d3jc3ahdjad7x7.cloudfront.net...© Harcourt † Grade 5 UNIT 1: USE WHOLE NUMBERS Chapter 1: Place...

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HSP

HSP

Grade 5

PRACTICE Workbook

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© Harcourt • Grade 5

UNIT 1: USE WHOLE NUMBERS

Chapter 1: Place Value, Addition, and Subtraction1.1 Place Value Through Millions ............PW11.2 Understand Billions ............................PW21.3 Compare and Order

Whole Numbers .................................PW31.4 Round Whole Numbers .....................PW41.5 Estimate Sums and Differences .........PW51.6 Add and Subtract Whole Numbers ...PW61.7 Problem Solving Workshop

Strategy: Work Backward ..................PW7

Chapter 2: Multiply Whole Numbers2.1 Mental Math: Patterns in

Multiples .............................................PW82.2 Estimate Products ...............................PW92.3 Multiply by 1-Digit Numbers ...........PW102.4 Multiply by Multi-Digit Numbers ....PW112.5 Problem Solving Workshop

Strategy: Find a Pattern ...................PW122.6 Choose a Method .............................PW13

Chapter 3: Divide by 1- and 2-Digit Divisors3.1 Estimate with 1-Digit Divisors .........PW143.2 Divide by 1-Digit Divisors ................PW153.3 Problem Solving Workshop Skill:

Interpret the Remainder ..................PW163.4 Zeros in Division ...............................PW173.5 Algebra: Patterns in Division ...........PW183.6 Estimate with 2-Digit Divisors .........PW193.7 Divide by 2-Digit Divisors ................PW203.8 Correcting Quotients .......................PW213.9 Practice Division ...............................PW223.10 Problem Solving Workshop Skill:

Relevant or Irrelevant Information ......................................PW23

Chapter 4: Expressions and Equations4.1 Write Expressions .............................PW244.2 Evaluate Expressions ........................PW254.3 Properties ..........................................PW264.4 Mental Math: Use the Properties ....PW274.5 Write Equations ................................PW284.6 Solve Equations ................................PW29

4.7 Functions ...........................................PW304.8 Inequalities .......................................PW314.9 Problem Solving Workshop

Strategy: Predict and Test ................PW32

UNIT 2: USE DECIMALS

Chapter 5: Understand Decimals5.1 Decimal Place Value .........................PW335.2 Equivalent Decimals .........................PW345.3 Compare and Order Decimals .........PW355.4 Problem Solving Workshop Skill:

Draw Conclusions .............................PW36

Chapter 6: Add and Subtract Decimals6.1 Round Decimals ................................PW376.2 Add and Subtract Decimals .............PW386.3 Estimate Sums and Decimals ...........PW396.4 Choose a Method .............................PW406.5 Problem Solving Workshop Skill:

Estimate or Find Exact Answer ........PW41

Chapter 7: Multiply Decimals7.1 Model Multiplication by

a Whole Number ..............................PW427.2 Algebra: Patterns in Decimal

Factors and Products ........................PW437.3 Record Multiplication by

a Whole Number ..............................PW447.4 Model Multiplication by

a Decimal ..........................................PW457.5 Estimate Products .............................PW467.6 Practice Decimal Multiplication ......PW477.7 Problem Solving Workshop Skill:

Multistep Problems .........................PW48

Chapter 8: Divide Decimals by Whole Numbers8.1 Decimal Division ...............................PW498.2 Estimate Quotients ..........................PW508.3 Divide Decimals by Whole

Numbers ............................................PW518.4 Problem Solving Workshop Skill:

Evaluate Answers for Reasonableness ................................PW52

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UNIT 3: DATA AND GRAPHING

Chapter 9: Data and Statistics9.1 Collect and Organize Data ..............PW539.2 Mean, Median, and Mode ...............PW549.3 Compare Data ..................................PW559.4 Analyze Graphs ................................PW569.5 Problem Solving Workshop

Strategy: Draw a Diagram ..............PW57

Chapter 10: Make Graphs10.1 Make Bar Graphs and

Pictographs .......................................PW5810.2 Make Histograms .............................PW5910.3 Algebra: Graph Ordered Pairs .........PW6010.4 Make Line Graphs ............................PW6110.5 Make Circle Graphs ..........................PW6210.6 Problem Solving Workshop

Strategy: Make a Graph .................PW6310.7 Choose the Appropriate Graph ......PW64

UNIT 4: NUMBER THEORY AND FRACTION CONCEPTS

Chapter 11: Number Theory11.1 Multiples and the Least Common

Multiple ............................................PW6511.2 Divisibility .........................................PW6611.3 Factors and Greatest Common

Factor ................................................PW6711.4 Prime and Composite Numbers ......PW6811.5 Problem Solving Workshop

Strategy: Make an Organized List ..PW6911.6 Introduction to Exponents ..............PW7011.7 Exponents and Square Numbers .....PW7111.8 Prime Factorization ..........................PW72

Chapter 12: Fraction Concepts12.1 Understand Fractions .......................PW7312.2 Equivalent Fractions .........................PW7412.3 Simplest Form ...................................PW7512.4 Understand Mixed Numbers ...........PW7612.5 Compare and Order Fractions

and Mixed Numbers .........................PW7712.6 Problem Solving Workshop

Strategy: Make a Model .................PW7812.7 Relate Fractions and Decimals ........PW79

UNIT 5: FRACTION OPERATIONS

Chapter 13: Add and Subtract Fractions13.1 Add and Subtract Like Fractions .....PW8013.2 Model Addition of Unlike

Fractions ............................................PW8113.3 Model Subtraction of Unlike

Fractions ............................................PW8213.4 Estimate Sums and Differences .......PW8313.5 Use Common Denominators ...........PW8413.6 Problem Solving Workshop

Strategy: Compare Strategies ........PW8513.7 Choose a Method .............................PW86

Chapter 14: Add and Subtract Mixed Numbers14.1 Model Addition of Mixed

Numbers ............................................PW8714.2 Model Subtraction of Mixed

Numbers ............................................PW8814.3 Record Addition and Subtraction ...PW8914.4 Subtraction with Renaming ............PW9014.5 Practice Addition and

Subtraction .......................................PW9114.6 Problem Solving Workshop

Strategy: Use Logical Reasoning .....PW92

Chapter 15: Multiply and Divide Fractions15.1 Model Multiplication of

Fractions ............................................PW9315.2 Record Multiplication of

Fractions ............................................PW9415.3 Multiply Fractions and Whole

Numbers ............................................PW9515.4 Multiply with Mixed Numbers ........PW9615.5 Model Fraction Division ...................PW9715.6 Divide Whole Numbers by

Fractions ............................................PW9815.7 Divide Fractions ................................PW9915.8 Problem Solving Workshop Skill:

Choose the Operation ...................PW100

UNIT 6: RATIO, PERCENT, AND PROBABILITY

Chapter 16: Ratios and Percents16.1 Understand and Express Ratios .....PW10116.2 Algebra: Equivalent Ratios and

Proportions .....................................PW102

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16.3 Ratios and Rates .............................PW10316.4 Understand Maps and Scales ........PW10416.5 Problem Solving Workshop

Strategy: Make a Table ..................PW10516.6 Understand Percent .......................PW10616.7 Fractions, Decimals, and

Percents ...........................................PW10716.8 Find Percent of

a Number ........................................PW108

Chapter 17: Probability17.1 Outcomes and Probability .............PW10917.2 Probability Experiments .................PW11017.3 Probability and Predictions ...........PW11117.4 Problem Solving Workshop

Strategy: Make an Organized List ................................PW112

17.5 Tree Diagrams .................................PW11317.6 Combinations and Arrangements .PW114

UNIT 7: GEOMETRY AND ALGEBRA

Chapter 18: Geometric Figures18.1 Points, Lines, and Angles ...............PW11518.2 Measure and Draw Angles ............PW11618.3 Polygons ..........................................PW11718.4 Problem Solving Workshop Skill:

Identify Relationships ....................PW11818.5 Circles ..............................................PW11918.6 Congruent and Similar Figures .....PW12018.7 Symmetry ........................................PW121

Chapter 19: Plane and Solid Figures19.1 Classify Triangles ............................PW12219.2 Classify Quadrilaterals ...................PW12319.3 Draw Plane Figures ........................PW12419.4 Solid Figures ...................................PW12519.5 Problem Solving Workshop

Strategy: Compare Strategies ......PW12619.6 Nets for Solid Figures .....................PW12719.7 Draw Solid Figures from

Different Views ..............................PW128

Chapter 20: Patterns20.1 Transformations .............................PW12920.2 Tessellations ....................................PW13020.3 Create a Geometric Pattern ..........PW131

20.4 Numeric Patterns ............................PW13220.5 Problem Solving Workshop

Strategy: Find a Pattern ................PW133

Chapter 21: Integers and the Coordinate Plane21.1 Algebra: Graph Relationships .......PW13421.2 Algebra: Equations and

Functions .........................................PW13521.3 Problem Solving Workshop

Strategy: Write an Equation ........PW13621.4 Understand Integers ......................PW13721.5 Compare and Order Integers ........PW13821.6 Algebra: Graph Integers on the

Coordinate Plane ...........................PW139

UNIT 8: MEASUREMENT

Chapter 22: Customary and Metric Measurements22.1 Customary Length ..........................PW14022.2 Metric Length .................................PW14122.3 Change Linear Units .......................PW14222.4 Customary Capacity and Weight ...PW14322.5 Metric Capacity and Mass ..............PW14422.6 Problem Solving Workshop Skill:

Estimate or Actual Measurement .................................PW145

22.7 Elapsed Time ...................................PW14622.8 Temperature ...................................PW147

Chapter 23: Perimeter23.1 Estimate and Measure

Perimeter ........................................PW14823.2 Find Perimeter ................................PW14923.3 Algebra: Perimeter Formulas ........PW15023.4 Problem Solving Workshop Skill:

Make Generalizations ....................PW15123.5 Circumference ................................PW152

Chapter 24: Area and Volume24.1 Estimate Area .................................PW15324.2 Algebra: Area of Squares and

Rectangles .......................................PW15424.3 Algebra: Relate Perimeter and

Area .................................................PW15524.4 Algebra: Area of Triangles ............PW15624.5 Algebra: Area of Parallelograms ..PW157

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24.6 Problem Solving Workshop Strategy: Solve a Simpler Problem ...........................................PW158

24.7 Surface Area ...................................PW15924.8 Algebra: Estimate and Find

Volume ............................................PW16024.9 Relate Perimeter, Area, and

Volume ............................................PW16124.10 Problem Solving Workshop

Strategy: Compare Strategies ........PW162

Spiral Review Week 1 ..........................................................SR1Week 2 ..........................................................SR2Week 3 ..........................................................SR3Week 4 ..........................................................SR4Week 5 ..........................................................SR5Week 6 ..........................................................SR6Week 7 ..........................................................SR7Week 8 ..........................................................SR8Week 9 ..........................................................SR9Week 10 ......................................................SR10Week 11 ......................................................SR11Week 12 ......................................................SR12Week 13 ......................................................SR13Week 14 ......................................................SR14Week 15 ......................................................SR15Week 16 ......................................................SR16Week 17 ......................................................SR17Week 18 ......................................................SR18Week 19 ......................................................SR19Week 20 ......................................................SR20Week 21 ......................................................SR21Week 22 ......................................................SR22Week 23 ......................................................SR23Week 24 ......................................................SR24Week 25 ......................................................SR25Week 26 ......................................................SR26Week 27 ......................................................SR27Week 28 ......................................................SR28Week 29 ......................................................SR29Week 30 ......................................................SR30Week 31 ......................................................SR31Week 32 ......................................................SR32Week 33 ......................................................SR33Week 34 ......................................................SR34Week 35 ......................................................SR35Week 36 ......................................................SR36

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Homework ManagementA 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.


Nu

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Prob

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Assig

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Nu

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Co

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Number of Problems

109876543210M

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Tue

Wed

Thu

Day


PW1 Practice© Harcourt • Grade 5

Name Lesson 1.1

Place Value Through MillionsWrite 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.

17. Fast Fact The diameter of Jupiter is 88,732 miles. How can Michael write the diameter of Jupiter in expanded form?

19. What is the value of the underlined digit in 729,340,233?

A 20,000

B 20,000

C 2,000,000

D 20,000,000

18. Clarrisa learns that the estimated 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 hundred thousands place?

A 0

B 2

C 3

D 5

13. 647,200 14. 40,000,000 � 20,000 � 1,000 � 80 � 5

What number makes the statement true?

15. 580,000 � 58 � 16. 2,760,000 � 276 �

Problem Solving and Test Prep


Name Lesson 1.2

Understand BillionsWrite 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


10. How many dimes equal the same total amount as 1,000,000,000 pennies?

12. What is the standard form of fifty-two million, six hundred eight thousand, thirty-nine?

A 52,680,390 C 52,608,039

B 52,608,390 D 52,068,039

11. During a year-long penny drive, a 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 the ten billions place?

A 5 C 2

B 3 D 0

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


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PW3 Practice


USE DATA For 13–14, use the table.


Name Lesson 1.3

Compare and Order Whole NumbersCompare. Write �, �, or � for each .

1. 6,574 6,547 2. 270,908 270,908 3. 8,306,722 8,360,272

4. 3,541,320 3,541,230 5. 670,980 680,790 6. 12,453,671 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

15. Which number is less than 61,534?

A 61,354

B 61,543

C 63,154

D 63,145

16. Which shows the numbers in order from greatest to least?

A 722,319; 722,913; 722,139

B 722,139; 722,319; 722,913

C 722,913; 722,139; 722,319

D 722,913; 722,319; 722,139

California

Minnesota

Oregon

Kansas

West Virginia

520,400,000

488,000,000

720,200,000

563,400,000

721,600,000

State Number of Quarters Minted

Quarters Minted in 2005

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.

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Name Lesson 1.4

Round Whole NumbersRound 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

9. 999,887,423 10. 76,805,439 11. 518,812,051 12. 657,388,369

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


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?

24. Name the place to which the number was rounded.

43,771,012 to 40,000,000

A hundred thousands C tens

B ten millions D millions

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?

25. Name the place to which the number was rounded.

622,192,013 to 622,200,000

A ten thousands C hundred thousands

B hundreds D ten millions

19. millions 20. hundred thousands 21. thousand

Round 34,251,622 to the place named.


Name Lesson 1.5

Estimate Sums and DifferencesEstimate 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

__

15. Brazil has a population of 186,112,794 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 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?

A Less than 12 mi

B Between 4 mi and 6 mi

C Between 15 mi and 20 mi

D More than 20 mi

16. What if the population of Brazil increased by 4 hundred thousand people, would that change your estimate for problem 22? Explain.

18. Estimate. Round to the nearest ten-thousand.

249,118 � 394,417

__

A 700,000

B 640,000

C 630,000

D 65,000



Name Lesson 1.6

Add and Subtract Whole NumbersEstimate. 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. 4,687,184

� 1,234,562

___

11. 542,002 � 319,428

___

12. 360,219 � 815,364

___

13. 32,109 � 6,234 � 4,827 14. 3,709,245 � 1,569,267 15. 200,408 � 64,159


16. How many more square miles of 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?

18. 328,954 � 683,681 �

A 901,535

B 1,001,535

C 1,012,635

D 1,012,645

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?

Michigan

Ontario

Erie

Huron

Superior

22,300

7,340

9,910

23,000

31,700

Lake Water Surface Area(in sq mi)

Great Lakes Facts



Name Lesson 1.7

Problem Solving Workshop Strategy: Work BackwardProblem Solving Strategy PracticeWork 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?

3. The latest Minke whale population is 55 times the latest gray whale population. What is the latest Minke whale population?

4. Write and solve an equation to find the decrease in the number of right whales from their original count.

5. Which type of whale had the greatest decrease in population? Explain how you know.

6. Pose a Problem Look back at Problem 4. Write a similar problem by changing the type of whale.

Mixed ApplicationUSE DATA For 3–5, use the table.

548,000

20,000

115,000

490,000

100,000

256,000

30,000

Whale Original Count

110,000

18,000

10,000

-

3,200

54,000

7,800

Latest Count

Whale Population Estimates

Bowhead

Fin

Gray

Humpback

Minke

Right

Sei


Name Lesson 2.1

Mental Math: Patterns in MultiplesFind the product.

1. 9 � 300

2. 3 � 100

3. 60 � 5

4. 5 � 7,000

5. 10 � 4,000

6. 700 � 200

7. 20 � 9,000

8. 1,000 � 10

9. 5,000 � 30

10. 6,000 � 80

11. 40 � 9,000

12. 7 � 200

13. 600 � 60

14. 100 � 600

15. 200 � 500

ALGEBRA Find the missing number.

16. 700 � 5,000 � 17. � 20 � 90,000 18. 600 � � 1,200


19. One colony of macaroni penguins has about 8,000 nests. If three penguins occupy each nest, how many penguins are there in all?

20. Each pair of macaroni penguins lays 2 eggs. How many eggs do 12,000,000 pairs of penguins lay?

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

22. A sedan at a car dealership sells for $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


Estimate ProductsEstimate 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



21. The Municipal Park Committee has budgeted $500 for 32 Japanese red maple trees for Green Park. Did the committee budget enough money? Estimate to solve.

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 48 � 54,090?

A 40 � 50,000

B 40 � 60,000

C 50 � 50,000

D 50 � 60,000

24. Which would give the best estimate for 108 � 276?

A 100 � 200

B 100 � 300

C 200 � 200

D 200 � 300

Name Lesson 2.2

Silver Maple

Red Maple

Japanese Red Maple

$11

$9

$18

Tree Cost

Green Park Expenses

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PracticePW10© Harcourt • Grade 5

Multiply by 1-Digit NumbersEstimate. Then find the product.

1. 47 � 6

2. 26 � 6

3. 207 � 3

4. 783 � 9

5. 428 � 5

6. 339 � 7

7. 518 � 5

8. 2,309 � 8

9. 8,014 � 3

10. 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 PrepUSE DATA For 23–24, use the table.

19. How much would it cost a family of 6 to fly roundtrip from Chicago to Vancouver?

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 8 � (800 � 70 � 3)?

A 8 � (800,703)

B 64 � 56 � 24

C 6,400 � 70 � 3

D 6,400 � 560 � 24

22. New windows cost $425 each. What is the total cost for 9 new windows?

A $3,725

B $3,825

C $4,725

D $4,825

Name Lesson 2.3

Honolulu, HI

London, England

Vancouver, WA

$619

$548

$282

Destination Cost in Dollars

Round Trip Airfares from Chicago, IL


Multiply by Multi-Digit NumbersEstimate. Then find the product.

1. 342 � 28

_

2. 451 � 61

_

3. 709 � 53

_

4. 622 � 34

_

5. 970 � 17

_

6. $229 � 77

7. 907 � 83

_

8. 1,345 � 23

__

9. 172 � 91

_

10. 4,029 � 67

__

11. 219 � 84

_

12. 727 � 33

_

13. $1,948 � 58

__

14. 1,220 � 42

__

15. 893 � 12

_

Problem Solving and Test Prep16. Abby wants to cycle 25 miles each

day for one full year, or 365 days. How many miles is Abby planning to cycle in all?

17. Rachel participated in a Bike-a-Thon. 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 competition on a pool in which onelap is 20 yards. Viola has swam8 laps. What distance has Viola swam?

A 160 yards

B 180 yards

C 1,600 yards

D 1,800 yards

19. Mon is training for a track and field event on a track where one lap is 400 meters. So far Mon has finished 2 laps. What distance has Mon ran?

A 220 meters

B 440 meters

C 800 meters

D 202 meters

Name Lesson 2.4


Name Lesson 2.5

© Harcourt • Grade 5PracticePW12

Problem Solving Workshop Strategy:Find a PatternProblem Solving Strategy PracticeFind a pattern to solve.

1. An art gallery has been open for a 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?

2. Prices for framing artwork in a framing 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?

3. An art-supply store sells sets of color 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?

4. A group of six statues made by a famous 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 PracticeUSE 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.

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 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?

32 inches

20inches


Choose a MethodFind the product. Choose mental math, paper and pencil, or a calculator.

1. 820 � 10

_

2. 5,129 � 18

__

3. 452 � 726

__

4. 304 � 21

_

5. 1,200 � 12

__

6. 500 � 12

7. 375 � 218

8. 40 � 5,000

9. 112 � 83

10. 400 � 320

11. 785 � 122

12. 93 � 11 � 34

13. 40 � 10 � 200


14. How many hours does a tiger sleep in one year?

15. In one year, how many more hours does a pig sleep more than a cow sleeps?

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 3,710 pounds

B 4,920 pounds

C 5,920 pounds

D 6,910 pounds

17. A typical giraffe may weigh about 145 pounds at birth. At maturity its weight is 18 times as great. What does a typical giraffe weigh at maturity?

A 1,075 pounds

B 1,305 pounds

C 2,380 pounds

D 2,610 pounds

Name Lesson 2.6

Tiger

Pig

Cow

16

9

4

Animal Time (hours per day)

Animal Sleep


PW14© Harcourt • Grade 5Practice

Name Lesson 3.1

Estimate with 1-Digit DivisorsEstimate 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


13. A shipment of motorcycles weighs 2,776 pounds. The shipment included 8 identical motorcycles. About how much did each motorcycle weigh?

14. Another shipment of motorcycles weighs 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 drove the same number of miles each day, what is the best estimate of how far Mr. Jones drove on the first day?

A 162 mi C 115 mi

B 140 mi D 96 mi

16. John traveled 885 miles in 3 days. If he traveled the same number of miles each day, what is the best estimate of how far John drove on the first day?

A 190 mi C 300 mi

B 268 mi D 250 mi



Divide by 1-Digit DivisorsName the position of the first digit of the quotient. Then find the first digit.

1. 4 � � 348

2. 7 � � 952

3. 5 � � 715

4. 6 � � 414

5. 9 � � 2,874

6. 3 � � 837

7. 8 � � 3,672

8. 7 � � 8,043

9. 9 � � 5,342

10. 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


21. There are 185 students going to a 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?

22. There are 185 students at the museum. 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?

23. One case can hold 9 boxes of cereal. How many cases are needed to hold 144 boxes of cereal?

A 1,296

B 16

C 17

D 9

24. A fifth-grade class made 436 cookies. The class put 6 cookies in each bag. How many cookies remained?

A 72 r4

B 2,616

C 4

D 72

Name Lesson 3.2



Problem Solving Workshop Skill: Interpret the RemainderTell how you would interpret the remainder. Then give the answer.

1. A total of 110 fifth graders are going on 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?

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?

3. A total of 124 players are riding a car to the soccer game. If 5 players can ride in each car, how many cars are needed?

4. There are 230 books in the storeroom. Each box holds 7 books. How many boxes are needed to store all of the books?

Mixed ApplicationsUSE 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?

6. If all bikers rode for 9 miles each day, who had to bike the least on the last day to finish their trip?

Sue

Pete

Brenda

Charlie

114

124

137

109

Biker Miles

Miles Biked on Vacation

Name Lesson 3.3

PracticePW17 PracticePW17© Hearcourt • Grade 5

Zeros in DivisionDivide.

1. 6 � � 912 2. 4 � � 716 3. 8 � � 829 4. 7 � � 941 5. 3 � � 1,373

6. 5 � � 634 7. 9 � � 1,681 8. 4 � � 871 9. 8 � � 1,163 10. 7 � � 791

11. 764 � 2 12. 834 � 9 13. 2,251 � 4 14. 3,676 � 6 15. 5,794 � 8


16. Each pack of marigold flowers can hold 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?

17. Each pack of tulips can hold 9 tulips. There are 956 tulips to be packed.How many tulips will be left? How many more tulips are needed to fill a9-pack container of tulips?

18. The population of the world in July 2006 was about 6,628,506,453. What is the value of the digit 2 in that number?

19. A pet store sells dog bones in packages of 6. How many packages can they make from 762 dog bones?

A 127

B 4,572

C 6

D 172

Name Lesson 3.4



Algebra: Patterns in DivisionUse 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 10. $2,000 � 10

11. 6,300 � 70

12. 4,200 � 60

13. 81,000 � 90 14. 80,000 � 2

15. 90,000 � 30

16. $35,000 � 50

Compare. Use ,, ., or � for each .

17. 350 � 7 3,500 � 70 18. 240 � 8 24 � 8 19. 360 � 40 360 � 4

Problem Solving and Test Prep20. A warehouse stored 10 crates of

paper. The paper weighed a total of 7,000 pounds. How much did one crate of paper weigh?

21. An office bought 8 office chairs for a total of $720. Each chair came with a $15 mail-in rebate. After the rebate, how much money did each chair cost?

22. A clothing store spends $4,500 on 9 clothing racks. How much does each clothing rack cost?

A $90

B $500

C $540

D $50

23. A business man spends $6,400 on 8 projectors for his company. How much does each projector cost?

A $80

B $800

C $640

D $8

Name Lesson 3.5


Estimate with 2-Digit DivisorsWrite 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

Estimate the quotient.

7. 24 � � 157 8. 31 � � $289 9. 72 � � 6,102

10. 181 � 35

11. 4,913 � 62

12. 55,208 � 87


13. The distance from the bottom of the first floor of an office building to the top of the 86th floor is 353 meters. About how many meters tall is each floor?

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?

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?

A 10

B 24

C 18

D 48

16. Heather spent 480 minutes practicing basketball last month. How many hours did Heather spend practicing basketball last month?

A 60

B 4

C 10

D 8

Name Lesson 3.6


Divide by 2-Digit DivisorsDivide. 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

bread each year. How many years would it take for the average person to eat 689 pounds of bread?

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?

15. The school auditorium has 756 seats arranged in 27 equal rows. How many seats are in each row?

A 27

B 28

C 29

D 30

16. A farmer planted a total of 768 corn seeds in 24 equal rows. How many corn seeds are there in each row?

A 28

B 30

C 32

D 34

Name Lesson 3.7



Correcting QuotientsWrite 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 7. 27 � � 259 8. 32 � � 6,730 9. 63 � � 234 10. 79 � � 5,688

11. 2,312 � 49

12. 734 � 56

13. 1,634 � 86

14. 6,324 � 62

15. 846 � 94


16. Robin needs to buy 250 coasters for a graduation party. Each package contains 18 coasters. How many packages should Robin buy?

17. A store orders 832 ounces of floor cleaner. Each bottle is 32 ounces and costs $3. How much does the store spend on the order?

18. The Comfortable Shoe Company can fit 16 boxes of shoes in a crate. How many crates will the company need to pack 576 boxes of shoes?

A 36

B 40

C 35

D 30

19. A Disc Jockey has a collection of 816 CDs. The CD case that he likes holds 24 CDs. How many cases will the Disc Jockey need to hold all his CDs?

A 43

B 30

C 34

D 40

Name Lesson 3.8



Practice DivisionDivide. 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

9. 582 � 6 10. 763 � 9

11. 1,516 � 47

12. 9,951 � 93


13. Julia can make a paper crane in 8 minutes. She spent 992 minutes making paper cranes for a party. How many paper cranes did Julia make?

14. Nathan spent 826 minutes making paper origami boxes. He can make a paper box in 7 minutes. How many origami boxes did Nathan make?

15. Sean has 6 piles of pennies. Each pile has 37 pennies. How many pennies does Sean have?

A 42

B 45

C 216

D 222

16. A school cafeteria used 232 pieces of bread yesterday equaling 8 full loaves. How many pieces of bread are in one loaf?

A 26

B 27

C 28

D 29

Name Lesson 3.9


Problem Solving Workshop Skill: Relevant or Irrelevant InformationProblem Solving Skill PracticeSolve.

1. A total of 47 fifth graders and 3 teachers 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?

2. James receives $15 each week from his 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?

3. Ryan’s collection of NFL cards is 5 times 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?

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?


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?

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 traveled on average 65 miles per hour. How many hours did Julie drive?

8. Sarah drove on average 50 miles per hour from Fairfax to Denver. Dan drove on average 55 from Redford to Denver. Who drove less time to reach Denver?

Fairfax,CA

Norland,FL

Redford,MI

Distance Between Cities (in miles)

Denver,COAustin,TXBoston,MA

1,050

1,780

3,080

1,210

1,430

740

1,360

1,260

860

Name Lesson 3.10


Write ExpressionsWrite a numerical expression. Tell what the expression represents.

1. William shared 8 apples equally among 4 friends.

2. Jillian bought 4 toys for $7 each.

3. 35 more than 18

Write an algebraic expression. Tell what the variable represents.

4. Jasmine has three times as many chores as her younger brother does.

5. Pedro swam some laps in the pool and then swam 2 more.

6. Neil spent 25 minutes on his math and some more time on his history homework.

Write an algebraic expression in words.

7. 3x � 8

8. 17 � m __ 4

9. n � 9


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. Write an algebraic expression to find the minimum number of gallons of water in the tank.

12. The temperature increased from a low of 62 degrees. Which expression best describes the new temperature? A 62 � t B 62 � t C 62t D t � 62

Bronze Cory

Clown Barb

Silver Dollar

3

5

8

Type of Fish Length (in inches)

Aquarium Fish

Name Lesson 4.1

Name Lesson 4.2


Evaluate ExpressionsEvaluate 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

11. 21 � 3c if c � 7

12. 4p � 6 if p � 1 1 _ 2

13. 3r � 4 � 2 � r if r � 7

14. 14 � (12 � y � 2) if y � 3

15. 3(x � 1) � (3 � x) if x � 2

16. 18 � 1 � 5y � y if y � 0.2

Use the expression to complete each table.

17. h 0 2 5 10 18. n 1 2 5 7

12h � 3 14 � 2n


19. Write an expression to represent the 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.

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 2k � 3?

A 8 C 11

B 9 D 24

22. The expression 5w shows the cost of 5 books. If w � $7.45, what is the total cost of the books?

A $35.00 C $37.25

B $39.45 D $12.45

Long Jump

Softball Throw

50-Meter Dash

800-Meter Run

28

s

89

r

Game Number of Players

Afternoon Games at Field Day


PropertiesName 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


11. Show the Commutative Property of 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.

13. The expression 30 � (8 � 7) shows the amount of money Daniel earned. Which expression represents the same amount of money?

A (30 � 8) � 7B (30 � 8) � (30 � 7)C (30 � 8) � (30 � 7)D (30 � 8) � (30 � 7)

14. The expression (20 � 4) � 12 shows the amount of money Josie earned. Which expression represents the same amount of money?

A (20 � 4) � 12B (12 � 20) � 4C 20 � (4 � 12)D (4 � 20) � 12

Cari’s Rock Collection

Type

of R

ock

Number of Pieces

Amethyst

Fluorite

Flint

Garnet

0 2 4 6 8 10 12

Name Lesson 4.3


Mental Math: Use the PropertiesUse 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


19. FAST FACT A group of sea lions 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?

20. Tell which property you would use to mentally find the value of 5 � 4 � 45. Then find the value.

21. There are 6 shelving units containing 5 shelves each. Each shelf holds 35 DVDs. Find the total number of DVDs on the shelving unit.

A 210

B 450

C 950

D 1,050

22. Tickets for the movies cost $13 each. James’ family buys 6 tickets. Explain how to use mental math to find the total cost of the movie tickets.

Name Lesson 4.4


Write EquationsWrite an equation for each. Tell what the variable represents.

1. Paulina has a photo album with 60 photos. Each page contains 5 photos. How many pages does the album have?

2. Jarrod practiced the trumpet and piano 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


5. Jaime has $130 in her savings account. 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.

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.

7. The Amsco building is 135 feet tall. 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.

A 135 � h � 30

B h � 135 � 30

C 135 � 30 � h

D h � 135 � 30

8. Tam had downloaded 25 songs for her 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 25 � s � 31

B s � 31 � 25

C s � 25 � 31

D 56 � s � 31

Name Lesson 4.5


Solve EquationsWhich 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 8. 72 � y � 12

9. d � 4 � 8 10. 6 � s � 84 11. v � 14 � 38 12. $24 � r � $61


13. Algebra A bear weighed 165 pounds 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.

14. Algebra Sam took 42 pictures of 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.

15. The equation $56 � p � $8 represents the total cost of some books and the cost per book. How many books were bought?

A 7

B 8

C 9

D 12

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.

Name Lesson 4.6


FunctionsWrite an equation to represent each function. Then complete the table.

1. c 0 1 2 3 4

d 8 10 11 12

2. m 0 1 2 3 4

p 0 4 12 16

3. g 0 2 4 6 8

h 21 19 17 13

4. j 0 2 4 6 8

k 1 2 3 4

5. v 12 15 18 21

w 3 6 9

6. x 5 6 7 8 9

y 5 9 11 13

7. a 0 2 4 6 8

b 1 11 21 31

8. y 3 6 9 12

z 9 21 45

9. s 5 10 15 20

r 2 7 9.5

Use the rule and the equation to make a function table.

10. Rule: Multiply by 4

m � 4 � r

11. Rule: Add 8

a � 8 � b


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 the balance in Dale’s savings account after x weeks. How much will be in the account after 10 weeks?

A $180 C $312

B $288 D $420

15. The equation y � 280 � 30x shows the 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 160 pages C 310 pages

B 250 pages D 400 pages

Name Lesson 4.7

m

r

a

b



InequalitiesWhich of the numbers 4, 6, 8, and 10 are solutions of each inequality?

1. x � 5 � 5

2. x � 6 � 2

3. x � 4 � 4

4. x � 9 � 15

5. x � 10 � 16

6. x � 10 � 0

7. x � 7 � 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 3 hours.

12. Magie, the cat, weighs less than 12 pounds.


13. Let a � age. What ticket price does a � 5 represent?

14. Let n � age. What ticket price does n � 12 � 6 represent?

15. The inequality s � 4 � 6 represents the least amount of money a snack costs at the county fair. Which amount is not a solution of the inequality?

A 1

B 2

C 3

D 4

16. The inequality s � 11 � 60 represents the greatest height in inches a person can be to ride a rollercoaster. Which amount is a solution of the inequality?

A 70

B 71

C 72

D 73

Name Lesson 4.8

Under 5

5–18/Child

Over 18/Adult

Free

$8

$15

Age Price

Circus Admission


Problem Solving Workshop Strategy: Predict and TestProblem Solving Strategy PracticePredict and test to solve the problem.

1. Andrea bought a total of 21 fish for her aquarium. She bought 9 fewer angelfish than guppies. How many angelfish and guppies did she buy?

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?

3. The sum of the ages of Michele and Clark’s ages is 27. Clark is twice as old as Michele. How old are Clark and Michele?

4. Loni is thinking of two numbers. One number is three times greater than the second number. Their sum is 32. What are the two numbers?

Mixed Strategy PracticeUSE 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 Barbs. The tank cost $180. How many Tiger Barbs did she buy?

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?

8. A gallon of water weighs 10 pounds. A fish tank weighs 35 pounds. How much does it weigh if it holds 15 gallons?

9. Open-Ended Bryce has $25 to spend on fish. He wants to purchase at least three fish of two different kinds. Which two kinds can he buy?

Silver Dollar

Clown Loach

Black Skirt Tetra

Tiger Barb

Keyhole Cichlid

$5

$8

$2

$3

$4

��

Name Lesson 4.9


Name Lesson 5.1


Decimal Place ValueWrite 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 6. 8.172

7. 0.831

8. 25.207

9. 87.759

10. 74.038

11. 1.3496

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 Prep17. A robber fly’s greatest length in meters

has 0 in the ones and tenths places and 5 in the hundredths place. What is this length of a robber fly in meters?

18. A honey bee is 0.017 m. A carpenter bee is 0.008 m longer than a honey bee. What is the length of a carpenter bee in expanded form?

19. What is the value of the underlined digit

in 8.536?

A 0.003

B 0.03

C 0.3

D 3.000

20. The decimal 0.9 is how many times greater than 0.009?

A 9

B 10

C 100

D 0.01


Equivalent DecimalsWrite 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

6. 1.800

7. 3.02

8. 8.640

9. 0.04

10. 45.100

11. 4.60

12. 2.70

Write the two decimals that are equivalent.

13. 3.007

3.700

3.7000

14. 0.930

0.093

0.93

15. 7.60

7.06

7.600

16. 3.0540

3.054

3.504

Problem Solving and Test Prep17. FAST FACT The 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.

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.

19. The calliope hummingbird lives in the mountains. It has been seen as high as 335.23 meters above sea level. Write an equivalent decimal for 335.23.

20. A banded calliope hummingbird was 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

Name Lesson 5.2


Compare and Order DecimalsCompare. Write ,, ., or � for each .

1. 0.37 0.370 2. 3.10 3.101 3. 0.579 0.576 4. 7.7 7.690

5. 0.812 0.821 6. 9.810 9.809 7. 0.955 0.95 8. 3.218 3.218

9. 5.202 5.220 10. 0.78 0.780 11. 4.17 4.017 12. 0.897 0.987

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


17. Which beetle has the shortest length? the longest length?

18. Another type of beetle is 1.281 cm long. Which beetle has a length less than 1.281 cm?

19. Some types of beetles can jump as high 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?

20. The depth the Japanese Beetle grub may hibernate underground is listed below. Which is the highest number?

A 29.103

B 29.300

C 29.301

D 29.004

Japanese Beetle

June Bug

Firefly

1.295

2.518

1.063

Beetle Size (in cm)

��

Name Lesson 5.3

Name Lesson 5.4


Problem Solving Workshop Skill:Draw ConclusionsProblem Solving Skill PracticeDraw a conclusion to solve the problem.

1. Mark planted 12 tomato plants. He 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?

2. Kim plants 3 rows of corn. The first row 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 ApplicationsUSE 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?

4. How much fertilizer will Nan give to all

her plants in a year?

5. Matt buys a plant for $1.35. He pays with

8 coins. Which coins does Matt use?

6. Tina has 25 plants on 5 shelves. Each shelf has 2 more plants than the shelf above it. How many plants are on each shelf?

A

B

C

D

E

1

2

3

4

5

Plant Number of Teaspoons

Amount of Fertilizer Per Week


Round DecimalsRound 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.

15. six hundred thirty-five thousandths 16. 50 � 9 � 0.8 � 0.005

Problem Solving and Test PrepUSE 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 6.49 pounds. To which place did she round?

A Ones

B Tenths

C Hundredths

D Thousandths

20. Neil rounded 9.135 pounds to 9.1 pounds. To which place did he round?

A Ones

B Tenths

C Hundredths

D Thousandths

Name Lesson 6.1

Practice

Name Lesson 6.2

PW38© Harcourt • Grade 5

Add and Subtract DecimalsFind the sum or difference.

1. 5 � 0.9

_

2. 11.7 � 3.04

__

3. 12.67 � 18.5

__

4. 16.08 � 3.49

__

5. 18.394 � 15.602

__

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

__

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


21. Until the 2002 Olympics, the record 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?

22. Beth and her grandmother paid $23.00 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?

23. Lynne buys a meal and a milk at the school cafeteria. If Lynne pays with a $5 bill, how much change should she receive?

A $1.06

B $1.55

C $2.96

D $3.94

24. Tim buys a daily planner and 1 pen at the school store. How much change should Tim receive from a $20.00 bill?

A $9.76

B $9.86

C $10.24

D $16.74

School CafeteriaItem Price

meal $3.45

fruit $0.80

milk $0.49

School StoreItem Price

notebook $4.55

12 pencils $2.14

1 pen $1.29

daily planner $8.95


Estimate Sums and DifferencesEstimate by rounding.

1. 6.71 �4.8

__

2. 10.238 � 7.842

__

3. 2.11 � 0.96

__

4. $14.54 �$7.35

__

5. 9.786 �8.914

__

6. $3.28 � $3.65

__

7. 9.276 6.419

�4.458

8. 0.63 � 0.31

__

9. 10.82 � 5.78

__

10. 1.53 � 0.15

__

11. $5.34 $1.06

�2.68

12. 4.29 �3.334

__

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


21. About how long would it take to listen to the 3 songs in the chart?

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 $16.29 and pens for $9.54. About how much money will she have left?

A $10

B $25

C $35

D $15

24. Heather and her husband have $99. They buy glassware for $19.49 and tablecloth for $22.53. About how much money would they have left?

A $50

B $45

C $38

D $57

Song Artist Playing Time(in minutes)

Top 3 Songs of 1956

Blue Suede Shoes

Hound Dog

Long Tall Sally

Elvis Presley

Elvis Presley

Little Richard

1.983

2.25

2.083

Name Lesson 6.3

$5.34$1.06

� $2.68


Choose a MethodChoose 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. 3.1 4.75

� 2.9

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. 2.9 � 1.5

__

13. 3.37 � 6.73

__

14. $57.19 � $ 2.68

__

15. 1.005 � 0.07

__

16. 2.4 � 3.75 � 1.8 17. 0.85 � 0.798 18. $1.95 � $7.65 19. 5.4 � 0.54


20. How much farther did Chistyakova jump in 1988 than Joyner-Kersee in 1994?

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, and 2 nickels. How much money does Lydia have? Show your work.

23. Dylan has 2 dollars, 3 quarters, 4 dimes, and a nickel. How much money does Dylan have? Show your work

Galina Chistyakova

Jackie Joyner-Kersee

Heike Dreschler

Anis oara Stanciu

Tatyana Kotova

Yelena Belevskaya

1988

1994

1992

1983

2002

1987

7.52

7.49

7.48

7.43

7.42

7.39

Name Year Distance (in meters)

Women’s Long Jump Records

Name Lesson 6.4



Problem Solving Workshop Skill: Estimate or Find Exact AnswerProblem Solving Skill PracticeTell whether you need an estimate or an exact answer. Then solve.

1. Serena is purchasing workout clothes in 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?

2. Alberto is purchasing a basketball for $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?

3. Jessa needs $140 to buy a bicycle. She saves $10 each week. She has already saved $60. How many weeks from now can Jessa buy the bicycle?

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?

Mixed Applications

5. Tom has 21 flowering plants in white, 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?

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.?

7. Each chicken has 2 legs, and each cow has 4 legs. How many legs do 9 chickens and 23 cows have?

8. Pose a Problem Look back at Exercise 6. Write a similar problem by changing the beginning temperature.

Name Lesson 6.5

PW42 Practice © Harcourt • Grade 5

Model Multiplication by a Whole NumberComplete the multiplication expression for each model. Find the product.

1.

� 0.34 �

2.

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

Name Lesson 7.1


Name Lesson 7.2

Algebra: Patterns in Decimal Factors and ProductsUse patterns to find the product.

1. 2.67 � 10 �

2.67 � 100 �

2.67 � 1,000 �

2. 1.789 � 10 �

1.789 � 100 �

1.789 � 1,000 �

3. 0.409 � 10 �

0.409 � 100 �

0.409 � 1,000 �

Multiply each number by 10, 100, 1,000, and 10,000.

4. 0.8

5. $3.99

6. 6.014

Find the value of n.

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

12. 0.004 � 1,000 � n


13. How many Earth years is 10 years on Jupiter?

14. How many Earth years is 1,000 years on Mercury?

A 0.000241 Earth years

B 0.0241 Earth years

C 241 Earth years

D 2,410 Earth years

15. A blank CD costs $0.36. How much will 100 blank CDs cost?

Mercury

Venus

Jupiter

Saturn

0.241 Earth years

0.615 Earth years

11.862 Earth years

29.457 Earth years

Planet Length of Year

Length of Planet Year


Name Lesson 7.3


15. It takes the planet Pluto 247.68 Earth years to revolve around the sun. How many Earth years does it take for Pluto to revolve around the sun five times?

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?

17. Ms. Salera’s class rode 3.8 miles to the observatory. The next closest observatory is 13 times as far. How many miles is the second observatory?

A 13 miles

B 49.4 miles

C 494 miles

D 4,940 miles

18. It takes the moon 29.5 days to go through all of its phases. How many days does it take the moon to go through all of its phases 30 times?

Record Multiplication by a Whole NumberFind and record the product.

1. 3.74 � 5

__

2. 6.81 � 7

__

3. 3.13 � 25

__

4. 4.92 � 16

__

5. 17.07 � 3

__

6. 61.3 � 4

7. 22.09 � 5

8. 48.2 � 36

9. 27.14 � 20

10. 6.067 � 19


11. 4.3 � 6 � n

12. 6 � n � 16.8

13. 52.45 � 3 � n

14. 4.1 � n � 24.6


Name Lesson 7.4

Model Multiplication by a DecimalUse the model to find the product.

1.

0.5 � 0.7 �

2.

0.3 � 0.6 �

3.

0.7 � 0.7 �

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 �


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 �


Estimate ProductsEstimate the product.

1. 34 � 2.1

__

2. 0.3 � 0.8

__

3. 0.7 � 0.9

__

4. 4.4 � 0.6

__

5. 5.5 � 6.2

__

6. 7.1 � 7.1

__

7. 26.3 � 5.4

__

8. 1.78 � 3.2

__

9. 44.7 � 2.5

__

10. $9.06 � 0.63

__

11. 352.4 � 0.46 12. 0.129 � 22.3

13. 7.035 � 61

14. $8.99 � 12

Problem Solving and Test Prep15. FAST FACT The fastest marine mammal,

the killer whale, can swim 35 miles per hour. How many miles can the whale swim in 10.25 hours?

16. Brittany earns $6.25 an hour working at the concession stand. How much does she earn in 7.5 hours?

17. A Ross seal at the aquarium weighs 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

B 2 � 430 D 3 � 430

18. A bottlenose dolphin eats an average of 155.75 pounds of fish per week. How much does the dolphin eat in 4.5 weeks?

Name Lesson 7.5


Practice Decimal MultiplicationFind 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

__

10. $13.00 � 0.007

__

11. 0.006 � 8.1

__

12. 0.44 � 0.05

__

13. 6.6 � 0.05

14. $2 � 0.04

15. 0.07 � 0.3

16. 0.07 � 0.09


17. Dustin has 8 guitar picks that are each 0.009 of an inch thick. What is the total height of the guitar picks if they are stacked on top of each other?

18. FAST FACT The smallest fish recorded 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 kilogram. How many kilograms do 4 sprouts weigh?

A 0.001 kilogram

B 0.01 kilogram

C 0.1 kilogram

D 1 kilogram

20. A light guitar string is 0.016 of an inch thick. A heavy guitar string is 2.25 times as thick. How thick is the heavy string?

A 0.036 in.

B 0.36 in.

C 3.6 in.

D 36 in.

Name Lesson 7.6


Name Lesson 7.7

Problem Solving Workshop Skill: Multistep ProblemsProblem Solving Skill PracticeDescribe the steps required to solve. Then solve the problem.

1. The crew of a fishing boat is paid $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?

2. A lobster boat captain pays its crew $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

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 a 6-hour fishing trip. Including himself, how many adults and children did Mr. Chopra pay for?

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?

Children

Children

Adult

Adult

$35

$65

$55

$95

6 hours

12 hours

6 hours

12 hours

Age Length of Trip

Captain Jack’s Fishing Adventure

Cost


Name Lesson 8.1


Decimal DivisionUse 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 �

Name Lesson 8.2


Estimate QuotientsFind 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 Prep21. During an 8-hour storm, it snowed

4.2 inches. Estimate the average hourly snowfall during this storm.

22. The greatest snowfall for one day was measured in Georgetown, Colorado on December 4, 1913. It snowed 63.0 inches in 24 hours. Estimate the hourly snowfall during this storm.

23. Which shows how you can best use compatible numbers to estimate 35.4 � 8?

A 32 � 8

B 35 � 8

C 38 � 9

D 40 � 8

24. Which shows how you can best use compatible numbers to estimate 58.3 � 6?

A 54 � 6

B 56 � 7

C 58 � 6

D 60 � 6


Name Lesson 8.3


Divide Decimals by Whole NumbersCopy the quotient and correctly place the decimal point.

1. 3 � � 77.7 2. 8 � � 0.704

3. 7 � � 5.95 4. 69 � � $92.46

Divide. Check by multiplying.

5. 3 � � 81.3 6. 36 � � 46.44 7. 49 � � 1.274 8. 21 � � 77.28

9. 7.83 � 9 10. $158.22 � 54 11. 2.208 � 8 12. 656.6 � 67

Problem Solving and Test Prep13. The fastest swimming record was set by

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?

14. The mako shark can swim more than 0.09 miles per minute for short amounts of time. About how far can it travel in one second at this speed?

15. 529.2 � 18.

A 0.294 C 29.4

B 2.94 D 294

16. The Gibsons paid $50.00 for a summer pass to Playland. If they went 20 times during the summer, what was the cost of each visit to Playland?

A $0.25 C $25.00

B $2.50 D $250.00

259 0088 085 $134



Problem Solving Workshop Skill: Evaluate Answers for ReasonablenessProblem Solving Skill Practice 1. Luis has 4 bottles of grape juice. Each

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.

2. Angela bought 1.65 pounds of green 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.


3. Hideko says 1 U. S. dollar equals 27.73 Russian rubles. David says 1 U. S. dollar equals 2.773 Russian rubles. Whose answer is reasonable?

4. Suppose you exchange 200 U. S. dollars for EU euros. How many euros will you receive? Which operation(s) did you use to solve?

5. John has 4.1 pizzas. He gave 2.7 pizzas away. How many pizzas does John have left? Is your solution an estimate or an exact answer?

Name Lesson 8.4

3

4

6

14

18

19.179 Australian Dollars

3.3 European Union (EU) Euros

706.8 Japanese Yen

388.22 Russian Ruble

139.662 Hong Kong Dollars

U. S. Dollars Currency

Currency Exchange Rates(April 2006)


Name Lesson 9.1

Collect and Organize DataA 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 400 children, ages 9–13

3. a random sample of 400 teachers

Make a line plot. Find the range of hours.

4.

Problem Solving and Test PrepUSE 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?

6. What is the range of the data Tammy collected about her classmates’ favorite subjects?

7. Which is the range for the following set of data: 14, 9, 11, 21, 7?

A 11

B 12

C 13

D 14

8. Which set of data has a range of 15?

A 4, 9, 2, 15, 18

B 9, 5, 20, 3, 25

C 8, 2, 15, 13, 17

D 5, 20, 7, 14, 21

2

4

5

7

4

10

6

2

Number of Hours Frequency

Volunter Hours Survey

Spelling

Reading

Science

Math

Social Studies

Favorite Subjects


Mean, Median, and ModeFind 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


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? 31, 27, 26, 25, 31

A 13

B 27

C 28

D 31

16. Explain how you can find the median for a set of data with an even number of data values.

Name Lesson 9.2

1

2

3

4

5

2

4

5

Game Number of Runs

Moreau Little League Team

Name Lesson 9.3


Compare DataCompare the mean, median, and range of the data sets.

1.

2.


3. Reasoning Hannah and Tyler count the 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?

4. Two data sets have different ranges and medians. Is the data in the data sets similar or different? Explain.

5. Which shows how the median for the sets of data compare?

A 111 � 111 C 48 � 45

B 111 � 98 D 120.3 � 110.3

6. Which shows how the mean for the sets of data compare?

A 52 � 47 C 34.5 � 40.5

B 19 � 19 D 42 � 39

Baseball Cards Saved 111 101 149

Football Cards Saved 124 87 98 132

Group A Pages Read47 33 52 36

Group B Pages Read42 39 47 28

A: Number of stamps collected13 25 19 32 66 22 19

B: Number of stamps collected6 13 21 20 15 13 24

Monday Homework Problems

2 3 6 2 6 3 4 5 4 5

Tuesday Homework Problems

10 4 2 5 3 4 6 9 6 1


Analyze GraphsFor 1–3, use the double-bar graph.

1. Which class period has the least number of right-handed students?

2. Which two class periods have the same number of students?

3. What is the total number of left-handed students in all four class periods?


4. Which sport has the greatest number of votes?

5. How many total votes are there for soccer and tennis?

6. A line graph shows a trend of less rain this week than 2 weeks ago. Explain what the line graph might look like.

7. Look at the double-bar graph at the top 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.

02468

1012141618

1 2 3 4

Num

ber o

f Stu

dent

s

Left-handedRight-handed

Class Period

Left-handed and Right-handedStudents

Name Lesson 9.4

Tennis

Soccer

Favorite sport

Key: Each � 3 votes.


Problem Solving Workshop Strategy: Draw a DiagramProblem Solving Strategy PracticeDraw a Venn diagram to solve.

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?

2. During a free period, 7 students used 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 PracticeFor 3–4, use the table. 3. Hank spent $26.06 on two supplies.

Which two supplies did he buy?

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

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.

6. Nora records the number of insects for 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?

Name Lesson 9.5

Ruler

Tongs

Graduated Cylinder

Hand Lens

Safety Goggles

$2.39

$11.50

$8.71

$19.95

$14.56

Science Supply Price

Science Supplies Sale


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.

Make a graph for the data set.

3.


4. Did the students have more CDs or more DVDs? How many more?

5. What is a reasonable scale and interval to graph the data?

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 C 10

B 25 D 5

Name Lesson 10.1

Joe’s Pet Store

Rabbit05

1015202535

Cat Dog Hamster

Pets

Num

ber o

f Pet

s

Book Type Number of Votes

Favorite Books

Mystery

Fantasy

Poetry

Sports

35

15

10

40

Name Number of CDs

Number of CDs and Movies

Chuck

Emily

Tim

10

14

13

Number of DVDs

2

5

2



Name Lesson 10.2

Make HistogramsFor 1–2, use the table.

2. Make a histogram of the data.

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.


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

old?

A 4 C 7

B 6 D 8

8. How many runners are 6–7 years old?

A 2 C 7

B 6 D 10

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

Weight(in pounds)

Number of Adult Dogs

43–45 3

46–48 8

49–51 10

Color of Bicycle Number of Bicycles

Red 16

Blue 23

Black 14

Ages of One-Mile Runners

4-50246

8

6-7 8-9 10-11 12-13Ages

Num

ber o

f Run

ners



Name Lesson 10.3

Algebra: Graph Ordered PairsUse the coordinate grid at the right. Write an ordered pair for each point.

1. A

2. B

3. C

4. D

Graph and label each point on the coordinate grid at the right.

5. E (4, 5) 6. F (2, 9)

7. G (8, 5) 8. H (3, 3)

9. I (0, 10) 10. J (7, 1)

Problem Solving and Test PrepUSE DATA For 11–14, use the map.Each unit represents 1 city block.

11. What ordered pair gives the location for the Playground?

12. What is the distance between Home and the Theater?

13. Use the map above. Suppose a museum is located at point D. What ordered pair locates this point?

A (3, 2)

B (2, 1)

C (1, 2)

D (2, 3)

14. Use the map above. Suppose a gym is located at point F. What ordered pair locates this point?

A (8, 4)

B (7, 4)

C (8, 3)

D (8, 5)

Library School

Playground

TheaterHome

N

W E

S

F

D

061 832 4 5 7 9 10

x

10

y

1

3

5

4

2

9

7

6

8

061 832 4 5 7 9 10

x

10

y

1

3

5

4

2

9

7

6

8

A

B

C

D


Practice© Harcourt • Grade 5

Name Lesson 10.4

PW61

Make Line GraphsUSE DATA For 1–2, use the table.

1. What would be an appropriate scale and interval to graph the data?

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.


4. What is the range in the number of inches in height for the first 7 years?

5. Between which years in the table did Tommy grow the most?

6. What would be an appropriate scale and interval to graph this data?

7. Suppose you made a line graph of this 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.

Weights of 2 Kittens (Cutie and Magic)

Month 0 1 2 3

Cutie 2 6 11 31

Magic 2.5 5 11.5 34

Tommy’s Height

Age (years) 1 3 5 7

Height (in.) 29 34 37 43

Weights of Cutie and Magic



Make Circle GraphsUse the data to make a circle graph.

1.

2.

3.

4.

Name Lesson 10.5

Apple

Orange

Banana

Pear

50

20

20

10

Fruit Number

Students’ Favorite Fruits

Flavor Number

3

1

2

2

Vanilla

Strawberry

Rocky Road

Pistachio

Chocolate 4

Ice Cream Flavors Ordered

Cupcakes

Crumb Cake

Muffins

Juice

Cookies

$50

$20

$15

$5

$10

Item Sold Earnings

Art Club Earnings From Bake Sale

Food

Clothing

Transportation

Savings

$35

$20

$15

$30

Item Cost

Celine’s Paycheck Celine's Paycheck

Favorite Fruits

Ice Cream Orders

Art Club Bake Sales


Problem Solving Workshop Strategy: Make a GraphProblem 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?

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?

Mixed Strategy Practice3. Paula has 1.5 times as many novels as

Carly. Carly has 12 novels. How many novels does Paula have? Show your work.

4. Pose a Problem Look back at Problem 1. How would your graph change if there were no scores above 93? Explain.

Name Lesson 10.6

78

75

99

94

81

98

84

71

92

96

101

104

76

97

90

82

88

80

93

88

Sarah’s Team Bowling Scores

72

72

73

80

74

71

74

74

84

68

78

69

71

68

69

81

83

79

79

77

May High Temperatures inSan Jose(°F)

Name Lesson 10.7


Choose the Appropriate GraphChoose the best type of graph or plot for the data. Explain your choice.

1. Hours Raul worked each of the past 6 days

2. Number of library books borrowed by 30 people

3. Water evaporated over 10 days

Draw the graph or plot that best displays each set of data. Tell whether the data is categorical or numerical.

4.

5.

Problem Solving and Test PrepUSE DATA For 6–7, use the table below.

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 data in table? Explain.

9. What set of data is categorical?A Runs scored by the team in 5 gamesB Items Ralph spent his allowance onC High temperature each month for

6 monthsD Votes given 10 congressman in

January

Paul’s Vacation BudgetActivity Amount

Food $9

Rides $7

Souvenirs $5

Weather Service AlmanacMonth Rainfall (inches)

May 16

June 22

July 18

Test Scores100 92 87 88 93 10084 95 100 75 97 93

Visitors To The Alamo By The Minute

Minute Visitors

1 14

2 30

3 45

4 65



Name Lesson 11.1

Multiples and the Least Common MultipleList 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


11. What are the least numbers of packs of yellow marbles and blue marbles a personwould have to buy to have the same number of each color of marble?

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 of 36?

A 5, 13, 18

B 4, 6, 18

C 6, 12, 18

D 6, 12, 16

14. Which set of numbers has an LCM of 12?

A 2, 3, 5

B 4, 6, 8

C 1, 5, 12

D 2, 4, 6

Yellow

Green

Blue

Orange

2

4

3

6

Color of Marble Number per Pack

Packs of Marbles


Practice PW66© Harcourt • Grade 5

Name Lesson 11.2

DivisibilityTest 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.



Name Lesson 11.3

Factors and Greatest Common FactorList 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


16. Sharon is dividing her green and blue 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?

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 and another number is 7. The second number is between 60 and 70. What is it?

19. Which number is not a common factor of 42 and 21?

A 7 C 21

B 6 D 3

Red

Yellow

Green

Blue

12

28

16

24

Color Number of Rocks

Sharon’s Rock Collection



Prime and Composite NumbersWrite 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

Name Lesson 11.4



Problem Solving Workshop Strategy: Make an Organized ListProblem Solving Strategy PracticeUse an organized list to solve.

1. During the month of May, Jean has 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.

2. Students are making picture frames. 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 Practice3. 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.

4. Carl spent $51.33 on three opera tickets. How much did each ticket cost? Show your work.

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?

Name Lesson 11.5

Which Type Of Book Is Your Favorite

Western,20% Adventure

24%

Humor,16%

Mystery,____

______ ,10%

______


Name Lesson 11.6

Introduction to ExponentsWrite in exponent form.

1. 10,000,000

2. 1,000

3. 10

4. 100,000,000

Find the value.

5. 103

6. 108

7. 104

8. 106

9. 105

10. 102

11. 107

12. 101

ALGEBRA Find the value of n.

13. 102 � n

14. 107 � n

15. 105 � n


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?

17. Kelly read the odometer on her parents’ car. She wrote down 105 miles. How many miles are shown on the odometer?

18. Which number represents 10 � 10 � 10?

A 100

B 101

C 102

D 103

19. Which number represents 10 � 10 � 10 � 10 � 10 � 10?

A 103

B 106

C 104

D 107



Exponents and Square NumbersWrite 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

6. 55

7. 73

8. 18

9. 115

10. 83

11. 46

12. 32

13. 113

14 57

Compare. Write ,, ., or �.

15. 53 23 16. 22 41 17. 54 78 18. 62 93

Problem Solving and Test PrepUSE DATA For 19–20, use the pattern in the table.

19. James earned 729 pennies. How many plates did James wash in all?

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?

A 27

B 43

C 52

D 41

22. What is the greatest square number that is even and is less than 300? What is the value of this square number?

Name Lesson 11.7

Start

1

2

3

1

3

9

27

Number of plateswashed

30

31

32

33

ExponentformPennies

Pennies Earned



Prime Factorization 1. Draw a factor tree to find the

prime factorization of 48. Writethe 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

10. 5 � 5 � 5 � 3

11. 52 � 112

12. 2 � 2 � 19

13. 11 � 2 � 2

14. 82 � 23

15. 32 � 63

16. 2 � 5 � 5 � 5


17. The prime factors of a number are the first four prime numbers. No factor is repeated. What is the number?

18. The prime factors of Patrick’s favorite number are 2, 7, and 3. Two is repeated once. What is Patrick’s favorite number?

19. Which numbers are two of the prime factors of 36?

A 2 and 3

B 11 and 3

C 5 and 2

D 4 and 13

20. What is the least number that is the product of two different primes that are squared?

Name Lesson 11.8



Understand FractionsWrite 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.

Write the fraction for each. 8. four fifths

9. five divided by ten

10. one sixth

11. two out of 9

Problem Solving and Test Prep12. A basket of fruit has 3 apples, 2 pears,

and 4 bananas. What fraction of the fruit are bananas?

13. A delivered pizza came cut in 6 equal slices. Mark ate 2 slices. Now 4 slices remain. What fraction of the pizza did Mark eat?

14. What fraction of the stars are gray?

A 1 __ 5 C 3 __

4

B 1 __ 4 D 4 __

5

15. What fraction of the triangles are gray?

A 1 __ 2 C 3 __

8

B 3 __ 5 D 5 __

8

G

10

H

10

I

10

Name Lesson 12.1

Name Lesson 12.2


Equivalent FractionsWrite an equivalent fraction.

1. 1 __ 8 2. 7 ___

10 3. 4 __

5 4. 6 __

8 5. 3 __

4 6. 1 __

3

7. 3 __ 6 8. 8 ___

12 9. 6 __

9 10. 10 ___

15 11. 10 ___

16 12. 5 __

6

Tell which fraction is not equivalent to the others.

13. 1 __ 2 , 5 ___

15 , 3 __

9 14. 2 __

6 , 1 __

4 , 4 ___

12 15. 5 ___

10 , 2 __

3 , 6 ___

12 16. 9 ___

12 , 3 __

4 , 2 __

5


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?

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 ?

A 3 ___ 10

B 4 ___ 10

C 7 ___ 10

D 3 __ 5

20. Which fraction is equivalent to 14 __ 16 ?

A 7 __ 8

B 7 __ 9

C 4 __ 6

D 2 ___ 16

Orange

Red

Purple

Blue

Green

Yellow

1

4

2

3

1

1

Color Number of PeopleWho Chose It

Preferred Colors


Name Lesson 12.3


Simplest FormName the GCF of the numerator and denominator.

1. 14 ___ 16

2. 3 __ 4 3. 12 ___

36 4. 9 ___

30 5. 10 ___

25

Write each fraction in simplest form.

6. 8 ___ 22

7. 17 ___ 34

8. 28 ___ 77

9. 16 ____ 100

10. 24 ___ 30

11. 10 ___ 10

12. 9 ___ 16

13. 20 ___ 60

14. 36 ___ 45

15. 12 ___ 57

16. 10 ___ 24

17. 15 ___ 25

18. 32 ___ 40

19. 70 ____ 100

20. 48 ___ 60

Problem Solving and Test Prep 21. Fast Fact Eight states border one or

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.

22. Twenty out of 75 salon clients made an appointment for a haircut. What fraction of the clients made a haircut appointment? Write the fraction in simplest form.

23. Which fraction shows 21 ___

28 in simplest

form?

A 1 __ 8

B 1 __ 7

C 3 __ 7

D 3 __ 4

24. Twelve of 30 students rode the bus today. What fraction of the students rode the bus? Write the fraction in simplest form.


Name Lesson 12.4


Understand Mixed NumbersWrite each mixed number as a fraction. Write each fraction as a mixed number.

1. 1 7 __ 8 2. 10 ___

9 3. 27 ___

4 4. 3 4 __

5 5. 1 11 ___

15 6. 4 1 ___

12

7. 41 ___ 10

8. 41 ___ 8 9. 61 ___

3 10. 5 9 ___

10 11. 3 1 __

9 12. 39 ___

5

13. 4 3 __ 7 14. 21 ___

4 15. 57 ___

7 16. 8 5 __

6 17. 9 4 __

9 18. 41 ___

6

19. 7 2 __ 3 20. 6 3 ___

10 21. 4 2 ___

15 22. 31 ___

4 23. 16 ___

5 24. 35 ___

6


25. How many times will Gayle fill a 1 _ 2 -cup ladel to serve 8 1 _ 2 cups of punch?

26. A recipe calls for 2 3 _ 4 cups of milk. What is 2 3 _ 4 written as a fraction?

27. Which fraction is the same as 2 4 _ 5 ?

A 8 __ 5

B 9 __ 5

C 14 ___

5

D 24 ___

5

28. Which mixed number is the same as 23 ___

4 ?

A 2 3 __ 4

B 3 1 __ 2

C 4 1 __ 4

D 5 3 __ 4


Name Lesson 12.5


Compare and Order Fractions and Mixed NumbersCompare. Write �, �, or � for each .

1. 4__9

5__9 2. 3__

43__5

3. 8___12

2__3 4. 5__

84__7

5. 9___11

8__9

6. 5___12

3__7

7. 6___10

4__5

8. 1 6__9

2 2__3

9. 4 5__8

4 3__4 10. 9 2__

6 8 3__

9

11. 3 4__5

3 5__6

12. 1 2___10

1 1__5

13. 4 4__6

3 3__4

14. 8 1__3

8 3__5 15. 6 3__

8 6 1__

4

Write in order from least to greatest.

16. 3 __ 8 , 3 __

4 , 1 __

4 17. 2 __

3 , 1 __

6 , 7 __

9 18. 1 5 __

8 , 1 3 __

4 , 1 5 __

6 19. 7 3 __

5 , 6 2 __

3 , 6 6 ___

10


20. Len paints and sells wooden flutes. List the flutes in order from shortest to longest.

21. Len created a new flute that is 6 2 _ 3 inches long. Which, if any, of his flutes are longer?

22. Kayla practiced violin 2 1 _ 4 hours on Monday, 2 3 __ 10 hours on Tuesday, and 1 4 _ 9 hours on Wednesday. On which day did she practice the longest?

A Tuesday C Monday

B Friday D Wednesday

23. Dean practiced trombone 1 2 _ 3 hours on Monday, 1 7 __ 12 hours on Tuesday, and 1 7 _ 9 hours on Wednesday. On which day did he practice the longest?

A Tuesday C Monday

B Wednesday D Saturday

Lily

Rose

Ivy

6

6

6

Flute Name Length, in inches

Len’s Flutes

34

58

712


Name Lesson 12.6


Problem Solving Workshop Strategy: Make a Model

Problem Solving Strategy PracticeMake a model to solve.

1. From home, Todd walked 3 blocks 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?

2. Kayla is putting up a picket fence on 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 PracticeSolve.

3. Lisa spent 10 minutes driving to the 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?

4. Pose a Problem Look back at 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.

Name Lesson 12.7


Relate Fractions and DecimalsWrite each decimal as a fraction or mixed number in simplest form.

1. 0.33 2. 0.06 3. 0.625 4. 0.35 5. 0.900

6. 1.05 7. 1.1 8. 1.12 9. 2.525 10. 4.08

11. 3.700 12. 0.205 13. 0.025 14. 4.98 15. 8.25

Write each fraction or mixed number as a decimal.

16. 7 _____ 1000

17. 8 ____ 100

18. 3 ___ 10

19. 9 ___ 20

20. 40 ___ 50

21. 1 6 ___ 25

22. 9 27 ___ 45

23. 5 6 ___ 15

24. 2 13 ___ 50

25. 3 36 ___ 40


26. A player’s batting average is 0.425. What fraction is equivalent to 0.425?

27. Kevin hit in 9 out of 40 at bats. What is his batting average?

28. Which fraction is NOT equivalent to 0.8?

A 4 __ 5 C 12

___ 15

B 8 ___ 10

D 3 __ 4

29. What decimal is equivalent to 1 4 __ 5 ?

A 1.8 C 1.5

B 1.4 D 1.3


Name Lesson 13.1


Add and Subtract Like FractionsFind the sum or difference. Write it in simplest form.

1. 1 __ 4 � 1 __

4 2. 2 __

7 � 1 __

7

3. 3 __ 5 � 1 __

5

4. 3 __ 7 � 2 __

7

5. 7 __ 8 � 5 __

8

6. 7 ___ 10

� 2 ___ 10

7. 4 __ 9 � 3 __

9

8. 4 __ 6 � 1 __

6

9. 3 __ 8 � 3 __

8

10. 2 __ 5 � 1 __

5

11. 8 ___ 10

� 5 ___ 10

12. 1 __ 6 � 2 __

6

13. 9 ___ 12

� 3 ___ 12

14. 2 __ 4 � 1 __

4

15. 3 ___ 10

� 5 ___ 10


16. Glaciers currently store 2 _ 3 of the world’s freshwater supply. If 1 _ 3 of those glaciers melted, how much would be left in glacier form?

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?

18. Iceberg Alley is where bergs from the glaciers of Greenland drift down to Newfoundland. If an iceberg floats 3 __ 10 mile in January, and 5 __ 10 mile in February, how far should it travel in order for the iceberg to have drifted 1 mile by March?

A 2 __ 10 mile

B 1 _ 5 mile

C 1 mile

D 1 1 _ 2 miles

19. Icebergs are usually white from millions 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 3 __ 8

B 2 __ 8

C 5 __ 8

D 1 3 __ 8



Model Addition of Unlike FractionsFind the sum. Write it in simplest form.

1.

1 __ 2 � 5 __

8 �

2.

3 __ 5 � 1 __

4 �

3.

1 __ 2 � 1 __

5 �

Find the sum using fraction bars. Write it in simplest form.

4. 1 __ 5 � 4 ___

10 � 5. 1 __

2 � 3 ___

10 � 6. 5 __

6 � 2 __

3 �

7. 1 __ 3 � 2 __

4 � 8. 1 __

2 � 1 __

8 � 9. 1 __

3 � 1 __

2 �

10. 5 __ 8 � 2 __

5 � 11. 5 __

8 � 3 __

4 � 12. 3 __

4 � 2 __

3 �

13. 3 __ 5 � 1 __

2 � 14. 2 __

6 � 3 __

9 � 15. 1 __

4 � 5 ___

12 �

16. 1 __ 2 � 2 __

6 � 17. 6 ___

10 � 1 __

3 � 18. 1 ___

12 � 3 __

4 �

12

18

18

18

18

18

15

15

15

14

15

12

Name Lesson 13.2

Name Lesson 13.3


Model Subtraction of Unlike FractionsUse fraction bars to find the difference. Write it in simplest form.

1. 5 __ 6 � 2 __

3 � 2. 3 __

4 � 1 __

5 � 3. 5 __

8 � 1 __

4 �

Find the difference using fraction bars. Write it in simplest form.

4. 2 __ 5 � 2 ___

10 � 5. 1 __

2 � 1 ___

12 � 6. 7 __

8 � 1 __

2 �

7. 3 __ 4 � 4 __

6 � 8. 2 __

3 � 1 __

5 � 9. 6 __

7 � 1 __

2 �

10. 4 __ 5 � 3 ___

10 � 11. 7 ___

12 � 1 __

3 � 12. 1 __

4 � 1 ___

10 �

13. 7 __ 8 � 3 __

8 � 14. 5 __

7 � 1 __

2 � 15. 8 __

9 � 1 __

3 �

16. 4 ___ 10

� 1 __ 4 � 17. 6 __

7 � 1 __

3 � 18. 3 __

4 � 1 __

2 �

16

13

13

16

16

16

16

?

14

15

14

14

?

18

14

18

18

18

18

?

Name Lesson 8.3


Name Lesson 13.4

Estimate Sums and DifferencesEstimate each sum or difference.

1. 5 __ 7 � 1 __

4 2. 1 __

6 � 3 __

7

3. 8 __ 9 � 2 __

5

4. 10 ___ 11

� 6 __ 9

5. 7 __ 8 � 1 __

2

6. 3 __ 5 � 2 __

8

7. 6 __ 7 � 3 __

4

8. 1 __ 8 � 5 __

6

9. 9 ___ 12

� 1 __ 9

10. 5 __ 8 � 4 __

5

Estimate to compare. Write , or . for each .

11. 1 __ 5 � 6 __

7 1 12. 7 ___

11 � 3 ___

10 1 __

2 13. 4 __

5 � 8 __

9 0 14. 7 __

9 � 3 __

5 1 __

2 15. 8 ___

12 � 2 ___

10 1


16. Maria is making burritos for dinner. Her recipe calls for 7 _ 8 cup of ground beef and 1 _ 6 cup of shredded cheese. Estimate the total amount of meat and cheese Maria uses in her recipe.

17. Jeremy rides his skateboard 2 miles from his home to school. After riding 3 _ 8 mile, he realizes he left his lunch money on the counter at home. About how far does Jeremy have left to travel when he realizes his mistake?

18. Gail is making a healthy snack for her weekend hike. She adds 3 _ 5 cup of raisins and 6 _ 7 cup of peanuts. Estimate the total amount that Gail adds.

A 1 1 __ 2 cups

B 1 cup

C 2 cups

D 1 __ 2 cup

19. Ling makes 1 gallon of fruit punch for 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?

A 1 __ 4 gallon

B 1 __ 8 gallon

C 3 __ 4 gallon

D 1 __ 2 gallon

PracticePW84

Name Lesson 13.5


Use Common DenominatorsFind the sum or difference. Write it in simplest form.

1. 4 __ 5 � 1 __

2

2. 7 __ 8 � 1 __

4

3. 1 ___ 10

� 1 __ 5

4. 7 ___ 12

� 1 __ 4

5. 2 __ 9 � 1 ___

10

6. 6 __ 7 � 3 __

8

7. 8 __ 9 � 1 __

2

8. 3 __ 4 � 1 __

5

9. 4 __ 5 � 4 ___

15

10. 7 ___ 10

� 1 __ 4


11. The lroquois tribe lived in the 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 _ 4 was used for skins or clothing, how much of the deer was utilized in all?

12. The lroquois tribe was skilled at tracking animals through the Adirondack Mountains. A favorite hunting trail was 7 _ 8 mile long, but the hunters only followed it for 1 _ 6 mile before spotting the first deer. How much more trail was there to hunt after the first sighting?

13. Which addition equation represents the fraction of beads that are black or gray?

A 5 ___ 12

� 1 __ 4 � 8 ___

12

B 5 ___ 12

� 1 __ 3 � 9 ___

12

C 4 __ 5 � 1 __

6 � 29 ___

30

D 3 __ 6 � 2 __

4 � 12 ___

12

14. Which addition equation represents the fraction of beads that are white or gray?

A 1 __ 2 � 2 __

8 � 6 __

8

B 3 __ 8 � 2 __

8 � 5 __

8

C 1 __ 8 � 1 __

3 � 11 ___

24

D 1 __ 3 � 4 __

8 � 5 __

6

Name Lesson 13.6


Problem Solving Workshop Strategy: Compare StrategiesProblem Solving Strategy Practice

1. Casey worked on memorizing her lines 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?

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?


3. Laurie wants to make 3 gowns. How many yards of yellow silk will she need for the gowns? Show your work.

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.

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?

Blue Chiffon

Yellow Silk

Gold Trim

Fabric Amount in Yards

Materials needed tomake 1 gown

3 12

2 35

2 67

Name Lesson 13.7


Choose a MethodChoose a method. Find the sum or difference. Write it in simplest form.

1. 2 __ 7 � 1 __

6

2. 2 __ 3 � 1 __

2

3. 3 __ 4 � 1 __

4

4. 6 ___ 22

� 1 ___ 11

5. 1 __ 5 � 3 __

5

6. 6 ___ 11

� 1 __ 6

7. 1 __ 3 � 3 __

8

8. 7 ___ 10

� 8 ___ 15

9. 4 ___ 15

� 5 ___ 12

10. 5 __ 6 � 1 __

6

11. 3 __ 7 � 1 __

2

12. 1 __ 8 � 2 __

5

13. 4 __ 5 � 1 __

4

14. 6 __ 7 � 5 __

7

15. 1 __ 7 � 4 ___

21

Problem Solving and Test Prep 16. Mark lives near the Empire State Building

in New York City. On Sunday, Mark spent 1 _ 4 of his day visiting the Empire State Building and 5 __ 12 of his day rollerblading in Central Park. What fraction of the day did Mark spend either visiting the Empire State Building or rollerblading?

17. Mark took a taxi ride from the Empire 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?

18. Lillian is practicing shooting marbles for 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?

19. Lillian is participating in the Holyoke 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.


Model Addition of Mixed NumbersUse fraction bars to find the sum. Write the answer in simplest form.

1. 3 1 __ 2 � 2 1 __

3 2. 1 1 __

4 � 3 3 __

8 3. 3 3 __

5 � 1 1 __

5 4. 5 3 ___

10 � 1 3 __

5

5. 2 1 __ 8 � 2 3 __

4 6. 5 1 __

4 � 1 1 __

6 7. 4 1 __

3 � 1 3 __

4 8. 2 1 __

5 � 3 3 ___

10

9. 1 5 __ 6 � 2 1 ___

12 10. 4 4 ___

10 � 1 1 __

2 11. 1 11 ___

12 � 1 2 __

3 12. 2 3 ___

10 � 2 1 __

2

13. 1 4 ___ 10

� 1 1 __ 2

__

14. 3 4 ___ 10

� 1 2 ___ 10

__

15. 1 1 __ 5

� 2 9 ___ 10

__

16. 3 2 __ 5

� 3 1 __ 2

_

17. 5 1 __ 3

� 2 4 __ 5

_

18. 1 5 __ 6

�4 5 ___ 12

_

19. 2 9 ___ 10

� 1 7 ___ 10

__

20. 4 3 __ 8

� 3 1 __ 4

_

21. 2 1 __ 4

� 2 1 __ 2

_

22. 3 1 __ 3

�3 7 ___ 12

_

23. 1 1 __ 4

� 5 1 __ 2

_

24. 3 1 __ 2

� 4 2 __ 5

_

Name Lesson 1.1Name Lesson 14.1


PW88 Practice

Model Subtraction of Mixed NumbersUse fraction bars, or draw a picture to find the difference. Write the answer in simplest form.

1. 3 8 ___ 10

�2 5 ___ 10

2. 5 5 __ 8 � 3 3 __

8 3. 6 1 __

2 � 1 1 __

4 4. 4 1 __

3 � 1 __

4

5. 3 3 __ 4 � 2 3 __

8 6. 5 3 __

5 � 3 1 __

2 7. 4 5 __

6 � 1 1 ___

12 8. 5 5 __

6 � 2 1 __

2

9. 3 7 ___ 12

� 1 1 __ 2 10. 5 2 __

3 � 4 1 __

4 11. 4 11 ___

12 � 2 1 __

6 12. 3 1 __

2 � 1 1 __

5

13. 4 7 __ 8

�1 1 __ 4

__

14. 5 7 ___ 10

�5 1 __ 5

__

15. 5 4 __ 5

�2 1 __ 2

__

16. 6 1 __ 2

�3 1 __ 6

__

17. 5 1 __ 2

�2 1 __ 3

__

18. 5 1 __ 2

�3 2 __ 5

__

19. 2 2 __ 3

�1 1 __ 2

_

20. 5 7 __ 8

�3 1 __ 4

__

21. 5 3 __ 4

�1 1 __ 3

_

22. 6 11 ___ 12

�5 1 __ 2

__

23. 4 9 ___ 10

�4 1 __ 5

__

24. 6 7 __ 8

�3 3 __ 4

__


Name Lesson 14.2


Name Lesson 14.3


Record Addition and SubtractionFind the sum or difference. Write the answer in simplest form.

1. 9 7 ___ 10

� 1 3 __ 5 � 2. 8 2 __

3 � 3 1 __

9 � 3. 9 1 __

4 � 5 2 __

3 �

4. 6 1 __ 2 � 1 4 __

9 � 5. 1 3 __

7 � 6 1 __

3 � 6. 10 3 __

4 � 5 1 __

6 �

7. 8 3 __ 6 � 2 4 ___

12 � 8. 12 11 ___

12 � 3 3 __

4 � 9. 8 5 __

6 � 9 3 __

4 �


10. How many miles did Sheryl run on Monday and Tuesday in all?

11. How much farther did Sheryl walk on Monday than on Tuesday?

12. Dan played guitar for 2 1 _ 2 hours on Saturday and 1 2 _ 5 hours on Sunday.

How many hours total did Dan playguitar in 2 days?

A 1 7 __ 10 hours

B 3 3 _ 7 hours

C 3 1 _ 2 hours

D 3 9 __ 10 hours

13. Ana spent 1 2 _ 3 hours cleaning her room, and Evelyn spent 1 8 _ 9 hours cleaning her room. How much longer did it take Evelyn to clean her room?

A 3 5 _ 9 hours

B 1 hour

C 2 _ 3 hour

D 2 _ 9 hour

Monday

Walking Running

Tuesday

Sheryl’s Training Record (In Miles)

1 124 1

32 1

4 2 59


PW90 Practice

Name Lesson 14.4


Subtraction with RenamingUse fraction bars to find the difference. Write the answer in simplest form.

1. 5 3 __ 8 � 1 5 __

8 2. 7 � 2 1 __

4 3. 4 1 __

2 � 3 __

4 4. 4 1 __

2 � 2 4 __

5

5. 6 1 ___ 10

� 2 9 ___ 10

6. 7 3 ___ 10

� 1 3 __ 5 7. 7 1 __

2 � 6 2 __

3 8. 4 1 __

3 �3 7 ___

12


9. Zack decided to reduce the amount of banana by 1 7 _ 8 ounces. How much banana did Zack use?

10. Zack’s recipe makes a 10 5 __ 12 -ounce smoothie. If blueberries were not included, how many ounces would the smoothie be?

11. Stacey buys 4 1 _ 4 yards of ribbon to make a bow. She uses 2 5 _ 8 yards. How much ribbon is left?

A 1 3 __ 8 yards

B 1 5 __ 8 yards

C 2 4 __ 8 yards

D 2 5 __ 8 yards

12. Jon used 5 1 _ 4 ounces of cranberry juice and 3 2 _ 3 ounces of orange juice to make fruit punch. How much more cranberry juice than orange juice did Jon use?

A 1 5 ___ 12

ounces

B 1 7 ___ 12

ounces

C 2 1 __ 7 ounces

D 2 7 ___ 12

ounces

Banana

Zack’s Large Fruit Smoothie

ounces

Ingredient Amount

ouncesStrawberry

ouncesBlueberry

4 34

2 16

3 12



Practice Addition and SubtractionEstimate. Then write the sum or difference in simplest form.

1. 1 1 __ 6 � 5 91 __

3 2. 14 3 __

4 � 9 5 __

6 3. 16 3 __

4 � 24 11 ___

12

4. 15 5 __ 8 � 11 5 __

6 5. 11 5 __

8 � 25 4 __

5 6. 8 � 1 5 __

7

Use a calculator to find the sum or difference.

7. 39 4 __ 5 � 17 1 __

2

8. 32 1 ___ 10

� 19 3 __ 5

9. 93 3 __ 4 � 28 7 ___

10


10. On which day did Cyndi spend the most time at fielding practice? The least?

11. How much time in all did Cyndi spendat 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 3 __ 8 minute

B 5 __ 8 minute

C 1 1 __ 8 minutes

D 1 5 __ 8 minute

13. Mary sold 33 3 _ 8 bushels of apples and 21 2 _ 3 bushels of pears. How many bushels of fruit did she sell in all?

A 54 1 ___ 24

bushels

B 54 5 ___ 24

bushels

C 55 1 ___ 24

bushels

D 55 5 ___ 24

bushels

Name Lesson 14.5

Cyndi’s Fielding Practice

hours

hours

38

1

1112

2

56

1 hours

Monday

Wednesday

Friday

Day Time



Name Lesson 14.6

Problem Solving Workshop Strategy: Use Logical ReasoningProblem Solving Strategy PracticeUse logical reasoning to solve.

1. Sue had softball practice for 3 2 _ 3 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?


3. The sum of the distances of the 3 homeruns hit in Game 1 is 278 11 __ 18 ft. What was the distance of Nina’s homerun in Game 1?

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?

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?

Carla

Game 2Game 1

Homerun Distance (Ft)

23

88 79

90

12

85

16

93

Nina

Maria



Model Multiplication of FractionsUse yellow and blue crayons to model the product.

1. 1 __ 2 � 4 __

5 � 2. 1 __

2 � 5 __

6 �

3. 2 __ 4 � 1 __

3 � 4. 2 __

3 � 1 __

2 �

Find the product.

5. 4 __ 9 � 5 __

6

6. 1 __ 3 � 1 __

4

7. 1 __ 8 � 2 __

3

8. 4 __ 7 � 2 __

5

9. 1 __ 2 � 2 __

9

10. 1 __ 3 � 3 __

4

11. 2 __ 5 � 1 __

7

12. 3 ___ 10

� 1 __ 2

13. 1 __ 9 � 2 __

3

14. 5 __ 7 � 1 __

4

Name Lesson 15.1



Record Multiplication of FractionsFind the product. Write the answer in simplest form.

1. 2 __ 3 � 9 ___

10

2. 6 __ 7 � 1 __

3

3. 5 __ 8 � 7 ___

12

4. 1 __ 4 � 3 __

7

5. 2 __ 9 � 4 __

7

6. 3 __ 8 � 5 ___

12

7. 9 ___ 10

� 4 __ 5

8. 3 __ 7 � 6 __

9

9. 4 ___ 10

� 7 __ 8

10. 5 __ 6 � 1 __

3

11. 1 __ 9 � 3 ___

10

12. 2 __ 5 � 3 ___

12

13. 4 __ 7 � 9 ___

10

14. 10 ___ 12

� 3 __ 5

15. 4 __ 9 � 3 __

8


16. Alexa uses 2 _ 3 of her backyard for a dog run. She has 1 _ 5 of the dog run fenced in. What fraction of Alexa’s backyard is fenced in?

17. Charles uses 1 _ 3 of his farm for a pumpkin patch. He uses 2 _ 7 of the pumpkin patch to grow white pumpkins. What fraction of the farm grows white pumpkins?

18. Jin picks 2 _ 3 of 1 _ 2 of his apple orchard to make apple cider. What fraction of the orchard did Jin pick?

A 1 __ 2

B 1 __ 6

C 1 __ 3

D 5 __ 9

19. Luisa planted 3 _ 5 of the last 2 _ 9 of her flower garden with daffodils. What fraction of her garden is daffodils?

A 5 ___ 20

B 1 __ 9

C 6 __ 7

D 2 ___ 15

Name Lesson 15.2


Multiply Fractions and Whole NumbersFind the product.

1. 5 � 9 ___ 10

2. 3 __ 4 � 2

3. 5 __ 6 � 3

4. 7 � 1 __ 9

5. 12 � 2 __ 7

6. 10 � 3 __ 5

7. 9 ___ 10

� 4

8. 5 __ 8 � 6

9. 1 __ 3 � 15

10. 9 � 4 __ 7

11. 8 � 5 __ 9

12. 5 � 6 __ 7

13. 11 � 1 __ 9

14. 8 __ 9 � 10

15. 3 ___ 10

� 11


16. Lloyd feeds his cats 2 _ 9 of a 5 pound bag of cat food each day. How many pounds of food does Lloyd feed his cats daily?

17. Kyra uses 3 _ 5 of a roll of yarn for each scarf she makes. How many rolls of yarn does she need to make 4 scarves?

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

B 20 ounces D 30 ounces

19. Shyla used 6 __ 7 of the 5 gallons of paint for

her fence. How many gallons of paint did Shyla use?

A 4 1 __ 2 gallons C 4 gallons

B 3 6 __ 7 gallons D 4 2 __

7 gallons

Name Lesson 15.3


Multiply with Mixed NumbersMake a model to find the product.

1. 2 1 __ 2 � 1 __

3 � 2. 1 __

4 � 1 1 __

2 � 3. 2 __

3 � 1 1 __

4 �

Find the product.

4. 5 � 4 1 __ 2

5. 2 � 1 3 __ 5

6. 8 � 2 1 __ 2

7. 2 1 __ 6 � 2 __

7

8. 1 3 __ 7 � 9

9. 2 __ 3 � 1 1 __

7 � 2 1 __

4

10. 1 3 __ 5 � 1 1 __

3 � 3 ___

10

11. 1 5 __ 7 � 1 __

3 � 3 __

5

12. 9 ___ 10

� 1 1 __ 4 � 2 1 __

2


13. Alejandro has 7 1 _ 3 pounds of flour. He uses 3 _ 4 of the flour to make bagels. How many pounds of flour did he use?

14. Isabel has 2 1 _ 2 gallons of scarlet paint. She uses 2 _ 3 of it to paint her dining room. How many gallons of paint did Isabel use?

15. Kim hiked 5 2 _ 3 miles on Saturday. She used 2 _ 5 of the time talking on the phone while hiking. How many miles did Kim talk on the phone while hiking?

A 2 4 ___ 15

B 3

C 2 11 ___ 12

D 4 1 __ 4

16. Joshua danced 3 1 _ 2 hours on Monday. Tess danced 3 _ 4 time as long. How many hours did Tess dance?

A 3 1 __ 9

B 2 3 __ 4

C 2 5 __ 8

D 1 9 ___ 10

Name Lesson 15.4


Model Fraction DivisionWrite a division number sentence for each model.

1. 2.

3. 4.

Use fraction bars to find the quotient.

5. 2 __ 9 � 1 __

6

6. 3 ___ 10

� 1 __ 4

7. 1 __ 4 � 1 __

8

8. 3 ___ 11

� 1 __ 4

9. 1 __ 2 � 1 ___

10

10. 4 __ 7 � 2 __

3

11. 1 � 1 __ 5

12. 6 � 4 __ 9

13. 5 � 1 __ 4

14. 7 ___ 10

� 1 __ 6

15. 4 � 1 __ 8

16. 2 � 1 __ 6

17. 8 � 1 __ 3

18. 8 ___ 11

� 1 __ 4

19. 2 � 1 __ 2

20. 4 � 1 __ 4

Name Lesson 15.5


Divide Whole Numbers by FractionsFind the quotient. Write it in simplest form.

1. 1 � 5 ___ 12

2. 2 � 1 __ 2

3. 7 � 2 __ 5

4. 9 � 1 __ 3

5. 6 � 3 __ 7

6. 4 � 1 __ 6

7. 3 � 7 __ 9

8. 8 � 5 ___ 12

9. 7 � 5 __ 6

10. 10 � 3 __ 5

11. 5 � 1 __ 4

12. 12 � 1 __ 3

13. 6 � 1 __ 3

14. 9 � 3 __ 4

15. 3 � 3 ___ 10


16. Students are painting the set for the 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?

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?

18. Henry cut a 10 foot log into 9 __ 10 foot pieces of firewood. How many pieces of firewood did Henry cut the log into?

A 10

B 11 1 __ 9

C 12 1 __ 3

D 9 5 __ 9

19. Melanie cut 5 feet of pretzel dough into 1 _ 3 foot pieces. How many pieces did Melanie cut the dough into?

A 12

B 15

C 18

D 20

Name Lesson 15.6


Name Lesson 15.7

Divide FractionsWrite a division sentence for each model.

1.

2.

Divide. Write the answer in simplest form.

3. 3 __ 8 � 5 ___

12

4. 5 __ 7 � 1 __

3

5. 6 __ 9 � 2 __

5

6. 7 ___ 10

� 3 __ 8

7. 2 1 __ 4 � 2 __

5

8. 3 1 __ 2 � 5 __

9

9. 2 1 __ 5 � 1 1 __

4

10. 5 ___ 12

� 3 __ 7

11. 4 __ 9 � 3 __

8

12. 1 2 __ 3 � 1 __

5


13. Bruce has 8 1 _ 2 feet of lumber to 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?

14. Cory has 10 1 _ 2 feet of paper to make banners. Each banner is 3 _ 4 of a foot long. How many banners can Cory make?

15. A baker has 7 1 __ 3 -cups of brown sugar.It takes 3 _ 4 -cup of brown sugar to make a loaf of banana bread. How many loaves of banana bread can the baker make?

16. Lila can walk 2 3 _ 4 miles in 4 _ 5 of an hour. How fast can she walk in miles per hour?

A 2 1 __ 5 miles per hour

B 3 1 __ 3 miles per hour

C 2 miles per hour

D 1 3 __ 4 miles per hour


Name Lesson 15.8

Problem Solving Workshop Skill: Choose the OperationProblem Solving Skill PracticeTell which operation you would use to solve the problem. Then solve.

1. Jacinda works 2 _ 5 of the days each month at the reference desk and 1 _ 3 of the days in the children’s room at the library. How often does Jacinda work 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?

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?

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 PracticeUSE DATA For 5–6, use the table.

5. Garrett plays for the Buffalos, and Lucy plays for the Bulldogs. They played 2 _ 3 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?

7. Ashley takes 1 _ 2 of the days each month for ballet lessons and 1 _ 6 for tap dance lessons. What fraction of the days each month does Ashley take dance lessons?

Bulldogs

Eagles

Buffalos

Lions

9

7

6

4

1

3

4

6

Team Wins Losses

Softball Tournament Results


Understand and Express RatiosWrite each ratio three ways. Then name the type of ratio.

1. flags with stripes: flags with stars

2. flags with a torch to flags with stripes

3. total number of flags to flags with a C

4. flags with stripes: total number of flags

5. flags with a torch to flags with a C

6. flags with stars to flags with a torch


7. The Arizona state flag has 7 red stripes and 6 gold stripes. What is the ratio of red stripes to gold stripes?

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.

9. Sara has 5 books about dogs and 3 books about horses. What is the ratio of books about horses to books about dogs?

A 5:3

B 8:3

C 3:5

D 5:8

10. Cody used 4 paper towels to clean up a mess. There are still 5 paper towels left on the roll. What is the ratio of used paper towels to total paper towels?

A 4:5

B 4:9

C 5:4

D 5:9

Name Lesson 16.1


Algebra: Equivalent Ratios and ProportionsWrite two equivalent ratios for each ratio. Use multiplication or division.

1. 1:7

2. 28 to 4

3. 5 __ 3

4. 9:27

Tell whether the ratios form a proportion. Write yes or no.

5. 1 __ 4 and 3 ___

12

6. 42 ___

9 and 14

___ 3

7. 13 ___

23 and 52

___ 99

8. 8 ___ 49

and 4 __ 9


9. Mia makes purple paint. For 1 gallon 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.

10. A flower bed has 7 red tulips and 9 yellow tulips. What is the ratio of red tulips to yellow tulips?

11. In the library, the ratio of mysteries to westerns is 4 to 1. The library has 32 mystery books. How many western books are there?

A 3

B 5

C 8

D 28

12. The ratio for making salad dressing is 3 cups oil to 1 cup of vinegar. Which is an equivalent ratio for 3 to 1?

A 3:1

B 5:15

C 6:1

D 9:6

Name Lesson 16.2



Ratios and RatesWrite each ratio in fraction form. Then find the unit rate.

1. 243 seconds for 81 jumping jacks

2. $3.52 for 4 pounds of bananas

3. 18 pages in 3 days

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


13. A package of 12 juice boxes is $2.76. A package of 16 juice boxes is $4.00. Which package is the better buy?

14. Fast Fact There are 124 calories in two cups of grapes. How many calories are there in 1 cup of grapes?

15. Sara buys 3 pounds of chicken for $17.97. What is the unit cost?

A $2.98

B $5.99

C $6.00

D $17.97

16. Alex spends $9.75 on 5 packages of baseball cards. What is the unit cost?

A $1.95

B $3.25

C $4.75

D $14.75

Name Lesson 16.3

MXENL08AWK5X_PHTE_C16_L03.Indd PW103MXENL08AWK5X_PHTE_C16_L03.Indd PW103 6/15/07 12:25:49 PM6/15/07 12:25:49 PM


Understand Maps and ScalesComplete the ratio table.

1.

2.

The map distance is given. Find the actual distance.

For 3–6, the scale is 1 in. � 300 mi. For 7–10, the scale is 2 cm � 8.4 km.

3. 2.2 in.

4. 7 in.

5. 0.4 in.

6. 5.4 in.

7. 0.25 cm

8. 6 cm

9. 3.1 cm

10. 8 cm

Problem Solving and Test Prep11. A map of Spain has a scale of

4 cm � 220 km. Another map of Spain is half the size. What is the scale of the smaller map?

12. The scale on a map showing Fargo and Grand Forks is 0.5 in. � 20 mi. The distance between these cities is 80 miles. What is the distance on the map?

13. Amber draws a map of her town using 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?

A 7.5 in.

B 7.5 ft

C 19.5 in.

D 19.5 ft

14. Nathan draws a map of his 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 1.9 cm

B 6.1 cm

C 8.2 cm

D 8.4 cm

Name

Map Distance, in 1 2 6

Actual Distance, mi 60 120 300 480

Map Distance, cm 1 8 9 13

Actual Distance, km 3.8 49.4 57

Lesson 16.4

MXENL08AWK5X_PHTE_C16_L04 .indd PW104MXENL08AWK5X_PHTE_C16_L04 .indd PW104 6/15/07 12:28:04 PM6/15/07 12:28:04 PM


Name Lesson 16.5

Problem Solving Workshop Strategy: Make a TableProblem Solving Strategy PracticeMake 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 PracticeUSE 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.

4. The height of the Empire State Building is 90 feet more than 4 _ 5 the height of the Sears Tower. How tall is the Empire State Building?

5. How much taller is the Taipei 101 building than the Empire State Building?

Taipei 101 Petronas Towers 1 & 2 1,450 ftSears Tower

1,380 ftJin Mao Building

Empire State Building



Understand PercentWrite 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.

Name Lesson 16.6



Name Lesson 16.7

Fractions, Decimals, and PercentsWrite 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.

9. 1 __ 4

10. 0.29

11. 7 ___ 10

12. 0.60

13. 0.178

14. 7 __ 8

15. 0.058

16. 3 ___ 15


17. California produces about 75% of the strawberries in the United States. What fraction of strawberries in the United States does California produce?

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?

19. Susan washed 3 _ 5 of her clothes. What percent of her clothes did she wash?

A 0.3

B 60%

C 0.35

D 53%

20. At the Corner Store, 85% of the 100 shelves contain food. What is the percent written as a decimal?

A 0.85

B 8.05

C 8.5

D 0.8


PW108

Name Lesson 16.8


Find Percent of a NumberComplete the sentence. Then, find the percent of each number.

1. 30% of 40

10 counters represent 100%, or 40.

So, each counter represents 10%, or

30% of 40 �

2. 60% of 15 � or 60 ____

100 of 15

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


Name Lesson 17.1


Outcomes and ProbabilityUse 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

spell out her name. What is the probability of pulling a vowel tile?

11. Daniel has a number cube labeled 1-6. What is the probability of rolling an odd number?

12. What is the probability that the pointer will land on stripes?

A 1 __ 8

B 2 __ 4

C 1 __ 4

D 1 __ 3

13. What is the probability of rolling a number greater than 4 on a number cube labeled 1 through 6?

PW109 Practice

A. 1 __ 6 C. 3 __

6 or 1 __

2

B. 2 __ 6 or 1 __

3 D. 5 __

6



Probability ExperimentsFor 1–4, use the table.

1. Rachel pulled a marble from a bag, 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

a red marble? a blue marble? a green marble? 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.

Number of pulls

Total

Red Blue Green White

Rachel’s Marble Experiment

5 12 6 7

Name Lesson 17.2

Name Lesson 17.3


Probability and PredictionsExpress 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;30 more tosses

2. 5 wins in 10 games;6 more games

3. 3 pink buttons in 9 pulls;12 more pulls

4. 12 blue socks in 48 pulls16 more pulls

5. 24 bananas out of 30 pieces of fruit;45 more pieces of fruit

6. 2 yellow shirts in 12 pulls6 more pulls

Problem Solving and Test Prep 7. George won 8 of the 12 games of

checkers he played with Mon. If they play once a day for the next9 days, how many games could George expect to win?

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?

9. Bobby lost 3 out of 9 chess matches. Predict how many times Bobby will lose in 12 more matches?

A 3 matches

B 4 matches

C 5 matches

D 6 matches

10. Perry’s soccer team won 4 out of 6 games. Predict how many times Perry‘s team will win in the next 15 games?

A 10 games

B 12 games

C 8 games

D 9 games

Name Lesson 17.4


Problem Solving Workshop Strategy:Make an Organized ListProblem Solving Strategy PracticeUSE DATA For 1–3, use the table.

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?

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 PracticeUSE DATA for 4–7, use the menu.

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?

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?

Thick

Thin

Marinara

Alfredo

Sausages

Olives

Mushrooms

Peppers

Crust Sauce Topping

Sal’s Pizza Parlor

Pancakes

Omelet

French toast

Quiche

Oatmeal or cold cereal

$4.80

$5.20

$4.50

$5.10

$3.70

Milk

Juice

Sparkling

$1.25

$1.75

$1.55

Breakfast Options

Beverages

Menu


Name Lesson 17.5


Tree DiagramsFor 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?

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?


4. If Ian rolls a die labeled 1-12 and tosses a coin, how many outcomes are possible?

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?

6. Imee can choose a gold, silver or string bracelet with red, green, blue, or yellow beads. How many bracelet and bead choices does Imee have?A 7

B 8

C 12

D 14

7. Matt can choose a plain, poppy seed, garlic, or sesame bagel with plain or herb cream cheese. How many bagel sandwich choices does Matt have?A 6

B 4

C 8

D 10

A IE P Q R


Name Lesson 17.6


Combinations and ArrangementsMake a list or draw a tree diagram to find the total number of possibilities.

1. ice-cream combinations: mint, vanillaor chocolate ice cream; chocolatechip, caramel syrup, or toffee topping

2. summer-camp activity combinations: hiking or horseback riding; 2-day, 3-day, or 4-day outings

3. ways to arrange a penny, nickel, and dime in a line

4. order in which Raymart, Nicole, Alissa, and Marie line up to start a raceacross the soccer field?


5. Kim needs to groom her 4 cats Cutie, Magic, Stitch, and Star. She grooms Cutie first. In how many different orders can Kim groom the remaining 3 cats?

6. Joy’s snack choices include 4 types of cookies and 2 types of drinks. If she chooses one cookie and one drink, how many possible combinations are there?

7. Kathy has 3 shirts and 4 pairs of shorts to choose from. How many possible choices does Kathy have?A 6

B 7

C 9

D 12

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 24

C 9

D 12


Points, Lines, and AnglesFor 1–6, use the figure. Name an example of each.

1. point 2. line segment

3. line 4. plane

5. vertex 6. vertical angles

For 7–14, use the figure above. Classify each angle. Write obtuse, acute, straight, or right.

7. �MNO 8. �KPS

9. �SPR

10. �JLQ

11. �JKS

12. �JLN

13. �LPQ

14. �QPR

Problem Solving and Test PrepUSE 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 the figure?

A parallel lines

B right angles

C point

D intersecting lines

18. Which is the least whole number of degrees an obtuse angle can have?

A 90�

B 91�

C 101�

D 45�

MJ K L

P N O

Q RS

Name Lesson 18.1


Measure and Draw AnglesEstimate the measure of each angle. Then use a protractor to find the measure.

1. �YXZ 2. �VXT

3. �TXZ 4. �UXZ

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 PrepUSE 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 angle?

A 82�

B 95�

C 105�

D 90�

11. What is the approximate measure of the angle below?

T

U V W

Y

X Z

Name Lesson 18.2

X

Z

Y


Practice

Name Lesson 18.3

PolygonsName 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�


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.

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.

10. Which of the following angles could form a triangle?

A 85, 42�, 63�

B 20�, 70�, 10�

C 80�, 50�, 50�

D 45�, 45�, 70�

11. Which polygon is not regular?

A

B

C

D



Problem Solving Workshop Skill: Identify RelationshipsProblem Solving Skill PracticeFor 1–2, identify the relationship. Then solve.

1. What relationship can you find between the length of a square’s sides and the perimeter?

2. Predict the perimeter, if the length of each side of a square is 14 inches?

Mixed Applications PracticeUSE DATA For 3–4, use the table.

3. Identify the relationship displayed in the table.

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?

Length Of Square Sides (In.) 3 4 5 6

Perimeter (In.) 12 16 20 24

Number Of Sides On A Prism Base 3 4 5 6 7

Number of Vertices 6 8 10 12 14

Name Lesson 18.4


CirclesFor 1–6, use the circle at the right.

1. Name 5 radii. 2. Name a diameter.

3. Name a chord.

4. Name the circle. 5. If ___

AC is 7 inches, how long is

___ BD ?

6. If ___

BD is 6.2 inches, how long is

___ AC ?

Complete 7–8. Then use a compass to draw each circle. Draw and label the measurements.

7. radius �

diameter � 1.4 cm

8. radius � 0.9 in.

diameter �

Problem Solving and Test PrepUSE DATA For 9–10, use the circle.

9. What is the unknown measure in the circle?

10. If 112˚ is changed to 95˚, what is the unknown measure of the circle?

11. Which is the measure of �AXC?

A 88�

B 124�

C 148�

D 184�

12. Which is the measure of �BXC?

A 90�

B 99�

C 109�

D 171�

Name Lesson 18.5

B

C

D

A E

F

99°112°

82°

A

C

88° B

X 124°

AB

C

171°

90°

X



Congruent and Similar FiguresWrite whether the two figures appear to be congruent, similar, or neither.

1. 2.

3.

4.

Identify the corresponding side or angle.

5. ___

UT

6. �S

7. ___

RS

8. �T

9. �U

10. ___

SU

11. �R

12. ___

TR

Problem Solving and Test PrepUSE DATA For 13–14, use the figures shown.

13. Do the figures appear to be congruent? Explain.

14. Do the figures appear to be similar? Explain.

15. Which best describes the two figures below?

A congruent

B similar

C regular polygons

D neither congruent nor similar

16. Quadrilaterals ABCD and EFGH are congruent. The measure of �C is 150�. What is the measure of the corresponding angle, �G ?

WXR

S

YZT U

F

T

V U

H G

Name Lesson 18.6



Name Lesson 18.7

SymmetryDraw 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.

9. 10.

11.

12.


13. Does a right triangle have lines of symmetry? rotational symmetry?

14. Brandon makes a design that has rotational symmetry every 1 __

2 -turn.

What angle measure describes the design’s symmetry?

15. Which figure has rotational symmetry?

A C

B D

16. Which figure has rotational symmetry?

A C

B D



Classify TrianglesClassify each triangle. Write isosceles, scalene, or equilateral.

1.

2.

3.

Classify each triangle. Write acute, right, or obtuse.

4.

5.

6.

Problem Solving and Test PrepFor 7–9, use the models of the sails.

7. What type of triangle is school A’s flag?

8. What type of triangle is school B’s flag?

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 type of triangle is it?

A scalene

B obtuse

C acute

D isosceles

11. James draws a triangle with angles that measure 45� and 60�. What is the measure of the third angle?

A 105�

B 90�

C 75�

D 45�

8 ft

7 ft4 ft7 cm7 cm

7 cm

5 m

9 m

9 m

18 in.

18 in.

10 in.

17 in.

21 in.

6 in. School A

School B

Name Lesson 19.1



Classify QuadrilateralsClassify 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.

5.

6.


7. Draw and name a quadrilateral with 4 right angles and 4 pairs of congruent sides.

8. Algebra One pair of congruent angles in a parallelogram each measure 54�. What is the measure of each of the missing angles?

9. A quadrilateral has 4 congruent angles and 2 pairs of congruent sides. What type of quadrilateral is it?

A rectangle

B trapezoid

C rhombus

D parallelogram

10. The sum of the measures of three angles in a quadrilateral is 280�. What is the measure of the fourth angle?

A 180�

B 120�

C 90�

D 80�

B C

A D A

D

B

C

Name Lesson 19.2


Draw Plane FiguresUse 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 3 inches; 2 congruent angles each measuring 45�

2. angles measuring 30�, 70�, 80�;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 measuring 2 inches and 1 pair of congruent sides measuring 4 inches

4. 2 pairs of congruent angles, 1 pair measures 75�; 4 congruent sides each measuring 3 inches

Name Lesson 19.3


Solid FiguresClassify 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 PrepUSE 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 base and 3 rectangular faces?

A pyramid

B rectangular prism

C triangular prism

D cube

11. Which solid figure has 0 faces, 0 edges and 0 vertices?

A sphere

B triangular prism

C pyramid

D pentagonal prism

Name Lesson 19.4

Name Lesson 19.5


Problem Solving Workshop Strategy:Compare StrategiesProblem Solving Strategy Practice 1. Sara is building prisms 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 build a pentagonal prism?

2. Bill is building a triangular pyramid by 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?

3. Sara also makes a pentagonal pyramid by using pieces of clay for the vertices and straws for the edges. How many pieces of clay and how many strawswill Sara need to make the pentagonal 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?

Mixed Strategy PracticeUSE DATA For 5–6, use the data in the diagram.

5. The diagram is of a new monument that will be installed in the town square of Duncan’s hometown. What type of polyhedron is it?

6. Duncan saw a model that was 1 _ 5 thesize of the actual monument. Write anequation to find the length of each side of the base in the model. Then solve it.

7. Duncan lives 1.3 miles from the town square. If he rode his bike to and from the town square twice in one day, how many miles did he ride in all?

10 m 10 m

15 m15 m



Nets for Solid FiguresMatch each solid figure with its net.

1. 2.

3.

4.

a. b. c. d.


5. Draw a net for a rectangular prism and for a triangular prism. Compare the nets by describing the shapes and number of bases and faces.

6. Draw a net for a pyramid and for a triangular pyramid. Compare the nets by describing the shapes and number of bases and faces.

7. How many rectangles will the net for a triangular prism contain?

A 2 C 4

B 3 D 5

8. How many triangles will the net for a pentagonal pyramid contain?

A 3 C 5

B 4 D 7

Name Lesson 19.6


Draw Solid Figures from Different ViewsIdentify the solid figure that has the given views.

1. 2. 3.

On the grids below, draw each figure from the top, the front, and the side.

4. 5. 6.

7. Write Math Explain which solid figures have a top view that is the same as the bottom view.

Top Front SideTop Front Side Top Front Side

Name Lesson 18.7Name Lesson 19.7

top view top view top view

front view front view front view

side view side view side view


TransformationsName 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?

A quadrilateral

B translation

C triangle

D circle

9. Which kind of transformation flips a figure over a line?

Name Lesson 20.1

PracticePracticePW130© Harcourt • Grade 5

TessellationsPredict 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.

Name Lesson 20.2


Name Lesson 20.3


Create a Geometric PatternTell 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.



PW132

Numeric PatternsIdentify 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 6first term: 43

11. rule: divide by 2first term: 88

12. rule: multiply by 3, add1 first term: 2


13. Em buys beads every month. By theend of 1 month she has 24 beads, bythe end of the second month she has48, and by the end of the third monthshe has 72. How many beads does shehave at the end of the fifth month ?

14. Henry is arranging his pennies into piles.The first pile has 1 penny, the secondhas 2 pennies, the third has 5 pennies,the fourth has 13 pennies, and the fifthhas 34 pennies. How many pennies arein the sixth pile ?

15. 30, 29, 27, 24, 20, 15, ...

A 10

B 12

C 9

D 7

16. 3, 9, 27, __, 243, 729

A 81

B 30

C 108

D 45

Name Lesson 20.4

Name Lesson 20.5


Problem Solving Workshop Strategy: Find a PatternProblem Solving Strategy Practice

1. When Ari’s figure has 1 side, Brenda’s 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?

2. Tonya makes a bracelet out of beads. Her design is shown below. What are the shapes of the next two beads in the design?

3. Julia builds a model using 105 blocks in 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?

4. Hector is painting a design around the 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, Brenda had a figure with 22 sides, how many sides does Ari’s figure have?

6. Rose made a border around a 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?



Algebra: Graph RelationshipsWrite the ordered pairs. Then graph them.

1.

2.


3. Mathew wrote the ordered pair (8,2)for 2 quadrilaterals with 8 interiorangles of 90�. What is his error?What should he have written?

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

B y-axis

C x-coordinate

D y-coordinate

6. What is the number 8 in the ordered pair (7,8)?

A x-axis

B y-axis

C x-coordinate

D y-coordinate

Number of quadrilaterals, x 1 2 3 4

Number of Interior Angles of 90°, y 4 8 12 16

6 5 4 3 2 1

0 2 3 1 4 5 7 8 9 10 11 12 13 14 15 166 x

y

5 4 3 2 1

0 2 3 1 4 5 7 8 9 106 x

y

Name Lesson 21.1

Number of rectangle faces, x 6 9 12 15

Number of triangular prisms, y 2 3 4 5

Number of cylinders, x 1 5 8 9

Number of square bases, y 0 0 0 0


Name Lesson 21.2


Algebra: Equations and FunctionsFind the rule to complete the function table. Then write an equation.

1.

x 27 21 18 15

y 9 8 7 6

2.

x 4 3 2 1 0

y 24 12 6

Use the equation to make a function table with at least 4 ordered pairs. Then graph the ordered pairs on the grid.

3. y � x � 4


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, which of the following pairs would you graph?

A (2,5)

B (5,2)

C (7,3)

D (3,7)

7. If you graph the equation y � 3x � 2, which of the following pairs would you graph?

A (2,7)

B (7,4)

C (4,14)

D (14,4)

6 78910

5 4 3 2 1

0 2 3 1 4 5 7 8 9 106 x

y

x

y

Practice PW135


Name Lesson 21.3


Problem Solving Workshop Strategy:Write an EquationWrite an equation to solve.

1. Carson spends $2.50 each weekday on a muffin and juice on his way to school. How much does Carson spend in 3 weeks?

2. Gesa parks her car at the subway stop at $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 PracticeUSE 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?

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.

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.

7. Each round-trip ferry ride costs $11.25.If Ms. Mallory takes the ferry anaverage of 15 times each month, how much does she spend on ferry fares in one year?

Seattle – Bainbridge IslandFerry Schedule

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.

minutes, x 5 10 15 20 25 30

fare, y $2.50 $5.00 $7.50 $10.00 $15.00



Understand IntegersIdentify 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|

13. |�19|

14. |�508|

15. |�29|


16. FAST FACT The coldest 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.

17. FAST FACT The warmest temperature recorded in Alaska happened in Fort Yukon. The temperature reached 100 degrees Fahrenheit on June 27, 1915. Write the temperature as an integer.

18. Which integer is the opposite of �513?

A �513

B �315

C �315

D �513

19. Which integer represents 4 years from now?

A �4,000

B �4

C �4

D �4,000

Name Lesson 21.4



Compare and Order IntegersCompare. Write ,, ., or � for each .

1. �7 �6 2. �90 �41 3. �12 �9 4. �18 �22

5. �7 �7 6. �56 �60 7. �19 �4 8. �54 �54

9. �3 �0 10. �14 0 11. �26 �26 12. �865 �864

Order each set of integers from greatest to least.

13. �1, �1, �5 14. �3, 0, �7, �10 15. �5, �2, �1, �6 16. �7, �9, �4, 0

17. �4, 4, 3, �2 18. 6, �9, 1, �2 19. 5, �5, �6, 7 20. �8, 6, 0, �3


21. The Brotulid family of fish live around �7000 meters. In what zone does this fish live?

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 �28

B �27

C �27

D �28

24. Which integer is greater than �8?

A �8

B �7

C �8

D �9

Name Lesson 21.5

Sunlight

Twilight

Midnight

Abyssal

Hadal

0 to –200–200 to –1,000

–1,000 to –4,000

–4,000 to –6,000

–6,000 to –11,000

Zone Name Range of depth (in meters)

Zones of the Oceans



Algebra: Graph Integers on the Coordinate PlaneFor 1–6, identify the ordered pair for each point.

1. point A

2. point E

3. point C

4. point F 5. point B

6. point D

For 7–12, graph and label the ordered pairs on the coordinate plane at the right.

7. M (5, �2) 8. N (�1, 1) 9. O (�3, 0)

10. P (3, 3) 11. Q (0, 2) 12. R (�5, �5)

Name the ordered pair that is described.

13. Start at the origin. Move 3 units to the left and 2 units up.

14. Start at the origin. Move 11 units to the left.


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?

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?

17. Start at the origin. Go to the left 1 unit. Go down 1 unit. What is the ordered pair?

A (1, 1)

B (�1, 1)

C (1, �1)

D (�1, �1)

18. Start at the origin. Move 3 units up. What is the ordered pair?

A (0, 3)

B (3, 0)

C (0, �3)

D (�3, 0)

Name Lesson 21.6

x-axis

y-axis

0-1

+1A

B

E

C

F

-2

+2

+2

-3

+3

+4

+5

+3 +4 +5

-4-5

+1-3 -2 -1-4-5

D



Customary Length Estimate the length of the stapler in inches. Then measure the length.

1. to the nearest inch:

2. to the nearest 1 __ 2 inch:

3. to the nearest 1 __ 8 inch:

4. In Exercises 5�7, which measurement is most precise? Explain.

Tell which measurement is more precise.

5. 4 1 __ 8 inches or 4 1 __

4 inches 6. 1 foot or 11 1 __

2 inches 7. 7 __

8 inches or 3 __

4 inches

Estimate the length in inches. Then measure to the nearest 1 __ 8 inch.

8.

Estimate:

Measurement:

9.

Estimate:

Measurement:

Name Lesson 22.1



Metric LengthEstimate 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 New York

4. width of a dictionary

5. height of the ceiling in your classroom

6. length of an apple stem

7. distance from Reno to Minneapolis

8. width of a key on a computer keyboard

Estimate and measure each.

9.

Estimate:

Measurement:

10.

Estimate:

Measurement:

11.

Estimate:

Measurement:

12.

Estimate:

Measurement:

Name Lesson 22.2



Change Linear UnitsChange the unit.

1. 10 yd � ft 2. 1,500 m � km 3. 93 ft � in.

4. 23 cm � mm 5. 3.5 mi � yd 6. 160 mm � m

7. 112 yd � ft 8. 19 km � m 9. 23 cm � 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 23. 1,000 m � � 1.5 km

24. 23 cm � � 1.24 m 25. 16 mm � � 2 cm


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?

27. There are 5 yards left of the fabric Bryce needs for a project. How many feet of fabric are left?

28. McKenna swam 1,250 meters. How many kilometers did she swim?

A 125 km

B 12.5 km

C 1.25 km

D 0.125 km

29. Chris cut 40 cm off a 1.5-m long string. How long is the string now?

A 1.46 m

B 1.4 m

C 1.1 m

D 0.9 m

Name Lesson 22.3


Name Lesson 22.4


Customary Capacity and WeightChange the unit.

1. 5 lb � oz 2. 16 c � qt 3. 8 gal � qt

4. 4,500 lb � T 5. 72 oz � lb 6. 12 fl oz � c

7. 16 qt � gal 8. 10 c � qt 9. 4.5 lb � oz


10. 7 lb 6 oz �4 lb 10 oz

___

11. 11 gal 2 c � 2 gal 1 c

___

12. 4 pt 1 c �1 pt 1 c

__

13. 23 lb 2 oz �20 lb 14 oz

___

14. 2 c 2 fl oz �4 c 6 fl oz

___

15. 3 qt 3 c �4 qt 2 c

__

16. 2 T 200 lb � 1 T 20 lb

___

17. 4 pt 2 fl oz �2 pt 6 fl oz

___


18. 1 c � � 2 qt 19. 12 fl oz � � 2 c

20. 33 oz � � 4 lb 21. 4 pt � � 4 gal

22. 2 c � � 1 gal 23. 1,500 lb � � 1 T

24. 2 fl oz � � 1 pt 25. 8 oz � � 3.5 lb

Problem Solving and Test Prep 26. Mrs. Moore handed out 4 ounces of

almonds to each of her 22 students. How many pounds of almonds did Mrs. Moore hand out?

27. Camryn made 3 gallons of iced tea for a party. How many cups of iced tea did Camryn make?

28. Tommy uses 4 ounces of cheese in each pizza he makes. How many pounds of cheese does Tommy need to make 28 pizzas? Explain.

29. Riley drank 8 cups of water during a soccer tournament. How many fluid ounces did he drink?

A 64 fl oz

B 32 fl oz

C 16 fl oz

D 64 qt


Name Lesson 22.5


Metric Capacity and MassChange the unit.

1. 80 L � kL 2. 900 mg � g 3. 7,500 mL � L

4. 18,000 mL � L 5. 5 kg � g 6. 130 mL � L

7. 336 g � mg 8. 8.25 L � mL 9. 1,200 mg � g


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 �


16. 4 g � � 250 mg 17. 1 L � � 2 mL


18. Jenna and Annie are making applesauce and need 5 kilograms of apples. How many grams are in 5 kilograms?

19. Cal drank 800 milliliters of water at school today and 500 milliliters at home. How many liters did Cal drink in all?

20. Kennedy’s dog weighs 34,000 g. How many kilograms does Kennedy’s dog weigh?

A 3,400 kg

B 340 kg

C 34 kg

D 3.4 kg

21. How many milliliters are in a 6.6 liter jug?

A 6,605 mL

B 606 mL

C 6,060 mL

D 6,600 mL


Practice

Name Lesson 22.6


Problem Solving Workshop Skill:Estimate or Actual MeasurementProblem Solving Skill PracticeTell whether you need an estimate or an actual measurement. Then solve.

1. Janet is making pendant necklaces 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?

.

2. Dominic is making a birdhouse and 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.


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?

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?

10-meter Satin cord spool

10-meter Elastic thread spool

10-meter Silver wire spool

10-meter Silk thread spool

Material Cost

$2.89

$2.31

$2.50

$8.63

Stringing Materials


Name Lesson 22.7


Elapsed TimeWrite the time for each.

1. Start: 7:14 A.M.Elapsed time: 2 hr 50 minEnd:

2. Start: Elapsed time: 12 hr 3 minEnd: 6:57 P.M.

3. Start: 4:12 P.M.Elapsed time: End: 6:43 P.M.

4. Start: January 1, 3:00 A.M.Elapsed time: 4 days 3 hr 30 minEnd:


6. Start: Monday, 2 P.M.Elapsed time: End: Tuesday, 6 A.M.

Add or subtract.

7. 3 days 2 hr � 1 day 10 hr

___

8. 12 min 22 sec � 2 min 32 sec

___

9. 2 hr 12 min � 1 hr 49 min

___

10. 6 wk 6 days � 4 wk 5 days

___

11. 32 min 9 sec � 40 min 10 sec

____

12. 6 hr 6 min � 4 hr 19 min

___

13. 1 day 12 hr � 2 days 14 hr

___

14. 5 wk 3 days � 4 wk 6 days

___


15. Christian checked out a book from the library that is due in 2 weeks. If he checked it out on April 3, what is the due date?

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?

17. Josh swam every Monday and Friday in June. How many days did he swim?

A 4 days

B 6 days

C 8 days

D 10 days

18. The movie started at 7:10 P.M. and lasted for 1 hour 54 minutes. What time did the movie end?

A 11:58 A.M.

B 9:04 P.M.

C 10:00 P.M.

D 9:40 P.M.


Name Lesson 22.8


TemperatureFind the change in temperature.

1. 56ºC to 20ºC

2. 7ºF to �17ºF

3. 88ºF to 101ºF

4. �16ºC to 30ºC

5. �6ºC to 2ºC

6. 100ºF to 0ºF

7. �16ºC to 20ºC

8. 7ºF to 17ºF

9. 18ºC to 49ºC

10. 1ºF to 26ºF

11. �16ºF to 9ºF

12. 0ºC to 0ºC

13. 50ºC to 50ºC

14. 7ºC to �1ºC

15. 50ºF to 100ºF

16. 77ºF to 0ºF

17. �30ºC to �10ºC

18. �14ºC to 22ºC


19. In Madrid, the temperature is 12°C, and in New York City, it is 48°C. What is the temperature difference in degrees C?

20. If the refrigerator is 38°F and the freezer is �1°F, what is the difference in temperature in degrees F?

21. What is the change in temperature from 41ºF to 23ºF?

A 62°F

B 32°F

C 24°F

D 18°F

22. What is the change in temperature from 12ºC to 20ºC?

A 5°C

B 7°C

C 8°C

D 10°C


Name Lesson 23.1


Estimate and Measure PerimeterEstimate 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.



Find PerimeterFind the perimeter of each polygon.

1.

2.

3.

4.

5.

6.

7.

8.


9. Cecil drew a diagram of a beehive 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?

10. Algebra Candace wants to build a 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.

11. The polygon below is a regular triangle.

What is the perimeter?

A 5 cm C 150 cm

B 15 cm D 1,500 cm

12. The flower is inside the square frame. What is the length of the frame that encloses the flower?

What is the perimeter?

A 1.4 cm C 10.4 cm

B 4.6 cm D 14 cm

29 in.29 in.

24 in.

24 in.1.5 m 1.8 m

2.3 m9 ft

11 ft

7 ft7 ft7 yd

5.7 m

5.9 m

4.3 m

3 m

3.1 m

30 in.

2.4 cm

2.6 cm

1 m

1.3 m

3 m

3.5 m

3 m

2.6 cm

5 cm

Name Lesson 23.2



Algebra: Perimeter FormulasFind the length of each regular polygon by using a formula.

1. 2.

3.

4.

5.

6.

7.

8.


9. ALGEBRA The perimeter of a regular hexagon is 42 yards. What is the length of each side?

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?

11. For which polygon could you use the formula P � 2l � 2w to find its perimeter?

A triangle

B parallelogram

C trapezoid

D pentagon

12. For which regular polygon could you use the formula P � 5x to find its perimeter?

A triangle

B square

C pentagon

D hexagon

121 yd

15 m

27 in.

18.5 in.

17 cm

7.2 mi

4.2 mi

19.1 mi

9 mi10 yd 10 yd

6 yd

1.75 in.

Name Lesson 23.3


Name Lesson 13.4

PracticePW151

Name Lesson 23.4


Problem Solving Workshop Skill: Make GeneralizationsProblem Solving Skill Practice Make generalizations to solve.

1. A rectangular shaped kitchen has 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?

2. The top of a table has a perimeter of 204 inches. A leaf extends the length of the top by 8 inches. What is the perimeter of the table top with the leaf?

3. Two boxes of cereal are the same 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?

4. The Pyramid of Khafre is the second 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 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?

.

6. Kerri has a tree house that is 5 feet by 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 and Carl are also identical twins. Can you find the ages of Brett and Bart? Explain.

8. Todd is cutting a rectangular piece of 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?



CircumferenceFor 1–3, complete the table.

1.

2.

3.

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?

Name Lesson 23.5

Object C d C � d

plate 25.12 in. 8 in.

wheel 81.64 in. 3.14

pizza 14 in. 3.14


Name Lesson 24.1


Estimate AreaEstimate the area of the shaded figure. Each square on the grid is 1 cm2.

1. 2.

3.


4. The jigsaw puzzle of a train at the right has 100 pieces. Estimate the area of the puzzle.

Train Puzzle (each square is 1 inch)

5. Estimate the area of the train in the jigsaw puzzle at the right.

6. Which is a reasonable estimate for the area of the figure?

A 15 in.2

B 9 in.2

C 4 in.2

D 2 in.2 � 1 in.2

7. Which of the following is a reasonable estimate for the area of the banner?

F 4 cm2

G 8 cm2

H 12 cm2

J 15 cm2 � 1 cm.2


Name Lesson 24.2


Algebra: Area of Squares and RectanglesFind the area of each figure.

1.

2.

16 cm

16 cm

3.

2 35 in.

6 14 in.

For each square or rectangle, find each missing measurement.

4. S = 7.5 m

A =

5. S = 5 in.

A =

6. S = 2 1 _ 4 ft

W = 3 ft

A =

7. S = 8.5 m

W = 11 m

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

B 540 tiles

C 900 tiles

D 630 tiles

11. What is the area of a 12 ft � 21 1 _ 2 ft driveway?

A 258 ft2

B 144 ft2

C 462 1 _ 2 ft2

D 326 1 _ 2 ft2

3.5 ft

8 ft5 ft

6 ft

Hickory

Pine

Oak

68 in.

54 in.

52 in.

40 in.

36 in.

48 in.

WoodPanel

Height Length


Name Lesson 24.3


Algebra: Relate Perimeter and AreaFor 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 aperimeter of 20 m. Describe thepatterns you see.

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 rectangle with a perimeter of 30 cm?

A 30 cm2

B 49 cm2

C 56 cm2

D 64 cm2

14. What is the least possible perimeter for a rectangle with an area of 169 ft2?

A 13 ft

B 52 ft

C 26 ft

D 152 ft

2

3

4

5

6

Width (m) Length (m) Area (m2)


Name Lesson 24.4


Algebra: Area of TrianglesFind the area of each triangle in square units.

1. 2.

3.

Find the area of each triangle.

4. base (b) = 5 m height (h) = 9 m Area (A) =

5. base (b) = 10 ft height (h) = 6 ft Area (A) =

6. base (b) = 7 in. height (h) = 12 in. Area (A) =

Problem Solving and Test PrepUSE 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 m2

B 50 m2

C 55 m2

D 60 m2

10. What is the area of the triangular figure?

A 45.5 in.2

B 91 in.2

C 55.5 in.2

D 20 in.2

12 ft

7 ft

9 in.

18 in.

3 cm

11 cm

height = 12 m

base = 10 m

7 in.

13 in.


Name Lesson 24.5


Algebra: Area of ParallelogramsFind the area of each parallelogram.

1. 2. 3.

4. 5. 6.

Problem Solving and Test Prep7. A yard is shaped like a parallelogram

with a base of 27 m and a height of 30 m. What is the area of the yard?

8. A parallelogram has a length of 15 cm and a height of 20 cm. It is divided into two congruent triangles. What is the area of each triangle?

9. What is the area of the parallelogram?

A 300 ft2

B 70 ft2

C 294 ft2

D 147 ft2

10. A playground is divided into two equal parallelograms. What is the area of the entire playground? Show your work.

5 m

6 m7 ft

3 ft

9 cm

5 cm

25 1 in.

in.8

13 ft

13 ft

10.4 yd

13.6 yd

14 ft

21 ft20 m

12 m

Name Lesson 24.6


Problem Solving Workshop Strategy: Solve a Simpler ProblemProblem Solving Strategy PracticeSolve.

1. Jane designed the figure below as a sun catcher. What is the area of the figure?

2. Luke made his sun catcher into a rocket. What is the area of the rocket?

Mixed Strategy PracticeUSE DATA For 3–4, use the diagram.

3. Chris designed his sun catcher to the right into an airplane. What is the area of Chris’ airplane?

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?

4 in. 14 in.6 in.

6 in. 8 in.

6 cm

5 cm

5 cm5 cm

6 cm

5 cm

18 cm

4 cm

5 cm1 cm

7 cm

4 cm

20 cm

11 cm

5 cm

Name Lesson 24.7


Surface AreaUse the net to find the surface area of each figure in square units.

1. Which faces on the net are congruent?

What is the area of the congruent faces?

What is the surface area of the prism?

2.

Find the surface area in ft2.

3.

.

4.

.

5.

.

6. WRITE Math Explain the difference between area and surface area.

E B A F

D

C

E

B

D A

C

Name Lesson 24.8


Algebra: Estimate and Find VolumeFind the volume of each rectangular prism.

1. 2.

3.


4. Which of the three pools has the greatest volume?

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 below?

A 15 units3

B 60 units3

C 20 units3

D 12 units3

7. Compare the volumes of the treasure chests. Which can hold more gold? Explain your answer.

12 yd5 yd

8 yd

2 cm

8 cm13 cm

3 ft

3 ft

3 ft2 ft 12

2 ft12

2 ft12

Pool A

Pool B

Pool C

17

15

15

9

8

7

20

25

30

Pool Length Width Depth

Swimming Pool Dimensions(in feet)

Name Lesson 24.9


Relate Perimeter, Area, and VolumeTell the unit you would use for measuring each. Write linear, square, or cubic.

1. how much tile needed to cover a floor

2. a door frame

3. the amount of water in a lake

4. how much wall paper needed to cover a wall

Write the units you would use for measuring each.

5. surface area of this prism

6. perimeter of this triangle

7. volume of this prism

Problem Solving and Test PrepUSE DATA for 8–9, use the picture of the aquarium.

8. What is the aquarium’s volume?

9. What is the area of the water’s surface that is exposed to the air?

10. Joe wraps a 9 in. � 6 in. � 4 in. gift. What unit should Joe use to decide how much wrapping paper he needs?

A inches

B square feet

C square inches

D cubic inches

11. Mary bought a 6 in. � 8 in. � 1 in. picture frame. What unit should she use to decide the width that is needed on a shelf for the picture frame?

A inches

B square feet

C square inches

D cubic inches

12 cm8 cm

5 cm

6 ft

6 ft 9 ft

4.5 m4 m

5 m

15 in.

18 in.

24 in.

Name Lesson 24.10

PracticePW162© Harcourt · Grade 5

Problem Solving Workshop Strategy: Compare Strategies

Problem Solving Strategy PracticeDraw 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?


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?

4. The sales clerk gave Carrie $5.26 back in change when he bought the toolbox that has a volume of 1,920 in.3. How much money did Carrie give the clerk?

5. Samantha is having her driveway paved. 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?

12

10

14

14

8

9

10

8

$54.99

$49.99

$74.99

$59.99

20

22

21

20

Length(in.)

Width(in.)

Heigth(in.) Price

Tool Chests

SPIRALREVIEW

Spiral Review

Name Week 1

Spiral ReviewSR1© Harcourt • Grade 5

For 13–14, tell whether thetwo figures are congruentand similar, similar, or neither.

13.

14.

For 12, make an organized list tosolve.

12. Ken is making tickets for the fair.Each type of ticket will be a differentcolor. There will be adult and childtickets. There will be 1-day, 2-day,and weekly tickets. How manydifferent ticket colors will there be?

For 1–4, round each numberto the place of the underlineddigit.

1. 124,516

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.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

11. start: 10:30 P.M.elapsed time: 2 hr 20 min

Spiral Review

Name Week 2

Spiral Review© Harcourt • Grade 5

SR2

For 9–10, use the thermometerto find the temperature in °F.

9.

10.

For 12–13, find a rule. Writethe rule as an equation. Findthe missing numbers.

12. Input, x 9 15 18 21 27

Output, y 3 5 6

13. Input, a 2 3 5 6 8

Output, b 16 24 40

For 11, use the frequency table. Tell whether the statementis true or false. Explain.

Favorite Type of MusicType of Music Votes

Country 43

Rock 37

Rap 34

11. More people chose rap than rock as their favorite.

For 1–8, estimate. Then find the product.

1. 26� 7

2. 672� 4

3. 429� 6

4. 783� 3

5. 842 � 5 6. 239 � 7

7. 3 � 462 8. 1,364 � 6

°F

-15

-25

-20

Spiral Review

Name Week 3


SR3

For 7–8, find the perimeter.

7.

8.

For 11–12, classify eachfigure in as many ways as possible.Write quadrilateral, parallelogram, rhombus, rectangle, square, ortrapezoid.

11.

For 9–10, for eachexperiment, tell whetherevents A and B are equally likely ornot equally likely. If they are not equallylikely, name the event that is more likely. 9. Experiment: Spin the pointer. Event A: gray Event B: white

10. Experiment: Toss a number cubenumbered 1–6.Event A: even numberEvent B: odd number

For 1–6, divide.

1. 8 � � 512 2. 4 � � 385

3. 5 � � 247 4. 3 � � 844

5. 821 � 6 � 6. 198 � 2 �

12.

Spiral Review

Name Week 4


For 1–4, use basic facts and patterns to find the missingquotient.

1. 30 � 10

2. 540 � 90

3. 4,200 � 6

4. $15,0000 � 30

For 5–6, divide. Check your answer.

5. 32 � � 426 6. 47 � � 529

For 17–18, place thenumbers where they belongin the Venn diagram.

17. 2, 6, 3, 9, 12, 4, 15, 18, 21

18. 23, 18, 6, 25, 8, 16, 37, 9, 11

For 19–29, use properties andmental math to find the value.

19. 43 + (16 + 24)

20. 29 + 28 + 21

21. 4 � 370

22. (46 + 58) + 4

23. 10 � 6 � 2

24. 6 � 7 � 5

25. 26 + 43 + 34

26. 4 � 8 � 5

27. 6 � 34

28. 87 + 61 + 3

29. 7 � 410

For 7–16, change each unit.

7. 24 in. � ft

8. 4 c � pt

9. 24 ft � yd

10. 2 T � lb

11. 2 c � fl oz

12. 2 gal � qt

13. 6 yd � ft

14. 5,280 ft � mi

15. 4 ft � in.

16. 3 lb � oz

Multiples of 2 Multiples of 3

Numbersless than 20

Numbersgreater than 10

Spiral Review

Name Week 5


For 12–13, name any line relationships you see in each figure. Write intersecting, parallel, or perpendicular.

12.

13.

For 10–11, use the double-bar graph.

10. What two sets of data are compared in

the graph?

11. Which careers have more men than

women?

For 1–4, write the value of theunderlined digit.

1. 2.65

2. 12.81

3. 5.97

4. 3.49


5. 6.35

For 6–9, find the perimeter of each figure.

6. 7.

8. 9.

9080706050403020100

TeacherEngineer Chemist Doctor

Men

Women

Careers

Career

Spiral Review

Name Week 6


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

5. 0.42 0.309

� 2.695

6. 18.7516.049

� 12.201

For 8–10, use the picture.List all possible outcomesof each experiment.

8. tossing a penny

9. spinning the pointer

10. tossing the penny and spinningthe pointer

For 11–12, write an algebraicexpression.

11. Caroline had 37 songs inher MP3 player. She deleted someof them.

12. Forty-three increased by somenumber.

For 13–14, find the value for each expression.

13. 17 – n for n = 4

14. p + 7 for p = 12

Find the perimeter and areaof the figure. Then drawanother figure that has the same perimeter but a different area.

7.

5 cm

3 cm

Spiral Review

Name Week 7


For 1–6 estimate. Then find theproduct.

1. 0.6� 0.7

2. 2.4� 0.8

3. 25.9� 0.3

4. 7.40� 2.7

5. 0.47 � 0.62 =

6. 0.452 � 3.6 =

For 9–10, find the medianand mode.

9. 1, 2, 3, 4, 5, 2, 1, 4, 1, 6

10. 6, 8, 1, 7, 3, 6, 9

For 11–12, tell whether the figure appears to have line symmetry, rotational symmetry, both, or neither.

11. 12.

For 13–14, draw all lines of symmetry.

13. 14.

For 7–8, find the area.

7.

6 ft

14 ft

8.

7 cm

7 cm

MXENL08AWK5X_SR_WK07.indd SR7MXENL08AWK5X_SR_WK07.indd SR7 6/15/07 2:26:37 PM6/15/07 2:26:37 PM

Spiral Review

Name Week 8


SR8

For 5-6, find the volume.

5.

6.

For 11-14, write an algebraicexpression for each phrase.

11. 15 books on each of b shelves

12. 22 more than m DVDs

13. $36 shared equally among y friends

14. 18 less than r

For 15–18, evaluate each expressionfor a = 6.

15. a + 27 16. 24 � a

17. 14 � a 18. 19 – a

For 7–10, choose 5, 10, or100 as the most reasonable interval for each set of data.

7. 90, 350, 260, 185, 415

8. 7, 23, 25, 18, 11

9. 52, 76, 24, 54, 61

10. 218, 371, 882, 119, 505

For 1–4, find the quotient.

1. 6 � � 20.4 2. 4 � � 9.66

3. 23 � � 59.11 4. 53 � � 75.26

MXENL08AWK5X_SR_WK08.indd SR8MXENL08AWK5X_SR_WK08.indd SR8 6/19/07 10:41:18 AM6/19/07 10:41:18 AM

Name Week 9

Spiral Review


For 1–4, complete tofind the sum or difference.

1. 54,639� 37,840

2. 738,521� 601,994

3. 4,193� 5,570

4. 65,574� 7,321

For 5–6, estimate. Then find the sum ordifference.

5. 84,679� 39,213

6. 5,807,436� 2,789,015

For 12–15, find the meanfor 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 findthe 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 solidfigure that is described.

19. one circular face

20. six rectangular faces

21. four vertices

For 22–23, would the net make a cube.Write yes or no.

22. 23.

For 7–9, find the elapsed time.

7. start: 10:45 a.m.end: 1:00 p.m.

8. start: 4:30 p.m.end: 7:15 p.m.

9. start: 8:30 p.m.end: 11:00 p.m.

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.elapsed time: 5 hr 45 mi

1B,7B9 1,34B,B1B

B,7B3 5B,2B3

Name Week 10

Spiral Review

6050403020100

Aug Sept Oct Nov DecMonth

T-Shirt Sales

Num

ber S

old


For 1–12, estimate the product.

1. 23 � 44 2. 61 � 28

3. 57 � 214 4. 46 � 697

5. 425 � 19 6. 768 � 86

7. 61 � 926 8. 584 � 73

9. 836 � 5,927 10. 2,483 � 369

11. 82 � 9,371 12. 46 � 34,672

For 23–25, use the graph.

23. During which month were 30 T-shirts sold?

24. How many T-shirts were sold in September?

25. Describe the change in T-shirt salesbetween October and November.

For 26–28, write analgebraic expression.

26. James had $34 in his wallet.He spent some of the money.

27. Twenty-six decreased by somenumber.

28. Anna had 14 DVDs. She boughtsome more DVDs

For 29–31, find the value for eachexpression.

29. 14 + n for n = 6

30. 9p for p = 11

31. 15 – b for b = 7

For 13–22, change each unit.

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

21. 400 mm = m

22. 60 m = cm

Spiral Review

Name Week 11


For 17–19, draw circle A witha 3-centimeter radius. Labeleach of the following.

17. radius BA

18. chord CD

19. diameter FG

For 13–16, use the picture tofind the probability of eachevent.

13. pulling a 1

14. pulling a 2 or 3

15. pulling a 1 or 4

16. pulling a tile that is not 3

For 1–11, find all the factors foreach product.

1. 24

2. 16

3. 27

4. 30

5. 42

6. 8

7. 14

8. 21

9. 5

10. 12

11. 10

Find the perimeter and areaof the figure below. Then drawanother figure that has the same area but a different perimeter.

12.

6 cm

8 cm

Spiral Review

Name Week 12

1 __ 3 , 5 __

6 , 1 __

6 2 5 __

6 , 3 2 __

3 , 2 4 __

9

1 __ 3 1 __

2 5 __

7 3 __

5

4 3 __ 7 4 2 __

5

2 7 ___ 12

2 5 __ 8

3 1 __ 3 3 4 ___

12

2 2 __ 3 1 8 ___

15


For 12–17, use counters toshow all arrays for eachnumber. Write prime or composite.

12. 35

13. 9

14. 29

15. 101

16. 75

17. 55

Make a bar graph to showthe data below.

13.

For 1–6, compare.Write <, >, or = for each

1. 2.

3. 4.

5. 6.

For 7–8, write in orderfrom least to greatest.

7. 8.

For 9–10, find the volume.

9.

10.

Joe’s MarblesRed Green Blue Brown

21 16 10 23

Spiral Review

Name Week 13

6 7 ___ 10

� 1 6 ___ 10

�

5 1 __ 3 � 7 2 __

3 � 9 5 __

9 � 2 2 __

9 �

3 1 __ 4 � 6 2 __

4 �

8 3 ___ 12

�3 1 ___ 12

_

4 1 __ 8

+ 3 5 __ 8

_


SR13

For 7–8, use the thermometer tofind the temperature in °C.

7. 60

50

55

°C

8. 0

-10

-5

°C

For 12–15, write parallel,intersecting, orperpendicular for each.

12. W

XY

Z

13. PL

MO

14.

R

Q

S

15. A

D

B

C

For 9–11, use the tally table.

9. Complete the total columnin the tally table.

10. How many family vacations last 10

days?

11. Which number of family vacation days

has the greatest total?

Length of Family Vacations Days Tally Total

5

10

15

20

For 1–6, add or subtract. Thenwrite the answer in simplest form.

1. 2.

3. 4.

5. 6.


Spiral Review

Name Week 14


For 14–15, write an equation. Tell what the variable represents.

14. Brad has 28 oranges. He gives some away. He now has 11 oranges. How many oranges does Brad give away?

15. Gina divides some crackers among her 4 friends. She gives each friend 6 crackers. How many crackers did Gina have?

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.

12. Experiment: Flip a coin Event A: heads Event B: tails

13. Experiment: Pick a marble Event A: gray Event B: black

For 1–6, write each fraction as a decimal.

1. 35

2. 5

25

3. 410

4. 37

100

5. 2850

6. 2

100

For 7–9, write each decimalas a fraction in simplest form.

7. 0.35 8. 0.45 9. 0.26


10. 3 m

7 m

11.

13 in.

13 in.

Spiral Review

Name Week 15


For 10–13, classify each triangle. Write isosceles, scalene, or equilateral. Then write right, acute, or obtuse.

10. 11.

12. 13.

For 7–9, use the bar graph.

7. Which planet has the greatest number

of moons?

8. Which planet has 1 more moon than

Earth?

9. How many moons does Neptune

have?

For 1–4, solve each problem.

1. What is the value of the underlined 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.

4. Write 9,641,508 in word form.


5.

6.

Spiral Review

Name Week 16


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)

For 12–15, use the picture to find the probability of each event.

12. pulling a gray marble

13. pulling a gray or black marble

14. pulling a white or gray marble

15. pulling a blue marble

For 1–8, find the sum or difference in simplest form.

1. 25 �

210

� 2. 34 �

13

�

3. 12 �

16

� 4. 23 �

16

�

5. 34 �

12

� 6. 14 �

38

�

7. 310

� 15

� 8. 58 �

14

�

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?

10. The pet store is having a sale on dog 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?


Spiral Review

Name Week 17


For 22–25, classify each solid figure. Write prism, pyramid, cylinder, cone, or sphere.

22. 23.

24. 25.

For 18–21, use the stem-and-leaf plot.

18. How many students earned a grade

of 76?

19. How many students earned a grade between 85 and 90?

20. Which grade occurred most often?

21. What is the difference between the highest grade and the lowest grade?


1. 23 � 44 2. 61 � 28

3. 57 � 214 4. 46 � 697

5. 425 � 19 6. 768 � 86

7. 61 � 926 8. 584 � 73

9. 86 � 597 10. 243 � 36

For 11–17, change the unit.

11. 5,000 m � km

12. 8 kL � L

13. 16 m � cm

14. 36 cm � mm

15. 200 cm � m

16. 6,000 L � kL

17. 71 km � m

Grades on a Science Test

Stem Leaf

6 7 9

7 0 3 4 6 6 9

8 2 4 4 6 7 8 8 9

9 1 3 5 5 5 8

6 | 7 represents 67

Name Week 18

Spiral Review


Make a tree diagram to find the number of possible combinations.

12. Activity choicesactivity: zoo, park, museumtime: morning, afternoon, evening

For 1–4, write an equivalent fraction.

1. 12 2.

39

3. 410

4. 315

For 5–8, tell which fraction is not equivalent to the others.

5. 25

, 410

, 38

6. 512

, 48

, 24

7. 13

, 59

, 26

8. 68

, 46

, 9

12

For 13–14, find the rule to complete the function table. Then write the rule as an equation.

13. input, x 24 18 12

output, y 8 4 2

14. input, x 2 6 8

output, y 4 10 16

For 9–10, find the perimeter of each polygon. 9. 23 cm

16 cm

11 cm 11 cm

10. 9 in.

Spiral Review

Name Week 19


Find the perimeter and area of the figure. Then draw another figure that has the same perimeter but a different area.

5. For 7–9, tell if the net would make a cube. Write yes or no.

7.

8.

9.

Use the data to make a circle graph.

6. Class President ElectionName Number of Votes

Sarah 30

Ty 50

Mike 20

For 1–4, multiply.

1. 308 � 52

_

2. 649 � 37

_

3. 582 � 41

_

4. 825 � 24

_

8 in.

2 in.

Class President Election


Spiral Review

Name Week 20


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

18. y � 3 � 49 � 13 19. 25 � 17 � 48 � b

For 9–11, use the double-bar graph.

2520151050

DramaClub

ScienceClub

PoetryClub

Soccer

Activity

Activities

BoysGirls

9. How many sets of data does the graph

show? 10. Which activity has the greatest number

of girls? 11. How many more girls than boys are

signed up for drama club?


1. 85.19 � 37.48

__

2. 251.895 � 75.362

__

3. 7.081 � 6.254

__

4. 3.582 � 0.763

__

5. 0.85 0.063

� 3.572

6. 11.804 6.137

� 15.749

For 7–8, find the volume of each rectangular prism.

7.

8.

7 ft

7 ft

7 ft

Spiral Review

Name Week 21

6 5

8910

11 12

7 6 543

21

65

8910

11 12

7 6 543

21

6

5

8910

11 12

7 6 543

21

8910

11 12

7 6 543

21


For 14–19, use the figure. Name an example of each.

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

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.

11. a random sample of 500 women, ages 18–40

12. a random sample of 500 people, ages 18–40

13. a random sample of 500 adults

For 1–4, use basic facts and patterns to solve.

1. 60 � 10

2. 630 � 70

3. 7,200 � 8

4. 48,000 � 60

For 5–6, divide.

5. 24 � � 318 6. 72 � � 609

For 7–10, write the time shown on the analog clock.

7. 8.

9. 10.

Spiral Review

Name Week 22


For 14–16, find the rule to complete the function table. Then write an equation.

14. x 0 1 2 4

y 0 6 18 24

15. x 12 10 8 6 4

y 6 4 2

16. x 13 11 9 7 5

y 9 5 3

Make a list or tree diagram to find all possible combinations.

13. Sandwich choices meat: ham, turkey, roast beef cheese: American, cheddar bread: wheat, white

For 1–6, compare.

Write �, �, or � for each .

1. 57

23

2. 45

67

3. 315

313

4. 146

123

5. 334

3712

6. 212

256

For 7–8, write in order from least to greatest.

7. 56

, 712

, 25

8. 334

, 359

, 313

For 9–12, write the time for each.

9. Start: 7:38 A.M. Elapsed time: 3 hr 52 min

End:

10. Start: Elapsed time: 2 hr 31 min End: 10:25 P.M.

11. Start: 11:16 A.M. Elapsed time: 1 hr 19 min

End:

12. Start: 2:37 P.M. Elapsed time: End: 4:19 P.M.

Spiral Review

Name Week 23

8 3 9

Red Blue Green

Marble Experiment

Number of Pulls

Total


For 15–16, classify each figure in as many ways as possible. Write quadrilateral, parallelogram, square, rectangle, rhombus, or trapezoid.

15.

16.

For 12–14, use the table. The table shows the results ofa marble experiment.

12. What is the experimental probability of pulling a red marble?

13. What is the experimental probability of pulling a blue marble?

14. What is the experimental probability of pulling a green marble?

For 1–3, compare. Write �, �,

or � for each .

1. 0.754 0.734

2. 1.09 1.10

3. 10 0.909

For 4–6, order from greatest to least.

4. 1.345; 1.305; 1.354

5. 0.101; 0.110; 0.100

6. 73.806; 7.386; 73.860

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

°F

–10

10

20

30

40

50

60

70

80

90

100

0

–10

10

20

30

40

50

60

70

80

90

100

0

Spiral Review

Name Week 24


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 PullsGreen Red Orange

12. number of wins in 36 more games

GamesWins Losses

For 1–8, find the sum or difference. Write it in simplest form.

1. 2 __ 5 � 2 __

5 � 2. 1 __

8 � 3 __

8 �

3. 4 __ 9 � 1 __

9 � 4. 5 __

7 � 2 __

7 �

5. 4 ___ 12

� 6 ___ 12

� 6. 3 __ 4 � 1 __

4 �

7. 6 ___ 10

� 2 ___ 10

� 8. 8 __ 9 � 2 __

9 �

For 9–10, estimate the area of the shaded figure. Each square on the grid is 1 cm2.

9.

10.

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

Spiral Review

Name Week 25


For 20–23, draw lines of symmetry. Tell whether each figure has rotational symmetry.Write yes or no.

20. 21.

22. 23.

Make a bar graph of the data.

19.

For 1–6, write two equivalent ratios for each ratio. Use multiplication and division.

1. 2 __ 3

2. 4 to 10

3. 3:5

4. 15 ___ 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.

Stock X PriceMonth Jan Feb Mar Apr

Price $46 $65 $52 $48


Spiral Review

Name Week 26

5

3

1

x-axis

y-ax

is

6789

101112

4

2

0 2 31 4 5 7 8 9 10 11 126


Write the ordered pairs. Then graph them.

11.

Make a list or draw a treediagram to find the totalnumber of arrangements.

10. ways to pull green, yellow, and blue tiles from a bag without looking

For 1–4, solve each problem.

1. Write 690,303,520,002 in expanded form.

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.

5. 0°C to 18°C

6. �20°C to �5°C

7. �15°C to 10°C

8. 75°C to 10°C

9. 0°C to �16°C

–30

–20

–10

0

10

20

30

–30

–20

–10

0

10

20

30

°C

x 0 1 2 3 4

y 0 3 6 9 12

Spiral Review

Name Week 27

Books Students ReadBooks Students Frequency

2

3

4

5


For 19–25, write acute, right, or obtuse for each angle.

19. � AFD

20. � BFA

21. � CFD

22. � BFE

23. � DFE

24. � CFA

25. � EFC

For 16–18, use the tally table.

16. Complete the frequency column in the table.

17. How many books read have the greatest frequency?

18. What is the range of the data?

For 1–4, find the product. Write it in simplest form.

1. 1 __ 3 � 3 __

7 � 2. 2 __

3 � 1 __

5 �

3. 2 __ 5 � 3 __

4 � 4. 5 __

6 � 3 ___

10 �

For 5–8, use a reciprocal to write a multiplication problem for the division problem.

5. 1 1 __ 2 � 2 � 6. 7 ___

12 � 1 __

4 �

7. 3 3 __ 4 � 2 __

3 � 8. 5 __

8 � 1 __

4 �

For 9–15, write the appropriate metric unit to measure each.

9. length of your hand

10. height of a house

11. length of an insect

12. distance from New York to Michigan

13. length of a soccer field

14. length of a classroom

15. length of a crayon

Spiral Review

Name Week 28

67

54321

0 2 31 4 5 76x-axis

y-ax

is


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)

For 9–11, use the Fundamental Counting Principle to find the total number of outcomes.

9. choosing an outfit with blue or tan pants and a green or red shirt

10. tossing a cube labeled 1 to 6 and flipping a penny

11. using two spinners, both with four equal sections of red, blue, green, and yellow

For 1–3, write each percent as a decimal and as a fraction in simplest form.

1. 36%

2. 74%

3. 40%

For 4–6, write each fraction or decimal as a percent.

4. 12 ___ 25

5. 0.06

6. 9 ___ 20

For 7–8, find the area of each figure.

7.

8.


Name Week 29

Spiral Review


For 1–8, estimate by rounding.

1. 29.63� 18.05

2. 87.905� 38.714

3. 4.139� 7.652

4. 2.763� 0.509

5. 93.47 � 62.13

6. 11.042 � 8.765

7. 43.869 � 10.062

8. 0.654 � 0.398

For 13–16, choose the best type of graph or plot for the data.

13. number of students in 7 classrooms

14. hours people spend fishing

15. different seating sections of a stadium

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.

18.

For 9–12, write the missing time for each.

9. Start: 9:45 A.M.Elapsed time: 2 hr 45 min

End:


11. Start: 10:29 A.M.Elapsed time: 2 hr 19 min

End:

12. Start: 3:15 P.M.Elapsed time: End: 4:57 P.M.

Name Week 30

Spiral Review


For 1–4, find the product.

1. 315 � 57

_

2. 642 � 38

_

3. 493 � 62

_

4. 510 � 26

_

Draw a tree diagram to find the total number of outcomes.

9. tossing a number cube labeled 1 to 6 and tossing a coin

For 10–15, use prime or composite.

10. 7

11. 27

12. 16

13. 81

14. 19

15. 12

For 5–8, find the perimeter of each regular polygon.

5. 6.

7. 8.

Spiral Review

Name Week 31


For 1–3, name the GCF of thenumerator and denominator.

1. 8

14 2.

1232

3. 1236

For 4–6, write each fraction in simplest form.

4. 6

15 5.

1628

6. 2540

For 7–9, complete.

7. 23

= 8

8. 30

= 16

9. 4

= 1221

For 18–20, use the line plot.

18. What is the median?

19. What is the mode?

20. What is the mean?

For 21–23, match each solid figure with its net.

21. a.

22. b

23. c


10. 3.50 cm � 2.7 m �

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

3 4 5 6 7 8 9 1021

Number of Miles Run

✗✗

✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗✗✗

✗ ✗ ✗ ✗ ✗✗ ✗✗


Spiral Review

Name Week 32


For 1–11, write the common factors for each pair of numbers.

1. 10, 35

2. 8, 32

3. 7, 42

4. 15, 45

5. 12, 30

6. 9, 27

7. 13, 26

8. 16, 40

9. 21, 63

10. 4, 20

11. 18, 24

For 14–16, express the experimental probability as a fraction in simplest form.

14. 3 green sections in 18 spins.How many green sections in 24 more spins?

15. 6 red marbles out of 15 pulls.How many red marbles in 35more pulls?

16. 10 losses in 16 games.How many losses in 40 more games?

Write the ordered pairs. Then graph them.

17. x 0 1 2 3 4

y 0 3 6 9 12

For 12–13, find the volume of each rectangular prism.

12.

13.

x-axis

y-ax

is

Spiral Review

Name Week 33


For 13–14, name each transformation. Write translation, reflection, or rotation.

13.

14.

For 11–12, use the graph.

11. What scale and interval are used in the line graph?

12. How would you change the graph if the temperature for August were 80° Fahrenheit?

For 1–4, write each mixed number as a fraction.

1. 1 45 2. 2 23

3. 1 27 4. 3 38

For 5– 8, write each fractionas a mixed number.

5. 85 6. 15

13

7. 178 8. 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.

9. tile for this floor

10. wrapping paper for this box

15 ft

12 ft

20 in.8 in.

8 in.

100

80

60

40

20

0May June July Aug Sept

Month

Average Monthly Temperature (°F)

Tem

pera

ture

(°F)

Spiral Review

Name Week 34


For 15-16, write a numerical expression. Tell what the expression represents.

15. Kate had $30. She spent $8 to see a movie and $15 to buy a shirt.

16. Tyler scored 12 points in the first half of the game and 17 points in the second half of the game.

For 10–14, write a fraction to show the probability of tossing a number cube labeled 1 to 6.

10. a 3

11. an odd number

12. a prime number

13. a number greater than 4

14. a number less than 8

For 1–7, compare. Write �, �, or � for each .

1. 0.643 0.629

2. 1.517 1.538

3. 3.249 2.221

4. 7.440 7.442

5. 0.820 0.82

6. 0.137 0.13

7. 2.228 3.282


8.

9.


Spiral Review

Name Week 35


For 14–15, classify each triangle. Write isosceles, scalene, or equilateral.

14. 8 cm 5 cm

11 cm

15.

9 ft

14 ft 14 ft

Classify each triangle. Write acute, right or obtuse.

16.

For 11–13, name the most appropriate graph.

11. Which type of graph would be most appropriate to record the growth of a plant over 5 weeks?

12. Which type of graph would be most 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?


1. 68 � 24 2. 83 � 49

3. 35 � 853 4. 73 � 985

5. 568 � 31 6. 828 � 76

7. 34 � 964 8. 672 � 95


9.

37 in.

14 in.

10.

9 m

12 m

15 m

Spiral Review

Name Week 36


For 22–24, find the rule to complete the function table.Then write the rule as an equation.

22.

23.

24.

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

20. spinning white or gray

21. spinning green

For 1–6, write each fraction as a decimal.

1. 4 __ 5 2. 7 ___

20

3. 3 ___ 10

4. 84 ____ 100

5. 35 ___ 50

6. 78 ____ 100

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

For 13–17, tell the units you would use for measuring each.Write linear, square, or cubic.

13. the amount of carpet needed to cover

a floor

14. the amount of water in a bathtub

15. the amount of wrapping paper needed

to cover a box

16. the height of a picture frame

17. the width of a door

input, x 24 20 16

output, y 6 4 3

input, x 15 19 21

output, y 17 19 23

input, x 5 9 11

output, y 35 49 77


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