __ 61 2 1 3 __ 6 __ __ 57 8 1 3 __ 4 __ __ 67 8 __ 3 3 4 __ Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C14_L02.indd PW88 6/15/07 12:56:04 PM Name Lesson 14.3 Record Addition and Subtraction Find the sum or difference. Write the answer in simplest form. 1. 7 __ 9 ___ 13 2. __ 3 1 __ 82 3. __ 5 2 __ 91 4. __ 1 4 __ 61 5. __ 6 1 __ 13 6. __ 5 1 __ 10 3 7. 4 __ 2 ___ 83 8. ___ 3 3 __ 12 11 9. __ 9 3 __ 85 10 2 6 5 9 12 3 9 7 3 12 4 4 3 4 6 6 4 Problem Solving and Test Prep USE DATA For 10–11, use the table. 10. How many miles did Sheryl run on Monday and Tuesday in all? Sheryl’s Training Record (In Miles) Walking 1 3 1 2 4 Monday 11. How much farther did Sheryl walk on 4 Tuesday Running 1 2 5 2 9 1 Monday than on Tuesday? 1 hours on 12. Dan played guitar for 2 _ 2 Saturday and 1 _52 hours on Sunday. How many hours total did Dan play guitar in 2 days? 2 hours cleaning her room, 13. Ana spent 1 _ 3 and Evelyn spent 1 8_9 hours cleaning her room. How much longer did it take Evelyn to clean her room? 7 hours A 1 __ 10 A 3 5_9 hours B 3 3_7 hours B 1 hour C 3 1_2 hours C _2 3 hour D _2 9 hour 9 D 3 __ hours 10 PW89 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C14_L03.indd PW89 6/28/07 1:16:02 PM Name Lesson 14.4 Subtraction with Renaming Use fraction bars to find the difference. Write the answer in simplest form. 1. __ 1 5 __ 53 5. 9 1 6 ___ 2 ___ 8 10 8 10 2. __ 721 6. 3 __ 7 ___ 13 4 10 5 3 1 3. 4 __ __ 2 4 1 4 4. 4 __ 2 __ 5 2 1 2 7. 7__ 6 __ 2 3 1 7 8. 4 __ 3 ___ 3 12 Problem Solving and Test Prep Zack’s Large Fruit Smoothie USE DATA For 9–10, use the table. Ingredient 9. Zack decided to reduce the amount of 1 _78 banana by ounces. How much banana did Zack use? Banana Strawberry Blueberry Amount 3 ounces 4 1 2 6 ounces 1 3 ounces 2 4 5 10. Zack’s recipe makes a 10 __ -ounce smoothie. If blueberries were not included, 12 how many ounces would the smoothie be? 11. Stacey buys 4 1_4 yards of ribbon to make a 12. Jon used 5 1_4 ounces of cranberry juice bow. She uses 2 5_8 yards. How much ribbon is left? and 3 2_3 ounces of orange juice to make fruit punch. How much more cranberry juice than orange juice did Jon use? 3 A 1 __ yards 8 5 B 1 __ yards 8 4 C 2 __ yards 8 5 __ D 2 yards 8 5 A 1 ___ ounces 12 7 B 1 ___ ounces 12 1 C 2 __ ounces 7 7 D 2 ___ ounces 12 PW90 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C14_L04.indd PW90 6/15/07 12:55:44 PM Name Lesson 14.5 Practice Addition and Subtraction Estimate. Then write the sum or difference in simplest form. 1 91 1. 1 __ ⫹ 5 __ 6 3 3 5 2. 14 __ ⫺ 9 __ 4 6 3 11 3. 16 __ ⫹ 24 ___ 4 12 5 5 4. 15 __ ⫺ 11 __ 8 6 5 4 5. 11 __ ⫹ 25 __ 5 8 5 6. 8 ⫺ 1 __ 7 Use a calculator to find the sum or difference. 4 1 7. 39 __ ⫹ 17 __ 5 2 3 1 8. 32 ___ ⫺ 19 __ 5 10 3 7 9. 93 __ ⫹ 28 ___ 4 10 Problem Solving and Test Prep USE DATA For 10–11, use the table. 10. On which day did Cyndi spend the most Cyndi’s Fielding Practice time at fielding practice? The least? Day Monday Wednesday Friday Time 1 3 hours 8 2 11 hours 12 1 5 hours 6 11. How much time in all did Cyndi spend at fielding practice on Wednesday and Friday? 12. Amber’s speech has to be 8 1_2 minutes long. If her speech is currently 7 7_8 minutes long, how much longer does her speech need to be? A B C D 13. Mary sold 33 3_8 bushels of apples and 3 __ minute 8 5 __ minute 8 __ minutes 11 8 5 1 __ minute 8 21 2_3 bushels of pears. How many bushels of fruit did she sell in all? 1 A 54 ___ 24 5 B 54 ___ 24 1 C 55 ___ 24 5 D 55 ___ 24 PW91 bushels bushels bushels bushels Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C14_L05.indd PW91 6/15/07 12:56:21 PM Name Lesson 14.6 Problem Solving Workshop Strategy: Use Logical Reasoning Problem Solving Strategy Practice Use logical reasoning to solve. 1. Sue had softball practice for 3 _32 hours. Sue’s mom came 3_4 hour after practice started, and left 5_6 hour before practice ended. How many hours of practice did Sue’s mom watch? 2. Mark, Dan, Brendan, and Alex sold popcorn for their baseball team. Dan sold twice as many pounds as Brendan. Alex and Mark sold the same amount. Brendan sold 12 1_2 pounds, 5 more pounds than Mark. How many pounds did each boy sell? Mixed Strategy Practice USE DATA For 3–4, use the table. 3. The sum of the distances of the 3 homeruns __ ft. What was the hit in Game 1 is 278 11 18 distance of Nina’s homerun in Game 1? Homerun Distance (Ft) Carla 4. The sum of the distances of the 3 homeruns hit in Game 2 is 9 1_2 ft less than the sum for Game 1. What was the distance of Maria’s homerun in Game 2? Game 1 Game 2 88 2 3 90 7 9 85 1 2 Nina Maria 93 1 6 5. Three pumpkins weigh 18 5_9 , 18 1_3 , and 18 5_6 pounds. Tim’s pumpkin weighs more than Denny’s, but they weigh the same when rounded to the nearest whole number. Rich’s pumpkin is lighter than Tim’s. How much does each boy’s pumpkin weigh? 6. The mailboxes are 41 1_2 , 40 1_4 , and 42 2_3 inches tall. Jill’s mailbox is 1 1_4 inches shorter than Ali’s. Abby’s mailbox is the tallest. How tall is each girl’s mailbox? PW92 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C14_L06.indd PW92 6/28/07 1:16:47 PM Name Lesson 15.1 Model Multiplication of Fractions Use yellow and blue crayons to model the product. 4 1 1. __ __ 5 2 1 __ 2. __ 5 6 2 1 2 3. __ __ 3 4 1 2 4. __ __ 2 3 Find the product. 4 __ 5. __ 5 6 9 1 __ 6. __ 1 4 3 1 2 7. __ __ 8 3 4 2 8. __ __ 7 5 1 2 9. __ __ 2 9 3 1 10. __ __ 3 4 2 1 11. __ __ 5 7 3 1 12. ___ __ 10 2 1 __ 13. __ 2 3 9 1 5 14. __ __ 4 7 PW93 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C15_L1.indd PW93 7/2/07 2:14:09 PM Name Lesson 15.2 Record Multiplication of Fractions Find the product. Write the answer in simplest form. 9 2 1. __ ⫻ ___ 3 10 6 1 2. __ ⫻ __ 7 3 7 5 3. __ ⫻ ___ 12 8 1 __ 4. __ ⫻3 7 4 2 __ 5. __ ⫻4 7 9 5 3 6. __ ⫻ ___ 12 8 4 9 7. ___ ⫻ __ 5 10 6 3 8. __ ⫻ __ 9 7 4 __ 9. ___ ⫻7 8 10 1 5 10. __ ⫻ __ 3 6 3 1 11. __ ⫻ ___ 10 9 3 2 12. __ ⫻ ___ 12 5 9 4 13. __ ⫻ ___ 10 7 3 10 14. ___ ⫻ __ 5 12 4 __ 15. __ ⫻3 8 9 Problem Solving and Test Prep 16. Alexa uses 2_3 of her backyard for a dog 17. Charles uses 1_3 of his farm for a pumpkin 18. Jin picks 2_3 of 1_2 of his apple orchard to 19. Luisa planted 3_5 of the last 2_9 of her make apple cider. What fraction of the orchard did Jin pick? flower garden with daffodils. What fraction of her garden is daffodils? 1 A __ 2 1 B __ 6 1 C __ 3 5 D __ 9 5 A ___ 20 1 B __ 9 6 C __ 7 2 D ___ 15 run. She has 1_5 of the dog run fenced in. What fraction of Alexa’s backyard is fenced in? patch. He uses 2_7 of the pumpkin patch to grow white pumpkins. What fraction of the farm grows white pumpkins? PW94 Practice © Harcourt • Grade 5 Name Lesson 15.3 Multiply Fractions and Whole Numbers Find the product. 9 1. 5 ___ 10 3 2. __ 2 4 5 3. __ 3 6 1 4. 7 __ 9 3 6. 10 __ 5 9 7. ___ 4 10 5 8. __ 6 8 1 9. __ 15 3 1 13. 11 __ 9 8 14. __ 10 9 5 11. 8 __ 9 6 12. 5 __ 7 2 5. 12 __ 7 4 10. 9 __ 7 3 15. ___ 11 10 Problem Solving and Test Prep 16. Lloyd feeds his cats 2_9 of a 5 pound bag 17. Kyra uses 3_5 of a roll of yarn for each of cat food each day. How many pounds of food does Lloyd feed his cats daily? 18. Pedro used 2_3 of a 33 ounce bottle of soap to wash his mother’s car. How many ounces of soap did Pedro use? A 22 ounces C 28 ounces 20 ounces D 30 ounces B scarf she makes. How many rolls of yarn does she need to make 4 scarves? 6 19. Shyla used __ of the 5 gallons of paint for 7 her fence. How many gallons of paint did Shyla use? 1 A 4 __ gallons 2 6 B 3 __ gallons 7 PW95 C 4 gallons D __ gallons 42 7 Practice © Harcourt • Grade 5 Name Lesson 15.4 Multiply with Mixed Numbers Make a model to find the product. 1 1 1 1 1. 2 __ __ 2. __ 1 __ 2 3 4 2 __ 3. __ 11 4 3 2 Find the product. 1 4. 5 4 __ 2 __ 2 1 __ __ 1 1 9. 2 7 4 3 3 5. 2 1 __ 5 1 6. 8 2 __ 2 3 3 1 10. 1 __ 1 __ ___ 5 3 10 __ __ 2 7. 2 1 7 6 5 3 1 11. 1 __ __ __ 7 5 3 3 8. 1 __ 9 7 9 1 1 12. ___ 1 __ 2 __ 10 4 2 Problem Solving and Test Prep 13. Alejandro has 7 1_3 pounds of flour. He 14. Isabel has 2 1_2 gallons of scarlet paint. 15. Kim hiked 5 2_3 miles on Saturday. She 16. Joshua danced 3 1_2 hours on Monday. uses 3_4 of the flour to make bagels. How many pounds of flour did he use? used 2_5 of the time talking on the phone while hiking. How many miles did Kim talk on the phone while hiking? She uses 2_3 of it to paint her dining room. How many gallons of paint did Isabel use? 1 A 3 __ 9 3 B 2 __ 4 5 C 2 __ 8 9 D 1 ___ 10 4 A 2 ___ 15 B 3 C ___ 2 11 D Tess danced 3_4 time as long. How many hours did Tess dance? 12 __ 41 4 PW96 Practice © Harcourt • Grade 5 Name Lesson 15.5 Model Fraction Division Write a division number sentence for each model. 1. 2. 3. 4. Use fraction bars to find the quotient. 2 1 5. __ ⫼ __ 9 6 1 1 9. __ ⫼ ___ 10 2 3 1 6. ___ ⫼ __ 10 4 1 __ 7. __ ⫼1 8 4 3 1 8. ___ ⫼ __ 11 4 4 __ 10. __ ⫼2 3 7 1 11. 1 ⫼ __ 5 4 12. 6 ⫼ __ 9 1 13. 5 ⫼ __ 4 7 __ 14. ___ ⫼1 6 10 1 15. 4 ⫼ __ 8 1 16. 2 ⫼ __ 6 1 17. 8 ⫼ __ 3 8 1 18. ___ ⫼ __ 11 4 1 19. 2 ⫼ __ 2 1 20. 4 ⫼ __ 4 PW97 Practice © Harcourt • Grade 5 Name Lesson 15.6 Divide Whole Numbers by Fractions Find the quotient. Write it in simplest form. 5 1. 1 ___ 12 1 2. 2 __ 2 2 3. 7 __ 5 1 4. 9 __ 3 3 5. 6 __ 7 1 6. 4 __ 6 7 7. 3 __ 9 5 8. 8 ___ 12 5 9. 7 __ 6 3 10. 10 __ 5 1 11. 5 __ 4 1 12. 12 __ 3 3 14. 9 __ 4 3 15. 3 ___ 10 1 13. 6 __ 3 Problem Solving and Test Prep 16. Students are painting the set for the 17. Gerard is cleaning a sculpture garden. He has 2 statues left to clean. It takes him 2 hours to clean 1_3 of the first statue. If he spends the same amount of time cleaning each statue, how many hours will it take Gerard to clean both statues? community theater’s upcoming play. It takes the students 3 hours to paint 2_5 of the set. If they spend the same amount of time painting each section, how many hours will it take the students to paint the whole set? 9 18. Henry cut a 10 foot log into __ 10 foot 19. Melanie cut 5 feet of pretzel dough pieces of firewood. How many pieces of firewood did Henry cut the log into? into 1_3 foot pieces. How many pieces did Melanie cut the dough into? A 10 A 12 B C D __ 11 1 9 __ 12 1 3 5 __ 9 9 B 15 C 18 D 20 PW98 Practice © Harcourt • Grade 5 Name Lesson 15.7 Divide Fractions Write a division sentence for each model. 1. 2. Divide. Write the answer in simplest form. 5 3 3. __ ___ 8 12 5 1 4. __ __ 7 3 1 5 8. 3__ __ 9 2 1 1 9. 2__ 1__ 4 5 2 6 5. __ __ 5 9 3 5 10. ___ __ 7 12 7 __ 6. ___ 3 8 10 1 2 7. 2__ __ 5 4 4 3 11. __ __ 9 8 2 1 12. 1__ __ 3 5 Problem Solving and Test Prep 13. Bruce has 8 1_2 feet of lumber to make 14. Cory has 10 1_2 feet of paper to make 1 -cups of brown sugar. 15. A baker has 7 __ 3 16. Lila can walk 2 3_4 miles in 4_5 of an hour. banners. Each banner is 3_4 of a foot long. How many banners can Cory make? part of the set for a school play. Each set part needs to be 1_4 feet tall. How many set parts can Bruce build? 3 _ 4 It takes -cup of brown sugar to make a loaf of banana bread. How many loaves of banana bread can the baker make? How fast can she walk in miles per hour? 1 A 2 __ miles per hour 5 1 B 3 __ miles per hour 3 C 2 miles per hour 3 D 1 __ miles per hour 4 PW99 Practice © Harcourt • Grade 5 Name Lesson 15.8 Problem Solving Workshop Skill: Choose the Operation Problem Solving Skill Practice Tell which operation you would use to solve the problem. Then solve. 1. Jacinda works 2_5 of the days each month _1 3 at the reference desk and of the days in the children’s room at the library. How often does Jacinda work at both places? 3. Padma cooks at the soup kitchen 3_5 of the days each month and at the hospital 1_4 of the days each month. What fraction of the days each month does Padma cook at both places? 2. Harrison has blue, red, green, and tiger eye marbles. Of the 15 marbles, 2_5 are tiger eye marbles. How many of Harrison’s marbles are tiger eye marbles? 4. Joaquin has 150 coins in his collection. He has pennies, nickels, dimes, quarters, and dollars. Of all the coins, 1_3 are quarters. How many of Joaquin’s coins are quarters? Mixed Applications Practice USE DATA For 5–6, use the table. Softball Tournament Results 5. Garrett plays for the Buffalos, and Lucy 2 _ 3 plays for the Bulldogs. They played of their teams’ winning games. How many more winning games did Lucy play than Garrett? 6. The Bulldogs won the league title after winning 90% of their games. How many more games did the Bulldogs win than the Lions? Team Wins Losses Bulldogs 9 1 Eagles 7 3 Buffalos 6 4 Lions 4 6 7. Ashley takes 1_2 of the days each month PW100 for ballet lessons and 1_6 for tap dance lessons. What fraction of the days each month does Ashley take dance lessons? Practice © Harcourt • Grade 5 Name Lesson 16.1 Understand and Express Ratios Write each ratio three ways. Then name the type of ratio. 1. flags with stripes: flags with stars 4. flags with stripes: total number of flags 2. flags with a torch to flags with stripes 3. total number of flags to flags with a C 5. flags with a torch to flags with a C 6. flags with stars to flags with a torch Problem Solving and Test Prep 7. The Arizona state flag has 7 red stripes and 6 gold stripes. What is the ratio of red stripes to gold stripes? 9. Sara has 5 books about dogs and 8. Fast Fact The state flag of Texas has 3 stripes. The blue stripe stands for loyalty, the white stripe stands for strength, and the red stripe stands for bravery. The blue stripe has a white star in its center. Write the ratio of blue stripes to total number of stripes in three ways. 10. Cody used 4 paper towels to clean up a 3 books about horses. What is the ratio of books about horses to books about dogs? mess. There are still 5 paper towels left on the roll. What is the ratio of used paper towels to total paper towels? A 5:3 A 4:5 B 8:3 B 4:9 C 3:5 C 5:4 D 5:8 D 5:9 PW101 Practice © Harcourt • Grade 5 Name Lesson 16.2 Algebra: Equivalent Ratios and Proportions Write two equivalent ratios for each ratio. Use multiplication or division. 1. 1:7 5 3. __ 3 2. 28 to 4 4. 9:27 Tell whether the ratios form a proportion. Write yes or no. 3 1 5. __ and ___ 4 12 13 52 7. ___ and ___ 23 99 42 14 6. ___ and ___ 9 3 8 4 8. ___ and __ 49 9 Problem Solving and Test Prep 9. Mia makes purple paint. For 1 gallon 10. A flower bed has 7 red tulips and of paint, she mixes 1 part red paint to 3 parts blue paint. Write a proportion that shows how many parts of each color Mia would need for 5 gallons of purple paint. 9 yellow tulips. What is the ratio of red tulips to yellow tulips? 11. In the library, the ratio of mysteries to 12. The ratio for making salad dressing is westerns is 4 to 1. The library has 32 mystery books. How many western books are there? 3 cups oil to 1 cup of vinegar. Which is an equivalent ratio for 3 to 1? A 3 A 3:1 B 5 B 5:15 C 8 C 6:1 D 28 D 9:6 PW102 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C16_L02.indd PW102 6/15/07 12:25:32 PM Name Lesson 16.3 Ratios and Rates Write each ratio in fraction form. Then find the unit rate. 1. 243 seconds for 81 2. $3.52 for 4 pounds of jumping jacks 3. 18 pages in 3 days bananas 4. $4.98 for 2 gallons of milk 5. 48 ounces in 3 cans 6. 64 doors on 16 cars 7. 96 books on 8 shelves 8. 300 miles in 5 hours 9. $24 for 4 hours of work 10. 144 peaches in 3 cases 11. 104 boxes in 8 stacks 12. 455 miles in 7 hours Problem Solving and Test Prep 13. A package of 12 juice boxes is $2.76. 14. Fast Fact There are 124 calories in two A package of 16 juice boxes is $4.00. Which package is the better buy? cups of grapes. How many calories are there in 1 cup of grapes? 15. Sara buys 3 pounds of chicken for 16. Alex spends $9.75 on 5 packages of $17.97. What is the unit cost? baseball cards. What is the unit cost? A $2.98 A $1.95 B $5.99 B $3.25 C $6.00 C $4.75 D $17.97 D $14.75 PW103 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C16_L03.Indd PW103 6/15/07 12:25:49 PM Name Lesson 16.4 Understand Maps and Scales Complete the ratio table. 1. 2. Map Distance, in 1 2 6 Actual Distance, mi 60 120 300 Map Distance, cm 1 8 9 13 3.8 Actual Distance, km 480 49.4 57 The map distance is given. Find the actual distance. For 3–6, the scale is 1 in. ⴝ 300 mi. For 7–10, the scale is 2 cm ⴝ 8.4 km. 3. 2.2 in. 4. 7 in. 5. 0.4 in. 7. 0.25 cm 8. 6 cm 9. 3.1 cm 6. 5.4 in. 10. 8 cm Problem Solving and Test Prep 11. A map of Spain has a scale of 12. The scale on a map showing Fargo 4 cm ⫽ 220 km. Another map of Spain is half the size. What is the scale of the smaller map? 13. Amber draws a map of her town using and Grand Forks is 0.5 in. ⫽ 20 mi. The distance between these cities is 80 miles. What is the distance on the map? 14. Nathan draws a map of his a scale of 1 in. ⫽ 50 ft. The actual distance between Amber’s house and the library is 975 feet. What is the distance on the map? neighborhood using a scale of 1 cm ⫽ 4 km. The distance on the map between Nathan’s house and Mr. Smith’s house is 2.1 centimeters. What is the actual distance? A 7.5 in. A 1.9 cm B 7.5 ft B 6.1 cm C 19.5 in. C 8.2 cm D 19.5 ft D 8.4 cm PW104 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C16_L04 .indd PW104 6/15/07 12:28:04 PM Name Lesson 16.5 Problem Solving Workshop Strategy: Make a Table Problem Solving Strategy Practice Make a table to solve. 1. Tara and her extended family are going to a theme park. Ticket prices are divided by age groups: 0–2; 3–9; and 10⫹. The ages of the people are 1, 8, 7, 11, 39, 2, 3, 21, 13, 14, 4, 38, and 24. How many people are in each group? 2. The prices for a single day theme park ticket are free for ages 0–2, $23 for ages 3–9, and $33 for ages 10⫹. What will the total cost of admission tickets be for Tara and her extended family? Mixed Strategy Practice USE DATA For 3–5, use the information in the picture. 3. The height of the Petronas Towers 1 & 2 is 33 feet more than the height of the Sears Tower. The Jin Mao Building is 290 feet shorter than the Taipei 101 building. Write the heights of the four buildings in order from shortest to tallest. Taipei 101 4. The height of the Empire State Building _4 5 is 90 feet more than the height of the Sears Tower. How tall is the Empire State Building? Petronas Towers 1 & 2 1,450 ft Sears Tower 1,380 ft Empire State Building Jin Mao Building 5. How much taller is the Taipei 101 building than the Empire State Building? PW105 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C16_L05.indd PW105 6/28/07 1:18:51 PM Name Lesson 16.6 Understand Percent Write a ratio and a percent to represent the shaded part. 1. 2. 3. 4. 5. 6. Write a decimal and a percent to represent the shaded part. 7. 8. 9. 10. 11. 12. PW106 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C16_L06.indd PW106 7/2/07 2:16:05 PM Name Lesson 16.7 Fractions, Decimals, and Percents Write each percent as a decimal and as a fraction in simplest form. 1. 10% 2. 45% 3. 30% 4. 26% 5. 18% 6. 59% 7. 82% 8. 67% Write each fraction or decimal as a percent. 1 9. __ 4 13. 0.178 10. 0.29 7 11. ___ 10 12. 0.60 7 14. __ 8 15. 0.058 3 16. ___ 15 Problem Solving and Test Prep 17. California produces about 75% of the strawberries in the United States. What fraction of strawberries in the United States does California produce? 19. Susan washed 3_5 of her clothes. What 18. If you eat about 10 medium strawberries you will get 9% of the vitamin B6 you should have every day. What fraction of vitamin B6 do you still need for that day? 20. At the Corner Store, 85% of the percent of her clothes did she wash? 100 shelves contain food. What is the percent written as a decimal? A 0.3 A 0.85 B 60% B 8.05 C 0.35 C 8.5 D 53% D 0.8 PW107 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C16_L07.indd PW107 6/15/07 12:27:18 PM Name Lesson 16.8 Find Percent of a Number Complete the sentence. Then, find the percent of each number. 1. 30% of 40 2. 60% of 15 ⫽ 10 counters represent 100%, or 40. 60 100 or ____ of 15 So, each counter represents 10%, or 30% of 40 ⫽ 60% of 15 ⫽ Find the percent of each number. 3. 20% of 20 4. 75% of 24 5. 25% of 12 6. 50% of 14 7. 40% of 15 8. 30% of 50 9. 10% of 80 10. 80% of 90 11. 10% of 10 12. 90% of 20 13. 75% of 8 14. 40% of 25 15. 25% of 20 16. 30% of 10 17. 50% of 6 18. 20% of 30 19. 25% of 80 20. 75% of 32 21. 30% of 30 22. 60% of 70 PW108 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C16_L08.indd PW108 6/15/07 12:28:20 PM Name Lesson 17.1 Outcomes and Probability Use the bag of marbles to write the probability of the event of pulling the marble described. 1. striped 2. black 3. white 4. gray or black 5. gray or white 6. gray, white, or black Use a number cube labeled 1 through 6 to write the probability of the event of tossing each number. Tell whether the event is likely, unlikely, certain, or impossible. 7. 5 8. a number greater than 2 9. a number less than 8 Problem Solving and Test Prep 10. Genevieve has a bag of letter tiles that 11. Daniel has a number cube labeled 1-6. spell out her name. What is the probability of pulling a vowel tile? What is the probability of rolling an odd number? 12. What is the probability that the pointer 13. What is the probability of rolling a will land on stripes? number greater than 4 on a number cube labeled 1 through 6? 1 A __ 8 1 A. __ 6 3 1 C. __ or __ 2 6 2 1 B. __ or __ 6 3 5 D. __ 6 2 B __ 4 1 C __ 4 1 D __ 3 PW109 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C17_L1.indd PW109 6/15/07 12:14:10 PM Name Lesson 17.2 Probability Experiments For 1–4, use the table. 1. Rachel pulled a marble from a bag, Rachel’s Marble Experiment recorded its color, and put the marble back in the bag. She did this 30 times and recorded her results in the table. What is the experimental probability of Rachel pulling Number of pulls a red marble? a green marble? a blue marble? Total Red Blue 6 7 Green White 5 12 a white marble? 2. Predict how many times out of 80 pulls that Rachel would pull a red marble from the bag. 3. Based on experimental probabilities, would you predict that Rachel would pull a red or a white marble more often if she pulled a marble from the bag 60 more times? Explain. 4. Predict the number of times out of 60 pulls that Rachel would pull a red or a green marble from the bag. 5. Predict the probability out of 60 pulls that Rachel would not pull a blue or a green marble from the bag. PW110 Practice © Harcourt • Grade 5 Name Lesson 17.3 Probability and Predictions Express the experimental probability as a fraction in simplest form. Then predict the outcome of future trials. For 3–6, items are returned after each trial. 1. 8 heads in 20 coin tosses; 2. 5 wins in 10 games; 30 more tosses 6 more games 3. 3 pink buttons in 9 pulls; 4. 12 blue socks in 48 pulls 12 more pulls 16 more pulls 5. 24 bananas out of 30 pieces of fruit; 6. 2 yellow shirts in 12 pulls 45 more pieces of fruit 6 more pulls Problem Solving and Test Prep 7. George won 8 of the 12 games of 8. Jojo rolled an even number on a number cube 4 out of 10 rolls. How many odd numbers could Jojo expect to roll in the next 15 rolls? checkers he played with Mon. If they play once a day for the next 9 days, how many games could George expect to win? 9. Bobby lost 3 out of 9 chess matches. 10. Perry’s soccer team won 4 out of 6 Predict how many times Bobby will lose in 12 more matches? games. Predict how many times Perry‘s team will win in the next 15 games? A 3 matches A 10 games B 4 matches B 12 games C 5 matches C 8 games D 6 matches D 9 games PW111 Practice © Harcourt • Grade 5 Name Lesson 17.4 Problem Solving Workshop Strategy: Make an Organized List Problem Solving Strategy Practice USE DATA For 1–3, use the table. Sal’s Pizza Parlor 1. Donita and her friends are trying to decide what kind of 1-topping pizza to order at Sal’s Pizza Parlor. How many different combinations of pizza crust, sauce, and topping are possible? Crust Sauce Topping Thick Marinara Sausages Thin Alfredo Olives Mushrooms Peppers 2. Sal is experimenting with a new pesto sauce. If he adds this to the menu, how many diffrent combinations of pizza crust, sauce, and topping would be possible? 3. Sal uses 3 different types of cheese on his pizza: parmesan, Romano, and mozzarella. If this category were added to the table, how many different combinations of pizza crust, sauce, topping, and cheese would be possible? Mixed Strategy Practice Menu USE DATA for 4–7, use the menu. Breakfast Options 4. If Jess and his 4 friends each order one breakfast option and one beverage, how many different combinations of breakfast options and beverage are possible? 5. Bea ran out of quiche. Now how many different combinations do Jess and his friends have for breakfast? Beverages Pancakes $4.80 Milk $1.25 Omelet $5.20 Juice $1.75 French toast $4.50 Sparkling $1.55 Quiche $5.10 Oatmeal or cold cereal $3.70 6. The total bill for breakfast is $30.85. If Jess and his friends pay with two $20 bills, how much change will they get back? 7. Jess owes $6.05 for breakfast. What two combinations could he have ordered? PW112 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C17_L4.indd PW112 6/18/07 10:21:10 AM Name Lesson 17.5 Tree Diagrams For 1–3, use the tiles and the spinner. Draw a tree diagram to find the total number of possible outcomes. 1. Draw a tile at random and spin the pointer. How many possible outcomes? A E I PQ R 3. Toss a number cube labeled 1 to 6 and spin the pointer. How many possible outcomes? 2. Toss coin and draw a tile at random. How many possible outcomes? Problem Solving and Test Prep 4. If Ian rolls a die labeled 1-12 and tosses 5. Liam Growser put his first name letter tiles in one bag and his last name letter tiles in another bag. How many outcomes are possible if he randomly removes one tile from each bag? a coin, how many outcomes are possible? 6. Imee can choose a gold, silver or string 7. Matt can choose a plain, poppy seed, bracelet with red, green, blue, or yellow beads. How many bracelet and bead choices does Imee have? A 7 garlic, or sesame bagel with plain or herb cream cheese. How many bagel sandwich choices does Matt have? A 6 8 B 4 C 12 C 8 D 14 D 10 B PW113 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C17_L5.indd PW113 6/15/07 12:14:41 PM Name Lesson 17.6 Combinations and Arrangements Make a list or draw a tree diagram to find the total number of possibilities. 1. ice-cream combinations: mint, vanilla 2. summer-camp activity combinations: hiking or horseback riding; 2-day, 3day, or 4-day outings or chocolate ice cream; chocolate chip, caramel syrup, or toffee topping 3. ways to arrange a penny, nickel, and 4. order in which Raymart, Nicole, Alissa, dime in a line and Marie line up to start a race across the soccer field? Problem Solving and Test Prep 5. Kim needs to groom her 4 cats Cutie, 6. Joy’s snack choices include 4 types of Magic, Stitch, and Star. She grooms Cutie first. In how many different orders can Kim groom the remaining 3 cats? 7. Kathy has 3 shirts and 4 pairs of shorts to choose from. How many possible choices does Kathy have? A 6 cookies and 2 types of drinks. If she chooses one cookie and one drink, how many possible combinations are there? 8. Leila has 4 pictures to hang on her wall in a single line. In how many different ways can she hang them? A 3 B 7 B 24 C 9 C 9 D 12 D 12 PW114 Practice © Harcourt • Grade 5 Name Lesson 18.1 Points, Lines, and Angles For 1–6, use the figure. Name an example of each. 1. point 2. line segment J 3. line M K L 4. plane P Q 5. vertex 6. vertical angles N R O S For 7–14, use the figure above. Classify each angle. Write obtuse, acute, straight, or right. 7. ⬔MNO 11. ⬔JKS 8. ⬔KPS 9. ⬔SPR 10. ⬔JLQ 12. ⬔JLN 13. ⬔LPQ 14. ⬔QPR Problem Solving and Test Prep USE DATA For 15–16, use the map. 15. Name three streets that are parallel to Historic Charles Street. 16. Chase Street forms a right angle with which street? 17. Which of the following best describes 18. Which is the least whole number of the figure? degrees an obtuse angle can have? A parallel lines A 90⬚ B right angles B 91⬚ C point C 101⬚ D 45⬚ D intersecting lines PW115 Practice © Harcourt • Grade 5 Name Lesson 18.2 Measure and Draw Angles Estimate the measure of each angle. Then use a protractor to find the measure. 1. ⬔YXZ 2. ⬔VXT 3. ⬔TXZ 4. ⬔UXZ U V W Y T X Z Use a protractor to draw each angle. Classify each angle. 5. 25⬚ 6. 90⬚ 7. an angle whose measure is greater than 135⬚ Problem Solving and Test Prep USE DATA For 8–9, use the clocks. 8. Look at the angle shown by the hands of the clock that shows 3:00. What is the measure of this angle? Explain how you know. 9. Estimate the measure of the angle formed by the hands of the clock that shows 4:00. Then measure the angle. 10. Which angle measure names an acute 11. What is the approximate measure of the angle? angle below? Z A 82⬚ B 95⬚ C 105⬚ X Y D 90⬚ PW116 Practice © Harcourt • Grade 5 Name Lesson 18.3 Polygons Name each polygon and tell whether it is regular or not regular. 1. 2. 3. 4. Tell if the given angles could form a triangle. 5. 60⬚, 65⬚, 60⬚ 6. 10⬚, 105⬚, 64⬚ 7. 77⬚, 53⬚, 50⬚ Problem Solving and Test Prep 8. Amelia is trying to draw a triangle. She wants to use the angle measures: 45⬚, 90⬚, and 45⬚. Can she draw a triangle using these angles? Explain. 10. Which of the following angles could 9. Dante is going to try to draw a triangle. He wants to use the angle measures: 47⬚, 84⬚, and 110⬚. Can he draw a triangle using these angles? Explain. 11. Which polygon is not regular? form a triangle? A 85, 42⬚, 63⬚ A B 20⬚, 70⬚, 10⬚ B C 80⬚, 50⬚, 50⬚ C D 45⬚, 45⬚, 70⬚ D PW117 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C18_L03.indd PW117 6/15/07 12:52:11 PM Name Lesson 18.4 Problem Solving Workshop Skill: Identify Relationships Problem Solving Skill Practice For 1–2, identify the relationship. Then solve. 1. What relationship can you find between the length of a square’s sides and the perimeter? Length Of Square Sides (In.) 3 4 5 6 Perimeter (In.) 12 16 20 24 2. Predict the perimeter, if the length of each side of a square is 14 inches? Mixed Applications Practice USE DATA For 3–4, use the table. 3. Identify the relationship displayed in the table. Number Of Sides On A Prism Base 3 4 5 6 7 Number of Vertices 6 8 10 12 14 4. How many vertices would a base with 9 sides have? 5. Dennis, Carl, Paul, and Jeremy live in the first four houses on Park Street. Dennis lives in the second house from the corner. Jeremy does not live next to Dennis. Paul lives on the corner. In what place is Carl’s house on the street? PW118 Practice © Harcourt • Grade 5 Name Lesson 18.5 Circles For 1–6, use the circle at the right. 1. Name 5 radii. 2. Name a 3. Name a chord. diameter. B C ___ 4. Name the circle. 5. If AC is 7 inches, ___ ___ D 6. If BD is 6.2 how long is BD? inches, ___ how long is AC ? E A F Complete 7–8. Then use a compass to draw each circle. Draw and label the measurements. 7. radius ⫽ 8. radius ⫽ 0.9 in. diameter ⫽ 1.4 cm diameter ⫽ Problem Solving and Test Prep USE DATA For 9–10, use the circle. 9. What is the unknown measure in the circle? 99° 112° 82° 10. If 112˚ is changed to 95˚, what is the unknown measure of the circle? 11. Which is the measure of ⬔AXC? A 88⬚ A B 88° B 124⬚ C 148⬚ X D 184⬚ C 12. Which is the measure of ⬔BXC? 124° A 90⬚ B 99⬚ C 109⬚ D 171⬚ PW119 A B 90° X 171° C Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C18_L05.indd PW119 6/15/07 12:51:26 PM Name Lesson 18.6 Congruent and Similar Figures Write whether the two figures appear to be congruent, similar, or neither. 1. 2. 3. 4. Identify the corresponding side or angle. ___ 6. ⬔S 5. UT 9. ⬔U ___ 10. SU ___ 7. RS 8. ⬔T 11. ⬔R 12. TR S R X W ___ T U Z Y Problem Solving and Test Prep USE DATA For 13–14, use the figures shown. 13. Do the figures appear to be congruent? Explain. F T V H 14. Do the figures appear to be similar? Explain. 15. Which best describes the two figures below? A congruent B similar C regular polygons U G 16. Quadrilaterals ABCD and EFGH are congruent. The measure of ⬔C is 150⬚. What is the measure of the corresponding angle, ⬔G ? D neither congruent nor similar PW120 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C18_L06.indd PW120 6/15/07 12:50:58 PM Name Lesson 18.7 Symmetry Draw all lines of symmetry. Then tell whether each figure has rotational symmetry by writing yes or no. 1. 2. 3. 4. 5. 6. 7. 8. Each figure has rotational symmetry. Tell the fraction and the angle measure of each turn. 10. 9. 11. 12. Problem Solving and Test Prep 13. Does a right triangle have lines of symmetry? rotational symmetry? 14. Brandon makes a design that has 1 rotational symmetry every __-turn. 2 What angle measure describes the design’s symmetry? 15. Which figure has rotational symmetry? 16. Which figure has rotational symmetry? A C A C B D B D PW121 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C18_L07.indd PW121 6/27/07 9:57:05 AM Name Lesson 19.1 Classify Triangles Classify each triangle. Write isosceles, scalene, or equilateral. 1. 2. 8 ft 4 ft 3. 7 cm 7 ft 9m 5m 7 cm 9m 7 cm Classify each triangle. Write acute, right, or obtuse. 4. 5. 6. Problem Solving and Test Prep For 7–9, use the models of the sails. 21 in. 7. What type of triangle is school A’s flag? 6 in. School A 17 in. 8. What type of triangle is school B’s flag? 18 in. 10 in. 9. Two of the angles in school A’s flag measure 75⬚ and 20⬚. What is the measure of the third angle? 10. A triangle has two equal sides. What School B 18 in. 11. James draws a triangle with angles that type of triangle is it? measure 45⬚ and 60⬚. What is the measure of the third angle? A scalene A 105⬚ B obtuse B 90⬚ C acute C 75⬚ D isosceles D 45⬚ PW122 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C19_L1.indd PW122 6/15/07 12:18:10 PM Name Lesson 19.2 Classify Quadrilaterals Classify each figure in as many ways as possible. Write quadrilateral, parallelogram, square, rectangle, rhombus, or trapezoid. 1. 2. 3. 4. For each quadrilateral name the parallel, perpendicular, and congruent sides. B 5. A C C 6. D D A B Problem Solving and Test Prep 7. Draw and name a quadrilateral with 8. Algebra One pair of congruent angles 4 right angles and 4 pairs of congruent sides. in a parallelogram each measure 54⬚. What is the measure of each of the missing angles? 9. A quadrilateral has 4 congruent angles 10. The sum of the measures of three and 2 pairs of congruent sides. What type of quadrilateral is it? angles in a quadrilateral is 280⬚. What is the measure of the fourth angle? A rectangle A 180⬚ B trapezoid B 120⬚ C rhombus C 90⬚ D parallelogram D 80⬚ PW123 Practice © Harcourt • Grade 5 Name Lesson 19.3 Draw Plane Figures Use a protractor and a ruler to draw each figure on a coordinate plane. Classify each figure by writing the name that best describes it. 1. 2 congruent sides each measuring 2. angles measuring 30⬚, 70⬚, 80⬚; 3 inches; 2 congruent angles each measuring 45⬚ no congruent sides Use a protractor and a ruler to draw each quadrilateral. Classify each quadrilateral by writing the name that best describes it. 3. 4 right angles; 1 pair of congruent sides 4. 2 pairs of congruent angles, 1 pair measuring 2 inches and 1 pair of congruent sides measuring 4 inches measures 75⬚; 4 congruent sides each measuring 3 inches PW124 Practice © Harcourt • Grade 5 Name Lesson 19.4 Solid Figures Classify each solid figure. Write prism, pyramid, cone, cylinder, or sphere. 1. 2. 3. 4. Write the number of faces, edges, and vertices. Then classify each solid figure. 5. 6. Problem Solving and Test Prep USE DATA For 7–9, use the solid figure to the right. 7. What is the shape of the base of the figure? 8. What is the shape of the sides of the figure? 9. How many faces, edges, and vertices does the figure have? 10. Which solid figure has a triangle as a 11. Which solid figure has 0 faces, 0 edges base and 3 rectangular faces? and 0 vertices? A pyramid A sphere B rectangular prism B triangular prism C triangular prism C pyramid D cube D pentagonal prism PW125 Practice © Harcourt • Grade 5 Name Lesson 19.5 Problem Solving Workshop Strategy: Compare Strategies Problem Solving Strategy Practice 1. Sara is building prisms by using pieces 2. Bill is building a triangular pyramid by of clay for the vertices and straws for the edges. How many pieces of clay and how many straws will Sara need to build a pentagonal prism? 3. Sara also makes a pentagonal pyramid using pieces of clay for the vertices and straws for the edges. How many pieces of clay and how many straws will Bill need to build a triangular pyramid? 4. Larissa made a model of a polyhedron using 8 pieces of clay for the vertices and 18 straws for the edges. What type of polyhedron did Larissa make? by using pieces of clay for the vertices and straws for the edges. How many pieces of clay and how many straws will Sara need to make the pentagonal pyramid? Mixed Strategy Practice USE DATA For 5–6, use the data in the diagram. 15 m 5. The diagram is of a new monument that 15 m will be installed in the town square of Duncan’s hometown. What type of polyhedron is it? 10 m 6. Duncan saw a model that was 1_5 the 10 m 7. Duncan lives 1.3 miles from the town size of the actual monument. Write an equation to find the length of each side of the base in the model. Then solve it. square. If he rode his bike to and from the town square twice in one day, how many miles did he ride in all? PW126 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C19_L5.indd PW126 6/15/07 12:17:27 PM Name Lesson 19.6 Nets for Solid Figures Match each solid figure with its net. 1. 2. 3. 4. a. b. c. d. Problem Solving and Test Prep 5. Draw a net for a rectangular prism and 6. Draw a net for a pyramid and for a for a triangular prism. Compare the nets by describing the shapes and number of bases and faces. 7. How many rectangles will the net for a triangular pyramid. Compare the nets by describing the shapes and number of bases and faces. 8. How many triangles will the net for a triangular prism contain? pentagonal pyramid contain? A 2 C 4 A 3 C 5 3 D 5 B 4 D 7 B PW127 Practice © Harcourt • Grade 5 Name 18.7 Lesson 19.7 Draw Solid Figures from Different Views Identify the solid figure that has the given views. 1. 2. Top Front Side 3. Top Front Side Top Front Side On the grids below, draw each figure from the top, the front, and the side. 4. 5. 6. top view top view top view front view front view front view side view side view side view 7. Write Math Explain which solid figures have a top view that is the same as the bottom view. PW128 Practice © Harcourt • Grade 5 Name Lesson 20.1 Transformations Name each transformation. 1. 2. 3. Draw figures to show a translation, a rotation, and a reflection of each. 4. 5. Problem Solving and Test Prep 6. Draw a translation of the figure. 7. Draw a rotation of the figure. 8. Which is a transformation? 9. Which kind of transformation flips a figure over a line? A quadrilateral B translation C triangle D circle PW129 Practice © Harcourt • Grade 5 Name Lesson 20.2 Tessellations Predict whether the figure or figures will tessellate. Trace and cut out several copies of each figure and then test your predictions. Write yes or no. 1. 2. 3. 4. 5. 6. 7. 8. PW130 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C20_L2.indd PW130 7/2/07 2:14:40 PM Name Lesson 20.3 Create a Geometric Pattern Tell how each pattern might have been created. 1. 2. 3. 4. Trace each figure. Then transform it to create a pattern. Sketch your design. 5. Translate the figure horizontally four times. 6. Draw a point of rotation. Rotate the figure clockwise 1_4 turn five times. PW131 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C20_L3.indd PW131 6/15/07 12:19:17 PM Name Lesson 20.4 Numeric Patterns Identify the rule for each pattern. 1. 8, 10, 12, 14, 16 ... 2. 5, 25, 125, 625, 3125 ... 3. 200, 100, 50, 25, 12.5 ... Find the missing number in each pattern. 4. 74, 69, ? , 59, 54 5. 3, ? , 23, 68, 203 6. 12, 14, 18, 24, ? Find the mistake in each pattern. Write the correct number. 7. 7, 10, 13, 14, 19 8. 1000, 500, 10, 1, 0.1 9. 56, 53, 50, 47, 45 Write the first four terms in each pattern. 10. rule: add 6 first term: 43 11. rule: divide by 2 12. rule: multiply by 3, add first term: 88 1 first term: 2 Problem Solving and Test Prep 13. Em buys beads every month. By the 14. Henry is arranging his pennies into piles. end of 1 month she has 24 beads, by the end of the second month she has 48, and by the end of the third month she has 72. How many beads does she have at the end of the fifth month ? 15. 30, 29, 27, 24, 20, 15, ... A 10 The first pile has 1 penny, the second has 2 pennies, the third has 5 pennies, the fourth has 13 pennies, and the fifth has 34 pennies. How many pennies are in the sixth pile ? 16. 3, 9, 27, __, 243, 729 A 81 B 12 B 30 C 9 C 108 D 7 D 45 PW132 Practice © Harcourt • Grade 5 Name Lesson 20.5 Problem Solving Workshop Strategy: Find a Pattern Problem Solving Strategy Practice 1. When Ari’s figure has 1 side, Brenda’s 2. Tonya makes a bracelet out of beads. figure has 4 sides. When Ari’s figure has 2 sides, Brenda’s figure has 6 sides. When Ari’s figure has 7 sides, how many sides does Brenda’s figure have? 3. Julia builds a model using 105 blocks in Her design is shown below. What are the shapes of the next two beads in the design? 4. Hector is painting a design around the the first row, 90 blocks in the second row, and 105 blocks in the third row. If Julia continues this pattern, how many blocks will she use in the fourth row? floor of his tree house. If he continues the pattern below, what will be the next four figures in Hector’s design? Mixed Strategy Practice 5. Pose a Problem If in exercise 1 above, 6. Rose made a border around a Brenda had a figure with 22 sides, how many sides does Ari’s figure have? painting. She used 40 figures in all, and used her pattern unit 8 times. How many figures are in Rose’s pattern unit? 7. Each student is given 36 yellow beads and 32 green beads. They need to put the beads into equal sized groups, each having the same number of yellow beads and green beads. What is the greatest number of yellow and green beads that can be in each group? PW133 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C20_L5.indd PW133 6/15/07 12:17:09 PM Name Lesson 21.1 Algebra: Graph Relationships Write the ordered pairs. Then graph them. 1. y Number of rectangle faces, x 6 9 12 15 Number of triangular prisms, y 2 3 4 5 6 5 4 3 2 1 0 2. Number of cylinders, x 1 5 8 9 Number of square bases, y 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 x y 5 4 3 2 1 0 x 1 2 3 4 5 6 7 8 9 10 Problem Solving and Test Prep USE DATA For 3–4, use the table. 3. Mathew wrote the ordered pair (8,2) for 2 quadrilaterals with 8 interior angles of 90⬚. What is his error? What should he have written? Number of quadrilaterals, x 1 2 3 4 Number of Interior Angles of 90°, y 4 8 12 16 4. Rick wrote the ordered pair (4,4) for 4 quadrilaterals with 16 interior angles of 90⬚. What is his error? What should he have written? 5. What is the number 5 in the ordered pair (5,7)? A x-axis 6. What is the number 8 in the ordered pair (7,8)? A x-axis B y-axis B y-axis C x-coordinate C x-coordinate D y-coordinate D y-coordinate PW134 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C21_L1.indd PW134 6/15/07 2:54:56 PM Name Lesson 21.2 Algebra: Equations and Functions Find the rule to complete the function table. Then write an equation. 1. 2. x 27 y 9 8 21 18 7 6 15 4 y 24 3 2 1 12 6 0 y Use the equation to make a function table with at least 4 ordered pairs. Then graph the ordered pairs on the grid. 3. x 10 9 8 7 6 5 4 3 2 1 y⫽x⫹4 x y 0 1 2 3 4 5 6 7 8 9 10 x Problem Solving and Test Prep Brice makes 3 more potholders an hour than Katie does. Use this information for 5 and 6. 4. Write an equation to show the relationship between how many potholders Brice and Katie make. 5. Choose four values for x in the equation you wrote. Create a function table in the box to the right. 6. If you graph the equation y ⫽ x ⫹ 3, 7. If you graph the equation y ⫽ 3x ⫹ 2, which of the following pairs would you graph? which of the following pairs would you graph? A (2,5) A (2,7) B (5,2) B (7,4) C (7,3) C (4,14) D (3,7) D (14,4) PW135 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C21_L2.indd PW135 6/15/07 12:51:46 PM Name Lesson 21.3 Problem Solving Workshop Strategy: Write an Equation Write an equation to solve. 1. Carson spends $2.50 each weekday on 2. Gesa parks her car at the subway stop at a muffin and juice on his way to school. How much does Carson spend in 3 weeks? $4 per day. Then she takes the subway to the amusement park. The price of a one-way ticket to the amusement park is $2. What is her total transportation cost for the day? Mixed Strategy Practice minutes, x USE DATA For 3–4, use the function table. 3. The table shows the amount of money a cab fare costs for rides of different lengths. How much is a 25-minute cab fare? fare, y 5 10 15 20 25 $2.50 $5.00 $7.50 $10.00 30 $15.00 4. If each cab ride starts with a $4 flat fee, what equation can you write to determine what a 35-minute cab fare would be? USE DATA For 5–7, use the ferry schedule. Seattle – Bainbridge Island Ferry Schedule 5. Ms. Mallory lives in Seattle and works on Bainbridge Island. It takes her 15 minutes to drive to work from the Bainbridge Island terminal. If she needs to be at work at 7:00 A.M., which ferry does she need to take? 6 Ms. Mallory lives 10 minutes from the Seattle ferry terminal. If she stops for an additional 10 minutes to get a bagel sandwich and juice on her way to the ferry terminal, how long is her trip from home to work. Depart Seattle Arrive Bainbridge 5:30 A.M. 6:35 A.M. 6:10 A.M. 6:45 A.M. 7:05 A.M. 7:40 A.M. 7:55 A.M. 8:30 A.M. 7. Each round-trip ferry ride costs $11.25. If Ms. Mallory takes the ferry an average of 15 times each month, how much does she spend on ferry fares in one year? PW136 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C21_L3.indd PW136 6/15/07 2:55:56 PM Name Lesson 21.4 Understand Integers Identify the integers graphed on the number line. 1. 2. $(' $/ $- $+ $) ' ") "+ "- "/ "(' $(' $/ $- $+ $) ' ") "+ "- "/ "(' Write an integer to represent each situation. 3. grow 5 inches 4. lost 2 pounds 5. break even Write the opposite of each integer. 6. 32 7. 41 8. 749 9. 802 10. 5,426 Write the absolute value of the integer. 11. | 1| 12. | 1| 14. |508| 13. | 19| 15. | 29| Problem Solving and Test Prep 16. FAST FACT The coldest temperature 17. FAST FACT The warmest temperature recorded in California happened in Boca. The temperature reached 45 degrees Fahrenheit below zero on January 20, 1937. Write the temperature as an integer. 18. Which integer is the opposite of 513? A B C D 513 recorded in Alaska happened in Fort Yukon. The temperature reached 100 degrees Fahrenheit on June 27, 1915. Write the temperature as an integer. 19. Which integer represents 4 years from now? A 315 B 315 C 513 D PW137 4,000 4 4 4,000 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C21_L4.indd PW137 6/18/07 10:21:38 AM Name Lesson 21.5 Compare and Order Integers Compare. Write ,, ., or ⴝ for each 1. 5. 9. ⫹ ⫹ 7 6 2. ⫹ ⫺ 7 6. ⫹ ⫺ 0 10. 7 3 . ⫺ ⫺ ⫺ ⫺ 90 56 ⫺ 14 41 3. 60 7. 0 11. ⫺ ⫹ 12 9 ⫺ ⫹ ⫺ ⫺ 19 4 26 4. 8. 26 12. 5, ⫺2, ⫹1, ⫺6 16. ⫹ ⫹ 18 22 ⫹ ⫹ 54 54 ⫺ ⫺ 865 864 Order each set of integers from greatest to least. 13. 17. ⫺ 1, ⫹1, ⫺5 ⫺ 4, 4, 3, ⫺2 14. ⫺ 3, 0, ⫺7, ⫹10 15. 18. 6, ⫺9, 1, ⫺2 ⫹ 19. 5, ⫺5, ⫺6, 7 20. ⫹ 7, ⫺9, ⫺4, 0 ⫺ 8, 6, 0, ⫺3 Problem Solving and Test Prep USE DATA For 21–22, use the table. 21. The Brotulid family of fish live around ⫺ 7000 meters. In what zone does this fish live? Zones of the Oceans Zone Name Sunlight ⫺ 22. A viper fish thrives 80 meters to ⫺ 1600 meters. Name the zones this fish lives in. ⫺ 23. Which integer is less than 27? A B C D Range of depth (in meters) 0 to –200 Twilight –200 to –1,000 Midnight Abyssal –1,000 to –4,000 –4,000 to –6,000 Hadal –6,000 to –11,000 ⫹ 24. Which integer is greater than 8? ⫺ 28 A ⫺ 27 B ⫹ 27 C ⫹ 28 D PW138 ⫺ 8 ⫺ 7 ⫹ 8 ⫹ 9 Practice © Harcourt • Grade 5 MXENL08AWK5X_PHTE_C21_L5.indd PW138 6/15/07 12:55:54 PM Name Lesson 21.6 Algebra: Graph Integers on the Coordinate Plane For 1–6, identify the ordered pair for each point. 1. point A 2. point E 3. point C y-axis +5 +4 4. point F 5. point B 6. point D F 10. P (3, 3) 8. N (⫺1, 1) 11. Q (0, 2) B +2 +1 C A -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 -1 -2 E -3 D 4 For 7–12, graph and label the ordered pairs on the coordinate plane at the right. 7. M (5, ⫺2) +3 9. O (⫺3, 0) x-axis -5 12. R (⫺5, ⫺5) Name the ordered pair that is described. 13. Start at the origin. Move 3 units to the 14. Start at the origin. Move 11 units to the left and 2 units up. left. Problem Solving and Test Prep 15. Allen was walking on a giant coordinate grid. He started at the origin and took 2 steps to the right. Then he took 5 steps up. What ordered pair did he walk to? 17. Start at the origin. Go to the left 1 unit. 16. Alexis was walking on a giant coordinate grid. She started at the origin and took 1 step to the left. Then she took 3 steps down. What ordered pair did she walk to? 18. Start at the origin. Move 3 units up. Go down 1 unit. What is the ordered pair? What is the ordered pair? A (1, 1) A (0, 3) ⫺ B ( 1, 1) B (3, 0) C (1, ⫺1) C (0, ⫺3) D (⫺1, ⫺1) D (⫺3, 0) PW139 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C21_L6.indd PW139 6/15/07 12:51:56 PM Name Lesson 22.1 Customary Length Estimate the length of the stapler in inches. Then measure the length. 1. to the nearest inch: 1 2. to the nearest __ inch: 2 1 3. to the nearest __ inch: 8 4. In Exercises 5⫺7, which measurement is most precise? Explain. Tell which measurement is more precise. 1 1 1 5. 4 __ inches or 4 __ inches 6. 1 foot or 11 __ inches 8 4 3 7 7. __ inches or __ inches 8 4 2 1 8 Estimate the length in inches. Then measure to the nearest __ inch. 8. 9. Estimate: Estimate: Measurement: Measurement: PW140 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C22_L1.indd PW140 6/15/07 2:56:06 PM Name Lesson 22.2 Metric Length Estimate the length of the pen in centimeters. Then measure the length. 1. to the nearest centimeter. 2. to the nearest millimeter. Write the appropriate metric unit for measuring each. 3. distance from Phoenix to 4. width of a dictionary 5. height of the ceiling in New York 6. length of an apple stem your classroom 7. distance from Reno to 8. width of a key on a Minneapolis computer keyboard Estimate and measure each. 9. 10. Estimate: Estimate: Measurement: Measurement: 11. 12. Estimate: Estimate: Measurement: Measurement: PW141 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C22_L2.indd PW141 6/15/07 2:55:20 PM Name Lesson 22.3 Change Linear Units Change the unit. 1. 10 yd ft 2. 1,500 m 4. 23 cm mm 5. 3.5 mi yd 6. 160 mm 7. 112 yd ft 8. 19 km m 9. 23 cm km 3. 93 ft in. m m Find the sum or difference. 10. 7 ft 6 in. 4 ft 10 in. ___ 11. 10 yd 1 ft 2 yd 2 ft __ 12. 13 ft 7 in. 12 ft 6 in. ___ 13. 1 yd 2 ft 1 yd 1 ft __ 14. 9 ft 4 in. 3 ft 8 in. __ 15. 3 yd 6 in. 4 yd 2 in. ___ 16. 14 ft 0 in. 0 ft 8 in. __ 17. 4 ft 1 in. 2 ft 10 in. ___ 18. 12 mm 12 cm 19. 7 km 0.6 km 20. 20 cm 0.2 m 21. 12 km 1,100 m ALGEBRA Find the missing measurement. 22. 1 ft 2 yd 24. 23 cm 23. 1,000 m 1.24 m 25. 16 mm 1.5 km 2 cm Problem Solving and Test Prep 26. Junie is 61.5 inches tall; Aaron is 5 feet, 3 inches tall. Who is taller, and what is the difference in their heights? 28. McKenna swam 1,250 meters. How 27. There are 5 yards left of the fabric Bryce needs for a project. How many feet of fabric are left? 29. Chris cut 40 cm off a 1.5-m long string. many kilometers did she swim? How long is the string now? A 125 km A 1.46 m B 12.5 km B 1.4 m C 1.25 km C 1.1 m D 0.125 km D 0.9 m PW142 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C22_L3.indd PW142 6/15/07 2:55:36 PM Name Lesson 22.4 Customary Capacity and Weight Change the unit. 1. 5 lb 4. 4,500 lb 7. 16 qt 2. 16 c oz 5. 72 oz T lb 8. 10 c gal 3. 8 gal qt qt 6. 12 fl oz c 9. 4.5 lb qt oz Find the sum or difference. 10. 7 lb 6 oz 4 lb 10 oz ___ 11. 11 gal 2 c 2 gal 1 c ___ 12. 14. 2 c 2 fl oz 4 c 6 fl oz ___ 15. 3 qt 3 c 4 qt 2 c __ 16. 4 pt 1 c 1 pt 1 c __ 2 T 200 lb 1 T 20 lb ___ 13. 17. 23 lb 2 oz 20 lb 14 oz ___ 4 pt 2 fl oz 2 pt 6 fl oz ___ ALGEBRA Find the missing measurement. 18. 1 c 20. 33 oz 22. 2 c 24. 2 fl oz 2 qt 19. 12 fl oz 4 lb 21. 4 pt 1 gal 23. 1,500 lb 1 pt 25. 8 oz 2c 4 gal 1T 3.5 lb Problem Solving and Test Prep 26. Mrs. Moore handed out 4 ounces of 27. Camryn made 3 gallons of iced tea for a almonds to each of her 22 students. How many pounds of almonds did Mrs. Moore hand out? party. How many cups of iced tea did Camryn make? 28. Tommy uses 4 ounces of cheese in 29. Riley drank 8 cups of water during a each pizza he makes. How many pounds of cheese does Tommy need to make 28 pizzas? Explain. soccer tournament. How many fluid ounces did he drink? A 64 fl oz B 32 fl oz C 16 fl oz D 64 qt PW143 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C22_L4.indd PW143 6/15/07 2:56:27 PM Name Lesson 22.5 Metric Capacity and Mass Change the unit. 1. 80 L ⫽ 2. 900 mg ⫽ kL 4. 18,000 mL ⫽ 7. 336 g ⫽ L mg 5. 5 kg ⫽ 3. 7,500 mL ⫽ g 6. 130 mL ⫽ g 8. 8.25 L ⫽ 9. 1,200 mg ⫽ mL L L g Find the sum or difference. 10. 12 mg ⫹ 12 mg ⫽ 11. 0.7 kL ⫺ 0.6 kL ⫽ 12. 20 mL ⫺ 0.2 mL ⫽ 13. 12 g ⫹ 1,100 g ⫽ 14. 13 kL ⫹ 121 kL ⫽ 15. 1,200 g ⫺ 729 g ⫽ ALGEBRA Find the missing measurement. 16. 4 g ⫺ ⫽ 250 mg 17. 1 L ⫺ ⫽ 2 mL Problem Solving and Test Prep 18. Jenna and Annie are making applesauce 19. Cal drank 800 milliliters of water at and need 5 kilograms of apples. How many grams are in 5 kilograms? school today and 500 milliliters at home. How many liters did Cal drink in all? 20. Kennedy’s dog weighs 34,000 g. How 21. How many milliliters are in a many kilograms does Kennedy’s dog weigh? 6.6 liter jug? A 3,400 kg A 6,605 mL B 340 kg B 606 mL C 34 kg C 6,060 mL D 3.4 kg D 6,600 mL PW144 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C22_L5.indd PW144 6/15/07 2:56:52 PM Name Lesson 22.6 Problem Solving Workshop Skill: Estimate or Actual Measurement Problem Solving Skill Practice Tell whether you need an estimate or an actual measurement. Then solve. 1. Janet is making pendant necklaces 2. Dominic is making a birdhouse and for 5 of her friends. She has a spool that has 2.2 m of leather string. If Janet needs 42 cm of leather string for each necklace, how much excess string will remain? needs to cut 3 pieces of trim that are 14, 31, and 44 cm long. Dominic has one 1-meter-long piece of trim. Is it long enough? Explain. . Mixed Applications USE DATA For 3–5, use the table. 3. Leslie is shopping for beading materials. She wants to make 51 20-cm bracelets with silver wire. How many 10-meter silver wire spools will Leslie need to buy? . 4. Mrs. Bisogno wants to make four 45-cm necklaces. If the store will let her buy her stringing material by the meter instead of by the spool, how many meters should Mrs. Bisogno ask for? Stringing Materials Material Cost 10-meter Satin cord spool $2.89 10-meter Elastic thread spool $2.31 10-meter Silver wire spool $2.50 10-meter Silk thread spool $8.63 5. Jeff and Mia buy 2 spools of silver wire and 4 spools of elastic thread. They pay with two $10 bills. How much change should they receive? PW145 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C22_L6.indd PW145 6/15/07 2:56:35 PM Name Lesson 22.7 Elapsed Time Write the time for each. 1. Start: 7:14 A.M. 2. Start: Elapsed time: 12 hr 3 min End: 6:57 P.M. Elapsed time: 2 hr 50 min End: 3. Start: 4:12 P.M. 4. Start: January 1, 3:00 A.M. Elapsed time: 4 days 3 hr 30 min End: Elapsed time: End: 6:43 P.M. 6. Start: Monday, 2 P.M. 5. Start: Elapsed time: 22 hr 12 min End: 11:12 P.M. Elapsed time: End: Tuesday, 6 A.M. Add or subtract. 7. 11. 3 days 2 hr 1 day 10 hr ___ 8. 12 min 22 sec 2 min 32 sec ___ 32 min 9 sec 12. 6 hr 6 min 4 hr 19 min 40 min 10 sec ___ ____ 9. 2 hr 12 min 1 hr 49 min ___ 10. 13. 1 day 12 hr 2 days 14 hr ___ 14. 6 wk 6 days 4 wk 5 days ___ 5 wk 3 days 4 wk 6 days ___ Problem Solving and Test Prep 15. Christian checked out a book from the 16. Mr. Lee requests that Ava and her classmates read for 25 minutes at home each weekday. How much time will they spend reading at home over 3 weeks? library that is due in 2 weeks. If he checked it out on April 3, what is the due date? 17. Josh swam every Monday and Friday in 18. The movie started at 7:10 P.M. and lasted June. How many days did he swim? for 1 hour 54 minutes. What time did the movie end? A 4 days A 11:58 A.M. B 6 days B 9:04 P.M. C 8 days C 10:00 P.M. D 10 days D 9:40 P.M. PW146 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C22_L7.indd PW146 6/15/07 12:15:34 PM Name Lesson 22.8 Temperature Find the change in temperature. 1. 56ºC to 20ºC 4. 7. ⫺ 16ºC to 30ºC ⫺ 16ºC to 20ºC 2. 7ºF to ⫺17ºF 5. 3. 88ºF to 101ºF ⫺ 6ºC to 2ºC 6. 100ºF to 0ºF 8. 7ºF to 17ºF 9. 18ºC to 49ºC ⫺ 10. 1ºF to 26ºF 11. 16ºF to 9ºF 13. 50ºC to 50ºC 14. 7ºC to ⫺1ºC 16. 77ºF to 0ºF 17. 12. 0ºC to 0ºC 15. 50ºF to 100ºF ⫺ 30ºC to ⫺10ºC 18. ⫺ 14ºC to 22ºC Problem Solving and Test Prep 19. In Madrid, the temperature is 12°C, and 20. If the refrigerator is 38°F and the freezer in New York City, it is 48°C. What is the temperature difference in degrees C? is ⫺1°F, what is the difference in temperature in degrees F? 21. What is the change in temperature from 22. What is the change in temperature from 41ºF to 23ºF? 12ºC to 20ºC? A 62°F A 5°C B 32°F B 7°C C 24°F C 8°C D 18°F D 10°C PW147 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C22_L8.indd PW147 7/2/07 2:15:22 PM Name Lesson 23.1 Estimate and Measure Perimeter Estimate perimeter. 1. Trace around the outline of a pen in the space below. Then use string and a ruler to estimate the perimeter in centimeters. 2. Using string and a ruler, estimate the perimeter of your desk or table top. Find the perimeter of each polygon in centimeters. 3. 4. 5. 6. PW148 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C23_L1.indd PW148 6/15/07 2:24:09 PM Name Lesson 23.2 Find Perimeter Find the perimeter of each polygon. 1. 2. 24 in. 29 in. 1.8 m 1.5 m 29 in. 3. 7 ft 2.3 m 7 ft 7 yd 9 ft 24 in. 5. 4. 11 ft 6. 5.7 m 7. 8. 3m 1.3 m 2.6 cm 3m 3m 5.9 m 2.4 cm 3.1 m 1m 30 in. 4.3 m 3.5 m Problem Solving and Test Prep 9. Cecil drew a diagram of a beehive 10. Algebra Candace wants to build a in the shape of a regular hexagon. The length of each side of the hexagon is 4.5 inches. What is the perimeter of Cecil’s model drawing? 11. The polygon below is a regular triangle. model of the Pentagon. She has enough balsa wood for a perimeter of 100 centimeters. Write an equation she could use to find the length of each side of the model. Then solve the equation. 12. The flower is inside the square frame. What is the length of the frame that encloses the flower? 5 cm 2.6 cm What is the perimeter? A 5 cm B 15 cm C 150 cm D 1,500 cm What is the perimeter? A 1.4 cm B PW149 4.6 cm C 10.4 cm D 14 cm Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C23_L2.indd PW149 6/15/07 2:23:26 PM Name Lesson 23.3 Algebra: Perimeter Formulas Find the length of each regular polygon by using a formula. 1. 2. 9 mi 27 in. 3. 4. 10 yd 10 yd 7.2 mi 19.1 mi 18.5 in. 4.2 mi 6 yd 5. 6. 7. 15 m 8. 121 yd 1.75 in. 17 cm Problem Solving and Test Prep 9. ALGEBRA The perimeter of a regular hexagon is 42 yards. What is the length of each side? 11. For which polygon could you use the 10. Each of the side chambers of the Lincoln Memorial are 38 feet wide and 63 feet long. What is the perimeter of one of the side chambers? 12. For which regular polygon could you use formula P ⫽ 2l ⫹ 2w to find its perimeter? the formula P ⫽ 5x to find its perimeter? A triangle A triangle B parallelogram B square C trapezoid C pentagon D pentagon D hexagon PW150 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C23_L3.indd PW150 6/15/07 2:22:15 PM Name Lesson 23.4 13.4 Problem Solving Workshop Skill: Make Generalizations Problem Solving Skill Practice Make generalizations to solve. 1. A rectangular shaped kitchen has 2. The top of a table has a perimeter of measurements of 12 feet by 16 feet. The perimeter of the kitchen is half the perimeter of the family room. What is the perimeter of the family room? 3. Two boxes of cereal are the same 204 inches. A leaf extends the length of the top by 8 inches. What is the perimeter of the table top with the leaf? 4. The Pyramid of Khafre is the second shape. The corn cereal box is 2 inches wide and 10 inches long. The perimeter of the wheat cereal box is 5 inches more than the corn cereal box. What is the perimeter of the wheat cereal box? largest pyramid in Giza. It is the same shape as the Great Pyramid. The perimeter of its base is 2,816 feet. How long is each side of its base? Mixed Applications 5. The length of the longest leg bone in a 6. Kerri has a tree house that is 5 feet by human, the femur, is 19.88 inches. The length of the longest arm bone in a human, the humerus, is 14.35 inches. What is the difference in length between the femur and the humerus? 7 feet. His circular table has a diameter of 6 feet. Will the table fit in his tree house? Explain. . 7. Brett and Bart are identical twins. Carly 8. Todd is cutting a rectangular piece of and Carl are also identical twins. Can you find the ages of Brett and Bart? Explain. cloth into smaller pieces. It measures 12 inches by 6 inches. If each smaller piece is 3 inches square, how many smaller pieces can he cut? PW151 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C23_L4.indd PW151 6/15/07 2:23:14 PM Name Lesson 23.5 Circumference For 1–3, complete the table. C⫼d Object C d 1. plate 25.12 in. 8 in. 2. wheel 81.64 in. 3. pizza 3.14 14 in. 3.14 4. Becca has a circular pillow. She wants to add a ribbon trim around its edge. If the diameter of the pillow is 20 centimeters, how many centimeters of ribbon does Becca need? To the nearest hundredth, find the circumference of a circle that has 5. a diameter of 16 yd 6. a radius of 2 m 7. a diameter of 2.5 km 8. a radius of 4 ft 9. a diameter of 14 in. 10. a radius of 22 cm 11. a diameter of 9 mi 12. a radius of 9 m 13. a diameter of 5.9 ft 14. a radius of 12.6 km 15. Reasoning If you double the diameter, what happens to the circumference? PW152 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C23_L5.indd PW152 6/15/07 2:22:45 PM Name Lesson 24.1 Estimate Area Estimate the area of the shaded figure. Each square on the grid is 1 cm2. 1. 2. 3. Problem Solving and Test Prep 4. The jigsaw puzzle of a train at the right Train Puzzle (each square is 1 inch) has 100 pieces. Estimate the area of the puzzle. 5. Estimate the area of the train in the jigsaw puzzle at the right. 6. Which is a reasonable estimate for the 7. Which of the following is a reasonable area of the figure? estimate for the area of the banner? A 15 in.2 F 4 cm2 B 9 in.2 G 8 cm2 C 4 in.2 H 12 cm2 D 2 in.2 1 in.2 J PW153 15 cm2 1 cm.2 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C24_L1.indd PW153 7/31/07 9:08:51 AM Name Lesson 24.2 Algebra: Area of Squares and Rectangles Find the area of each figure. 1. 2. 8 ft 3. 6 1 in. 4 5 ft 6 ft 16 cm 3.5 ft 2 3 in. 5 16 cm For each square or rectangle, find each missing measurement. S = 7.5 m 4. 5. A= S = 5 in. S = 2 1_4 ft 6. A= 7. S = 8.5 m W = 3 ft W = 11 m A= A= Problem Solving and Test Prep For 6–7, use the table. 8. Cassie plans to paint the hickory wood panel. What is its area? 9. Which panel has an area of about 2,500 in. ? 2 10. How many 1 in.2 tiles are needed to cover an 18 in. ⫻ 30 in. countertop? A 324 tiles Wood Panel Height Length Hickory 68 in. 40 in. Pine 54 in. 36 in. Oak 52 in. 48 in. 11. What is the area of a 12 ft ⫻ 21 1_2 ft driveway? A 258 ft2 B 540 tiles B 144 ft2 C 900 tiles C 462 1_2 ft2 D 630 tiles D 326 1_2 ft2 PW154 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C24_L2.indd PW154 6/15/07 12:16:00 PM Name Lesson 24.3 Algebra: Relate Perimeter and Area For the given perimeter, find the length and width of the rectangle with the greatest area. Use whole numbers only. 1. 80 ft 2. 36 yd 3. 6 mi 4. 200 cm 5. 76 m For the given area, find the length and width of the rectangle with the least perimeter. Use whole numbers only. 6. 50 mm2 7. 16 in.2 8. 48 yd2 9. 65 mi2 10. 144 ft2 Problem Solving and Test Prep 11. Complete the table to find the areas of rectangles with a perimeter of 20 m. Describe the patterns you see. Width (m) Length (m) Area (m2) 2 3 4 5 6 12. Using 200 feet of fencing, what is the greatest area that can be fenced? The least area? Use whole numbers. 13. What is the greatest possible area for a 14. What is the least possible perimeter for rectangle with a perimeter of 30 cm? a rectangle with an area of 169 ft2? A 30 cm2 A 13 ft B 49 cm2 B 52 ft C 56 cm C 26 ft 2 D 64 cm2 D 152 ft PW155 Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C24_L3.indd PW155 7/16/07 5:27:22 PM Name Lesson 24.4 Algebra: Area of Triangles Find the area of each triangle in square units. 1. 9 in. 2. 3 cm 3. 7 ft 11 cm 18 in. 12 ft Find the area of each triangle. 4. base (b) = 5 m 5. base (b) = 10 ft height (h) = 9 m Area (A) = 6. base (b) = 7 in. height (h) = 6 ft Area (A) = height (h) = 12 in. Area (A) = Problem Solving and Test Prep USE DATA For 7–8, use the pattern. 7. Kate bought blue tiles to fill the middle of the pattern. How many blue tiles did she buy? 8. Reasoning The tiles in the pattern are right isosceles triangles. The two shorter sides of each triangle are each 1 inch long. Estimate the area of the shaded part of the pattern. 9. What is the area of the triangle? A 120 m B 50 m2 C 55 m D 60 m 2 10. What is the area of the triangular figure? A 45.5 in.2 height = 12 m 2 2 base = 10 m B 91 in.2 C 55.5 in. D 20 in.2 PW156 7 in. 2 13 in. Practice © Harcourt • Grade 5 MXENL08AWK5X_PH_C24_L4.indd PW156 6/15/07 12:16:26 PM Name Lesson 24.5 Algebra: Area of Parallelograms Find the area of each parallelogram. 1. 2. 3. 9 cm 6m 7 ft 5m 5 cm 3 ft 4. 5. 6. 13 ft 1 5 2 in. 10.4 yd 8 in. 13 ft 13.6 yd Problem Solving and Test Prep 7. A yard is shaped like a parallelogram 8. A parallelogram has a length of 15 cm with a base of 27 m and a height of 30 m. What is the area of the yard? 9. What is the area of the and a height of 20 cm. It is divided into two congruent triangles. What is the area of each triangle? 10. A playground is divided into two equal parallelogram? parallelograms. What is the area of the entire playground? Show your work. 14 ft A 300 ft2 B 70 ft2 C 294 ft2 12 m 21 ft 20 m D 147 ft2 PW157 Practice © Harcourt • Grade 5 Name Lesson 24.6 Problem Solving Workshop Strategy: Solve a Simpler Problem Problem Solving Strategy Practice Solve. 1. Jane designed the figure below as a sun catcher. What is the area of the figure? 4 in. 2. Luke made his sun catcher into a rocket. What is the area of the rocket? 6 cm 14 in. 6 in. 5 cm 5 cm 18 cm 6 in. 5 cm 8 in. 5 cm 6 cm Mixed Strategy Practice 4 cm 11 cm USE DATA For 3–4, use the diagram. 5 cm 3. Chris designed his sun catcher to the 1 cm right into an airplane. What is the area of Chris’ airplane? 7 cm 5 cm 20 cm 4 cm 4. Chris bought the materials for the sun catcher. He paid $1.50 each for each rectangle, $2.25 for each triangle, $1.75 for each parallelogram, $3.00 for stain and 3 feet of chain for $4.50 a foot. How much did Chris spend in all? 5. Joy made a sun catcher with alternating blue and red squares. She began with a blue square. The sun catcher has 9 rows of 5 squares each. How many squares of each color are there? PW158 Practice © Harcourt • Grade 5 Name Lesson 24.7 Surface Area Use the net to find the surface area of each figure in square units. 1. Which faces on the net are congruent? C What is the area of the congruent faces? E B A F D What is the surface area of the prism? 2. B D A E C Find the surface area in ft2. 3. 4. . 5. . . 6. WRITE Math Explain the difference between area and surface area. PW159 Practice © Harcourt • Grade 5 Name Lesson 24.8 Algebra: Estimate and Find Volume Find the volume of each rectangular prism. 1. 2. 3. 8 yd 8 cm 13 cm 5 yd 12 yd 2 cm Problem Solving and Test Prep USE DATA For 4–5, use the table. 4. Which of the three pools has the Swimming Pool Dimensions (in feet) greatest volume? Pool 5. In the winter, Pool A is filled to a depth of only 2 feet. What is the volume of the Pool A? 6. What is the volume of the prism Length Width Depth Pool A 20 17 9 Pool B 25 15 8 Pool C 30 15 7 7. Compare the volumes of the treasure below? chests. Which can hold more gold? Explain your answer. 2 21 ft 3 ft 2 ft 3 21 ft 2 21 ft 3 ft A 15 units3 B 60 units3 C 20 units3 D 12 units3 PW160 Practice © Harcourt • Grade 5 Name Lesson 24.9 Relate Perimeter, Area, and Volume Tell the unit you would use for measuring each. Write linear, square, or cubic. 2. a door frame 1. how much tile 3. the amount of water in a lake needed to cover a floor 4. how much wall paper needed to cover a wall Write the units you would use for measuring each. 5. surface area of this 6. perimeter of this triangle 7. volume of this prism prism 5 cm 5m 9 ft 6 ft 4m 8 cm 6 ft 12 cm 4.5 m Problem Solving and Test Prep USE DATA for 8–9, use the picture of the aquarium. 8. What is the aquarium’s volume? 15 in. 9. What is the area of the water’s surface that is exposed to the air? 18 in. 24 in. 10. Joe wraps a 9 in. ⫻ 6 in. ⫻ 4 in. gift. 11. Mary bought a 6 in. ⫻ 8 in. ⫻ 1 in. What unit should Joe use to decide how much wrapping paper he needs? picture frame. What unit should she use to decide the width that is needed on a shelf for the picture frame? A inches A inches B square feet B square feet C square inches C square inches D cubic inches D cubic inches PW161 Practice © Harcourt • Grade 5 Name Lesson 24.10 Problem Solving Workshop Strategy: Compare Strategies Problem Solving Strategy Practice Draw a conclusion to solve the problem. 1. Joyce is replacing the hardwood flooring in her rectangular shaped dining room. The area of the floor is 238 ft2. The length of the floor is 17 ft. What is the width of the floor? 2. Anthony’s plans to mow his lawn that is in the shape of a rectangle. He knows that the lawn is 15 m wide and has an area of 345 m2. What is the length of Anthony’s lawn? Mixed Strategy Practice USE DATA For 3–4, use the table. 3. Reasoning The height of the tool chest that John bought is more than 8 in. The width is less than 22 in. What is the volume of his toolbox? How much did John pay for it? Tool Chests Length (in.) Width (in.) Heigth (in.) Price 12 20 8 $54.99 10 22 9 $49.99 14 21 10 $74.99 14 20 8 $59.99 4. The sales clerk gave Carrie $5.26 back 5. Samantha is having her driveway paved. in change when he bought the toolbox that has a volume of 1,920 in.3. How much money did Carrie give the clerk? She wants the driveway to be the same width as her garage and have an area of 748 ft2. If the length of her driveway is 34 ft, how wide is her driveway? PW162 Practice © Harcourt · Grade 5 SPIRAL REVIEW Week 1 Name Spiral Review For 1–4, round each number to the place of the underlined digit. For 12, make an organized list to solve. 12. Ken is making tickets for the fair. 1. 124,516 Each type of ticket will be a different color. There will be adult and child tickets. There will be 1-day, 2-day, and weekly tickets. How many different ticket colors will there be? 2. 6,732 3. 25,019 4. 3,723,801 For 5–6, name the place to which each number was rounded. 5. 76,812 to 80,000 6. 251,006,475 to 251,006,480 For 7–9, find the elapsed time. 7. start: 11:15 A.M. end: 2:00 P.M. 8. start: 3:30 P.M. For 13–14, tell whether the two figures are congruent and similar, similar, or neither. 13. end: 6:45 P.M. 9. start: 9:30 P.M. end: 4:15 A.M. For 10–11, find the ending time. 10. start: 4:00 P.M. elapsed time: 5 hr 15 min 14. 11. start: 10:30 P.M. elapsed time: 2 hr 20 min SR1 Spiral Review © Harcourt • Grade 5 Week 2 Name Spiral Review For 1–8, estimate. Then find the product. 1. 26 ⫻ 7 2. 672 ⫻ 4 For 11, use the frequency table. Tell whether the statement is true or false. Explain. Favorite Type of Music Type of Music 3. 429 ⫻ 6 4. 5. 842 ⫻ 5 783 ⫻ 3 6. 239 ⫻ 7 Votes Country 43 Rock 37 Rap 34 11. More people chose rap than rock as 7. 3 ⫻ 462 their favorite. 8. 1,364 ⫻ 6 For 9–10, use the thermometer to find the temperature in °F. 9. & For 12–13, find a rule. Write the rule as an equation. Find the missing numbers. 12. 10. Input, x 9 15 18 Output, y 3 5 6 Input, a 2 3 5 Output, b 16 24 40 21 27 6 8 -15 -20 13. -25 °F SR2 Spiral Review © Harcourt • Grade 5 Week 3 Name Spiral Review For 1–6, divide. 1. 8 512 2. 4 385 3. 5 247 4. 3 844 For 9–10, for each experiment, tell whether events A and B are equally likely or not equally likely. If they are not equally likely, name the event that is more likely. 9. Experiment: Spin the pointer. Event A: gray Event B: white 5. 821 ⫼ 6 ⫽ 6. 198 ⫼ 2 ⫽ 10. Experiment: Toss a number cube numbered 1–6. Event A: even number Event B: odd number For 7–8, find the perimeter. 7. For 11–12, classify each figure in as many ways as possible. Write quadrilateral, parallelogram, rhombus, rectangle, square, or trapezoid. 11. 8. 12. SR3 Spiral Review © Harcourt • Grade 5 Week 4 Name Spiral Review For 1–4, use basic facts and patterns to find the missing quotient. For 17–18, place the numbers where they belong in the Venn diagram. 17. 2, 6, 3, 9, 12, 4, 15, 18, 21 1. 30 10 Multiples of 2 Multiples of 3 2. 540 90 3. 4,200 6 4. $15,0000 30 For 5–6, divide. Check your answer. 18. 23, 18, 6, 25, 8, 16, 37, 9, 11 Numbers less than 20 5. 32 426 Numbers greater than 10 6. 47 529 For 7–16, change each unit. For 19–29, use properties and mental math to find the value. 7. 24 in. ft 8. 4 c pt 9. 24 ft yd 21. 4 370 10. 2 T lb 22. (46 + 58) + 4 11. 2 c fl oz 23. 10 6 2 12. 2 gal qt 24. 6 7 5 13. 6 yd ft 14. 5,280 ft mi 15. 4 ft in. 28. 87 + 61 + 3 16. 3 lb oz 29. 7 410 19. 43 + (16 + 24) 20. 29 + 28 + 21 25. 26 + 43 + 34 26. 4 8 5 27. 6 34 SR4 Spiral Review © Harcourt • Grade 5 Week 5 Name Spiral Review For 1–4, write the value of the underlined digit. For 10–11, use the doublebar graph. 1. 2.65 Careers 90 80 70 60 50 40 30 20 10 0 2. 12.81 3. 5.97 4. 3.49 Men Women Engineer Teacher Chemist Doctor Career Write the number in two other forms. 10. What two sets of data are compared in 5. 6.35 the graph? 11. Which careers have more men than women? For 6–9, find the perimeter of each figure. 6. 7. For 12–13, name any line relationships you see in each figure. Write intersecting, parallel, or perpendicular. 12. 8. 9. 13. SR5 Spiral Review © Harcourt • Grade 5 Week 6 Name Spiral Review For 1–6, find the sum or difference. 1. 91.47 ⫹ 23.76 2. 105.308 ⫺ 61.487 3. 8.759 ⫹ 5.413 4. 2.704 ⫺ 0.285 For 8–10, use the picture. List all possible outcomes of each experiment. 8. tossing a penny 9. spinning the pointer 5. 0.42 0.309 ⫹ 2.695 6. 18.751 6.049 ⫹ 12.201 Find the perimeter and area of the figure. Then draw another figure that has the same perimeter but a different area. 10. tossing the penny and spinning the pointer For 11–12, write an algebraic expression. 11. Caroline had 37 songs in her MP3 player. She deleted some of them. 7. 3 cm 5 cm 12. Forty-three increased by some number. For 13–14, find the value for each expression. 13. 17 – n for n = 4 14. p + 7 for p = 12 SR6 Spiral Review © Harcourt • Grade 5 Week 7 Name Spiral Review For 1–6 estimate. Then find the product. For 9–10, find the median and mode. 9. 1, 2, 3, 4, 5, 2, 1, 4, 1, 6 1. 0.6 ⫻ 0.7 2. 2.4 ⫻ 0.8 3. 25.9 ⫻ 0.3 4. 7.40 ⫻ 2.7 10. 6, 8, 1, 7, 3, 6, 9 5. 0.47 ⫻ 0.62 = 6. 0.452 ⫻ 3.6 = For 7–8, find the area. 7. 14 ft 6 ft For 11–12, tell whether the figure appears to have line symmetry, rotational symmetry, both, or neither. 11. 8. 12. 7 cm 7 cm For 13–14, draw all lines of symmetry. 13. SR7 14. Spiral Review © Harcourt • Grade 5 MXENL08AWK5X_SR_WK07.indd SR7 6/15/07 2:26:37 PM Week 8 Name Spiral Review For 1–4, find the quotient. 1. 6 20.4 2. 4 9.66 For 7–10, choose 5, 10, or 100 as the most reasonable interval for each set of data. 7. 90, 350, 260, 185, 415 8. 7, 23, 25, 18, 11 3. 23 59.11 9. 52, 76, 24, 54, 61 4. 53 75.26 10. 218, 371, 882, 119, 505 For 5-6, find the volume. 5. For 11-14, write an algebraic expression for each phrase. 11. 15 books on each of b shelves 12. 22 more than m DVDs 13. $36 shared equally among y friends 6. 14. 18 less than r For 15–18, evaluate each expression for a = 6. 15. a + 27 16. 24 ⫼ a 17. 14 ⫻ a 18. 19 – a SR8 Spiral Review © Harcourt • Grade 5 MXENL08AWK5X_SR_WK08.indd SR8 6/19/07 10:41:18 AM Week 9 Name Spiral Review For 1–4, complete to find the sum or difference. 1. 3. 738,521 ⫹ 601,994 54,639 ⫺ 37,840 2. 1B,7B9 1,34B,B1B 4,193 ⫹ 5,570 4. B,7B3 65,574 ⫺ 7,321 5B,2B3 For 5–6, estimate. Then find the sum or difference. 5. 84,679 ⫹ 39,213 6. 5,807,436 ⫹ 2,789,015 For 7–9, find the elapsed time. 7. start: 10:45 a.m. end: 1:00 p.m. For 12–15, find the mean for each set of data. 12. 13, 8, 11, 9, 14 13. 68, 73, 86, 61 14. 234, 186, 213 15. 78, 63, 98, 27, 44 For 16–18, use the given mean to find the missing value in each set of data. 16. 17, 12, 18, ; mean: 13 17. 69, 84, 73, ; mean: 81 18. 78, 93, 86, ; mean: 82 For 19–21, name a solid figure that is described. 19. one circular face 8. start: 4:30 p.m. end: 7:15 p.m. 9. start: 8:30 p.m. 20. six rectangular faces end: 11:00 p.m. 21. four vertices For 10–11, find the ending time. 10. start: 3:00 p.m. elapsed time: 4 hr 20 mi 11. start: 8:30 p.m. For 22–23, would the net make a cube. Write yes or no. 22. 23. elapsed time: 5 hr 45 mi SR9 Spiral Review © Harcourt • Grade 5 Week 10 Name Spiral Review For 1–12, estimate the product. 2. 61 ⫻ 28 3. 57 ⫻ 214 4. 46 ⫻ 697 5. 425 ⫻ 19 6. 768 ⫻ 86 T-Shirt Sales Number Sold 1. 23 ⫻ 44 For 23–25, use the graph. 60 50 40 30 20 10 0 Aug Sept Oct Month Nov Dec 23. During which month were 30 T-shirts 7. 61 ⫻ 926 sold? 8. 584 ⫻ 73 24. How many T-shirts were sold in 9. 836 ⫻ 5,927 10. 2,483 ⫻ 369 September? 25. Describe the change in T-shirt sales between October and November. 11. 82 ⫻ 9,371 12. 46 ⫻ 34,672 For 13–22, change each unit. For 26–28, write an algebraic expression. 13. 500 cm = m 14. 30 mm = cm 15. 8 cm = mm 16. 10 m = cm 17. 700 mm = cm 18. 20 cm = m 19. 5 m = mm 20. 2,000 = m For 29–31, find the value for each expression. 21. 400 mm = m 29. 14 + n for n = 6 22. 60 m = cm 26. James had $34 in his wallet. He spent some of the money. 27. Twenty-six decreased by some number. 28. Anna had 14 DVDs. She bought some more DVDs 30. 9p for p = 11 31. 15 – b for b = 7 SR10 Spiral Review © Harcourt • Grade 5 Week 11 Name Spiral Review For 1–11, find all the factors for each product. 1. 24 For 13–16, use the picture to find the probability of each event. 2. 16 3. 27 4. 30 13. pulling a 1 5. 42 6. 8 14. pulling a 2 or 3 7. 14 8. 21 9. 5 15. pulling a 1 or 4 10. 12 11. 10 16. pulling a tile that is not 3 Find the perimeter and area of the figure below. Then draw another figure that has the same area but a different perimeter. For 17–19, draw circle A with a 3-centimeter radius. Label each of the following. 12. 8 cm 6 cm 17. radius BA 18. chord CD 19. diameter FG SR11 Spiral Review © Harcourt • Grade 5 Week 12 Name Spiral Review For 1–6, compare. Write <, >, or = for each 1 1. __ 3 5 2. __ 7 1 __ 2 3 __ 3. 4 7 7 ___ 5. 2 12 Make a bar graph to show the data below. __ 42 5 __ 25 8 __3 13. 5 1 __ 4. 3 3 4 3 ___ 12 __ 22 8 1 ___ 6. 3 Joe’s Marbles Red Green Blue Brown 21 16 10 23 15 For 7–8, write in order from least to greatest. 5 1 __ , 5 __ , 1 __ __ 2 __ 4 __ 7. 8. 2 , 3 , 2 3 6 6 6 For 9–10, find the volume. 9. 3 9 For 12–17, use counters to show all arrays for each number. Write prime or composite. 12. 35 13. 9 14. 29 10. 15. 101 16. 75 17. 55 SR12 Spiral Review © Harcourt • Grade 5 Week 13 Name Spiral Review For 1–6, add or subtract. Then write the answer in simplest form. 1. __ 41 2. 8 5 + 3__ 8 _ For 9–11, use the tally table. Length of Family Vacations 3 8 ___ 12 1 ⫺3___ 12 _ Days Tally Total 5 10 15 20 __ ⫹ 7 2 __ ⫽ 3. 5 1 3 3 __ ⫺ 2 2 __ ⫽ 4. 9 5 9 9. Complete the total column 9 in the tally table. 10. How many family vacations last 10 6 7 5. 6 ___ ⫺ 1 ___ ⫽ 10 10 __ ⫹ 6 2 __ ⫽ 6. 3 1 4 4 days? 11. Which number of family vacation days has the greatest total? For 7–8, use the thermometer to find the temperature in °C. 7. For 12–15, write parallel, intersecting, or perpendicular for each. 60 12. 55 13. W Y X L P O M A B D C Z 50 °C Q 14. 8. 15. 0 R S -5 -10 °C SR13 Spiral Review © Harcourt • Grade 5 MXENL08AWK5X_SR_WK13.indd SR13 7/2/07 2:17:09 PM Week 14 Name Spiral Review For 12–13, for each experiment, tell whether events A and B are equally likely or not equally likely. If they are not equally likely, name the event that is more likely. For 1–6, write each fraction as a decimal. 1. 3 5 2. 5 25 3. 4 10 4. 37 100 28 5. 50 12. Experiment: Flip a coin Event A: heads Event B: tails 2 6. 100 For 7–9, write each decimal as a fraction in simplest form. 7. 0.35 8. 0.45 13. Experiment: Pick a marble 9. 0.26 Event A: gray Event B: black For 10–11, find the area. 10. For 14–15, write an equation. Tell what the variable represents. 3m 14. Brad has 28 oranges. He gives some away. He now has 11 oranges. How many oranges does Brad give away? 7m 11. 13 in. 15. Gina divides some crackers among 13 in. her 4 friends. She gives each friend 6 crackers. How many crackers did Gina have? SR14 Spiral Review © Harcourt • Grade 5 Week 15 Name Spiral Review For 1–4, solve each problem. For 7–9, use the bar graph. 1. What is the value of the underlined .UMBEROF-OONS digit in 4,239,561? 2. Write 2,345,587 in expanded form. 3. Write the standard form of three hundred three million, five hundred twenty-six thousand, ninety-one. .EPTUNE 3ATURN 5RANUS 0LANET -ARS %ARTH 7. Which planet has the greatest number of moons? 8. Which planet has 1 more moon than 4. Write 9,641,508 in word form. Earth? 9. How many moons does Neptune have? For 10–13, classify each triangle. Write isosceles, scalene, or equilateral. Then write right, acute, or obtuse. For 5–6, find the perimeter. 5. )+`e% 10. ,Zd 11. ,`e% *`e% ,Zd +`e% ,Zd *.`e% 6. 12. 0d (,d 0d (0d (+d 13. /]k /]k ,]k ()d SR15 Spiral Review © Harcourt • Grade 5 Week 16 Name Spiral Review For 1–8, find the sum or difference in simplest form. 1. 2 2 ⫺ ⫽ 5 10 2. 3 1 ⫹ ⫽ 4 3 3. 1 1 ⫹ ⫽ 2 6 4. 2 1 ⫺ ⫽ 3 6 For 12–15, use the picture to find the probability of each event. 12. pulling a gray marble 5. 7. 3 1 ⫺ ⫽ 4 2 6. 3 1 ⫹ ⫽ 10 5 8. 1 3 ⫹ ⫽ 4 8 5 1 ⫺ ⫽ 8 4 13. pulling a gray or black marble 14. pulling a white or gray marble 15. pulling a blue marble For 9–11, use a calendar to solve. 9. The zoo will be offering discount tickets from January 3 to January 29. How many days will tickets be discounted? For 16–21, graph and label the following points on the coordinate grid. 16. A (4,3) 17. B (2,5) 18. C (0,7) 19. D (3,4) 20. E (6,4) 21. F (5,1) 10. The pet store is having a sale on dog p and cat food from February 1 to February 16. How many days will the food be on sale? / . , + * ) ( 11. Delia paid for her newspaper delivery on July 1. She last paid for it three weeks and four days ago. When did she last pay for her newspaper delivery? ' SR16 ( ) * + , - . / o Spiral Review © Harcourt • Grade 5 MXENL08AWK5X_SR_WK16.indd SR16 7/31/07 9:37:59 AM Week 17 Name Spiral Review For 1–10, estimate the product. 1. 23 ⫻ 44 2. 61 ⫻ 28 For 18–21, use the stem-andleaf plot. Grades on a Science Test Stem 3. 57 ⫻ 214 4. 46 ⫻ 697 5. 425 ⫻ 19 6. 768 ⫻ 86 6 7 8 9 Leaf 7 9 0 3 4 6 6 9 2 4 4 6 7 8 8 9 1 3 5 5 5 8 6 | 7 represents 67 18. How many students earned a grade of 76? 7. 61 ⫻ 926 8. 584 ⫻ 73 19. How many students earned a grade between 85 and 90? 20. Which grade occurred most often? 9. 86 ⫻ 597 10. 243 ⫻ 36 21. What is the difference between the highest grade and the lowest grade? For 11–17, change the unit. 11. 5,000 m ⫽ 12. 8 kL ⫽ 13. 16 m ⫽ 14. 36 cm ⫽ 15. 200 cm ⫽ 16. 6,000 L ⫽ 17. 71 km ⫽ km L For 22–25, classify each solid figure. Write prism, pyramid, cylinder, cone, or sphere. 22. 23. 24. 25. cm mm m kL m SR17 Spiral Review © Harcourt • Grade 5 Week 18 Name Spiral Review For 1–4, write an equivalent fraction. 1. 3. 1 2 2. 4 10 4. 3 9 Make a tree diagram to find the number of possible combinations. 12. Activity choices activity: zoo, park, museum time: morning, afternoon, evening 3 15 For 5–8, tell which fraction is not equivalent to the others. 2 4 3 5 4 2 5. , , 6. , , 5 10 8 12 8 4 7. 1 5 2 , , 3 9 6 8. 6 4 9 , , 8 6 12 For 9–10, find the perimeter of each polygon. 9. 23 cm For 13–14, find the rule to complete the function table. Then write the rule as an equation. 13. 11 cm 11 cm input, x 24 output, y 8 4 2 input, x 2 6 8 output, y 4 18 12 16 cm 10. 9 in. 14. SR18 10 16 Spiral Review © Harcourt • Grade 5 Week 19 Name Spiral Review For 1–4, multiply. 1. 3. 308 ⫻ 52 _ 2. 582 ⫻ 41 _ 4. Use the data to make a circle graph. 649 ⫻ 37 _ 6. 825 ⫻ 24 _ Name Number of Votes Sarah 30 Ty 50 Mike 20 Class President Election Find the perimeter and area of the figure. Then draw another figure that has the same perimeter but a different area. 5. Class President Election For 7–9, tell if the net would make a cube. Write yes or no. 8 in. 7. 2 in. 8. 9. SR19 Spiral Review © Harcourt • Grade 5 MXENL08AWK5X_SR_WK19.indd SR19 7/2/07 2:18:41 PM Week 20 Name Spiral Review For 1–6, find the sum or difference. 1. 3. 85.19 37.48 __ 2. 7.081 6.254 __ 4. For 9–11, use the doublebar graph. Activities 251.895 75.362 __ Boys Girls 25 20 15 10 5 0 3.582 0.763 __ Drama Club Science Club Poetry Club Soccer Activity 9. How many sets of data does the graph 5. 0.85 0.063 3.572 6. 11.804 6.137 15.749 For 7–8, find the volume of each rectangular prism. show? 10. Which activity has the greatest number of girls? 11. How many more girls than boys are signed up for drama club? For 12–19, solve each equation. 12. 39 15 r 13. 3 n 75 14. a 8 8 15. 36 w 20 16. 4 y 20 17. 80 h 4 7. *p[ *p[ (,p[ 8. 7 ft 7 ft 18. y 3 49 13 19. 25 17 48 b 7 ft SR20 Spiral Review © Harcourt • Grade 5 Week 21 Name Spiral Review For 11–13, tell whether each sample represents the population. If it does not, explain. A food company wants to know if people ages 18–40 like their new pasta. For 1–4, use basic facts and patterns to solve. 1. 60 ⫼ 10 2. 630 ⫼ 70 11. a random sample of 500 women, ages 18–40 3. 7,200 ⫼ 8 4. 48,000 ⫼ 60 12. a random sample of 500 people, ages 18–40 For 5–6, divide. 5. 24 318 6. 72 609 For 7–10, write the time shown on the analog clock. 7. 9. 11 12 1 2 10 9 3 4 8 7 6 5 5 6 11 12 1 2 10 9 3 4 8 7 6 5 8. 10. 13. a random sample of 500 adults For 14–19, use the figure. Name an example of each. 11 12 1 2 10 9 3 4 8 7 66 55 6 11 12 51 2 10 9 3 4 8 7 6 5 < A 9 ; ? 8 = > : 14. ray 15. point 16. line 17. vertex 18. line segment 19. vertical angles For 20–21, use the figure above. Classify each angle. Write acute, obtuse, straight, or right. 20. ⬔DAB 21. ⬔BAC SR21 Spiral Review © Harcourt • Grade 5 Week 22 Name Spiral Review For 1–6, compare. Write ⬍, ⬎, or ⴝ for each 1. 5 7 2 3 2. Make a list or tree diagram to find all possible combinations. . 4 5 13. Sandwich choices 6 7 3. 3 1 5 3 1 3 4. 1 4 6 1 2 3 5. 3 3 4 3 7 12 6. 2 1 2 2 5 6 meat: ham, turkey, roast beef cheese: American, cheddar bread: wheat, white For 7–8, write in order from least to greatest. 7. 5 7 2 , , 6 12 5 3 4 5 9 8. 3 , 3 , 3 For 9–12, write the time for each. 9. Start: 7:38 A.M. Elapsed time: 3 hr 52 min 1 3 For 14–16, find the rule to complete the function table. Then write an equation. 14. End: x 0 1 y 0 6 x 12 10 y 6 x 13 y 9 2 4 18 24 6 4 10. Start: Elapsed time: 2 hr 31 min End: 10:25 P.M. 15. 8 4 2 11. Start: 11:16 A.M. Elapsed time: 1 hr 19 min End: 16. 12. Start: 2:37 P.M. 11 9 7 5 3 5 Elapsed time: End: 4:19 P.M. SR22 Spiral Review © Harcourt • Grade 5 Week 23 Name Spiral Review For 12–14, use the table. The table shows the results of a marble experiment. For 1–3, compare. Write ⬍, ⬎, or ⫽ for each 1. 0.754 2. 1.09 3. 10 . 0.734 Marble Experiment 1.10 0.909 Red Blue Green 8 3 9 Number of Pulls Total For 4–6, order from greatest to least. 12. What is the experimental probability of 4. 1.345; 1.305; 1.354 pulling a red marble? 5. 0.101; 0.110; 0.100 13. What is the experimental probability of pulling a blue marble? 6. 73.806; 7.386; 73.860 14. What is the experimental probability of pulling a green marble? For 7–11, use the thermometer to find the change in temperature. 7. 12°F to 31°F 8. 0°F to 35°F 9. 10°F to 7°F – 10. 74°F to 88°F 11. 0°F to –6°F 100 100 90 90 80 80 70 70 60 60 50 50 40 40 30 30 20 20 10 10 0 0 –10 For 15–16, classify each figure in as many ways as possible. Write quadrilateral, parallelogram, square, rectangle, rhombus, or trapezoid. 15. –10 16. °F SR23 Spiral Review © Harcourt • Grade 5 Week 24 Name Spiral Review For 1–8, find the sum or difference. Write it in simplest form. 2 2 1. __ __ 5 5 3 1 2. __ __ 8 8 For 11–12, use the table to find the experimental probability. Then predict the outcome of future trials. 11. number of green tiles in 40 more pulls Tile Pulls __ __ 1 3. 4 9 9 2 5 4. __ __ 7 7 6 4 5. ___ ___ 12 12 1 3 6. __ __ 4 4 Green Red Orange 12. number of wins in 36 more games Games 2 6 7. ___ ___ 10 10 Wins 2 8 8. __ __ 9 9 For 9–10, estimate the area of the shaded figure. Each square on the grid is 1 cm2. Losses For 13–20, solve each equation. 13. 49 h 17 14. 24 a 8 15. 9 n 54 16. $42 w $35 17. 3 y 42 18. h 7 4 19. d 9 21 3 20. 34 8 n 10 9. 10. SR24 Spiral Review © Harcourt • Grade 5 Week 25 Name Spiral Review For 1–6, write two equivalent ratios for each ratio. Use multiplication and division. Make a bar graph of the data. 19. __ 1. 2 3 Stock X Price Month Jan Feb Mar Apr Price $46 $65 $52 $48 2. 4 to 10 3. 3:5 15 4. ___ 18 5. 1 to 7 6. 15:5 For 7–18, change the unit. 7. 36 in. ft 8. 28 qt gal 9. 5 lb oz 10. 24 ft yd 11. 4 pt fl oz 12. 3 T lb 13. 3 mi ft 14. 36 qt gal 15. 48 c qt 16. 2.5 T lb 17. 2 ft 4 in. in. 18. 6 yd 3 ft in. For 20–23, draw lines of symmetry. Tell whether each figure has rotational symmetry. Write yes or no. 20. 21. 22. 23. SR25 Spiral Review © Harcourt • Grade 5 MXENL08AWK5X_SR_WK25.indd SR25 6/15/07 2:28:02 PM Week 26 Name Spiral Review Make a list or draw a tree diagram to find the total number of arrangements. For 1–4, solve each problem. 1. Write 690,303,520,002 in expanded form. 10. ways to pull green, yellow, and blue tiles from a bag without looking 2. What is the value of the underlined digit in 32,405,922,287? 3. Write the standard form of five billion, six hundred ninety-six million, three hundred seventy-five thousand, twelve. 4. What digit is in the ten billions place in 670,050,213,604? For 5–9, use the thermometer to find the change in temperature. 30 5. 0°C to 18°C 20°C to ⫺5°C 6. ⫺ 7. ⫺ Write the ordered pairs. Then graph them. 30 20 20 10 10 0 0 11. x 0 1 2 3 4 y 0 3 6 9 12 8. 75°C to 10°C 9. 0°C to 16°C –10 –10 –20 –20 –30 –30 y-axis 15°C to 10°C ⫺ °C 12 11 10 9 8 7 6 5 4 3 2 1 0 SR26 1 2 3 4 5 6 7 8 9 10 11 12 x-axis Spiral Review © Harcourt • Grade 5 Week 27 Name Spiral Review For 1–4, find the product. Write it in simplest form. 3 1 1. __ ⫻ __ ⫽ 7 3 For 16–18, use the tally table. Books Students Read Books 2 1 2. __ ⫻ __ ⫽ 5 3 Students Frequency 2 3 3 2 3. __ ⫻ __ ⫽ 5 4 5 3 4. __ ⫻ ___ ⫽ 6 10 For 5–8, use a reciprocal to write a multiplication problem for the division problem. 1 5. 1__ ⫼ 2 ⫽ 2 7 1 6. ___ ⫼ __ ⫽ 2 3 7. 3__ ⫼ __ ⫽ 3 4 5 1 8. __ ⫼ __ ⫽ 8 4 12 4 5 16. Complete the frequency column in the table. 17. How many books read have the greatest frequency? 4 For 9–15, write the appropriate metric unit to measure each. 18. What is the range of the data? For 19–25, write acute, right, or obtuse for each angle. 9. length of your hand : ; 9 10. height of a house 11. length of an insect 8 = < 19. ⬔ AFD 20. ⬔ BFA 12. distance from New York to Michigan 13. length of a soccer field 21. ⬔ CFD 22. ⬔ BFE 23. ⬔ DFE 14. length of a classroom 24. ⬔ CFA 25. ⬔ EFC 15. length of a crayon SR27 Spiral Review © Harcourt • Grade 5 Week 28 Name Spiral Review For 1–3, write each percent as a decimal and as a fraction in simplest form. For 9–11, use the Fundamental Counting Principle to find the total number of outcomes. 1. 36% 9. choosing an outfit with blue or tan 2. 74% pants and a green or red shirt 3. 40% For 4–6, write each fraction or decimal as a percent. ___ 4. 12 25 10. tossing a cube labeled 1 to 6 and flipping a penny 11. using two spinners, both with four 5. 0.06 equal sections of red, blue, green, and yellow 9 6. ___ 20 For 7–8, find the area of each figure. 7. )-]k (*]k 8. For 12–17, graph and label the ordered pairs on the coordinate plane. 12. A (3,1) 13. B (0,5) 14. C (4,2) 15. D (4,1) 16. E (5,2) 17. F (3,2) y-axis (,Zd (,Zd 7 6 5 4 3 2 1 0 SR28 1 2 3 4 5 6 7 x-axis Spiral Review © Harcourt • Grade 5 MXENL08AWK5X_SR_WK28.indd SR28 6/15/07 2:26:10 PM Week 29 Name Spiral Review For 1–8, estimate by rounding. 1. 29.63 ⫹ 18.05 2. 87.905 ⫺ 38.714 For 13–16, choose the best type of graph or plot for the data. 13. number of students in 7 classrooms 3. 4.139 ⫹ 7.652 4. 2.763 ⫺ 0.509 14. hours people spend fishing 5. 93.47 ⫺ 62.13 6. 11.042 ⫹ 8.765 15. different seating sections of a stadium 7. 43.869 ⫺ 10.062 8. 0.654 ⫺ 0.398 For 9–12, write the missing time for each. 9. Start: 9:45 A.M. Elapsed time: 2 hr 45 min End: 16. deer population over a 6-year period For 17–18, classify each figure in as many ways as possible. Write quadrilateral, parallelogram, square, rectangle, rhombus, or trapezoid. 17. 10. Start: Elapsed time: 3 hr 25 min End: 8:15 P.M. 11. Start: 10:29 A.M. Elapsed time: 2 hr 19 min End: 18. 12. Start: 3:15 P.M. Elapsed time: End: 4:57 P.M. SR29 Spiral Review © Harcourt • Grade 5 Week 30 Name Spiral Review For 1–4, find the product. 1. 3. 315 57 _ 2. 493 62 _ 4. Draw a tree diagram to find the total number of outcomes. 642 38 _ 9. tossing a number cube labeled 1 to 6 and tossing a coin 510 26 _ For 10–15, use prime or composite. For 5–8, find the perimeter of each regular polygon. 5. ()Zd 6. /d 10. 7 11. 27 12. 16 7. 8. 13. 81 )(*p[ 14. 19 /%)]k 15. 12 SR30 Spiral Review © Harcourt • Grade 5 Week 31 Name Spiral Review For 1–3, name the GCF of the numerator and denominator. 1. 8 14 2. 12 32 3. For 18–20, use the line plot. ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ 12 36 For 4–6, write each fraction in simplest form. 6 4. 15 16 5. 28 1 2 3 4 5 ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ 6 7 8 9 10 Number of Miles Run 25 6. 40 18. What is the median? For 7–9, complete. 19. What is the mode? 7. 2 8 = 3 8. 30 = 1 6 9. 4 = 12 21 20. What is the mean? For 10–17, find the sum or difference. For 21–23, match each solid figure with its net. 10. 3.50 cm ⫹ 2.7 m ⫽ 21. a. 22. b 23. c 11. 15 m ⫹ 25 cm ⫽ 12. 54 mm ⫺ 5.4 cm ⫽ 13. 2.036 m ⫺ 36 mm ⫽ 14. 6 ft 5 in. ⫹ 3 ft 6 in. 15. 12 yd 2 ft ⫹ 5 yd 1 ft 16. 9 ft 3 in. ⫺ 7 ft 4 in. 27. 12 yd ⫺ 3 yd 2 ft SR31 Spiral Review © Harcourt • Grade 5 MXENL08AWK5X_SR_WK31.indd SR31 6/15/07 2:28:21 PM Week 32 Name Spiral Review For 1–11, write the common factors for each pair of numbers. 1. 10, 35 For 14–16, express the experimental probability as a fraction in simplest form. 14. 3 green sections in 18 spins. 2. 8, 32 How many green sections in 24 more spins? 3. 7, 42 4. 15, 45 5. 12, 30 15. 6 red marbles out of 15 pulls. How many red marbles in 35 more pulls? 6. 9, 27 7. 13, 26 8. 16, 40 16. 10 losses in 16 games. 9. 21, 63 How many losses in 40 more games? 10. 4, 20 11. 18, 24 For 12–13, find the volume of each rectangular prism. Write the ordered pairs. Then graph them. 12. 17. -Zd x 0 1 2 3 4 y 0 3 6 9 12 ,Zd (/Zd .`e% 13. .`e% y-axis (*`e% () (( (' 0 / . - , + * ) ( ' ( ) * + , - . / 0 (' (( () x-axis SR32 Spiral Review © Harcourt • Grade 5 Week 33 Name Spiral Review For 11–12, use the graph. For 1–4, write each mixed number as a fraction. Average Monthly Temperature (°F) 100 3. 1 Temperature (°F) 2 4 1. 1 5 2. 2 3 2 7 4. 3 8. 8 20 June July Aug Sept Month 11. What scale and interval are used in the line graph? 12. How would you change the graph if 13 7. 17 40 May 6. 15 5 60 0 3 8 For 5– 8, write each fraction as a mixed number. 5. 8 80 the temperature for August were 80° Fahrenheit? 37 12 For 9–10, write whether you need to find perimeter, area, or volume to solve the problem. Then solve using the appropriate formula. For 13–14, name each transformation. Write translation, reflection, or rotation. 13. 9. tile for this floor 12 ft 15 ft 14. 10. wrapping paper for this box 8 in. 20 in. 8 in. SR33 Spiral Review © Harcourt • Grade 5 Week 34 Name Spiral Review For 1–7, compare. Write ⬍, ⬎, or ⫽ for each . For 10–14, write a fraction to show the probability of tossing a number cube labeled 1 to 6. 1. 0.643 0.629 2. 1.517 1.538 3. 3.249 2.221 11. an odd number 4. 7.440 7.442 12. a prime number 5. 0.820 0.82 6. 0.137 0.13 7. 2.228 3.282 For 8–9, find the area. 8. 10. a 3 13. a number greater than 4 14. a number less than 8 For 15-16, write a numerical expression. Tell what the expression represents. 15. Kate had $30. She spent $8 to ()]k see a movie and $15 to buy a shirt. (/]k 9. 16. Tyler scored 12 points in the first half /`e% of the game and 17 points in the second half of the game. (+`e% SR34 Spiral Review © Harcourt • Grade 5 MXENL08AWK5X_SR_WK34.indd SR34 7/2/07 2:19:07 PM Week 35 Name Spiral Review For 1–8, estimate the product. 1. 68 ⫻ 24 2. 83 ⫻ 49 For 11–13, name the most appropriate graph. 11. Which type of graph would be most 3. 35 ⫻ 853 appropriate to record the growth of a plant over 5 weeks? 4. 73 ⫻ 985 12. Which type of graph would be most 5. 568 ⫻ 31 6. 828 ⫻ 76 7. 34 ⫻ 964 8. 672 ⫻ 95 appropriate to show the attendance for a week at the state fair? 13. Which type of graph would be most appropriate to show how a person’s income is spent each month? For 9–10, find the perimeter. 9. For 14–15, classify each triangle. Write isosceles, scalene, or equilateral. 14 in. 14. 8 cm 5 cm 37 in. 15. 14 ft 14 ft 11 cm 9 ft 10. 15 m 9m 12 m Classify each triangle. Write acute, right or obtuse. 16. SR35 Spiral Review © Harcourt • Grade 5 Week 36 Name Spiral Review For 1–6, write each fraction as a decimal. __ 1. 4 5 7 2. ___ 20 3 3. ___ 10 84 4. ____ 100 35 5. ___ 50 78 6. ____ 100 For 18–21, use the spinner. Write the probability of each event. Tell whether the event is certain, likely, unlikely, or impossible. 18. spinning black 19. spinning gray For 7–12, write each decimal as a fraction in simplest form. 7. 0.2 8. 0.38 9. 0.57 10. 0.46 11. 0.65 12. 0.44 20. spinning white or gray 21. spinning green For 13–17, tell the units you would use for measuring each. Write linear, square, or cubic. For 22–24, find the rule to complete the function table. Then write the rule as an equation. 13. the amount of carpet needed to cover 22. a floor input, x 24 output, y 6 4 3 input, x 15 19 21 output, y 17 input, x 5 output, y 35 20 16 14. the amount of water in a bathtub 23. 15. the amount of wrapping paper needed 19 23 to cover a box 16. the height of a picture frame 24. 9 49 11 77 17. the width of a door SR36 Spiral Review © Harcourt • Grade 5 MXENL08AWK5X_SR_WK36.indd SR36 6/19/07 10:41:55 AM

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