practiceprogress graphs for students to chart progress throughout the week suggested homework...

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HSP

HSPTEACHER EDITION Grade 4

PRACTICE Workbook

Copyright © by Harcourt, Inc.

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ISBN 13: 978-0-15-356768-1

ISBN 10: 0-15-356768-6

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1 2 3 4 5 6 7 8 9 10 073 16 15 14 13 12 11 10 09 08 07

© Harcourt • Grade 4

UNIT 1: UNDERSTAND WHOLE NUMBERS AND OPERATIONS

Chapter 1: Understand Place Value1.1 Place Value Through Hundred

Thousands ...........................................PW11.2 Model Millions ...................................PW21.3 Place Value Through Millions ............PW31.4 Compare Whole Numbers .................PW41.5 Order Whole Numbers .......................PW51.6 Problem Solving Workshop

Strategy: Use Logical Reasoning .......PW6

Chapter 2: Add and Subtract Whole Numbers2.1 Algebra: Relate Addition and

Subtraction .........................................PW72.2 Round Whole Numbers

Through Millions ................................PW82.3 Mental Math: Estimate Sums and

Differences ..........................................PW92.4 Mental Math Strategies ...................PW102.5 Problem Solving Workshop Skill:

Estimate or Exact Answer ................PW112.6 Add and Subtract to 4-Digit

Numbers ............................................PW122.7 Choose a Method .............................PW13

Chapter 3: Algebra: Use Addition and Subtraction3.1 Addition Properties ..........................PW143.2 Write and Evaluate Expressions ......PW153.3 Addition and Subtraction

Equations ..........................................PW163.4 Problem Solving Workshop

Strategy: Work Backward ................PW173.5 Patterns: Find a Rule ........................PW18

UNIT 2: MULTIPLICATION AND DIVISION FACTS

Chapter 4: Multiplication and Division Facts4.1 Algebra: Relate Operations .............PW194.2 Algebra: Relate Multiplication

and Division ......................................PW204.3 Multiply and Divide Facts

Through 5 .........................................PW214.4 Multiply and Divide Facts

Through 10 .......................................PW224.5 Multiplication Table Through 12 ....PW234.6 Patterns on the Multiplication

Table ..................................................PW244.7 Problem Solving Workshop Skill:

Choose the Operation .....................PW254.8 Algebra: Find Missing Factors .........PW26

Chapter 5: Algebra: Use Multiplication and Division Facts

5.1 Multiplication Properties .................PW275.2 Multiplication and Division

Expressions ........................................PW285.3 Order of Operations ........................PW295.4 Multiplication and Division

Equations ..........................................PW305.5 Problem Solving Workshop

Strategy: Predict and Test ................PW315.6 Explore Inequalities .........................PW325.7 Patterns: Find a Rule ........................PW33

UNIT 3: TIME, TEMPERATURE, AND DATA

Chapter 6: Time and Temperature6.1 Telling Time ......................................PW346.2 Elapsed Time .....................................PW356.3 Elapsed Time on a Calendar ............PW366.4 Algebra: Change Units of Time .......PW376.5 Problem Solving Workshop Skill:

Sequence Information .....................PW386.6 Temperature .....................................PW396.7 Explore Negative Numbers ..............PW40


Chapter 7: Collect and Organize Data7.1 Collect and Organize Data ..............PW417.2 Venn Diagrams .................................PW427.3 Find Mean, Median, and Mode ......PW437.4 Line Plots ..........................................PW447.5 Choose a Reasonable Scale .............PW457.6 Problem Solving Workshop Skill:

Make Generalizations ......................PW46

Chapter 8: Interpret and Graph Data8.1 Bar Graphs ........................................PW478.2 Make Bar and Double-Bar

Graphs ...............................................PW488.3 Circle Graphs ....................................PW498.4 Algebra: Use a Coordinate Grid ......PW508.5 Line Graphs .......................................PW518.6 Make Line Graphs ............................PW528.7 Problem Solving Workshop

Strategy: Make a Graph ..................PW538.8 Choose an Appropriate Graph ........PW548.9 Algebra: Graph Relationships .........PW558.10 Problem Solving Workshop Skill:

Identify Relationships ......................PW56

UNIT 4: MULTIPLY BY 1-DIGIT AND 2-DIGIT NUMBERS

Chapter 9: Multiply by 1-Digit Numbers9.1 Mental Math: Multiplication

Patterns .............................................PW579.2 Mental Math: Estimate Products ....PW589.3 Model 2-Digit by 1-Digit

Multiplication ...................................PW599.4 Record 2-Digit by 1-Digit

Multiplication ...................................PW609.5 Multiply 3-Digit and 4-Digit Numbers

and Money .......................................PW619.6 Multiply with Zeros ..........................PW629.7 Problem Solving Workshop Skill:

Evaluate Reasonableness .................PW63

Chapter 10: Multiply by 2-Digit Numbers10.1 Mental Math: Multiplication

Patterns .............................................PW6410.2 Multiply by Tens ...............................PW6510.3 Mental Math: Estimate Products ....PW6610.4 Problem Solving Workshop

Strategy: Solve a Simpler Problem ..PW6710.5 Model 2-Digit by 2-Digit

Multiplication ...................................PW6810.6 Record 2-Digit by 2-Digit

Multiplication ...................................PW6910.7 Multiply 2-Digit and 3-Digit

Numbers and Money .......................PW7010.8 Choose a Method .............................PW7110.9 Problem Solving Workshop Skill:

Multistep Problems ..........................PW72

UNIT 5: DIVIDE BY 1-DIGIT AND 2-DIGIT DIVISORS

Chapter 11: Understand Division11.1 Divide with Remainders ...................PW7311.2 Model 2-Digit by 1-Digit Division ...PW7411.3 Record 2-Digit by 1-Digit Division ...PW7511.4 Problem Solving Workshop

Strategy: Draw a Diagram ...............PW7611.5 Mental Math: Division Patterns ......PW7711.6 Mental Math: Estimate Quotients ..PW7811.7 Place the First Digit ..........................PW79

Chapter 12: Practice Division12.1 Problem Solving Workshop Skill:

Interpret the Remainder ..................PW8012.2 Divide 3-Digit Numbers

and Money .......................................PW8112.3 Zeros in Division ...............................PW8212.4 Choose a Method .............................PW83

Chapter 13: Divide by 2-Digit Divisors13.1 Mental Math: Division Patterns ......PW8413.2 Model Division by 2-Digit Divisors ..PW8513.3 Record Division .................................PW8613.4 Correcting Quotients .......................PW8713.5 Problem Solving Workshop Skill:

Too Much/Too Little Information ....PW88


Chapter 14: Number Theory and Patterns14.1 Factors and Multiples .......................PW8914.2 Divisibility Rules ...............................PW9014.3 Prime and Composite Numbers ......PW9114.4 Number Patterns ..............................PW9214.5 Problem Solving Workshop

Strategy: Find a Pattern ...................PW93

UNIT 6: FRACTIONS AND DECIMALS

Chapter 15: Understand Fractions and Mixed Numbers

15.1 Read and Write Fractions ................PW9415.2 Model Equivalent Fractions .............PW9515.3 Compare and Order Fractions .........PW9615.4 Read and Write Mixed Numbers .....PW9715.5 Compare and Order Mixed

Numbers ............................................PW9815.6 Problem Solving Workshop Skill:

Sequence Information .....................PW99

Chapter 16: Add and Subtract Fractions and Mixed Numbers

16.1 Model Addition ..............................PW10016.2 Model Subtraction .........................PW10116.3 Record Addition and

Subtraction .....................................PW10216.4 Problem Solving Workshop

Strategy: Write an Equation ..........PW10316.5 Add and Subtract Mixed

Numbers ..........................................PW10416.6 Model Addition and Subtraction

of Unlike Fractions .........................PW105

Chapter 17: Understand Decimals and Place Value

17.1 Relate Fractions and Decimals ......PW10617.2 Decimals to Thousandths ...............PW10717.3 Equivalent Decimals .......................PW10817.4 Relate Mixed Numbers and

Decimals ..........................................PW10917.5 Compare and Order Decimals .......PW11017.6 Problem Solving Workshop Skill:

Draw Conclusions ...........................PW111

Chapter 18: Add and Subtract Decimals and Money

18.1 Round Decimals ..............................PW11218.2 Estimate Decimal Sums and

Differences ......................................PW11318.3 Model Addition ..............................PW11418.4 Model Subtraction .........................PW11518.5 Record Addition and Subtraction .PW11618.6 Make Change .................................PW11718.7 Problem Solving Workshop

Strategy: Compare Strategies ........PW118

UNIT 7: GEOMETRY

Chapter 19: Lines, Rays, Angles, and Plane Figures19.1 Points, Lines, and Rays ...................PW11919.2 Measure and Classify Angles .........PW12019.3 Line Relationships ..........................PW12119.4 Polygons ..........................................PW12219.5 Classify Triangles ............................PW12319.6 Classify Quadrilaterals ...................PW12419.7 Circles ..............................................PW12519.8 Problem Solving Workshop

Strategy: Compare Strategies ........PW126

Chapter 20: Motion Geometry20.1 Congruent and Similar Figures .....PW12720.2 Turns and Symmetry ......................PW12820.3 Transformations .............................PW12920.4 Problem Solving Workshop

Strategy: Act It Out ........................PW13020.5 Tessellations ....................................PW13120.6 Geometric Patterns ........................PW132

Chapter 21: Solid Figures21.1 Faces, Edges, and Vertices .............PW13321.2 Draw Figures ..................................PW13421.3 Patterns for Solid Figures ..............PW13521.4 Different Views of Solid Figures ...PW13621.5 Problem Solving Workshop

Strategy: Make a Model ................PW13721.6 Combine and Divide Figures .........PW138


UNIT 8: MEASUREMENT AND PROBABILITY

Chapter 22: Customary and Metric Measurement 22.1 Measure Fractional Parts .............PW13922.2 Algebra: Change Customary

Linear Units ..................................PW14022.3 Weight ..........................................PW14122.4 Customary Capacity .....................PW14222.5 Problem Solving Workshop

Strategy: Compare Strategies .....PW14322.6 Metric Length ...............................PW14422.7 Algebra: Change Metric

Linear Units ..................................PW14522.8 Mass ..............................................PW14622.9 Metric Capacity ............................PW14722.10 Problem Solving Workshop

Strategy: Make a Table ................PW148

Chapter 23: Perimeter, Area, and Volume23.1 Estimate and Measure

Perimeter ......................................PW14923.2 Algebra: Find Perimeter ..............PW15023.3 Area of Plane Figures ..................PW15123.4 Algebra: Find Area .......................PW15223.5 Problem Solving Workshop Skill:

Use a Formula ..............................PW15323.6 Relate Perimeter and Area ..........PW15423.7 Estimate and Find Volume of

Prisms ............................................PW155

Chapter 24: Probability24.1 List All Possible Outcomes ...........PW15624.2 Problem Solving Workshop

Strategy: Make an Organized List ..............................PW157

24.3 Predict Outcomes of Experiments ..................................PW158

24.4 Probability as a Fraction ..............PW15924.5 Experimental Probability .............PW16024.6 Combinations and

Arrangements ..............................PW161

SPIRAL REVIEWWeek 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

My Homework Progress

0

2

4

68

10

ThuWed Tue Mon

Number of Problems Assigned

Number of Problems Correct

Day

Num

ber o

f Pro

blem

s

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 problems 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

mb

er of

Prob

lems

Assig

ned

Nu

mb

er of

Prob

lems

Co

rrect

My H

om

ewo

rk Prog

ress

Number of Problems

109876543210M

on

Tue

Wed

Thu

Day


Lesson 1.1Item Suggested rationale

2numbers through hundred thousands

3numbers through hundred thousands

6expanded form and place value

9 value of underlined digit

12writing numbers in multiple forms

13 multiple choice; place value


1 multiples of thousands

4 multiples of hundreds

7recognize situations where numbers are less than a million

11recognize situations where numbers are large enough to be a million

19digits in the ten-thousands place

20numbers with different numbers of digits

25numbers with the same number of digits

PracticePW1© Harcourt • Grade 4

Place Value Through Hundred ThousandsWrite each number in two other forms.

1. 50,000 � 3,000 � 700 � 5

2. eight hundred thousand, nine hundred thirty-seven

3. 420,068

4. 78,641

Complete.

5. 290,515 � two hundred ninety , five hundred fifteen � � 90,000 � � 10 � 5

6. � 10,000 � 3,000 � 100 � 80 � 9 � 413,1 �

four hundred thirteen thousand, one eighty-nine

Write the value of the underlined digit in each number.

7. 705,239

8. 417,208

9. 914,325

10. 360,044

Problem Solving and Test Prep11. In 2005, there were 20,556 Bulldogs

registered in the American Kennel Club. Write the number of registered Bulldogs in two other forms.

12. In 2005, the Labrador Retriever was the most popular breed of dog in the American Kennel Club, with 137,867 registered Labrador Retrievers. Write 137,867 in two other forms.

13. What is the value of the digit 9 in 390,215?

A 900B 9,000C 90,000D 900,000

14. In February, eighty-five thousand, six hundred thirteen people went to the Westminster Dog Show. What is this number in standard form?

A 850,630 C 850,613

B 85,630 D 85,613

Name Lesson 1.1

Circled problems are suggested homework problems.

53,705; fifty-three thousand, seven hundred five

800,937; 800,000 � 900 � 30 � 7

four hundred twenty thousand, sixty-eight; 400,000 � 20,000 � 60 � 8

seventy-eight thousand, six hundred forty-one; 70,000 � 8,000 � 600 � 40 � 1

thousand

89

5,000 10,000 20 4

20,000 � 500 � 50 � 6; twenty thousand, five hundred fifty-six

one hundred thirty-seven thousand, eight hundred sixty-seven; 100,000 � 30,000 � 7,000 � 800 � 60 � 7

500200,000

hundred400,000

C

D


Model MillionsSolve.

1. How many hundreds are in 100,000?

3. How many thousands are in 1,000,000?

5. How many hundreds are in 1,000,000?

2. How many thousands are in 10,000?

4. How many hundreds are in 10,000?

6. How many thousands are in 100,000?

Tell whether the number is large enough to be in the millions or more. Write yes or no.

7. the number of people at a baseball stadium for one game

9. the number of leaves on the trees in a forest

11. the number of cars people own in the United States

13. the number of bags of trash a family makes in one month

15. the number of fourth graders in the United States

17. the number of gallons of water in the ocean

8. the distance in miles to the nearest star outside our solar system

10. the distance in feet across a swimming pool

12. the number of trips a bus might make in one day

14. the distance in miles from one city to another in your state

16. the number of miles from the Earth to the Moon

18. the number of stars in the solar system

Choose the number in which the digit 5 has the greater value.

19. 435,767 or 450,767

20. 510,000 or 5,100,000

21. 125,000,000 or 521,000,000

22. 435,003 or 4,300,500

23. 1,511,672 or 115,672

24. 40,005,400 or 350,400,300

25. 135,322,000 or 9,450,322

26. 35,000,000 or 3,500,000

Name Lesson 1.2

1,000 thousands

1,000 hundreds 10 thousands

100 hundreds

10,000 hundreds 100 thousands

no

no

yes

yes yes

no

no

no

no

yes

450,767 5,100,000

521,000,000

1,511,672

435,003

350,400,300

135,322,000 35,000,000


yes

yes

PW1-PW2© Harcourt · Grade 4

MXENL08AWK4X_PHTE_Rat.indd PW1-PW2MXENL08AWK4X_PHTE_Rat.indd PW1-PW2 6/19/07 3:11:41 PM6/19/07 3:11:41 PM


2numbers through one-hundred million

3numbers through one-hundred million

7 place value through millions

11word problem; place value through ten thousands

13multiple choice; place value in the ten millions place


8comparing hundred thousands; equal number of digits

10comparing millions; unequal number of digits

12comparing millions; unequal number of digits

14algebra; place value; find missing digit

16use a table to compare value in ten thousands

19multiple choice; comparing value in hundreds


Place Value Through MillionsWrite each number in two other forms.

1. ninety-five million, three thousand, sixteen

2. four hundred eighty-five million, fifty-two thousand, one hundred eight

3. 507,340,015

4. 20,000,000 � 500,000 � 60,000 � 1,000 � 300 � 40

Use the number 78,024,593.

5. Write the name of the period that has the digits 24.

6. Write the digit in the ten millions place.

7. Write the value of the digit 8.

8. Write the name of the period that has the digit 5.

Find the sum. Then write the answer in standard form.

9. 7 thousands 3 hundreds 4 ones � 8 ten thousands 1 thousand 5 hundreds

Problem Solving and Test Prep10. The average distance from the Earth to

the Sun is 92,955,807 miles. What is the value of the digit 2 in 92,955,807?

11. The average distance from the Earth to the Sun is one hundred forty-nine million, six hundred thousand kilometers. Write this number in standard form.

Name Lesson 1.3

12. What is the value of the digit 8 in 407,380,510?

A 8,000,000 C 80,000B 800,000 D 8,000

13. What is the value of the digit 4 in 43,902,655?

A 400,000 C 40,000,000B 4,000,000 D 400,000,000

95,003,016; 90,000,000 � 5,000,000 � 3,000 � 16

485,052,108; 400,000,000 � 80,000,000 � 5,000,000 � 50,000 � 2,000 � 100 � 8

five hundred seven million, three hundred forty thousand, fifteen; 500,000,000 � 7,000,000 � 300,000 � 40,000 � 15

twenty million, five hundred sixty-one thousand, three hundred forty; 20,561,340

thousands 7

8,000,000 ones

88,804

2,000,000 149,600,000


C C


Compare Whole NumbersUse the number line to compare. Write the lesser number.

1. 3,660 or 3,590

2. 3,707 or 3,777

3. 3,950 or 3,905

Compare. Write <, >, or = for each .

4. 5,155 5,751 5. 6,810 6,279 6. 45,166 39,867

7. 74,288 74,288 8. 891,023 806,321 9. 673,219 73,551

10. 3,467,284 481,105 11. 613,500 1,611,311 12. 4,000,111 41,011

ALGEBRA Find all of the digits that can replace each �.

13. 781 � 78�

14. 2,4�5 � 2,465

15. �,119 � 9,119

Problem Solving and Test PrepUSE DATA For 16–17, use the table.

16. Which mountain is taller: Mt. Logan or Mt. McKinley?

17. Which mountain is taller than 29,000 feet?

18. Which number is greatest?

A 34,544

B 304,544

C 43,450

D 345,144

19. Ernie wants to collect 140 books each week for the school book drive. In each of four weeks, he collected 147 books, 129 books, 163 books, and 142 books. Which number of books was less than Ernie’s weekly goal?

A 147 books C 129 books

B 163 books D 142 books

Name Lesson 1.4

3,500 3,600 3,700 3,800 3,900 4,000

Tallest Mountains

Mountain Height (in feet)

Everest 29,028

McKinley 20,320

Logan 19,551

3,590 3,707 3,905

� � �

� � �

� � �

0, 2, 3, 4, 5, 6, 7, 8, 9

0, 1, 2, 3, 4, 5, 7, 8, 9 1, 2, 3, 4, 5, 6, 7, 8

Mt. McKinley

Mt. Everest


D

C




2ordering millions, equal numbers of digits

3ordering hundred thousands, equal number of digits

7ordering numbers with unequal numbers of digits

14word problem; comparing dollar amounts in the hundred thousands


2problem Solving: logical reasoning

3problem solving; make a model

4problem solving: guess and check


Order Whole NumbersWrite the numbers in order from greatest to least.

1. 74,421; 57,034; 58,925

2. 2,917,033; 2,891,022; 2,805,567

3. $409,351; $419,531; $417,011

4. 25,327,077; 25,998; 2,532,707

5. 621,456; 621,045,066; 6,021,456

6. $309,423; $305,125; $309,761

7. 4,358,190; 4,349,778; 897,455

8. 5,090,115; 50,009,115; 509,155

ALGEBRA Write all of the digits that can replace each �.

9. 389 � 3�7 � 399

10. 5,601 � 5,�01 � 5,901

Problem Solving and Test Prep USE DATA For 11–12, use the table.

11. Which lake has the smallest area?

12. Write the names of the lakes in order

from least area to the greatest area.

13. Which shows the numbers in order from greatest to least?A 92,944; 92,299; 92,449

B 159,872; 159,728; 159,287

C 731,422; 731,242; 731,244

D 487,096; 487,609; 487,960

14. Automobile sales for four weeks are $179,384, $264,635, $228,775, and $281,413. Which amount is the greatest?

Name Lesson 1.5

Largest Lakes

Lake Area(in square miles)

Victoria 26,828

Huron 23,000

Superior 31,700

Caspian Sea 143,244

74,421; 58,925; 57,034 2,917,033; 2,891,022; 2,805,567

25,327,077; 2,532,707; 25,988$419,531; $417,011; $409,351

$309,761; $309,423; $305,125

621,045, 066; 6,021,456; 621,456

4,358,190; 4,349,778; 897,455

50,009,115; 5,090,115; 509,155

9 7, 8

Lake Huron

Lake Huron, Lake Victoria, Lake Superior, The Caspian Sea

$281,413Circled problems are suggested homework problems.

B


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

1. The stadium store sells team shirts on Friday, Saturday, and Sunday. The numbers of shirts sold for three days were 473, 618, and 556. The least number of shirts were sold on a Friday. More than 600 shirts were sold on Saturday. How many shirts were sold on Sunday?

2. Anton, Rachel, and Lamont each like different teams. The teams are the Rugby Ghosts, the Yellow Bees, and the Tan Cougars. Anton’s favorite team does not have a color in its name. Lamont does not like the Tan Cougars. Which team does Rachel like?

Mixed Strategy Practice 3. Beth, Paulo, Lee, Maya, and Rob are

standing in line to get into the movies. Beth is in front of Maya. Maya is not last in line. Rob is first. Lee is after Maya. Paulo is not last. In what order are they standing in line? Make a model in the box at the right to solve.

USE DATA For 4–5, use the information shown in the art.

4. Claire buys two items. She spends less than $100 total. Which two items does Claire buy?

5. Alex plans to save money to buy the hockey stick. He already has $8 in his savings. If he saves and adds $22 each week to his savings, how many weeks will it take to save $72?

Name Lesson 1.6

$72

$79

$34$54

556 shirts the Tan Cougars

Rob, Paulo, Beth, Maya, Lee

baseball glove and soccer ball

3 weeksCircled problems are suggested homework problems.

MXENL08AWK4X_PHTE_C01_L6.indd PW6 7/2/07 10:23:18 AM


MXENL08AWK4X_PHTE_Rat.indd PW5-PW6MXENL08AWK4X_PHTE_Rat.indd PW5-PW6 7/2/07 11:58:07 AM7/2/07 11:58:07 AM


1 write a related fact




11 write fact families

13problem solving; write related facts

15multiple choice; recognizing a related fact


2rounding money to thousands place

4 rounding to hundreds

5rounding to hundred thousands

6 rounding to millions

8rounding larger numbers to multiple places

10rounding to millions using a chart

12multiple choice; rounding to ten thousands by choosing from a list


Algebra: Relate Addition and SubtractionWrite a related fact. Use it to complete the number sentence.

1. � 7 � 8

2. 4 � � 13

3. � 9 � 14

4. 8 � � 11

5. � 4 � 8

6. 17 � � 9

7. � 5 � 5

8. 13 � � 5

9. � 7 � 16

Write the fact family for each set of numbers.

10. 6, 8, 14

11. 7, 5, 12

12. 9, 6, 15

Problem Solving and Test Prep13. Byron can do 12 pull-ups. Malik can

do 7 pull-ups. How many more pull-ups can Byron do than Malik? What related facts can you use to solve this problem?

14. Jim can do 16 pull-ups. Andy can do 11 pull-ups. Selma can do more pull-ups than Andy but fewer than Jim. What are the possible number of pull-ups that Selma could have done?

15. Which of the following sets of numbers cannot be used to make a fact family?

A 25, 10, 15 C 15, 9, 6

B 2, 2, 4 D 7, 3, 14

16. Which of the following sets of numbers can be used to make a fact family?

A 5, 6, 11 C 7, 6, 12

B 11, 12, 13 D 19, 9, 11

Name Lesson 2.1

7 � 8 � 15 13 � 4 � 9 14 � 9 � 5

11 � 8 � 3 8 � 4 � 12 17 � 9 � 8

5 � 5 � 10 13 � 5 � 8 16 � 7 � 9

6 � 8 � 14;

8 � 6 � 14;

14 � 8 � 6;

14 � 6 � 8

7 � 5 � 12;

5 � 7 � 12;

12 � 5 � 7;

12 � 7 � 5

9 � 6 � 15;

6 � 9 � 15;

15 � 6 � 9;

15 � 9 � 6

5 more pull-ups;

12 � 7 � 5; 7 � 5 � 12 12, 13, 14, 15


Possible answersare given.

AD

15 9 5

8123

10 8 9



Round Whole Numbers Through MillionsRound each number to the place value of the underlined digit.

1. 7,803

2. $4,097

3. 23,672

4. 627,432

5. 34,809,516

6. 671,523,890

Round each number to the nearest ten, thousand, hundred thousand, and million.

7. 6,086,341

8. 79,014,878

9. 821,460,934


10. Which state has a population that rounds to 5,700,00?

11. What is the population of Maryland rounded to the nearest thousand?

12. Which number rounds to 45,000?

A 44,399 C 44,890

B 44,098 D 45,987

13. To which place do you round to find the rounded number that is closest to 9,760,000?

Name Lesson 2.2

79,014,880; 79,015,000; 79,000,000;79,000,000

821,460,930; 821,461,000; 821,500,000;821,000,000

8,000 $4,000 20,000

627,400 34,800,000 672,000,000

6,086,340; 6,086,000; 6,100,000; 6,000,000

Tennessee

5,296,000

ten thousands


C





2rounding to estimate differences

3 rounding to estimate sums

6font-end estimation to estimate differences

7font-end estimation to estimate sums

11 using compatible numbers

13 adjusting the estimate

15problem solving; adding by estimating in the ten thousands

17multiple choice; estimate in the ten thousands


2subtracting mentally using friendly numbers

4adding mentally using friendly numbers

5adding mentally using friendly numbers

7 subtracting using swapping

9subtracting using friendly numbers

19multiple choice; adjust the addends; explaining how to use swapping

20multiple choice; choosing the correct adjustment to find the sum


Mental Math: Estimate Sums and DifferencesUse rounding to estimate.

1. 6,356 � 1,675

__

2. 8,267 – 2,761

__

3. 3,818,707 � 2,978,392

___

4. 75,428 – 19,577

__

Use front-end estimation to estimate.

5. 187 � 519

__

6. 6,489 � 1,807

__

7. 2,314,655 � 5,901,683

___

8. 61,075 � 29,732

__

Use compatible numbers to estimate.

9. 5,432 � 652

10. 45,221 � 6,167

11. 392 � 47 � 89

Adjust the estimate to make it closer to the exact sum or difference.

12. 6,285 � 2,167

Estimate: 8,000

13. 42,819 � 11,786

Estimate: 30,000

14. 17,835 � 45,199

Estimate: 65,000

Problem Solving and Test Prep 15. Steve travels abroad to visit a friend

and then comes back home. He travels 10,945 miles one way. About how far does Steve travel round trip?

17. A plane flies 13,867 miles in one week. The next week it flies 9,276 miles. Which is the best estimate of how many miles the plane flew in these two weeks?

A 23,000 miles C 15,000 miles

B 40,000 miles D 16,000 miles

16. A train travels 5,742 miles this week. Last week it traveled 1,623 fewer miles than this week. About how many miles did the train travel last week?

18. Last month, Chad sold 523 CDs at his store. This month, he sold 167 more CDs than last month. About how many CDs in all did Chad sell this month and last month? Explain how you got your answer.

Name Lesson 2.3

8,000 5,000 7,000,000 55,000

600 5,000 7,000,000 40,000

5,000 � 700 � 4,300

45,000 � 6,000 � 51,000

400 � 50 � 100 � 550

6,300 � 2,200 � 8,500

43,000 � 12,000 � 31,000

18,000 � 45,000 � 63,000

Possible answer: about 4,000 miles

about 1,200 CDs; Possible answer: I rounded 523 to 500 and 167 to 200. 500 + 200 = 700. 500 + 700 = about 1,200 CDs.

Possible estimates are given.



Possible answer: about 22,000 miles

A




Mental Math StrategiesAdd or subtract mentally. Tell the strategy you used.

1. 73 � 15

2. 87 � 48

3. 57 � 91

4. 152 � 68

5. 542 � 148

6. 515 � 151

7. 799 � 231

8. 387 � 73

9. 945 � 425

10. 452 � 339

11. 396 � 265

12. 594 � 496

Find the sum or difference.

13. 78 � 46

14. 61 � 16

15. 40 � 24

16. 37 � 19

Problem Solving and Test Prep

17. Vicky has 32 baseball cards and29 soccer cards. Use mental math to find how many sports cards Vicky has in all.

18. Kareem bowls 78 the first game and 52 the second game. Use mental math to find the difference of Kareem’s scores.

19. Jason sells 27 tickets on Monday and 34 on Tuesday. He adds 3 to 27 to find the total mentally. How should Jason adjust the sum to find the total?

A Add 3 to 34.

B Add 4 to 34.

C Subtract 3 from 34.

D Subtract 4 from 34.

20. Haley buys a baseball bat and glove that cost $25 and $42. She subtracts $2 from $42 to find the total mentally. How should Haley adjust the sum to find the total?

A Add $2 to $25.

B Subtract $2 from $25.

C Add $5 to $25.

D Subtract $5 from $25.

Name Lesson 2.4


88 39 148 84

690 364 568 460

520 791 661 98

61 sports cards 26

124 45 64 18

CB

Strategies may vary.




1 exact answer or estimate



8 multi-step problem


3 regrouping twice

4 regrouping twice

5regrouping hundreds, tens, and ones

8regrouping hundreds, tens, and ones

17 algebra involving regrouping

23multiple choice; subtracting by regrouping

24problem solving; subtracting by regrouping


Problem Solving Workshop Skill: Estimate or Exact AnswerProblem Solving Skill PracticeExplain whether to estimate or find an exact answer. Then solve.

1. A plane has 5 seating sections that can hold a total of 1,175 passengers. Today, the sections held 187, 210, 194, 115, and 208 passengers. Was the plane filled to capacity?

2. A small plane carries 130 gallons of fuel. It needs 120 gallons to fly a 45-mile trip. Does the pilot have enough fuel to make a 45-mile trip?

3. A movie theater has a total of 415 seats. There are 187 adults and 213 children seated in the theater. How many empty seats are there in the theater?

4. Bob drives 27 miles round trip each day for three days. Has Bob traveled more or less than 250 miles?

Mixed Applications 5. The movie theater sells 213 tickets on

Monday, 187 tickets on Tuesday, and 98 tickets on Wednesday. Are there more than, or less than 600 tickets sold for all three days.

6. The movie theater sells 209 tickets for “Canyon Trail” and 94 tickets for “A Light in the Sky”. How many more tickets are sold at the theater for “Canyon Trail” than for “A Light in the Sky”?

7. Sara sells 87 tickets for a school benefit. Josh sells 43 tickets. Marc sells 28 tickets. How many more tickets does Sara sell than Marc and Josh sell altogether?

8. A stamp album contains 126 stamps. Another album contains 67 stamps. Each album can hold up to 150 stamps. How many stamps do both albums contain altogether?

Name Lesson 2.5

Exact; No, there were only 914 passengers.

Estimate; yes

Estimate; Less, Bob has traveled about 90 miles.

less than 600 tickets sold 115 more tickets

Exact; 15 empty seats

16 more tickets 193 stamps

Circled problems are suggested homework problems.PracticePW12


Add and Subtract 3-Digit and 4-Digit NumbersEstimate. Then find the sum or difference.

1. 414 � 727

__

2. 784 � 149

__

3. 5,305 � 848

__

4. 7,322 � 616

__

5. 2,673 � 4,548

__

6. 3,357 � 1,219

__

7. 8,452 � 2,621

__

8. 9,344 � 5,667

__

9. 4,955 � 978

__

10. 9,999 � 901

__

11. 7,593 � 1,475

__

12. 8,891 � 1,490

__

13. 3,069 � 956

__

14. 6,560 � 5,699

__

15. 1,948 � 1,052

__

16. 7,326 � 2,673

__

ALGEBRA Find the missing digit.

17. 9 8 � 247

__

1,175

18. 7,895

� 1,23

__

6,661

19. ,689 � 726

__

3,963

20. 1,357

� 7 6

__

2,113

Problem Solving and Test Prep21. Jan drove 324 miles on Monday, then

483 miles on Tuesday. How many miles did Jan drive in all?

22. A baseball team scores 759 runs in a season. The next season the team scores 823 runs. How many runs does the team score in all?

23. An airplane will fly a total of 4,080 miles this trip. The plane has flown 1,576 miles so far. How many more miles will the plane fly this trip?

A 2,504

B 2,514 C 2,594D 5,656

24. There are 5,873 soccer fans at the first game. There are 3,985 fans at the second game. How many more fans are at the first game? Explain.

Name Lesson 2.6

1,100; 1,141 700; 635 6,000; 6,153 6,000; 6,706

3,000; 3,677 5,000; 5,831 8,000; 7,221 4,000; 4,576

6,000; 5,933 9,000; 9,098 9,000; 9,068 8,000; 7,401

4,000; 4,025 1,000; 861 1,000; 896 10,000; 9,999

54

42

807 miles 1,582 runs

1,888 more fans; I subtracted 3,985 from 5,873 to get my answer.



A





2 mental math

3 paper and pencil or calculator

5 mental math

7 paper and pencil or calculator

9algebra; regroup to find the sum

13problem solving; subtract using mental math

16multiple choice; addition using paper and pencil


2 use the commutative property

5 use the identity property

6 use the associative property

9use the commutative and associative properties

11problem solving using a table; use the associative property

12problem solving using a table; use the commutative and associative properties

13problem solving; use commutative and associative properties


Choose a MethodFind the sum or difference. Write the method you used.

1. 256,684 � 157,925

__

2. 845,002 � 32,000

__

3. 5,369,021 � 1,488,627

___

4. 390,451 � 189,693

__

5. 4,244,500 � 110,001

___

6. 7,056,634 � 869,378

___

7. 5,351,842 � 1,409,876

___

8. 6,411,809 � 411,809

___


9. 32 ,164 � 651,247

__

974,411

10. 722, 85 � 134,761

__

588,124

11. 314,678

� 1 2,657

__

182,021

12. 7,1 9,236 � 1,292,459

___

8,481,695

Problem Solving and Test Prep13. Jupiter’s moon, Callisto, is

1,883,000 kilometers away from Jupiter. Jupiter’s other moon, Ganymede, is 1,070,000 kilometers away from Jupiter. What is the difference of these two distances?

14. Jessie scores 304,700 points in a video game. Raquel scores294,750 points. How many more points does Jessie score than Raquel scores?

15. Last year, 456,197 fans attended a minor league’s baseball games. This year, 387,044 fans attended. What is the total number of fans that attended this year and last year all together?

16. Plane A travels 108,495 miles. Plane B travels 97,452 miles. How many miles do both planes travel in all?

A 195,847 miles

B 205,847 miles

C 205,887 miles

D 205,947 miles

Name Lesson 2.7

414,609 6,857,648813,002 200,758

4,354,501 7,926,012 3,941,966 6,000,000

3 83

8

813,000 kilometers 9,950 points

843,241 fans


Methods may vary.

D



Addition PropertiesFind the missing number. Name the property you used.

1. � � 0 � 0 � 23 2. 15 � 5 � � � 15 3. 12 � (2 � 7) � (� � 2) � 7

4. � � 7 � 7 � 36 5. � � 45 � 45 � 0 6. (22 � �) � 11� 22 � (44 � 11)

Change the order or group the addends so that you can add mentally. Find the sum. Name the property you used.

7. 120 � 37 � 280

8. 25 � 25 � 30

9. 60 � 82 � 40

10. 28 � 21 � 32 � 19


11. Use the Associative Property to find the total number of marbles in Sam’s collection.

12. Sam buys another 15 Shooter Stripes. How many marbles are in Sam’s collection now?

13. Joe has 12 blue marbles, 13 red marbles, and 38 green marbles. Explain how to use addition properties to find the total number of marbles Joe has. Then solve the problem.

14. Luke has 150 green marbles, 22 yellow marbles, 48 blue marbles, and 40 red marbles. Explain how to use addition properties to find the total number of marbles Luke has. Then solve the problem.

Name Lesson 3.1

Blue Chinese Checkers

Cat’s Eyes

Speckled Spots

Shooter Stripes

32

81

18

59

Type Number

Sam’s Marble Collection

23, identity 5, commutative 12, associative

36, commutative 0, identity 44, associative

(120 � 280) � 37 � 437 (25 � 25) � 30 � 80

(60 � 40) � 82 � 182 (28 � 32) � (21 � 19)� 100

190 marbles

205 marbles

Commutative Property to re-order, the Associative Property to add; 63 marbles

Commutative Property to re-order, then the Associative Property to add 260 marbles


Possible answers are shown. Properties may vary.




2practice evaluating expressions



11 practice writing expressions

12 practice writing expressions

15practice writing situations to match expressions

16practice writing situations to match expressions

17multiple choice; finding an expression to match the variables in a word problem


1practice writing equations when given words

3practice solving a subtraction equation

6practice solving an addition equation

8practice writing situations to match equations

12problem solving; practice writing and solving equations

13multiple choice; finding an equation from a word problem


Write and Evaluate ExpressionsFind the value of each expression.

1. 12 � (4 � 3)

2. 5 � (15 � 3)

3. 17 � � if � � 8

4. 5 � (m � 2) if m �12

5. (18 � 22)�15

6. (31 � 16) � 8

7. � � 25 if � = 9

8. b � (31 � 5) if b � 52

Write an expression with a variable. Tell what the variable represents.

9. Sally gave away 5 apples.

10. Ali had 9 fish and bought some more.

11. Theresa put $15 in her bank account.

12. Glenn gave away some of his 20 pins.

Write an expression to match the words.

13. Bob has some stamps. He gave Sam 5 stamps.

14. Todd caught 12 crickets. He then caught some more.

Problem Solving and Test Prep15. Sean gave away 20 hats. He gave

some hats to his brother. Write an expression to show how many hats Sean gave to his brother.

16. What is the value of the expression 15 � (c � 3) if c � 5?

17. Edie ran 2 miles more than Joan. Which expression shows how far Joan ran?

A e � 2 C e � 3

B 2 � e D e � 2

18. There are 6 kittens in a closet. The mother cat removes 3 kittens. Write an expression that shows the number of kittens left in the closet. How many kittens are left in the closet?

Name Lesson 3.2

9 15

1634725

a � number of apples Sally had; a � 5

f � number of fish Ali bought; 9 � f

m � former amount of money in Theresa’s bank account; m � $15

p � number of pins Glen gave away; 20 � p

Possible answer: h � number of hats he gave to his brother; 20 � h

7

5 17

6 � 3 � 3; 3 leftCircled problems are suggested homework problems.

D

t � 5 12 � k


Addition and Subtraction EquationsWrite an equation. Use �, �, or � for each .

1. Rickie has 15 model cars. Some are red, a, and 8 are blue.

15 a 8

2. Wendy had $12. Her mother gave her some more money, a. Now she has $17.

$12 a $17

Solve the equation.

3. 19 � 4 � n

4. 6 � � � 19

5. r � 12 � 21

6. t � 14 � 31

Write words to match the equation.

7. b � 5 � 12 8. a � 9 � 2

9. 16 � w � 4 10. y � 7 � 29


Name Lesson 3.3

11. Thirteen dogs graduated in May. There were 5 assist dogs, 4 service dogs, and some tracking dogs. Write an equation that shows the total number of dogs that graduated in May.

12. Eight service dogs graduated in February, 5 in May, and 9 in November. Write and solve an equation that shows how many service dogs graduated in all.

13. Jed watched 10 minutes of previews

and a 50-minute movie about dogs. Which equation shows the total time Jed was in the theater?A 10 � 50 � t

B 50 � t � 10

C t � 10 � 60

D t � 10 � 50

14. Haley’s favorite picture book is 27 pages long. Eleven of the pages have pictures of dogs. The rest have pictures of birds. Which equation can be used to find how many pages have picture of birds?

A 27 � 11 � b C b � 11 � 27

B 27 � b � 16 D b � 11 � 27

n � 15 � � 13 r � 33 t � 17


Possible variables are given

Check students’ problems.

8 + 5 + 9 = d; d = 22 service dogs5 + 4 + t = 13

A

D

� � � �




1practice the work-backward strategy



6practice the draw-a-diagram strategy

7use a table to write and solve an equation


2practice defining and extending a pattern

4practice defining and extending a pattern

6 practice extending a pattern

8 finding the value of a variable

9multiple choice; translating data from a table into an equation

Name Lesson 3.4


Problem Solving Workshop Strategy: Work Backward

Problem Solving Strategy PracticeWork backward to solve.

1. Leon arrived at the preserve at 11:00 A.M. He began the morning by taking 45 minutes to feed his pets at home and driving 2 hours to get to the preserve. What time did Leon begin?

2. Kit read a 25-page book about lions. Seven pages were about hunts, 15 pages were about habitat, and the rest were about prides. How many pages were about prides?

3. Twelve lions in the pride did not go on a hunt. When the lions returned from the hunt, there were 21 lions. How many lions went on the hunt?

4. Polly ate lunch and then took 15 minutes to walk to Cher’s house. They rode bikes for 35 minutes and then studied for 20 minutes. If they finished at 2:30, when did Polly finish lunch?

Mixed Strategy Practice 5. Five prides were sent from the zoo to

a preserve. Two prides were returned. Now there are 17 prides at the zoo. How many prides were at the zoo before the 5 were sent away?

6. Red, blue, green, and brown teams lined up for their assignments. The brown team directly was ahead of the red team. The blue team was not last. The green team was first. Which team was last?

7. USE DATA Use the information in the table. Write and solve an equation that shows how many lions are in the preserve in all. Then solve for the variable.

Cubs

Adolescents

Mature

Older

18

14

2

7

Age Number

Preserve Lion Population

8:15 A.M.

9 lions

3 pages

1:20 P.M.

the red team20 prides

18 � 14 � 2 � 7 � p; p � 41


Name Lesson 3.5


Patterns: Find a RuleFind a rule. Write your rule as an equation. Use the equation to extend your pattern.

1.

2.

3.

4.

Use the rule and equation to make an input/output table.

5. Add 7 to m.m � 7 � n

6. Subtract 14 from a.a � 14 � b


7. A figure is made of a row of squares. One square has a perimeter of 4. Two squares has a perimeter of 6, and so on. Finish the input-output table to show the pattern.

8. If a rule for a table is written as an equation as a � 6 � b, then what is the value of b if a equals 24?

9. Which equation describes the data in

the table?

A d � 13 � c C c � 13 � d

B c � 13 � d D d � 13 � c

10. What equation describes the data in the table?

A g � 5 � h C g � 4 � h

B g � 4 � h D g � h � 2

Input f 10 15 20 25 30

Output g 5 10 15 � �

Input c 88 86 84 � �Output d 66 64 62 60 58

Input s � � 9 12 15

Output t 70 66 62 58 54

Input x 15 14 13 12 11

Output y � � 28 27 26

Input m � � � �Output n � � � �

Input a � � � �Output b � � � �

Input s 1 2 3 4 5

Output p 4 6 � � �

Input c 0 2 3 4

Output d 13 15 16 17

Input g 1 3 5 7

Output h 5 7 9 11

subtract 5 from f; f � 5 � g; 20, 25

subtract 22 from c; c � 22 � d; 82, 80

add 53 to s; s � 53 � t; 17, 13

add 15 to x; x � 15 � y; 30, 29

Check students’ input/output tables.

8, 10, 12 30


B C

Possible rules are given.




2relate repeated addition and multiplication

3relate repeated subtraction and division

5relate multiplication and addition

6relate multiplication and addition

7 problem solving; division

10 multiple choice; division


2 understand fact families

3 understand fact families

6find the value of a variable and relate operations

11find the value of a variable and relate operations

13problem solving; multiplication

16 multiple choice; multiplication


Algebra: Relate OperationsWrite the related multiplication or division sentence. Draw a picture that shows the sentence.

1. 18 � 6 � 6 � 6 � 0

2. 5 � 5 � 5 � 15

3. 6 � 2 � 2 � 2 � 0

Tell whether the number sentence is true or false. If false, explain how you know.

4. 5 � 5 � 5 � 5 �? 4 � 5 5. 3 � 4 �? 4 � 4 � 4 � 4

6. 2 � 7 �? 7 � 7 � 7


7. A class of 21 students will go on 3 different rides at the fair. The same number of students will go on each ride. How many students will go on each ride?

8. Jake plays 7 different games at the fair. He plays each game 2 times. What is the total number of games that Jake plays?

9. An amusement park ride has 4 cars. Each car holds 4 people. How many people can go on the ride at one time?

A 4

B 8

C 12

D 16

10. Shane needs 2 tickets to ride the carousel one time. Shane has 8 tickets. How many times can Shane ride the carousel?

A 2

B 4

C 6

D 8

Name Lesson 4.1


18 � 6 � 3

true false; 4 should be added 3 times, not 4 times

false; 7 should be added 2 times, not 3 times

7 students 14 games

5 � 3 � 15 6 � 2 � 3

D B

For 1–3, check students’ drawings.


Algebra: Relate Multiplication and DivisionWrite the fact family for the set of numbers.

1. 4, 2, 8

2. 7, 2, 14

3. 8, 9, 72

4. 6, 1, 6

Find the value of the variable. Then write a related sentence.

5. 4 � 7 � c

6. 81 � m � 9

7. 16 � j � 4

8. 8 � n � 16

9. 64 � 8 � r

10. 7 � 8 � w

11. 9 � 5 � p

12. 10 � 3 � a

Problem Solving and Test Prep 13. Laura colors every picture in each of

her 5 coloring books. There are 9 pictures in each book. How many pictures does Laura color in all?

14. Carlos has 63 crayons. He puts them into 7 equal groups for his classmates to use. How many crayons are in each group?

15. A crayon box holds 72 crayons. There are 9 equal rows of crayons in the box. How many crayons are in each row?

A 7

B 8

C 9

D 10

16. Mr. Lee draws a picture with 3 different crayons. A student uses 4 times as many crayons as Mr. Lee uses. How many crayons does the student use?

A 12

B 15

C 9

D 10

Name Lesson 4.2


4 � 2 � 82 � 4 � 88 � 2 � 48 � 4 � 2

7 � 2 � 142 � 7 � 1414 � 2 � 714 � 7 � 2

8 � 9 � 729 � 8 � 7272 � 8 � 972 � 9 � 8

6 � 1 � 61 � 6 � 66 � 1 � 66 � 6 � 1

28 � 7 � 4 9 � 9 � 81 4 � 4 � 16 16 � 2 � 8

9 crayons45 pictures

8 � 8 � 64 56 � 8 � 7 45 � 5 � 9 30 � 3 � 10

c � 28

Possible sentences are given.

AB

w � 56

m � 9 j � 4 n � 2

r � 8 a � 30 p � 45




2 division practice

3 multiplication practice

9 division practice



16 division practice

18find the value of a variable and practice multiplication

20find a value of a variable and practice multiplication




2choosing strategies for multiplication practice

6choosing strategies for division practice





PW21 Practice© Harcourt • Grade 4

Multiply and Divide Facts Through 5Find the product or quotient.

1. 4 � 3

2. 5 � 1 3. 4 � 8 4. 3 � 5

5. 2 � 7 6. 8 � 2 7. 35 � 5 8. 32 � 4

9. 16 � 4 10. 3 � 7 11. 4 � 10 12. 14 � 2

13. 1 � 7 14. 3 � 8 15. 20 � 4 16. 9 � 3

ALGEBRA Find the value of a � 3 for each value of a.

17. a � 2 18. a � 5 19. a � 1 20. a � 4

Problem Solving and Test Prep 21. Sue has 32 marbles and wants to put

them into 4 equal groups. How many marbles will be in each group?

22. Joe eats 5 apples every week. How many apples will Joe eat in 6 weeks?

23. Laurie makes a quilt pattern that is 10 squares wide and 3 squares long. How many squares are in the quilt pattern in all?

A 3

B 10

C 13

D 30

24. Mrs. Long delivers 30 quilts to a hospital. She delivers the same number of quilts on each of 6 floors. How many quilts does Mrs. Long deliver to each floor?

A 5

B 6

C 7

D 8

Name Lesson 4.3

12 5 32 15

14 4 7 8

4 21 40 7

7 24 5 3

6 15 3 12

8 marbles 30 apples


DA


Multiply and Divide Facts Through 10Find the product or quotient. Show the strategy you used.

1. 8 � 8 2. 7 � 9 3. 8 � 5 4. 9 � 6

5. 56 � 8 6. 81 � 9 7. 100 � 10 8. 72 � 9

9. 10 � 9

_

10. 7 � 8

_

11. 9 � 8

_

12. 6 � 6

_

13. 8 � � 64 14. 9 � � 36 15. 7 � � 49 16. 6 � � 54

ALGEBRA Find the value of the coins.

17. 18.

Problem Solving and Test Prep 19. Jeff had 10 checkers left at the end of

each game he played. How many checkers did Jeff have left at the end of 7 games?

20. Kim played checkers for 6 days and won a total of 24 games. She won the same number of games each day. How many games did Kim win each day?

21. There are 6 rows of chairs with 7 chairs in each row. How many chairs are there? Describe the strategy you used to find the product.

22. Lauren has 4 stacks of cards. There are 9 cards in each stack. How many cards does Lauren have? Describe the strategy you used to find the product.

Name Lesson 4.4

Dimes 2 3 5 7 9

Cents 20

Nickels 1 2 3 4 5

Cents 25

64 63 40 54

7 9 10 8

70 checkers 4 games

42 chairs; Descriptions will vary.


90 56 72 36

8 4 7 9


5 10 15 20 30 50 70 90

36 cards; Descriptions will vary.








17algebra; find missing numbers in an input/output table

18algebra; find missing numbers in an input/output table


2 finding square numbers



6finding patterns on the multiplication table

8problem solving; using square numbers

10multiple choice; using multiples


Multiplication Table Through 12Find the product or quotient. Show the strategy you used.

1. 110 � 11

2. 8 � 11

3. 12 � 9

4. 99 � 11

5. 7 � 12

6. 6 � 11

7. 84 � 12

8. 48 � 12

9. 11 � 11

10. 132 � 11

11. 108 � 12

12. 12 � 12

13. 60 � 12

14. 63 � 7

15. 11 � 9

16. 11 � 12

ALGEBRA Use the rule to find the missing numbers.

17. Multiply the input by 11.

18. Multiply the input by 12.

19. Divide the input by 11.

20. What could the missing factors be in � � � � 36?

Find as many factor pairs as you can. Explain how you found these factors.

Name Lesson 4.5

Input Output

2

4

6

Input Output

3

48

5

Input Output

99

10

121

10 88 108 9

84 66 7 4

121 12 9 144

5 9 99 132

66 60

110

1 and 36; 2 and 18; 3 and 12; 4 and 9; 6 and 6



44

22 36

4

9

11

Explanations may vary.


Patterns on the Multiplication TableFind the square number.

1. 9 � 9

2. 5 � 5

3. 10 � 10

4. 4 � 4

5. 2 � 2

For 6–7, use the multiplication table.

6. What pattern do you see in the first 9 multiples of 11?

7. What pattern do you see in the first 9 multiples of 9?

Problem Solving and Test Prep 8. Niko has a square number that is less

than 50. The digits add up to 9. What is Niko’s number?

9. Use the rule 1 less than 3 times the number to make a pattern. Start with 5. What is the 4th number in the pattern?

10. The multiples of which number are four times the multiples of 2?

A 1

B 8

C 5

D 20

11. The multiples of which number are three times the multiples of 4?

A 8

B 12

C 40

D 84

0 1

0 0 0

2

0

3

0

4

0

5

0

6

0

7

0

8

0

9

0

10

0

11

0

12

0

1 0 1 2 3 4 5 6 7 8 9 10 11 12

2 0 2 4 6 8 10 12 14 16 18 20 22 24

3 0 3 6 9 12 15 18 21 24 27 30 33 36

4 0 4 8 12 16 20 24 28 32 36 40 44 48

5 0 5 10 15 20 25 30 35 40 45 50 55 60

6 0 6 12 18 24 30 36 42 48 54 60 66 72

7 0 7 14 21 28 35 42 49 56 63 70 77 84

8 0 8 16 24 32 40 48 56 64 72 80 88 96

9 0

0

9 18 27 36 45 54 63 72 81 90 99 108

10 10 20 30 40 50 60 70 80 90 100 110 120

11 0 11 22 33 44 55 66 77 88 99 110 121 132

12 0 12 24 36 48 60 72 84 96 108 120 132 144

Name Lesson 4.6

Possible patterns are given.


81 25 100 16 4

The multiples have the same digits in their ones and tens place: 11, 22, 33, 44, 55, 66, 77, 88, 99

The ones digits are counting numbers from 9–1, the tens digit are counting numbers from 0–9

Possible answer: 36 122

BB




1 choose the operation; division

3 choose the operation

4problem solving; write a number sentence

5problem solving; too much, too little information


2 algebra; solve for a variable






16problem solving; multiplication practice

17problem solving; write a number sentence


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

1. Sally takes 24 gallons of juice to the school picnic. The students at the picnic drink 2 gallons of juice every hour. How many hours will it take the students to drink all the juice?

2. Each student in Lori’s class brings 12 cookies to the bake sale. There are 12 students in Lori’s class. How many cookies does Lori’s class bring to the bake sale?

Mixed Applications3. Greg sold 108 mini muffins at the bake sale. He sold the mini muffins in bags of 12.

Which fact family can you use to find out how many bags of mini muffins Greg sold? How many bags of mini muffins did Greg sell?

4. Julie wants to know how many workbooks she will use for the school year. The subjects she is studying are math, science, and reading. Each subject has 2 workbooks. What number sentence can be used to find the total number of workbooks Julie will use for the school year?

USE DATA For 5–6, use the table below.

5. At the bake sale, 9 people bought slices of pie. Each person bought the same number of slices for $2 each. How many slices of pie did each person buy?

6. How many cookies, brownies, and cupcakes were sold in all?

Name Lesson 4.7

Bake Sale Final Sales

Item Number Sold

cupcakes 147

cookies 211

slices of pie 54

slices of cake 39

brownies 97


division; 12 hours

multiplication; 144 cookies

12 � 9 � 108; 9 � 12 � 108; 108 � 12 � 9; 108 � 9 � 12; 9 bags

3 � 2 � 6

6 slices

455


Algebra: Find Missing FactorsFind the missing factor.

1. 4 � g � 20

2. y � 3 � 27

3. 8 � w � 48

4. 7 � a � 49

5. � � 2 � 24

6. 9 � r � 81

7. 4 � � � 36

8. 7 � s � 77

9. 5 � � � 23 � 2

10. 8 � � � 20 � 4

11. 6 � � � 11 � 7

12. 10 � � � 15 � 5

13. 7 �

� � 12 � 2

14. 3 � � � 16 � 5

15. 4 � � � 13 � 3

Problem Solving and Test Prep 16. Each season, a total of 32 tickets are

given away. Each chosen family is given 4 free tickets. Write a number sentence that can be used to find the number of families that will receive tickets.

17. The manager of the Antelopes orders 4 uniforms for each new player. This year, the manager orders 16 uniforms. Write a number sentence that can be used to find the number of new players.

18. The Ants won 121 games this year. They won the same number of games for each of 11 months. Which number sentence can be used to find the number of games the Ants won each month?

A 121 � � � 11

B 11 � � � 121

C 12 � 12 � 144 � �

D 10 � � � 100

19. The community softball club has 120 members. They need to hire one coach for every 12 players. How many coaches will the community softball club need to hire?

A 0

B 11

C 12

D 10

Name Lesson 4.8

g = 5

a = 7

� = 9

y = 9 w = 6

� = 2

� = 2

� = 12 r = 9

� = 5

� = 2

� = 4

s = 11

� = 3

� = 7

Possible answer: � � 4 � 32 Possible answer: � � 4 � 16


B D




2 use the associative property

3 use the zero property

4 use the identity property

10identify the associative property

12 make a model to solve

13make a model to find the product

16 place parentheses

18solve a problem using the distributive property

19multiple choice; word problem that needs to be grouped with parentheses


2practice writing multiplication expressions

4practice writing division expressions



10determine the meaning of an expression

12problem solving; practice writing expressions

14multiple choice; practice relating words to an expression


Multiplication PropertiesUse the properties and mental math to find the product.

1. 3 � 4 � 2

2. 4 � 5 � 5

3. 7 � 4 � 0

4. 7 � 12 � 1

Find the missing number. Name the property you used.

5. (5 � 3) � 4 � 5 � (� � 4)

6. 3 � 5 � 5 � �

7. 8 � � � (2 � 10) � (6 � 2)

8. 3 � (7 � �) � 3

9. 8 � (5 � 3 � 2) � �

10. 3 � (2 � 4) � � � (2 � 3)

Make a model and use the Distributive Property to find the product.

11. 14 � 6

12. 5 � 15

13. 9 � 17

Show two ways to group by using parentheses. Find the product.

14. 2 � 5 � 6

15. 4 � 3 � 2

16. 9 � 3 � 4

Problem Solving and Test Prep17. The pet store window has 5 kennels

with 4 puppies in each and 6 kennels with 6 kittens in each. Are there more puppies or kittens? How many more?

18. Jake takes his dog on a long walk 3 times each week. They walk for 4 blocks. They pass 12 houses on each block. How many houses do Jake and his dog pass each week on their long walk?

19. Each box of cat toys has 10 packets. Each packet contains 2 toys. How many cat toys are there in 5 boxes?

A 200 C 100

B 190 D 150

20. Each student receives 3 workbooks. Each workbook contains 12 pages. How many pages do 3 students receive?

A 108 C 36

B 48 D 72

Name Lesson 5.1

24 100 0 84

3; associative 3; commutative

4; distributive 6; identity

0; zero 4; associative

84 75 153

2 � (5 � 6); (2 � 5) � 6; 60

more kittens; 16 more 144 houses

4 � (3 � 2); (4 � 3) � 2; 24

9 � (3 � 4); (9 � 3) � 4; 108


C A

Check students’ models


Multiplication and Division ExpressionsWrite an expression that matches the words. Tell what the expression represents.

1. stamps, s, divided equally in 6 rows

2. some peas, p, in each of 10 pods

3. some marbles, m, on sale at 15¢ each

4. 42 cookies divided among several students, s

Find the value of the expression.

5. y � 5 if y � 6

6. 63 � b if b � 7

7. 9 � a if a � 2

8. r � 6 if r � 54

Match the expression with the words.

9. (4 � t) � 8

10. (t � 12) � 4

11. (t � 2) � 8

a. a number, t, divided by 2 minus 8

b. 4 times a number, t, plus 8

c. a number, t, times 12 and separated into 4 pieces

Problem Solving and Test Prep12. Ella has some pages with 9 stickers

on each page. Write an expression for the number of stickers Ella has.

13. Look at Exercise 12. Suppose Ella has 12 pages. How many stickers does Ella have in all?

14. Robert has 7 times as many soap box racers as Xavier. Let r represent the number of soap box racers Robert has. Which expression shows the number of soap box racers Robert has?

A 7 � rB r � 7C 7 � rD r � 7

15. Fran needs to write 121 letters. She writes the same number of letters each day. Write an expression for the number of days it takes Fran to write all the letters. How many days does it take Fran to write all the letters if she writes 11 letters each day? Explain.

Name Lesson 5.2


s � 6; stamps in each row p � 10; total number of peas

15¢ � m; total price of marbles

42 � s; cookies per student

30 9 18 9

b c a

p � 9 108 stickers

let d � number of days; 121 � d; 11 days since 121 � 11 � 11.

C




1practice following the order of operations

4practice following the order of operations

5determine whether the order of operations has been followed correctly

8determine whether the order of operations has been followed correctly

9follow the order of operations to make a number sentence true

11follow the order of operations to make a number sentence true

13solve a problem using the order of operations

14multiple choice; finding the value of an expression using order of operations


3 practice writing an equation

4 practice writing an equation

7practice solving multiplication equations

10practice solving division equations

12practice solving multiplication equations

13practice solving a problem by multiplying

15multiple choice; finding the value of an expression with a variable


Order of OperationsFollow the order of operations to find the value of each expression.

1. 7 � 10 � 3

2. (41 � 5) � 6

3. 7 � 25 � 5

4. 31 � 72 � 8

Write correct if the operations are listed in the correct order. If not, write the correct order of operations.

5. (7 � 8) � 4 Multiply, divide

6. 36 � 7 � 3 Subtract, multiply

7. 4 � 6 � 3 Add, multiply

8. 28 � (4 � 6) � 12 Subtract, multiply, add

Use the numbers listed to make a true number sentence.

9. 5, 6, and 42

� � � 42

10. 3, 15, and 21

� � � 12

11. 7, 9, and 81

� � � 2

Problem Solving and Test Prep12. Students get $2 off the price of

admission at a local museum. If admission is $8 and 5 students and 2 teachers will visit, how much will their admissions cost in all?

13. At the museum, Wally buys 2 books for $8 each and a kazoo for $12. Kent buys one book for $9, a statue for $13, and 4 pens for $3 each. Who spends more money: Wally or Kent? How much more?

14. Find the value of 56 � 49 � 7 � 4.

A 5

B 24

C 52

D 53

15. Find the value of 5 � 45 � 5 � 5.

A 5

B 10

C 19

D 15

Name Lesson 5.3

37 6 12 40

correct multiply, subtract

multiply, add multiply, subtract, add

6 15 81

$46 Kent spends $6 more


D C

5 42 21 3 9 7


Multiplication and Division EquationsWrite an equation for each. Choose the variable for the unknown. Tell what the variable represents.

1. Three students divide 27 bracelets equally among themselves.

2. Two bags of beads with equal pounds makes a total of 50 pounds.

3. Maddie plants 3 seeds in each of15 pots.

4. Jesse divides 36 ornaments equally and puts them into 9 bags.

Solve the equation.

5. a � 6 � 48

6. d � 4 � 7

7. 3 � w � 27

8. 63 � n � 9

9. b � 5 � 5

10. 22 � t � 11

11. 4 � k � 3 � 24

12. 5 � h � 3 � 45

Problem Solving and Test Prep13. Phyllis is making rings. Each ring has

3 beads. If Phyllis can make 7 rings, how many beads does she have?

14. Ted divided 56 blocks equally among 8 bags. How many blocks were in each bag?

15. In which equation does t � 3?

A t � 12 � 4

B 36 � t � 12

C t � 5 � 30

D 15 � t � 60

16. Seven friends paid a total of $21 to enter a craft fair. Write an equation to show the price of one admission. Then solve the equation.

Name Lesson 5.4

Possible variables are given.

27 � b � 3, b is bracelets per student

2 � b � 50, b is total number of bags

3 � 15 � p, p is total number of seeds

36 � r � 9, r is ornaments in each bag

d � 28a � 8 w � 9 n � 7

b � 25 t � 2 k � 2 h � 3

21 beads 7 blocks

21 � 7 � p; admission is $3 per person


B




2determine whether a number meets definition of an inequality

4determine whether a number meets definition of an inequality

5choose numbers that meet the definition of an inequality

6choose numbers that meet the definition of an inequality

7 write an inequality

10 write an inequality

11multiple choice; finding the value of inequalities with variables


2predict and test to solve a problem



6use logical reasoning to solve a problem




Problem Solving Workshop Strategy: Predict and Test

Problem Solving Strategy PracticePredict and test to solve.

1. Betty likes to solve number puzzles. Here is the most recent one she found. The product of two numbers is 48. Their sum is 14. What are the two numbers?

2. Kim is thinking of two numbers. The quotient is 4 and the difference is 27. What are the two numbers?

3. Kyle and Ellie played basketball. Kyle scored half as many points as Ellie. Together they scored 27 points. How many points did each player score?

4. Don bought two puzzle books. Together, they cost $19. One book cost $5 more than the other. How much did each book cost?

Mixed Strategy Practice USE DATA For 5–10, complete the table.

Name Lesson 5.5

Sum Product Difference Two Numbers

5. 10 21 4 ,

6. 10 0 ,

7. 10 16 ,

8. 18 3 ,

9. 15 54 ,

10. 8 0 ,


6 and 8 9 and 36

Ellie: 18 points; Kyle: 9 points $7 and $12

7 3

5 5

8 2

6 9

4 4

6 3

25

6

3

16

9


Explore InequalitiesWhich of the numbers 8, 9, 10, and 11 make the inequality true?

1. m � 9

2. 9 � x

3. b � 4 � 13

4. x � 6 � 2

Use the number lines below to graph three whole numbers that make the inequality true.

5. 4 � y 6. 8 � m � 3

Write an inequality to match the words. Choose the variable for the unknown. Tell what the variable represents.

7. June’s watering can holds up to 5 quarts of water.

8. Tom will add less than 4 tablespoons of plant food.

Problem Solving and Test Prep 9. April spilled more than 3 teaspoons of

pumpkin seeds. Write an inequality to show how many seeds, p, April spilled.

10. A Scotch pine can grow to a height of 50 feet. Write an inequality to show how high a Scotch pine, p, can grow.

11. Which value of r makes the inequality true?

r � 7

A r � 8

B r � 6

C r � 17

D r � 19

12. Which value of p makes the inequality true?

p � 4 � 8

A p � 3

B p � 2

C p � 1

D p � 4

Name Lesson 5.6

2 3 4 5 6 7 8 9 1010 2 3 4 5 6 7 8 9 1010

8, 9 10, 11 10, 11 9, 10, 11

Check students’ number lines.

c � 5; c is the amount of water in the can

f � 4; f is the amount of plant food added

p � 3 p � 50


B D




3write a rule as an equation to find missing numbers in a table

4write a rule as an equation to find missing numbers in a table

5make a table using a rule and an equation

6make a table using a rule and an equation

7solve a problem by writing an equation for a rule

8finding a rule from data in a table


2recognize more than one way to tell time

6recognize more than one way to tell time; estimate time

7recognize more than one way to tell time; estimate time

11relate time measurement to common events or activities

13 estimate time

15multiple choice; recognize more than one way to tell time


Patterns: Find a RuleFind a rule. Write your rule as an equation. Use your rule to find the missing numbers.

1.

2.

3.

4.

Use the rule and the equation to make an input/output table.

5. Multiply a by 3, subtract 1.(a � 3) � 1 � b

6. Divide c by 2, add 1.(c � 2) � 1 � d

Problem Solving and Test Prep 7. USE DATA Use the milk label. Hal has

3 servings of milk each day. How many grams of protein will Hal get in 5, 6, and 7 days? Write an equation.

8. What equation shows a rule for the table?

9. What equation shows a rule for the table?

Name Lesson 5.7

Input, c 4 8 32 128 512

Output, d 1 2 8

Input, r 4 5 6 7 8

Output, s 8 10 12

Input, a 10 20 30 40 50

Output, b 1 2 3

Input, m 85 80 75 70 65

Output, n 17 16 15

Input, a

Output, b

Input, c

Output, d

Input, p (pints) 1 2 3 4 5

Output, c (cups) 2 4 6 8 10

Input, p 2 4 6 8 10

Output, g 6 12 18 24 30

Amount per serving

Total Carb. 32mg

Sodium 50mg

Protein 8g

Divide c by 4; c � 4 � d Multiply r by 2; r � 2 � s

Divide a by 10; a � 10 � b Divide m by 5; m � 5 � n

120, 144, 168 grams; equations may vary; p � 3 � 8 � d where p is the number of grams of protein total and d is the number of days.



32 128 14 16

144 5 13

Check students’ tables.

Possible answer: p � 2 � c Possible answer: p � 3 � g


Telling TimeWrite the time as shown on a digital clock.

1. two fifty-two

2. 12 minutes after eight

3. half past six

Write two ways to read the time. Then estimate to the nearest 5 minutes.

4.

5.

6.

7.

8.

9.

Tell whether to use seconds, minutes, hours, or days to measure the time.

10. to travel around the world

11. to look up the meaning of a word

12. to make a model plane from scratch

Problem Solving and Test PrepUSE DATA For 13–14, use the clock at the right.

13. To the nearest 5 minutes, what time is it?

14. Write the time in two other ways.

15. Jose has lunch at a quarter after eleven in the morning. Which time is it?

A 10:45 A.M. C 11:30 A.M.

B 11:15 A.M. D 11:45 A.M.

16. Greg says that it is 11 minutes until three in the afternoon. Which time is it?A 3:11 P.M. C 2:49 P.M.

B 2:49 A.M. D 3:11 A.M.

Name Lesson 6.1

2:33 P.M. 4:16 A.M 6:47 P.M.

8910

11 12

7 6 543

21

8910

11 12

7 6 543

21

8910

11 12

7 6 543

21

8910

11 12

7 6 543

21

A.M.

2:52 8:12 6:30

days min hours

8:45 A.M.

8:44 A.M.; sixteen minutes until 9

10:04:31; twenty-nineseconds before ten-o-five; 10:05

sixteen minutes after four in the morning; four sixteen; 4:15 A.M.

thirty-three minutes after two in the afternoon; two thirty-three; 2:35 P.M.

7:57:58; 2 minutes three seconds to eight; 8:00

8:12:55; five seconds before eight thirteen; 8:15

Possible answers are given.

forty-seven minutes after six in the evening; six forty-seven; 6:45 P.M.


BC




1reinforce the concept of elapsed time

3reinforce the concept of elapsed time

5find starting time when given end and elapsed times

7find starting time when given end and elapsed times

9find start time when given end and elapsed times

11find start time when given end and elapsed times

14find elapsed time to the nearest second

15multiple choice; find elapsed time


1 find elapsed time using weeks

3 find elapsed time using days

4find beginning time when ending and elapsed times are given

7explain the concept of holidays not on the same date each year

9multiple choice; find elapsed time using days


Elapsed TimeFind the elapsed time.

1. start: 8:15 A.M. end: 8:55 A.M.

2. start: 6:50 P.M. end: 7:20 P.M.

3. start: 7:35 A.M. end: 7:15 P.M.

4. start: 9:55 A.M. end: 1:45 P.M.

Find the start time.

5. end: 11:35 P.M. elapsed time: 6 hr 55 min

6. end: 6:25 A.M. elapsed time: 55 min

7. end: 11:41 A.M. elapsed time: 2 hr 12 min

8. end: 8:15 P.M. elapsed time: 12 hr 25 min





Problem Solving and Test PrepFor 13–14, use the table.

13. At which stop did the bus spend the most time?

14. The bus arrived at the library at 3:12 P.M. To the nearest second, when did it leave the library?

15. The basketball team starts practice right after the school day ends. They finish practice at 6:00 P.M., which is 2 hours and 30 minutes after the school day ends. What time does the school day end?

A 6:30 P.M.

B 4:00 P.M.

C 3:30 P.M.

D 2:30 P.M.

16. Ms. Smith’s social studies class starts at 10:15 A.M. and ends at 11:20 A.M. How long is the class?

A 1 hour

B 1 hour 5 minutes

C 1 hour 15 minutes

D 1 hour 20 minutes

Name Lesson 6.2

Time Spent at Bus Stops

Stop Elapsed Time (min:sec)

Avery School 2:05

Central Mall 3:15

Library 1:34

Post Offi ce 1:12

40 min 30 min 11 hr 40 min 3 hr 50 min

4:40 P.M. 5:30 A.M. 9:29 A.M. 7:50 A.M.

8:30 A.M. 11:09 P.M. 7:35 A.M. 6:30 A.M.

Central Mall

3:13:34 P.M.


B

C

MXENL08ASE4X_PH_C06_L2.indd PW35 7/2/07 9:56:28 AM


Elapsed Time on a CalendarFor 1–5, use the calendars.

1. About how many weeks are there between May 13 and June 26?

2. Lyle practices for 16 days in preparation for a recital on June 8. When did Lyle start practicing?

3. Ginger has an appointment May 16. Today is May 5. How many days are there until Ginger’s appointment?

4. Flag Day is June 14. Todd is going on vacation 3 weeks and 3 days before Flag Day. When is Todd going on vacation?

5. Beginning on May 28, there is a sale at the department store. The sale lasts for 12 days. What is the last date of the department store’s sale?

Problem Solving and Test PrepFor 6–9, use the calendars above.

6. How many days are there between National Teacher’s Day (May 6) and Memorial Day (May 26)?

7. National Teacher’s Day is always the first Tuesday in May. Explain why it will not always fall on May 6 every year.

8. If today is June 15, how many days have passed since May 13?

A 15 days C 26 days

B 32 days D 16 days

9. Mrs. Greer returned home from a trip on June 29 at 12:01 A.M. If she left on Flag Day (June 14) at 12:01 A.M., how many days was Mrs. Greer gone?A 15 days C 2 days

B 16 days D 12 days

Name Lesson 6.3

May

Sun Mon Tue Wed Thu Fri Sat

1 2 3

4 5 6 7 8 9 10

11 12 13 14 15 16 17

18 19 20 21 22 23 24

25 26 27 28 29 30 31

June

Sun Mon Tue Wed Thu Fri Sat

1 2 3 4 5 6 7

8 9 10 11 12 13 14

15 16 17 18 19 20 21

22 23 24 25 26 27 28

29 30

about 6 weeks

May 23

11 days

May 21 June 8

20 days

Possible answer: because dates do not fall on the same day each year


B

A




2 convert months to years

3 convert days to hours

5convert years and months to months

6 convert years and days to days

7 compare hours and days

10 compare weeks and days

12 compare and order events

13multiple choice; convert weeks to days


1sequence information to determine elapsed time

2sequence information to make a timeline

3sequence information to determine elapsed time

5sequence information by working backward

6 determine unit cost


Algebra: Change Units of TimeComplete. Tell whether you multiply or divide.

1. 192 hours � days 2. 84 months � years

3. 14 days � hours 4. minutes � 300 seconds

5. years months � 32 months 6. 4 years days � 1,475 days

Compare. Write �, �, or � for each .

7. 180 hours 7 days 8. 1,080 hours 8 weeks

9. 660 seconds 15 minutes 10. 208 weeks 1,456 days

Problem Solving and Test PrepFor 11–12, use the table.

11. How many hours do the females fish at sea?

12. Which penguin fact represents the least amount of time? the greatest amount of time?

13. Matt goes to camp for 13 weeks. How many days does Matt go to camp?

A 91 days

B 86 days

C 67 days

D 70 days

14. The Reagan family has a 15-year mortgage loan on their home. How many months will it take the Reagan family to repay the loan?

A 150 months

B 200 months

C 120 months

D 180 months

Name Lesson 6.4

Emperor Penguins: Facts

Event or Activity Approximate Time

Females make and lay egg 2 months 1 week

Females keep egg warm 2 hours

Males keep egg warm 63 days

Females fi sh at sea 8 weeks

Males may go without food 4 months

Males fi sh at sea 24 days

Longest recorded dive for food 22 minutes

8

5

152

. ,

�

336

,

1,344 hours

longest recorded dive for food; males may go without food.


8

7

AD

divide divide

multiply divide

divide divide


Problem Solving Workshop Skill: Sequence InformationProblem Solving Skill PracticeUse a timeline to sequence the information.Then solve the problem.For 1–3, use the table.

1. The first hamburger stand opened in Tulsa, Oklahoma, 13 years after the first hamburger was eaten on a bun. What year did the first hamburger stand open?

2. Use the table and the information in Exercise 1 to make a timeline to sequence the information.

Mixed Applications 3. The largest burger chain opened in California in 1954. How long was that after

burgers first became the rage at the St. Louis World’s Fair?

4. Make your own timeline of the first time you tried some of your favorite activities. Use the Hamburger Timeline as a model.

5. It took Sandra 2 hours to run her errands. She went to the bank first. Then she spent 25 minutes at the hair salon and 40 minutes getting groceries. Sandra arrived home at 6:30 P.M. How long was Sandra at the bank?

6. The market’s regular price for a jar of pickles is 95 cents. This week, there is a sale: two jars of pickles for 98 cents. What is the difference between the sale price per jar and the regular price per jar?

Name Lesson 6.5

19301880

History of the Hamburger Timeline

History of the Hamburger

Event Date

First hamburger chain opens 1921

Hamburgers become the rage at the St. Louis World’s Fair

1904

First hamburger eaten between slices of bread

1885

First hamburger eaten on a bun 1891

1904

Check students’ timelines.

50 years

Check students’ timelines.

55 minutes

46 cents





2practice reading ºF and ºC thermometers

7practice reading ºF and ºC thermometers

9practice reading and estimating ºF and ºC thermometers

10practice reading and estimating ºF and ºC thermometers

11practice finding change in temperature

13practice finding change in temperature

18 practice ordering temperature

20multiple choice; determine change in temperature


2locate positive and negative numbers on a number line

4locate positive and negative numbers on a number line

6graph and compare positive and negative numbers on a number line

8graph and compare positive and negative numbers on a number line

10relate positive and negative numbers to real situations

13relate positive and negative numbers to real situations

14recognize whether a number is positive or negative in real situations

16multiple choice; order positive and negative numbers


TemperatureUse the thermometer to find the temperature shown by each letter.

1. A

2. B

3. C

4. D

5. E

6. F

7. G

8. H

Write each temperature. Then estimate to the nearest 5 degrees.

9.

10.

Use a thermometer to find the change in temperature.

11. 20�F to 5�F

12. 13�F to 72�F

13. �8�C to 35�C

14. 63�C to 42�C

Choose the better estimate.

15. hot tea: 30�C or 95�C

16. lake: 50�F or 100�F

17. ice cream: 3�C or 40�C


18. Order the temperatures below from greatest to least. 100�C; �45�C; �12�C, 32�C

19. Bruce measures the temperature outside one morning and it is 45�F. What is the temperature the next morning if the temperature increases by 20 degrees?

20. The temperature dropped from 15�C to �8�C. What was the change in temperature?

A 23º C C 8º C

B 15º C D 7º C

21. Which of the following is most likely to have a temperature of 212�F?

A Ice cream C Pond

B Oven D Pool

°F °C

–10

0

10

20

30

50

–20

20

10

–10

0

30 E

B

40

60

70

80

FC

D

AG

H

Name Lesson 6.6

0

-10

-5

°C °F

70

60

65

25�F 70�F 55�F 40�F

�5�F85�F 50�F 32�F

�4�C; �5�C 62�F; 60�F

15�F 43�C59�F 21�C

95�C 50�F 3�C

100�C; 32�C; �12�C; �45�C; 65�F


AB

PW40© Harcourt • Grade 4

Practice

Explore Negative NumbersName the number represented by each letter.

1. A 2. B 3. C 4. D 5. E

Draw a number line and graph the numbers. Compare using � or �.

6. �6 �8 7. �5 �11 8. �3 �4 9. �15 �15

Write a positive or negative number to represent each situation.

10. Fred spends all of his $8 allowance.

11. Mary buys 12 roses.

12. Ruth wins the game by 15 points.

13. Sam and Saya eat the last 7 apples.

Problem Solving and Test Prep14. Hans answers 10 questions correctly

on the test. Is this a positive or a negative number?

15. Martin loses five dollar bills in the laundry. Is this a positive or a negative number?

16. Order from least to greatest:�5, �2, �3, and �6.

A �2, �3, �5, �6

B �3, �5, �2, �6

C �2, �6, �3, �5

D �6, �2, �3, �5

17. Order from greatest to least:�6, �9, �4, and 0.

A �9, �6, 0, �4

B �4, 0, �6, �9

C 0, �4, �6, �9

D �9, �6, �4, 0

Name Lesson 6.7

-20 -10 0 +10 +20

AE BCD

0 �13 �9 �4 �18

. , . ,

�$8 �12

�15 �7

positive


AD

negative




2read and interpret data in a table

5calculate to interpret data in a table

7determine whether data are categorical or numerical

9calculate to interpret data in a table

10 calculate totals from a table

11multiple choice; solve a problem using a table


2interpret data in a Venn diagram

3 place data in a Venn diagram

5 draw a Venn diagram

7interpret data from a Venn diagram

9multiple choice; interpret data from a Venn diagram


Collect and Organize DataFor 1–2, use the Favorite Snacks frequency table.Tell whether each statement is true or false. Explain.

1. More students chose carrots than bananas as their favorite snack.

2. More students chose carrots and celery as their favorite than chose apples and bananas.

For 3–5, use the Sports Participation frequency table.

3. How many more boys participate in volleyball than tennis?

4. How many more girls participate in golf than in tennis?

5. How many more boys and girls together play softball than volleyball?

Tell whether the data are numerical or categorical.

6. shoe size

7. rainfall

8. bird population

Problem Solving and Test PrepUSE DATA For 9–10, use the Sports Participation table above.

9. Which is the most popular sport for girls? for boys?

10. Who has the largest overall participation in sports: girls or boys?

11. How many people were surveyed?

A 186

B 194

C 196

D 200

12. What question would you ask if you were taking a survey about favorite sports?

Students’ Favorite SnacksSnack Votes

Apple 12Banana 7Carrots 8Celery 4

Sports ParticipationSport Boys Girls

Golf 12 19Softball 18 17Tennis 9 11Volleyball 13 12

Favorite Sport VotesGolf 37Softball 63Tennis 52Volleyball 44

Name Lesson 7.1

True. 8 chose carrots, 7 chose bananas

False. 19 chose apples and bananas, 12 chose carrots and celery

4 more boys

8 more girls

10 more boys and girls

categorical numerical numerical

girls- golf, boys- softball girls

Possible answer: What is your favorite sport?


C


Venn DiagramsFor 1–4, use the Venn diagram.

1. Describe and label the data for Sections B and C?

2. Why are the numbers 20 and 40 sorted in Section B of the diagram? 4. If Section A were multiples of 45 and

Section C were multiples of 71, would Section B contain a number less than 100? Explain.

3. In which section would you sort the number 60? Explain.

For 5–6, use the Breakfast Choices table.

5. Show the results in the Venn diagram at the right.

6. What data overlaps? Explain.

Problem Solving and Test PrepFor 7–8, use the Breakfast Choices table.

7. How many students chose either cereal or fruit?

8. What would need to change in order for there to be no overlapping data?

9. Look at the Multiples Venn diagram at the top of the page. Which number belongs in Section C?

A 22 C 204

B 28 D 250

10. Look at the Multiples Venn diagram at the top of the page. Which number belongs in Section B?

A 30 C 80

B 50 D 65

Name Lesson 7.2

Breakfast ChoicesFood Student NamesCereal Jane, Mani, Liddy, Steve, Ana

Fruit Ben, Cecee, Beth Both Dave, Raiza

of 4 :

of :

of :

4 8

1216

2040

5 10

2515

A B CMultiples

Multiples of 4 and 5, multiples of 5.

They are multiples of both 4 and 5.

Section B, multiples of both 4 and 5.

No, there are no multiples of both 45 and 71 that are less than 100

Check students’ diagrams.

Dave and Raiza. They chose both fruit and cereal.

8 studentsDave and Raiza would have to change their answer.


D C




2mean, median, and mode from a table

3use tables to compare the median of the data

4 use tables to compare data

5multiple choice; find the median

6 multiple choice; find the mode


1practice making tally sheets and line plots from data

3 analyze data

4 draw conclusions from data

6practice finding measures of central tendency in a data set

7multiple choice; find the mean from a data set


Find Mean, Median, and ModeFind the mean, median, and mode.

1.

Mean

Median

Mode

2.

Mean

Median

Mode

For 3–4, use the graphs.

3. What is the difference between the median number of T-Shirts sold in May and the median number of T-Shirts sold in June?

4. How many more total T-Shirts were sold in June than in May?

Problem Solving and Test Prep 5. What is the median of the following

set of data?

4, 7, 10, 9, 9, 5, 7, 8, 8, 9.

A 5

B 8C 9

D 10

6. Look at the T-Shirts Sold in June bar graph above. What is the mode for the data?

A 9

B 10

C 15

D 18

Name Lesson 7.3

RainfallMonth Nov Dec Jan Feb MarInches 1 2 7 8 2

Animals FedDays Mon Tue Wed Thu Fri SatNumber 5 12 5 9 10 7

181614121086420

Red Blue Green White

T-Shirts Sold in May

181614121086420

Red Blue Green White

T-Shirts Sold in June

4 8

B

22

85


1 tee10 more tees

C


Line PlotsFor 1–4, use the Tourist Souvenir Survey data.

1. Use the data to fill in the tally table and line plot at the right.

2. Are there clumps in the data? Explain.

3. Is there a hole in the data? Explain.

4. Did most people buy 1 or 2 souvenirs or buy 5 or 6 souvenirs?

Problem Solving and Test PrepFor 5–8, use the line plot you made above.

5. The people who bought 4 souvenirs spent $2 for each one. How much did all the people who bought 4 souvenirs spend in all?

6. Find the mode, the median, and the total number of souvenirs bought.

7. What is the mean of the number of souvenirs bought?

A 3

B 6

C 15

D 18

8. What is the range of the number of souvenirs bought?

A 3

B 5

C 8

D 10

Tourist Souvenir Survey

Question: How many souvenirs did you buy at the gift shop while at the Kennedy Space Center Visitor Complex?

Responses: 2, 1, 5, 4, 1, 2, 5, 2, 1, 6, 1, 1, 2, 4, 6, 5, 2, 1, 1, 6, 2, 5, 2, 6, 2

Number of Souvenirs Tally

1

2

3

4

5

6

Name Lesson 7.4

2 3 4 5 6 7 8 910Number of Souvenirs Bought

Check students’ tally tables and line plots.

yes, between 1 and 2

yes, no one bought 3 souvenirs

1 or 2

$16mode: 2, median: 2, total: 75


AB




1determine an appropriate interval

2determine an appropriate interval

3use a bar graph to find the scale and interval

4find how the length of bars in a bar graph change with the length of intervals

7analyze the data in a bar graph

8analyze the data in a bar graph

9multiple choice; recognize the interval used in a bar graph


1 complete a chart using data

3make generalizations from data

4make generalizations from data

5problem solving; choose the operation

6extend a pattern from data in a table


Choose a Reasonable Scale and IntervalFor 1–2, choose 5, 10, 25, or 100 as the most reasonable interval for each set of data. Explain your choice.

1. 35, 55, 77, 85, 20, 17

2. 125, 200, 150, 75, 275, 300

For 3–6, use the Favorite Summer Sport graph.

3. What are the scale and the interval used in the graph?

4. How would the length of the bars change if the interval were 10?

5. How many votes were cast in all?

6. How many more votes did swimming

get than croquet and volleyball combined?

Problem Solving and Test PrepUSE DATA For 7–10, use the FavoriteWinter Sport graph.

7. What is the least favorite winter sport?

10. What is the scale for the Favorite Winter Sport graph?

A 0–80 C 0–100

B 0–50 D 0–20

8. How many fewer people voted for sledding than skiing and ice skating combined?

9. What is the interval for the Favorite Winter Sport graph?

A 5 C 15

B 10 D 20

Name Lesson 7.5

Num

ber o

f Vot

es

4540353025201510

50

Volleyball Croquet Swimming HikingSport

Favorite Summer Sport

Num

ber o

f Vot

es

100908070605040302010

0Sledding Ice Skating Skiing Basketball

Sport

Favorite Winter Sport

10 25

scale: 0�45; interval: 5

Bars would be shorter.

105 votes

10 more votes

skiing

25


Explanations will vary.

B C


Problem Solving Workshop Skill: Make Generalizations

Problem Solving Skill PracticeFor 1–3, use the table. Make a generalization. Then solve the problem.

1. Complete the chart below with the data from the table at the right.

2. Kosi is 5’9” tall. What is a healthy weight range for Kosi?

3. Gwen is a healthy adult who weighs 135 pounds. According to the chart, what might be Gwen’s range in height?

Mixed ApplicationsFor 4–7, use the table above.

4. How much greater is the weight range of a healthy adult who is 6’0” tall than one who is 5’7”?

5. Gino weighs 180 pounds. About how much more does Gino weigh than Jo who is at maximum weight for 5’9”?

6. If the pattern continues, what will be the range of healthy weights for an adult who is 6’1” tall?

7. Look at Exercise 4. Change the numbers to write a new problem.

Known Information

The table shows the healthy weight range for adults. Adults who are tall should weigh between and 184 pounds. Healthy adults who weigh between 139 and 174 pounds may be about tall. An adult who is 5’7” should weigh between and

.

• Minimum weights increase in -pound increments.

• Maximum weights increase in -pound increments.

Height (ft, in)

Adult Weight Ranges (in pounds)

Minimum Maximum

5’7” 127 159

5’8” 131 164

5’9” 135 169

5’10” 139 174

5’11” 143 179

6’0” 147 184

Name Lesson 7.6

135–169

5’7”–5’9”

5 pounds 11 pounds

151–189 pounds



6’0”

127

147

5’10”

159

4

5





1determine the range of the data

3 interpret a bar graph



9multiple choice; interpret a bar graph


1 practice making a bar graph

2practice making a double-bar graph

3 interpret data in a bar graph

5 interpret data in a bar graph

8interpret data in a double-bar graph


Bar GraphsFor 1–6, use the Distance of Planets bar graph.

1. An Astronomical Unit (AU) is the average distance between the Earth and the Sun. Scientists use Astronomical Units to help represent other large distances. According to the data shown in the graph, what is the range of AU shown?

2. Which planet in the graph is farthest from the sun?

3. Which planet is 6 times farther away from the Sun than Jupiter?

4. Which planet’s distance from the Sun is the median of the data?

5. List the names of the planets in the

graph in order from the greatest average distance from the Sun to the least average distance from the Sun.

6. Of the planets shown in the graph, which planet do you think is the coldest? the warmest? Explain.

Problem Solving and Test PrepUSE DATA For 7–10, use the Average Distance of Planets bar graph above.

7. How many AU further is Uranus’ average distance from the Sun than Jupiter’s average distance from the Sun?

8. How many AU closer is Earth’s average distance from the Sun than Saturn’s average distance from the Sun?

9. How many AU is the average distance from the sun to the planet Uranus?

A 5 C 19B 10 D 30

10. How many AU is the average distance from the Sun to Neptune?

A 5 C 19B 10 D 30

Name Lesson 8.1

Average Distance of Planetsfrom the Sun

Neptune

Uranus

Saturn

Jupiter

Earth

Distance (rounded to the nearest AU)

(one AU = 93 million miles)

Plan

et

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 320

29 AU

Neptune

Neptune Saturn

Neptune, Uranus, Saturn,

Jupiter, Earth

Neptune because it is far from the heat of the sun. Earth because it is close to the heat of the sun.

14 AU 9 AU


C D


Make Bar and Double-Bar GraphsFor 1–2, use the data in the Average Rainfall table to make two bar graphs. Then make a double-bar graph.

1.

2.

For 3–6, use the graphs you made.

3. Which city gets the most rainfall from January through March?

4. During which month does Boulder get the most rainfall?

5. Which city has a greater range of inches of rainfall in the three months?

6. Look at Exercise 2. During which month is the difference in rainfall the greatest? How great?

For 7–8, use the double-bar graph at the right.

7. What is the range of the data?

8. How many more girls than boys like soccer the most?

Average Rainfall (in inches)City Jan Feb Mar

Portland, OR 6 5 5Boulder, CO 1 1 2

Num

ber o

f Stu

dent

s

SportFootball Baseball Soccer

Favorite Sports to Watch

02468

10

Tennis

BoysGirls

Name Lesson 8.2

Average Rainfall in Portland, OR

Aver

age

Rain

fall

(in In

ches

)

Jan Feb Mar01234567

Month

Average Rainfall in Boulder, CO

Aver

age

Rain

fall

(in In

ches

)

Jan Feb Mar01234567

Month

Average Rainfall (in inches)

MonthJan Feb Mar

Boulder, CO

01234567

Aver

age

Rain

fall

(in In

ches

)

Check students’ graphs.


Portland

March

neither, they both have a range of 1 inch

January, 5 inches

7

6 more girls



Portland, OR




1 interpret circle graphs


4compare and interpret circle graphs


7multiple choice; interpret circle graphs, total participants


1find points on the coordinate grid

4find points on the coordinate grid

5plot points on the coordinate grid




11use a coordinate grid to describe a path

12multiple choice; understand the meaning of an ordered pair


Name Lesson 8.3

Macaroni

Hot Dogs Pizza

Fish

Cat

Dog

A B C

Fish

Cat

Dog

Dog

Fish

Cat

Circle GraphsFor 1–3, use the Favorite School Lunch graph.

1. Which school lunch received less than 1 _ 4 of the votes?

2. Which school lunch received half of the votes?

3. Which school lunch received the least number of votes?

For 4, use Graphs A, B, and C.

4. Dana asked 8 friends about their favorite pet. Three people voted for dogs, 3 for cats and 2 for fish. She says Graph C matches the data. Describe Dana’s error. Tell which graph matches the set of data.

Problem Solving and Test PrepFor 5–8, use the Favorite Vegetable graph.

5. Which vegetable received the least number of votes?

6. How many more people voted for carrots than potatoes?

7. In all, how many people voted for a favorite vegetable?

A 200 C 125

B 150 D 100

8. Which is the most favorite vegetable?

A Carrots B Corn

C Broccoli D Potatoes

Broccoli73 votes

Potatoes44 votes

Corn32 votes

Carrots51 votes

Favorite Vegetable

Favorite School Lunch


Macaroni

Pizza

Graph C shows 5 votes for dogs, 2 for cats and 1 for fish. The votes were 3 for dogs, 3 for cats and 2 for fish. So Graph A is the correct graph.

Corn

7 people

A C

Macaroni


Algebra: Use a Coordinate GridWrite the point for each ordered pair on the coordinate grid at the right.

1. (0,5) �

2. (7,6) �

3. (4,4) �

4. (1,7) �

Graph each point and label it usingthe ordered pair.

5. (6,4) 6. (1,1)

7. (6,6) 8. (1,9)

9. What polygon is formed by the points (6,4), (1,1), (6,6), and (1,9)?

Problem Solving and Test PrepFor 10–11, use the map at the right.

10. Kevin leaves Garden Grocery. He walks 6 units left and 2 units up. Where is Kevin now?

11. Jill leaves Tony’s Toy store to go to Joe’s Art store. Describe Jill’s path.

12. How many units above the origin is (4,7)?

A 11 C 4

B 7 D 3

13. Which of the points in the ordered pairs (8,5) and (4,2) are on the x-axis?

A 8 and 4 C 4 and 5

B 5 and 2 D 8 and 2

Name Lesson 8.4

678910

54321

0 2 3x-axis

y-ax

is

1 4 5 7 8 9 106

678910

54321

0 2 31 4x-axis

y-ax

is

5 7 8 9 106

Tony’s Toy Store

Joe’s Art Store

Garden Grocery

Mike’s Market

678910

54321

0x-axis

y-ax

is

31 4 5 7 8 9 106

A D

E

F

G

H

B

CC

G

D

B

Check students’ graphs

trapezoid

toy store (1, 8)

1 unit down, 3 units right

B A





1 interpret line graphs




9multiple choice; interpret trends in line graphs


1 make a line graph

2 make a line graph

3make and interpret line graphs

4make and interpret line graphs


Line GraphsFor 1–5, use the graph at the right.

1. Which is the highest average temperature in Honolulu?

2. During what months are the trends level?

3. What is the range of average high temperatures in Honolulu?

4. Is the trend in the average high temperature increasing or decreasing from January to June?

5. What is the average temperature in Honolulu for February?

Problem Solving and Test PrepFor 6–7, use the Rosemary Plant graph.

6. How tall was the plant when Hughgot it?

7. If the trend seen in weeks 0 through 4 continues, what will happen to the rosemary plant in week 5?

8. A line slanting downward on a line graph shows that the data are

A increasing. C staying the same.

B decreasing. D too small to graph.

9. A line slanting upward on a line graph shows that the data are

A increasing. C staying the same.

B decreasing. D too small to graph.

Average Highs in Honolulu

Tem

per

atu

re (

in º

F)

MonthJan Apr May JunMarFeb

86858483828180

87888990

Growth of Hugh’s Rosemary plant

00 1

2

2 3

4

4

6

8

10

12

14

Time (in weeks)

Gro

wth

(in

Inch

es)

Name Lesson 8.5

87 degrees

Jan–Feb

80–87 degrees

increasing

4 in.

the plant will grow 5 inches

80�F


B A


Make Line GraphsFor 1–2, use the data in each table to make a line graph.

1.

2.

3. Use the data in the table below to make a line graph in the space at the right. How much money will Bill raise if he swims 100 laps?

4. Use the data in the table below to make a line graph in the space at the right. How many rows will Jenna knit if she knits for 12 hours?

Daily TemperatureDay Mon Tue Wed ThuTemperature(in ºF) 65 70 85 75

Name Lesson 8.6

Touchdowns MadeYear 2004 2005 2006Number ofTouchdowns 10 12 18

Daily Temperature Touchdowns Made

Bill’s Bike-a-Thon

Number of Laps 20 40 60 80

Amount raised $25 $50 $75 $100

Jenna’s Knitting

Number of hours 2 4 6 8

Number of rows 8 16 24 32

Bill’s Bike-a-Thon

Number of Laps

Am

ount

Rai

sed

(in d

olla

rs)

0 20 40 60 80 100

25

50

75

100

125

Jenna’s Knitting

Number of Hours

Num

ber o

f Row

s

0 2 4 6 8 10

48

12162024283236404448

$125

48 rows






1make a graph to solve a problem

3make a graph to solve a problem

5explain your choice of graphs to show data

6use the solve-a-simpler-problem strategy

7 use the act-it-out strategy


1apply criteria for the best type of graphs



8choose the best graph for a set of data


Problem Solving Workshop Strategy: Make a Graph

Problem Solving Strategy PracticeFor 1–3, use the Visitors Spending table.Make a graph to solve.

1. Use the space provided at the right to make either a line graph or bar graph to display the data. Label your data.

2. What trend in the data does your graph show?

3. What if you wanted to add that in the year 2000 visitors spent $45 billion. Would that change the trend in the data ?

Mixed Strategy Practice 4. Look at the graph you made above.

What is the range of the data?

5. Explain why you chose one graph type over the other.

6. In the first quarter of 2004, 11,800,000 visitors came to Florida by air and 9,800,000 came by other means of transportation. How many more visitors traveled by air than by other means of transportation?

7. Jeff, Sean, Ida, and Paul are in line to buy souvenirs. Neither Sean nor Paul are first. Jeff is second and Paul is ahead of Sean. In what order are they in line?

Name Lesson 8.7

Visitors Spending in FloridaYear Billions of Dollars

2001 49

2002 50

2003 52

2004 57

2005 62

30

40

50

60

70

20

10

0 20012002

20032004

2005


Spending is increasing.

No, spending would still be increasing.

$13 billionAnswers will vary.

2 million Ida, Jeff, Paul, Sean




Choose an Appropriate GraphFor 1–6, choose and explain the best type of graph or plot for the data.

1. how Drew spends one afternoon

2. the amount of rainfall in a given day

3. favorite toys preferred by cats and dogs in a pet daycare

4. number of students who make As in three different grading periods

5.

6.

Problem Solving and Test PrepFor 7, use the line graph at the right.

7. Why is a line graph not the best choice to show the number of students in study hall?

8. Which type of graph would best display the numbers of four different car models sold in a weekend?

A Bar graph C Line graphB Circle graph D Pictograph

9. Which type of graph would best display how many hours students in class spent on homework over 5 days?

A Bar graph C Line graphB Circle graph D Line plot

Mileage Traveled

Day Mon Tues Wed Thurs Fri

Miles 75 30 30 90 120

Bird Wingspan

Bird Hummingbird Crane Goose

Inches 4 84 54

Name Lesson 8.8

Students in Study Hall

Num

ber o

fSt

uden

ts

Class Period

01st 2nd 3rd 4th

51015

circle graph; compares

parts of whole

line graph; shows how

data changes over time

double-bar graph; compares data from two different groups

bar graph; compares

different groups of data

bar graph; compare data

about different categoriesbar graph; compares

different groups of data

A bar graph would be better, because it compares data about different groups.

Circled problems are suggested homework problems

AD






2write an equation to compare an input/output table

3use an equation to make a function table and list and graph the ordered pairs

4use an equation to find ordered pairs

5use an equation to find ordered pairs

6multiple choice; find missing numbers in a function table


1practice the skill of identifying relationships

3practice the skill of identifying relationships

5solve problems using the choose-the-operation skill

6solve problems using using time and the work-backward strategy


Algebra: Graph RelationshipsFind the rule. Write your rule as an equation. Use the equation to find the missing numbers.

1.

2.

Make a function table. Write the input /output values asordered pairs. Graph the ordered pairs.

3. y � x � 1

ordered pairs:

� , �

� , �

� , �

� , �

Problem Solving and Test Prep 4. In Exercise 2, what will be the ordered

pair if x is 55?

5. In Exercise 1, what will be the ordered pair if y is 55?

6. Based on the information in the table, how many miles will be traveled in 6 hours?

A Divide 32 by 6. C Add 7.B Multiply 6 by 8. D Add 37.

7. Describe what happens to the value of y when the value of x decreases in the equation y � x � 10?

Input, x 2 4 5 6

Output, y 11 12 13 14 16

Input, x 5 10 20 25

Output, y 1 2 4 6

Name Lesson 8.9

Hours, h 1 2 4 6

Miles, m 8 16 32

6 7 8

9

5

4

3 2

1

0 2 3 1 4 5 7 8 9 6

Input, x

Output, y

y � x � 10 y � x � 5

Check students’ tables and graphs.

(55, 11) (45, 55)

The value of y also

decreases.


Possible equations are given.

1 315

153 5

30

B



Problem Solving Workshop Skill: Identify RelationshipsProblem Solving Skill Practice 1. Amber is making a design for her

sweater. She is using 4 equilateral hexagons. How is the perimeter of an equilateral hexagon related to the length of one side of the hexagon? Complete the function table and graph the ordered pairs in the box at the right to help solve.

2. What if Amber adds another hexagon that is 8 inches on each side. What would be the perimeter of that hexagon?

Mixed Applications 3. Tom is fencing a pentagonal pen that

is 5 yards on each side. Hank is fencing a pentagonal pen that is 7 yards on each side. How much more fencing will Hank use than Tom use?

4. Alter the length of the sides of Amber’s hexagons to change the perimeters. Complete a new function table below.

5. Lynn needs 11 sections of garden edging for each of 8 trees. How many sections of edging will Lynn need in all?

6. Ned’s doctor appointment is at 3:30. He will drive 15 minutes to the gym and spend 45 minutes there. Next, he will drive 3 minutes to a class and spend 25 minutes there. Then he will drive 10 minutes to the doctor’s. At what time must Ned start his trip?

Length of a Side (in inches), l 1 2 4

Perimeter (in inches), p 6 12

Each | | = 1 inch

Name Lesson 8.10


Perimeter is 6 times the

length of one side.

3

10 yards

1:5288 sections

18 24

48 in





Lesson 9.1 Item Suggested rationale

1identifying patterns in multiplication

3Identifying patterns in multiplication

6use patterns and mental math to multiply

7use patterns and mental math to multiply

8 algebra; solve for the variable

10 algebra; solve for the variable

12problem solving; multiply and compare

14multiple choice; use patterns to find missing numbers


2 estimate products

3 estimate products

7 estimate products

8 estimate products

10 estimate products



17problem solving, using estimation

19multiple choice; find the best estimate

20multiple choice; number sentence for best estimate


Mental Math: Multiplication PatternsUse mental math to complete the pattern.

1. 7 � 6 � 42

7 � 60 �

7 � 600 �

7 � 6,000 �

2. 3 � 8 � 24

3 � 80 �

3 � � 2,400

3 � 8,000 �

3. 9 � 7 � 63

9 � � 630

9 � 700 �

9 � � 63,000

Use patterns and mental math to find the product.

4. 2 � 30

5. 3 � 700

6. 9 � 4,000

7. 7 � 800

ALGEBRA Find the value of n.

8. 2 � n � 42,000

9. 7 � 400 � n

10. 8 � n � 16,000

11. n � 500 � 4,500

Problem Solving and Test Prep12. Windsurfing costs $20 a day at New

State Park. Jen windsurfed for 5 days. Paul windsurfed for 7 days. How much more did Paul pay than Jen paid?

13. Every carload of people entering the state park pays $7. In January, there were 200 cars that entered the park. In July, there were 2,000 cars that entered the park. How much more money did the park collect in July than in January?

14. Which number is missing from this equation?

� � 7 � 3,500

A 50

B 500

C 5,000

D 50,000

15. Which number is missing from this equation?

8 � � � 32,000

A 40

B 400

C 4,000

D 40,000

Name Lesson 9.1

60 2,100 36,000 5,600

n � 2,800 n � 2,000 n � 9

$40 more $12,600 more


4204,20042,000

240800

24,000

706,300

7,000

B C

n � 21,000

PracticePW58

Name Lesson 9.2


Mental Math: Estimate ProductsEstimate the product. Write the method.

1. 2 � 49

2. 7 � 31

3. 5 � 58

4. 4 � 73

5. 3 � 27

6. 8 � 26

7. 4 � 25

8. 5 � 82

9. 6 � 53

10. 9 � 47

11. 6 � 71

12. 5 � 31

14. 88 � 2

_

14. 29 � 8

_

15. 65 � 4

_

16. 39 � 7

_


17. About how many pencils will Haley use in 8 months?

18. How many more pencils will Haley use in ten months than Abby will use in ten months?

19. Which number sentence would give

the best estimate for 6 � 17?

A 6 � 20 � �

B 6 � 25 � �

C 6 � 10 � �

D 6 � 5 � �

20. Which number sentence would give the best estimate for 6 � 51?

A 6 � 5 � �

B 6 � 45 � �

C 6 � 50 � �

D 6 � 55 � �

Pencils Used Each Month

Name Number of Pencils

Haley 18

Abby 12

Bridget 17

Kelsey 21

100; rounding

210; compatible numbers

300; rounding


90; rounding

240; rounding

80 or 120; compatible numbers

300; rounding


180; rounding


280; rounding

280; rounding

Possible answer: 160 pencils

60 more pencils



A C

420; rounding



MXENL08AWK4X_PH_C09_L2.indd PW58 7/2/07 10:14:13 AM




5understanding relationship between multiplication and modeling



9 use base-ten blocks to model

11 base-ten modeling





2 multiply whole numbers

3 multiply with money

6use partial products to multiply

7use partial products to multiply

9algebra; use a rule to find missing numbers in a function table

122 step problem solving using addition and multiplication

13multiple choice; multi-step problem solving with money


Model 2-Digit by 1-Digit MultiplicationFind the product.

1.

4 � 14 �

2.

6 � 21 �

3.

8 � 18 �

4.

9 � 19 �

5.

2 � 13 �

6.

5 � 17 �

7.

3 � 24 �

8.

3 � 25 �

Use grid paper or base-ten blocks to model the product. Record your answer.

9. 2 � 18

10. 5 � 16

11. 4 � 17

12. 3 � 31

13. 6 � 17

14. 8 � 18

15. 7 � 31

16. 9 � 33

Name Lesson 9.3

56 126

144 171

26 85

72 75

36 80 68 93

102 144 217 297


Check students’ models.



Record 2-Digit by 1-Digit MultiplicationEstimate. Then record the product.

1. 53 � 5

_

2. 34 � 3

_

3. $49 � 2

_

4. 6 � 71

_

Write each partial product. Then record the product.

5. 9 � 62

6. 3 � 41

7. 5 � 38

8. 2 � 49

ALGEBRA Write a rule. Find the missing numbers.

9.

Rule:

10.

Rule:


11. Mr. Lewis gets in his car at 11:15 A.M. He drives for 2 hours and 45 minutes. What time is it when Mr. Lewis stops driving?

12. A gardener had 21 tulip bulbs. She bought 7 more. How many rows of 4 tulips each can the gardener now plant?

13. Jan and Beth count their savings. Jan has seven $1 bills and one $5 bill. Beth has three $10 bills. How much more do they need to save to have $50 total?

A $11

B $42

C $8

D $39

14. If the pattern in the number sentences below continues, could 180 be one of the products in this pattern? Explain.3 � 3 � 93 � 3 � 3 � 273 � 3 � 3 � 3 � 81

Name Lesson 9.4

Number of Quarts, q 2 3 4 5 6

Number of Cups, c 8 12 20

Number of Yards, y 1 2 3 4 5

Number of Feet, f 3 9 12

250; 265 90; 102 $100; $98 420; 426

18, 540; 558

3, 120; 123

40, 150; 190

18, 80; 98

Rule: multiply q by 4 Rule: multiply y by 3

2:00 P.M. 7 rows

Possible answer: no, 180 is an even number and cannot have odd factors.



16 24 6 15

C





4estimate and find products with money

7 estimate and find products

10algebra; find missing digits in factors

15compare products using money

18word problem; demonstrate multiplication with larger numbers

19word problem; multiply a 4-digit number and money


2 estimate and find the product

5estimate and find the product with money

8estimate and find the product with money

12 multiplication of 4-digit factor

15estimate and multiply a 4-digit number with zeros

17word problem; multiplication using money

19multiple choice; multiplication using money

20multiple choice; multiply a 3-digit number with zeros


Multiply 3-Digit and 4-Digit Numbers and Money Estimate. Then find the product.

1. 116 � 3

_

2. 2,247 � 7

__

3. 209 � 2

_

4. $19.99 � 4

__

5. 323 � 7

6. 3 � 8,124

7. 9,347 � 7

8. 443 � 5

ALGEBRA Find the missing numbers.

Compare. Write �, �, or � for each .

13. 4 � $2,085 5 � $1,875 14. 7 � 3,006 8 � 2,493

15. 4 � 2,163 2 � 4,326 16. 6 � $2,227 5 � $3,323

Problem Solving and Test Prep17. A Boston bookstore sells Make Way for

Ducklings for $8 a copy. If 1,223 people buy a copy, what are the total sales?

18. It costs $15.95 for each adult and $8.95 for each child to visit the New England Aquarium in Boston. Altogether, how much does it cost for 7 adults and 7 children to visit?

19. Ice skate rental at the Boston Common Frog Pond costs $8 for adults. In February, 1,791 adults rented skates. What were the total sales from ice skate rentals for February? Show your work.

20. Jean bought 4 key chains for $2.95 each. She paid with a $20-bill. How much change did Jean receive? Show your work.

Name Lesson 9.5

10. 45 � 2

__

1,290

9. 2 3 � 8__

, 84

11. ,4 8 � 3

__

7, 8

12. 1,5 � 9___

, 23

300;348 14,000;15,729 400;418 $80;$79.96

2,100;2,261 24,000;24,372 63,000;65,429 2,000;2,215

6

, .

�

$174.30$9,784

$14,328; 8 � 1,791 � 14,328 $8.20; 4 � $2.95 � $11.80, $20 � $11.80 � $8.20



,

2

71

2 2

42 1 3 9

4 7


Multiply with ZerosEstimate. Then find the product.

1. 3,044 � 3

__

2. 4,700 � 5

__

3. $75.05 � 6

__

4. $43.05 � 4

__

5. 8,077 � 2

__

6. 1,130 � 7

__

7. $30.45 � 6

__

8. $51.03 � 8

__

9. 4 � 2,340

10. 6 � $30.55

11. 7 � $1,023

12. 5 � 3,405

13. 3,240 � 3

14. 4,063 � 5

15. 2,402 � 8

16. 7,861 � 9

Problem Solving and Test Prep17. It costs $35.90 for one ticket to the

circus. How much does it cost for 8 tickets to the circus?

18. Raul buys 3 packs of sports stickers. Each pack has 105 stickers. How many total stickers does Raul buy?

19. Mr. Bench buys 4 pairs of pajamas for $20.98 each. How much does Mr. Bench spend?

A $80.92

B $81.92

C $82.92

D $83.92

20. Carl buys 6 books to read over the summer. Each book has 203 pages. How many pages will Carl read over the summer?

A 1,209 pages

B 818 pages

C 1,218 pages

D 809 pages

Name Lesson 9.6

9,000; 9,132

23,000; 23,500

$420; $450.30

$160; $172.20

16,000; 16,154

7,000; 7,910

$180; $182.70

$400; $408.24

8,000; 9,360

$180; $183.30

7,000; 7,161

15,000; 17,025

9,000;9,720

20,000;20,315

16,000;19,216

72,000;70,749


315$287.20


DC




2 multiplication of money

3multiplication, of a 4-digit number with money

4 guess and check

5multiplication of 3-digit numbers

6 multi-step problem

7recognizing and using patterns


2 multiply by multiple of 10

7 multiply by multiple of 10

9multiply by multiples of 10 to complete a function table

13multiply by multiples of 10 to complete a function table

16use a table to compare products

17multiple choice; multiply using multiples of 10


Problem Solving Workshop Skill:Evaluate ReasonablenessProblem Solving Skill PracticeSolve the problem. Then evaluate the reasonableness of your answer.

1. Mr. Kohfeld buys a $1.37 carton of eggs each week. How much does Mr. Kohfeld spend on eggs in 4 weeks?

2. Vivian spends $6.49 on lunch every day. How much does Vivian spend on lunch in 7 days?

3. Yoshi is an athlete who eats a breakfast of 1,049 calories each morning. How many calories does Yoshi eat at breakfast in 7 days?

4. Together Elise and Chris spelled 27 words correctly. Chris spelled 5 more words correctly than Elise. How many words did each student spell correctly?

Mixed Applications 5. The Miller family eats 9 bowls of cereal

each day. How many bowls of cereal does the Miller family eat in a year (365 days)? How do you know your answer is reasonable?

6. Joe spent $25.87 for groceries. He bought cereal for $6.25, eggs for $5.37, pancake mix for $3.67, bacon for $7.25, and juice. How much did Joe spend on juice?

USE DATA For 7–8, use the information from the stone wall.

7. Tanya is building this wall from stone. If the pattern continues, how thick will the next stone be?

8. If the finished wall is 6 stones high, what is the overall height of the wall?

Name Lesson 9.7

5 in.?

9 in.7 in.

13 in.

11 in.

$5.48; yes because it is between $4.80 and $8.00.

$45.43; yes, because it is between $35.00 and $42.

7,343 calories; yes because it is between 7,000 and 8,400.

Chris: 16; Elise: 11

3,285 bowls; possible answer:it is between my estimates of 2,700 and 3,600

$3.33

3 inches

48 inches



Mental Math: Multiplication PatternsUse patterns and mental math to find the product.

1. 50 � 3,000

2. 7 � 40

3. 8 � 1,000

4. 50 � 700

5. 12 � 2,000

6. 70 � 200

7. 11 � 120

8. 90 � 80

ALGEBRA Complete the tables by using mental math.

9. 1 roll � 20 nickels 10. 1 roll � 60 dimes

11.

12.

13.

14.


15. What if you wanted to magnify a termite 6,000 times? How long would the termite appear to be?

16. Which would appear longer, a termite magnified 1,200 times or a wasp magnified 900 times?

17. How many zeros are in the product of 400 � 500?

A 4 C 6

B 5 D 7

18. How many zeros must be in the product of 1,000 and any factor?

A no more than 3 C none

B at least 3 D always 12

Name Lesson 10.1

Rolls 20 30 40 50 600

Nickels 400

Rolls 20 30 40 50 600

Dimes 1,200

� 7 60 700 8,000

40 2,800

60 480,000

� 8 40 500 9,000

50 400

90 810,000

Insect LengthsInsect Length (in mm)

Carpenter Bee 19

Fire Ant 4

Termite 12

Wasp 15

150,000 280 8,000 35,000

24,000 14,000 1,320 7,200

600; 800; 1,000; 12,000 1,800; 2,400; 3,000; 36,000

11. 2,400; 28,000; 320,000 12. 420; 3,600; 42,000

13. 2,000; 25,000; 450,000 14. 720; 3,600; 42,000

72,000 mm

the termite


B B

MXENL08ASE4X_PHTE_C10_L1.indd PW64 8/7/07 9:26:32 AM




2 practice multiplying by 10s



9use algebra to find missing digits in factors

12use algebra to find missing digits in factors

13use algebra to find missing digits in products

16 solve a multistep problem

17multiple choice; use multiplication

18multiple choice; multiply money


3practice 2-digit by 2-digit estimation






19multiple choice; estimate products


Multiply by TensChoose a method. Then find the product.

1. 20 � 17

2. 15 � 60

3. 66 � 50

4. 78 � 30

5. 96 � 40

6. 90 � 46

7. 52 � 80

8. 70 � 29

ALGEBRA Find the missing digit in the number.

9. 22 � 3� � 660

10. 60 � 37 � 2,�20

11. 5� � 80 � 4,480

12. �0 � 77 � 3,080

13. 40 � 44 � �,760

14. 90 � 83 � 7,4�0


15. How many frames does it take to produce 60 seconds of Snow White?

16. Are there more frames in 30 seconds of Pinnocchio or 45 seconds of The Enchanted Drawing?

17. Sadie runs 26 miles each week. How many miles will Sadie run in 30 weeks?

A 780

B 720

C 690

D 700

18. If gourmet cookies cost $12 a pound, how much does it cost to buy 30 pounds of cookies?

A $360

B $3,600

C $36

D $36,000

Name Lesson 10.2

Animated Productions

Title Date Released

Frames Per Second

The Enchanted Drawing © 1900 20

Little Nemo © 1911 16

Snow White and the Seven Dwarfs © 1937 24

Pinocchio © 1940 19

The Flintstones TM 1960-1966 24


340 900 3,300 2,340

3,840 2,0304,140 4,160

0

4

2

1

6

7

1,440

The Enchanted Drawing

A A


Mental Math: Estimate ProductsEstimate the product. Choose the method.

1. 34 � 34

2. 27 � 42

3. 41 � 55

4. 17 � 39

5. 72 � 21

6. 54 � 67

7. 58 � 49

8. 64 � 122

9. 93 � 93

10. 19 � 938

11. 42 � 666

12. 71 � 488

13. 54 � 32

14. 97 � 93

15. 549 � 65

16. 486 � 74

Problem Solving and Test Prep17. A serving of watermelon has 27 grams

of carbohydrates. About how many grams of carbohydrates do 33 servings of watermelon contain?

18. There are 52 homes in Kyle’s neighborhood. Each home has one refrigerator. The door on each refrigerator is opened 266 times a week. About how many times are the doors opened in all?

19. Choose the best estimate for the product 48 � 637.

A 20,000

B 24,000

C 30,000

D 34,000

20. Choose the best estimate for the product 64 � 271.

A 12 ,000

B 14,000

C 18,000

D 35,000

Name Lesson 10.3

Possible estimates are given. Methods will vary.

900 1,200 2,400 800

1,400 3,500 3,000 7,200

8,000 18,000 28,000 35,000

900 grams about 15,000 times


1,500 9,000 35,000 35,000

C A




2practice solving a simpler problem



5use a table to practice solving a simpler problem

7rewrite a previous problem by changing some data


1practice solving 2-digit-by2-digit multiplication using a grid model

5practice solving 2-digit-by2-digit multiplication using a grid model

8problem solving; practice solving 2-digit-by2-digit multiplication

9 model a product using a grid


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

1. For a year, Greta counted the birds in her backyard. She counted an average of 20 each day. About how many birds did Greta count in all during the year (365 days)?

2. Participants in the Backyard Birdcount reported seeing 843,635 Canadian geese and 710,337 snow geese. How many more Canadian geese were counted than snow geese?

3. Participants reported seeing 486,577 European starlings and 254,731 American robins. How many starlings and robins were reported in all?

4. The 93 counties in Nebraska reported seeing an average of 5,245 birds. About how many birds were reported in Nebraska?

Mixed Strategy Practice 5. USE DATA Jim saw a hummingbird

that was only 4 inches long. Which bird from the table at the right has a length that is 5 times as long as the hummingbird?

6. Bird watchers in Lincoln, Nebraska, reported seeing 311,214 birds. Bird watchers in Hutchinson, Kansas, reported seeing 133,288. How many birds were seen in all?

7. Look back at Exercise 4. Write a similar problem by changing the number of counties and the average number of birds seen.

Name Lesson 10.4

Type of Bird Maximum Speed(in miles per hour)

Maximum Length(in inches)

Carrion Crow 31

31

41

34

20

6

26

48

House Sparrow

Mallard

WanteringAlbatross

Possible estimate: about 7,000 133,298

741,308 Possible estimate: 450,000

444,502

Carrion Crow

Answers will vary.




Model 2-Digit by 2-Digit MultiplicationUse the model and partial products to solve.

1. 15 � 29

2. 17 � 32

3. 19 � 25

4. 14 � 27

5. 16 � 28

6. 19 � 24

Problem Solving and Test Prep 7. The apples from an average sized tree

will fill 20 bushel-sized baskets. If an orchard has 17 average sized trees, how many bushel-sized baskets of apples can it produce?

8. Each student eats about 65 apples a year. How many total apples will the 27 students in Mrs. Jacob’s class eat in one year?

9. Draw a model in the space below that could represent the product 64.

10. What product is shown by the model?

.

Name Lesson 10.5

435 544 475

378 448 456

1,755 apples340 baskets

442


Check students’ drawings; possible models, 32 � 2; 16 � 4; 8 � 8





3Practice multiplying 2-digit by 2-digit numbers with money

5Practice multiplying 2-digit by 2-digit numbers

7Practice multiplying 2-digit by 2-digit numbers

8Practice multiplying 2-digit by 2-digit numbers with money

10use a bar graph to practice multiplying 2-digit by 2-digit numbers

11multiple choice; multiply with money

12multiple choice; multiply 2-digit numbers


1practice multiplying 2-digit numbers

2practice multiplying 2- and 3- digit numbers and money

5practice multiplying 2- and 3- digit numbers and money

8practice multiplying 2- and 3- digit numbers

9practice multiplying 2- and 3-digit numbers with money

13 use the break apart strategy




Record 2-Digit by 2-Digit MultiplicationEstimate. Then choose either method to find the product.

1. 28 � 19

_

2. 36 � 53

_

3. $76 � 25

_

4. 64 � 31

_

5. 76 � 83

6. 41 � 69

7. 57 � 65

8. 82 � $48

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

9. Last summer, 19 people rented parasails on each of the windy days. How many people in all parasailed last summer on windy days?

10. If 13 people rented parasails on each of the windy and cold days, how many people rented parasails in all?

11. Willa bought 16 oak trees for her backyard. Each tree cost $33. How much did the trees cost in all?

A $300 C $528

B $480 D $600

12. There are 47 members in the Fun in the Sun Parasail Club. Each member spent 88 hours parasailing last year. How many hours in all did the club members spend parasailing last year?

A 6,413 C 4,230

B 4,136 D 7,236

Name Lesson 10.6

Tota

l Num

ber o

f Day

s Re

nted

Sun Beach Parasail

300

250

200

150

100

50

0

300

2813 22

Sunny Days

Rainy D

ays

Windy Days

Cold Days

Weather

600; 532 2,000; 1,908 $2,400; $1,900 1,800; 1,984

6,400; 6,308 2,800; 2,829 4,200; 3,705 $4,000; $3,936

247 riders

455 riders



B

C



Multiply 2-Digit and 3-Digit Numbers and MoneyEstimate. Then find the product.

1. 58 � 39

_

2. $4.28 � 45

__

3. 622 � 76

__

4. 199 � 37

_

5. $3.97 � 36

6. 544 � 47

7. 37 � $638

8. 747 � 23

9. $9.32 � 42 10. 81 � 422

11. $1.23 � 71

12. 15 � 602


13. Sally found 9 � 15 by using the break apart strategy. Show how Sally found the product.

14. Each of 41 electric cars can drive 50 miles an hour. How many miles in all do the cars travel in one hour?

15. Ken bought 52 loaves of multigrain bread for $3.89 a loaf. How much did Ken spend on bread in all?

A $202.28 B $206.17

C $206.89 D $208.21

16. How many minutes are there in 24 hours? Explain how you found your answer.

Name Lesson 10.7

2,400; 2,262

$200; $192.60

48,000; 47,272

8,000; 7,363

$160;$142.92

25,000; 25,568

$24,000; $23,606

14,000; 17,181

$360;$391.44

32,000; 34,182

$70; $87.33

12,000; 9,030

9 � 5 � 45; 9 � 10 � 90; 45 � 90 � 135

10,080; 7 � 24 � 60 � 10,080.


2,050


A





2choose and implement a practical multiplication method

7choose and implement a practical multiplication method with money

8choose and implement a practical multiplication method

12choose and implement a practical multiplication method with money




1practice solving multistep problems






Choose a MethodEstimate. Then find the product. Write the method you used.

1. 22 � 30

_

2. 653 � 31

__

3. 5,000 � 70

__

4. 322 � 23

__

5. 312 � 20

__

6. 666 � 11

__

7. $87.15 � 59

__

8. 9,000 � 80

__

9. 343 � 22

10. 505 � 90

11. 612 � 27

12. $52 � 375

Problem Solving and Test Prep13. Junie had a party at home. The

special plates she bought cost $12.39 each. If there were a total of 23 people at the party including June, how much did the plates cost in all?

14. A local store sells silver balloons at $28.75 a case. Frank bought 48 cases. How much did the balloons cost?

15. Carol sold pot holders at a craft fair. If she sold 40 pot holders for $8.25 each, how much money did she make?

A $330.00

B $320.00

C $32.50

D $32.00

16. Tatum bought 13 hair braids for $2.65 each. How much did Tatum spend in all?

A $10.50

B $26.50

C $34.45

D $47.45

Name Lesson 10.8

mental math; 660

paper and pencil; 20,243

mental math; 350,000


mental math; 6,240


calculator; $5,141.85

mental math; 720,000


mental math; 45,450

calculator; 16,524

paper and pencil; $19,500

$284.97 $1,380


AC

Methods may vary.



Problem Solving Workshop Skill: Multistep Problems

Problem Solving Skill Practice 1. The London Eye water ride has 18

boats. Each boat holds 22 people and runs 30 times a day. How many people ride the London Eye each day if all the boats are full all the time?

2. Bus A travels 532 miles one way. Bus B travels 1,268 miles round-trip. Which bus travels the most round-trip miles if Bus A makes 6 trips and Bus B makes 5 trips?

3. There are 62 students in all. Twenty-five students take only band class. Thirty-four students take only art class. The rest take both band and art class. How many students take both band and art?

4. Trin bought 6 T-shirts at $12.57 each. Ron bought 7 T-shirts at the same price. How much did Ron and Trin spend altogether?

Mixed ApplicationsUSE DATA For 5–6, use the table.

5. How many more inches does a magnolia grow in 5 years than a holly?

6. Len planted a 24-inch mountain laurel. About how tall will it be in 7 years?

7. A Ferris wheel has 20 cars that seat 4 people each. Each ride is 10 minutes long. How many people ride the Ferris wheel in 3 hours if all the cars are full all the time?

8. Rosa rode the Ferris wheel, the go-carts for 10 minutes, the merry-go-round for 25 minutes, and the roller coaster for 35 minutes. She rode a total of 1 hour and 30 minutes. How long did Rosa ride the Ferris wheel?

Name Lesson 10.9

Arborvitae

Holly

Magnolia

Mountain laurel

24 in.

12 in.

30 in.

10 in.

Tree Average Yearly Growth(in inches)

Popular Landscaping Trees


11,880 Bus A

3 students $163.41

1,440 people 20 minutes

90 inches

94 inches





2find the quotient and remainder




13problem solving; find the quotient and remainder

16multiple choice; identify the problem when given the model


1practice division using base-ten blocks









Divide with RemaindersUse counters to find the quotient and remainder.

1. 27 � 5 � 2. 34 � 8 � 3. 18 � 4 �

4. 57 � 7 � 5. 41 � 6 � 6. 53 � 9 �

Divide. You may wish to use counters or draw a picture to help.

7. 26 � 3 � 8. 34 � 4 � 9. 50 � 9 �

10. 9 � � 75 11. 8 � � 54 12. 7 � � 60

Problem Solving and Test Prep13. Five students are playing a card game

using a deck of 54 cards. If the cards are divided evenly among each player, how many will each student get? How many cards will be left over?

14. Bill made up a game using 10 each of purple, yellow, green, blue, orange, and red marbles. If Bill divides the marbles equally among 8 players, how many will be left over?

15. Which problem does the model describe?

A 34 � 5

B 28 � 5

C 34 � 6

D 20 � 6

16. Which problem does the model describe?

A 30 � 6

B 42 � 4

C 30 � 7

D 24 � 4

Name Lesson 11.1

5 r2 4 r2 4 r2

8 r1 6 r5 5 r8

8 r2 5 r5

8 r3 6 r6 8 r4

10 cards; 4 left over 4 marbles left over



8 r2

A C



Model 2-Digit by 1-Digit DivisionUse base-ten blocks to find the quotient and remainder.

1. 37 � 2 � 2. 53 � 5 � 3. 92 � 7 � 4. 54 � 4 �

5. 56 � 3 � 6. 89 � 9 � 7. 78 � 6 � 8. 92 � 8 �

9. 4 � � 65 10. 7 � � 79 11. 6 � � 89 12. 4 � � 87

Divide. You may wish to use base-ten blocks.

13. 3 � � 77 14. 2 � � 67 15. 4 � � 66 16. 5 � � 67

17. 37 � 3 � 18. 98 � 4 � 19. 91 � 6 � 20. 72 � 7 �

21. 8 � � 93 22. 6 � � 57 23. 4 � � 77 24. 9 � � 59

Name Lesson 11.2

18 r1 10 r3 13 r1 13 r2

18 r2 9 r8 13 11 r4

16 r1 11 r2 14 r5 21 r3

25 r2 33 r1 16 r2 13 r2

13 r1 24 r2 15 r1 10 r2

6 r519 r19 r311 r5






2practice dividing 2-digit by 1-digit numbers



14algebra; practice dividing 2-digit by 1-digit numbers to complete a function table

15problem solving; interpret the remainder

16problem solving; interpret the quotient

18multiple choice; identify the remainder


2solve a problem using the draw-a-diagram strategy



5 solve a problem using a table

6 order data in a table

7solve a problem using the predict-and-test strategy


Record 2-Digit by 1-Digit DivisionChoose a method. Then divide and record.

1. 4 � � 93 2. 7 � � 75 3. 5 � � 97

4. 49 � 3 � 5. 61 � 2 � 6. 95 � 7 �

7. 9 � � 87 8. 6 � � 87 9. 8 � � 99

Use multiplication to check each answer.

10. 93 � 7 � 13 r2 11. 89 � 8 � 11 r1 12. 51 � 4 � 12 r3

ALGEBRA Complete each table.

13. 14.

Problem Solving and Test Prep15. Sixty-three students signed up to play

golf. The coach divided them into teams with 4 student in each group. How many students were left over?

16. There will be 6 runners on each relay team. If a total of 77 runners signed up, how many teams could there be?

17. Four students divided 85 building blocks equally. How many building blocks did each student receive?

A 20 C 22

B 21 D 24

18. Three students divided 46 building blocks equally. How many building blocks were left over?

A 4 C 2

B 3 D 1

Name Lesson 11.3

Number of Cups 4 20 28 36 44

Number of Quarts 1 5

Number of Pints 64 72 80 88 96

Number of Gallons 8 9

23 r1 10 r5 19 r2

16 r1

14 r3

13 r4

9 r6

30 r1

12 r3

3 students 12 teams


13 � 7

_

91 � 2

_

93

B D

11 � 8

_

88 � 1

_

89

12 � 4

_

48 � 3

_

51

1197 121110

Methods may vary.


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

1. Fiona’s dog is 4 times as long as Rod’s dog. End to end, they are 60 inches long. How long is Fiona’s dog?

2. Davey divided 112 ounces of rabbit food equally into 7 containers. How many ounces did each container hold?

3. Dina walked 3 blocks west and 5 blocks north from her home to get to the pet store. If now she walks 1 block east, 4 blocks north, and another 2 blocks east, how far is Dina from her home?

4. Mel collects baseball cards. He wants 7 of each of his 13 favorite players. He now has a total of 87 cards. How many additional cards does Mel need to make his set of 7 cards each complete?

Mixed Strategy PracticeUSE DATA For 5–6, use the table below.

5. Together the height of Dan’s 3 dogs is 38 inches. What breeds are they?

6. Order the dogs in the table from shortest to tallest.

7. Altogether, Haille’s dog statue collection weighs 20 pounds. One statue weighs 8 pounds and the rest each weigh half as much. How many dog statues does Haille have?

8. Use the information from Exercise 5 to write a new problem that asks to explain the answer.

Name Lesson 11.4

48 inches 16 ounces

9 blocks 4 additional cards

Bichon Frise, Border Collie, Chichuahua

Chihuahua, Bichon Frise, Shar-Pei, Border Collie, Siberian Husky, Labrador Retriever, Irish Setter


Circled problems are suggested homework problems.4 statues




3 estimate 2-digit quotients



10 compare estimated quotients



16compare estimated quotients using data in a table



2recognize and use division patterns



8 use division patterns

10 use division patterns

16problem solving; use division patterns

18multiple choice; division of money


Mental Math: Division PatternsUse mental math to complete the pattern.

1. 72 � 8 � 9

720 � 8 �

7,200 � 8 �

72,000 � 8 �

2. 42 � 7 �

� 7 � 60

4,200 � 7 �

42,000 � 7 �

3. � 6 � 4

240 � 6 �

� 6 � 400

24,000 � 6 �

4. 30 � 3 �

� 3 � 100

3,000 � 3 �

� 3 � 10,000

5. � 5 � 8

400 � 5 �

� 5 � 800

40,000 � 5 �

6. 28 � 4 �

� 4 � 70

2,800 � 4 �

� 4 � 7,000

Use mental math and patterns to find the quotient.

7. 1,600 � 4

8. 28,000 � 7

9. 50 � 5

10. 900 � 3

11. 32,000 � 4

12. 2,000 � 5

13. 600 � 2

14. 3,500 � 7

Problem Solving and Test Prep15. Maria has 4,500 stamps in her collection.

She puts an equal number of stamps into each of 9 books. How many stamps are in each book?

16. Tex wants to put 640 stickers in his sticker book. If 8 stickers can fit on each page, how many pages will Tex fill?

17. The circus sells tickets for $4 each. If the circus collected a total of $2,000, how many tickets did they sell?

A 50

B 500

C 5,000

D 50,000

18. Dee collected $60 for selling tickets to the school play. If Dee sold 5 equally priced tickets in all, how much did each ticket cost?

A $12

B $24

C $30

D $45

Name Lesson 11.5

909009,000

6420

6006,000 4,000

2440

2,400

10300

1,00030,000

4080

4,0008,000 28,000

7280

700

400 4,000 10 300

8,000 400 300 500

500 stamps 80 pages


B

A


Mental Math: Estimate QuotientsEstimate the quotient.

1. 392 � 4

2. 489 � 6

3. 536 � 9

4. 802 � 8

5. 632 � 7

6. 32,488 � 4

7. 3,456 � 5

8. 7,820 � 8

Estimate to compare. Write �, �, or � for each .

9. 272 � 3 460 � 5 10. 332 � 6 412 � 5 11. 527 � 6 249 � 3

12. 138 � 2 544 � 9 13. 478 � 7 223 � 3 14. 3,112 � 8 1,661 � 8


15. About how many more times does a mouse’s heart beat in one minute than a dog’s heart beat in one minute?

16. About how many times does a human’s heart beat in 1 minute?

17. A common loon beats its wings about 1,250 times in 5 minutes. Which is the best estimate of the number of times it beats its wings in one minute?

A 20

B 40

C 250

D 400

18. Nine equal-length Arizona Black Rattlesnakes laid in a row measure 378 inches. What is the best estimate of the length of 1 rattlesnake?

A 20

B 40

C 200

D 400

Name Lesson 11.6

100 80 60 100

90 8,000 700 1,000

�

,

.

. .

,

Possible answer:about 400 more times

Possible answer: about 70 times



C B




1identify where to place the first digit and divide



9divide a 3-digit by a 1-digit number

16divide a 3-digit number by a 1-digit number

18problem solving; divide 3-digit by a 1-digit number

20multiple choice; place the first digit


3determine how to interpret the remainder



7exchange information to solve a new problem

8work backward to solve a problem


Place the First DigitTell where to place the first digit. Then divide.

1. 4 � � 511

2. 7 � � 621

3. 2 � � 124

4. 3 � � 423

5. 136 � 2

6. 215 � 5

7. 468 � 6

8. 357 � 8

Divide.

9. 3 � � 166 10. 9 � � 785 11. 4 � � 334 12. 6 � � 577

13. 116 � 2 � 14. 425 � 5 � 15. 627 � 7 � 16. 436 � 8 �

Problem Solving and Test Prep17. Petra picked 135 petals from the

flowers of sweet pea plants. Each flower had 5 petals. How many flowers did Petra pull petals from?

18. Todd wants to place some thyme plants equally into 8 areas in his garden. If he has 264 plants, how many thyme plants can Todd place in each area?

19. In which place is the first digit in the quotient 118 � 4?

A Ones C Hundreds

B Tens D Thousands

20. In which place is the first digit in the quotient 1,022 � 5?

A Ones C Hundreds

B Tens D Thousands

Name Lesson 11.7

hundreds tens tens hundreds

tens; 68 tens; 43 tens; 78 tens; 44 r5

55 r1 87 r2 83 r2 96 r1

58 85 89 r4 54 r4

27 flowers 33 thyme plants


B C

127 r3 88 r5 62 141



Problem Solving Workshop Skill: Interpret the RemainderProblem Solving Skill PracticeSolve. Write a, b, or c to explain how to interpret the remainder.

a. Increase the quotient by 1. b. Quotient stays the same.Drop the remainder.

c. Use the remainder as the answer.

1. The crafts teacher gave 8 campers a total of 55 beads to make necklaces. If the teacher divided the beads equally among the campers, how many did each camper receive?

2. In all, campers from each 3 tents brought 89 logs for a bonfire. Two tents brought equal amounts but the third brought more. How much more?

3. Gene had 150 cups of water to divide equally among 9 campers. How many cups did Gene give each camper?

4. Camp leaders divided 52 cans of food equally among 9 campers. How many cans of food were left over?

Mixed Applications 5. Gail had 34 hot dogs. She gave

3 camp counselors 2 hot dogs each before dividing the rest equally among the 7 campers. How many hot dogs did Gail give each camper?

6. The morning of a hiking trip the temperature was 54�F. By mid afternoon, the temperature had risen to 93�F. How much warmer was the afternoon temperature?

7. Pose a Problem In Exercise 5, suppose Gail gave 8 counselors 2 hotdogs each. How many hotdogs did Gail give each camper?

8. Wynn bought these camping tools: a flashlight, an axe for $15, a lantern for $12, and a camp stool for $23. If Wynn spent a total of $57, how much did the flashlight cost?

Name Lesson 12.1

6 beads; b 2 logs more; c

16 cups; b 7 cans; c

4 hot dogs 39�

2 hot dogs with 4 left over $7






2divide money and check the answer

6 divide and check the answer

10 find the missing divisor

13find the missing digit in the dividend

15 find the missing remainder

16use logical reasoning to find the unit cost

18 multiple choice; dividing


2write the number of digits in the quotient

7write the number of digits in the quotient

11practice dividing and checking the quotient

12practice dividing and checking the quotient




Divide 3-Digit Numbers and MoneyDivide and check.

1. 147 � 5 � 2. $357 � 7 � 3. 575 � 4 �

4. 6 � � $844 5. 9 � � 874 6. 8 � � 766

7. 137 � 4 � 8. 325 � 3 � 9. $924 � 7 �


10. 577 � � 115 r2 11. 10� 2 � $405

12. 9 � � 593

13. 1 4 5 r2 14. 71 r4 15. 7 � � 488

Problem Solving and Test Prep16. In all, Alfred paid $18 for 12 bundles of

asparagus at a local grocery store. If the bundles were in a buy-one-get-one-free sale, how much did each bundle cost before the sale?

17. Eva wants to divide 122 yards of yarn into 5-yard lengths to make potholders. How many potholders can Eva make? How many yards will be left over?

18. Ed divided 735 football cards equally among 8 friends. How many cards did each friend get?

A 98

B 91

C 99

D 99r3

19. Four cans of spaghetti are on sale for $4.64. How much does one can of spaghetti cost?

Name Lesson 12.2

5 r8

� � 572

69 r

4 � � 5 2

$3 24; 2 yards left over

$1.16


29 r2 $51 143 r3

140 r4 97 r1 95 r6

34 r1 108 r1 $132

B

5 8

68 8

5


Zeros in DivisionWrite the number of digits in each quotient.

1. 366 � 3

2. 5 � � 374

3. 635 � 7

4. 4 � � 923

5. 672 � 8

6. 5 � � 811

7. 9 � 921

8. 6 � � 597

9. 816 � 2

10. 7 � � 177

Divide and check.

11. 495 � 5 � 12. 719 � 6 �

13. 3 � � 735 14. 3 � � 735

Problem Solving and Test Prep15. Yoshi has a collection of 702

miniature cars that he displays on 6 shelves in his bookcase. If the cars are divided equally, how many are on each shelf?

16. In 5 days, scouts made a total of 865 trinkets for a fundraiser. If they made the same number each day, how many did they make in 1 day?

17. Greta has 594 flyers in stacks of 9 flyers each. How many stacks of flyers will Greta make?

A 55

B 66

C 77

D 88

18. Susan has 320 slices of banana bread. She wants to fill bags with 8 slices of banana bread each. How do you find the number of bags Susan will fill? Explain.

Name Lesson 12.3

3 digits 2 digits 2 digits 3 digits 2 digits

3 digits 3 digits 2 digits 3 digits

99

2 digits

245 224 r1

117 cars 173 trinkets

Divide the number of slices by the number of slices per bag. 320 � 8 � 40


119 r5

B





1practice dividing a 3-digit number



13algebra; find the missing dividend

15problem solving; practice dividing a 3-digit number

17multiple choice; divide to solve a problem


1use compatible numbers to estimate quotients of 3-digit by 2-digit numbers




10practice estimating quotients using data

11practice estimating quotients in word problems

14multiple choice; choose the best estimate of a division problem


Choose a MethodDivide. Write the method you used.

1. 2 � � 643

2. 2 � � 2,418

3. 4 � � 6,458 4. 5 � � 1,467 5. 3 � � 2,483

6. 7 � � 8,123 7. 8 � � 7,467 8. 3 � � 5,105 9. 7 � � 6,111 10. 4 � � 9,600

ALGEBRA Find the dividend.

11. � � 3 � 178

12. � � 4 � 733

13. � � 7 � 410

Problem Solving and Test Prep14. Leona’s team scored a total of

854 points in 7 days. Pilar’s team scored a total of 750 points in 6 days. Which team scored more points per day?

15. Vicki has 789 seeds to put into packets. If she puts 9 seeds in each packet, how many packets will Vicki need? How many seeds will be left over?

16. Seth donated a total of $3,336 over 6 months. He donated the same amount each month. How much did Seth donate each month?

A $210

B $333

C $336

D $556

17. Joe calculated that he drove 1,890 miles a year roundtrip, to and from work. If each round trip is 9 miles, how many days did Joe work?

A 210

B 333

C 336

D 556

Name Lesson 12.4


321 r1 403 1,614 r2 293 r2 827 r2

1,160 r3 933 r3 1,701 r2 873 2,400

534 2,932 2,870

Pilar’s team87 packets with 6 seeds left over

D A

Methods may vary.


Estimate QuotientsWrite the compatible numbers you would use to estimate the quotient. Then estimate.

1. 564 � 21 �

2. 878 � 11 �

3. 421 � 52 �

4. 72 � � 4,218

5. 93 � � 2,644

6. 27 � � 564

7. 3,611 � 42 �

8. 91 � � 6,942

9. 29 � � 5,764

10. USE DATA About how many more times does a human heart beat in one minute than a brown bear’s heart beats in one minute?

Problem Solving and Test Prep11. A sea lion’s heart beats 1,615 times in

17 minutes. About how many times does a sea lion’s heart beat in one minute?

12. A group of 23 mature female sea lions weigh 9,706 pounds. Estimate the average weight of one sea lion in this group.

13. What is the best estimate of 887 � 32?

A 10

B 20

C 30

D 40

14. What is the best estimate of 626 � 63?

A 20

B 60

C 26

D 10

Name Lesson 13.1

Animal Heart Rates

Animal Average Number of Heart Beats in 35 minutes

Human 2,520

Brown bear 1,365


600 � 20; 30 900 � 10; 90 400 � 50; 8

4,200 � 70; 60

2,700 � 90; 30

600 � 30; 20

Possible answer: about 40 more times

Possible answer: about 80 times

Possible answer: about 500 pounds

C D

4,000 � 40; 100

7,200 � 90; 80

6,000 � 30; 200






1dividing a 2-digit by 2-digit number using base-ten blocks



11dividing 3-digit by 2-digit money amounts by drawing a picture

12dividing 3-digit by 2-digit number by drawing a picture

14dividing a 3-digit by 2-digit number

16dividing a 3-digit by 2-digit money amount


1divide a 3-digit by 2-digit number



6divide a 4-digit number by a 2-digit number

9algebra; find the missing dividend of a 4-digit by 2-digit division problem

10algebra; find the missing remainder of a 3-digit by 2-digit division problem

12problem solving; solve a 3-digit by 2-digit division word problem

13problem solving; solve a 4-digit by 2-digit division word problem


Name Lesson 13.2

Model Division by 2-Digit DivisorsUse base-ten blocks to divide.

1. 87 � 21

2. 50 � 12

3. 58 � 16

4. 78 � 21

5. 37 � 14

6. 71 � 15

7. 67 � 18

8. 98 � 23

Draw a picture to divide.

9. 131 � 17

10. 168 � 25

11. $208 � 52

12. 192 � 32

Divide. You may use base-ten blocks or draw a picture.

13. 76 � 18

14. 31 � � 164

15. 19 � � 157

16. $105 � 15


4 r3 4 r2 3 r10 3 r15


2 r9 4 r11 3 r13 4 r6

7 r12 6 r18 $4 6

4 r4 5 r9 8 r5 $7

Check students’ pictures.


Name Lesson 13.3

Record DivisionDivide and record.

1. 276 � 42 �

2. 806 � 31 �

3. 668 � 23 �

4. 651 � 45 �

5. 14 � � 98 6. 44 � � 1,872 7. 32 � � 709 8. 51 � � 478

ALGEBRA Find the missing number.

9. � 18 � 97 10. 822 � 43 � 19 r 11. 289 � 26 � r3

Problem Solving and Test Prep12. Annie has a collection of 433 nickels.

If she puts them into rolls of 20 nickels each, how many rolls will Annie make? How many nickels will Annie have left over?

13. Mr. Keele recently packed up his collection of 1,033 family photos. If each box held 35 photos, how many boxes did Mr. Keele use? How many photos were left over?

14. June always puts 16 stamps on each page of her stamp album. Her aunt just bought her 284 stamps. Explain how to use division to find how many pages June will fill in her album.

15. Herb has 2,435 stickers to divide equally among his 29 classmates. How many stickers will be left over?

A 11

B 27

C 28

D 83


6 r24

C

26 29 r1 14 r21

7 42 r24 22 r5 9 r19

1,7465 11

21 rolls, 13 left 29 boxes, 18 left

Possible explanation: Estimate to place the first digit in the quotient. Then divide. Write the remainder next to the quotient.




2adjust the estimated digit in the quotient



7algebra; find the value of a variable

9algebra; find the value of a variable




1determine if there’s too much or too little information to solve a word problem

2determine if there’s too much or too little information to solve a word problem

3problem solving; use data from a chart

5problem solving; determine the possible combinations from among 3 choices

6 solve a multi-step problem


Name Lesson 13.4

Adjusting QuotientsAdjust the estimated digit in the quotient, if needed. Then divide.

1. 19 � � 118 2. 53 � � 268

3. 37 � � 296

4. 21 � � 1,974 5. 48 � � 1,928

6. 64 � � 1,422


7. 860 � 43 � n

n �

8. 1,092 � 13 � n

n �

9. 1,064 � n� 56

n �

10. n � 32 � 46

n �

Problem Solving and Test Prep11. Mr. James drove 225 miles to visit his

brother. He maintained a speed of 45 miles per hour. How many hours did Mr. James drive?

12. A commuter train can hold a total of 1,978 passengers in 23 equally sized cars. How many passengers can the train carry in each car?

13. Ms. Grey’s car travels 32 miles per gallon of gas. Explain how to estimate how many gallons of gas Ms. Grey will need to travel 2,816 miles.

14. The cafeteria staff put 833 carrotsticks into bags. Each bag held 22 carrot sticks. Which is the best estimate of how many bags they filled?

A 30

B 40

C 50

D 60

7 5 7

1 4 3


20

6 r4 5 r3 8

94 40 r8 22 r14

84 19 1,472

5 hours 86 passengers

Possible explanation:

Round. 3,000 � 30 � 100,

so she would need about

100 gallons.

B



Name Lesson 13.5

Problem Solving Workshop Skill: Too Much/Too Little InformationProblem Solving Skill Practice

Decide if the problem has too much or too little information. Then, solve if possible. If there is too little information, identify the missing information.

1. Rocky has a collection of 954 trading cards. He divides the trading cards equally into boxes. The boxes are 5 inches by 7 inches. In how many boxes does Rocky store his trading cards?

2. Wendy’s assignment is to divide 567 gold stars equally into 21 bags. The stars are to be used for school craft projects over the next 6 weeks. How many gold stars can Wendy put into each bag?

Mixed ApplicationsUSE DATA For 3–6, use the sign below.

3. Janis wants to buy 11 of her friends a gift from the Last Chance CD Sale. How much money will Janis need to save if she buys each friend a Top-10 CD? Will your answer be an estimate or an exact answer?

4. Jaime decided to buy 5 top-10 CDs and 4 soundtracks. How much more do the 5 top-10 CDs cost than the 4 soundtracks cost?

5. Lisa has $38 to buy 3 CD gifts for her friends. What possible combinations could Lisa buy?

6. Nelly will buy 1 book on CD and 3 soundtracks. Kyle will buy 3 top-10 CDs and 1 soundtrack. Who will spend more: Nelly or Kyle?

Last Chance CD SaleTop-10 $13 Books on CD $14Soundtracks $11


too little; number of

boxes available

too much; 27 gold stars

$143; exact answer $21 more

1 ea.; 3 soundtracks; 2 S, 1 top

10; 2 soundtracks, 1 book on

CD; 2 top-10, 1 soundtrack Kyle





3practice finding all the factors of composite numbers

6 practice finding multiples

9decide if one number is a factor of another



16Practice finding a pattern of multiples

18 finding a factor of a number

19multiple choice; finding factors of a number


2decide if a number is divisible by another



14 practice the divisibility rules

15 practice the divisibility rules

17problem solving; divide by multiples of 10

19multiple choice; decide if a number is divisible by another


Factors and MultiplesUse arrays to find all of the factors of each product.

1. 12

2. 18

3. 30

4. 21

List the first twelve multiples of each number.

5. 11

6. 4

7. 9

Is 8 a factor of each number? Write yes or no.

8. 16

9. 35

10. 56

11. 96

Is 32 a multiple of each number? Write yes or no.

12. 1

13. 16

14. 13

15. 8

Problem Solving and Test Prep16. Tammy wants to make a pattern

of multiples of 2, that are also factors of 16. What will be the numbers in Tammy’s pattern?

17. Which multiples of 4 are also factors of 36?

18. What multiple of 7 is a factor of 49?

19. Fred is placing 10 cups on a table, in equal rows. In what ways can Fred arrange the cups?

A Rows of 1, 2, or 6

B Rows of 2, 4, or 6

C Rows of 1, 2, 5 or 10

D Rows of 10, 20, or 30

Name Lesson 14.1

1, 2, 3, 4, 6, 12

1, 2, 3, 6, 9, 18

1, 2, 3, 5, 6, 10, 15, 30

1, 7, 21

11, 22, 33, 44,

55, 66, 77, 88,

99, 110, 121, 132

4, 8, 12, 16, 20,

24, 28, 32, 36,

40, 44, 48

9, 18, 27, 36,

45, 54, 63, 72,

81, 90, 99, 108

yes

2, 4, 8, 16

yes yesno

yesyes no yes

4, 12


7

C



Divisibility RulesTell whether the number is divisible by 2, 5, 10, or 25.

1. 825

2. 312

3. 466

4. 745

5. 250

6. 155

7. 380

8. 455

9. 676

10. 695

11. 300

12. 266

Write true or false for each statement. Explain.

13. All numbers divisible by 25 are also divisible by 2.




Problem Solving and Test Prep17. Ace wants to divide 86 blocks equally

among 10 students. Will Ace have any blocks left over? If yes, how many?

18. Can Greta divide 760 scorecards equally among 25 teammates? If yes, how many will each teammate receive? If no, why not?

19. Which number is divisible by 5 and 10?

A 2,245 C 2,446

B 2,300 D 2,557

20. If a number is divisible by 15, is it also divisible by 5 and 10? Explain.

Name Lesson 14.2

5, 25 2 2 5

2, 5, 10, 25 5 2, 5, 10 5

false; numbers divisible by 2 have to be even; some numbers divisible by 25 are not even.

true; 10 is divisible by 5.

yes; 6 no; 760 is not equally divisible by 25.

2 5 2, 5, 10, 25 2

false; numbers divisible by 5 end in 5 or 0; numbers divisible by 1 include all numbers.

true; 5 is divisible by 1.

It is divisible by 5 but not necessarily by 10.


B




2use a model to determine a prime or composite number




9determine whether a number is prime or composite





23multiple choice; determine which number is prime


1find a rule and extend the pattern

3find a rule and extend the pattern

6use a rule to find missing numbers in a pattern

8use a rule to find missing numbers in a pattern

10 develop a pattern



14 write a rule for a pattern

15multiple choice; find a rule for a pattern


Prime and Composite NumbersMake arrays to find the factors. Write prime or composite for each number.

1. 9

2. 17

3. 24

4. 36

5. 41

6. 2

7. 27

8. 57

Write prime or composite for each number.

9. 54

10. 37

11. 29

12. 40

13. 45

14. 33

15. 51

16. 88

17. 42

18. 11

19. 21

20. 67

Problem Solving and Test PrepUSE DATA For 21–22, use the picture of stickers.

21. In what other ways could the stickers be arranged in equal rows?

22. Is 49 prime, or composite? Explain.

23. Which of the following is a prime number?

A 20 C 24

B 21 D 29

24. Which of the following is a composite number?

A 19 C 36

B 23 D 41

Name Lesson 14.3

Check students’ arrays.

1, 3, 9; composite

1, 17; prime

Possible answer: no other way or in one row of 49 stickers

composite; it has more than two factors

1, 2, 3, 4, 6, 8, 12, 24; composite

1, 2, 3, 4, 9, 12, 18, 36; composite

1, 3, 9, 27; composite

composite prime prime composite

primecomposite composite composite

composite prime composite prime


1, 41; prime

1, 2; prime

1, 3, 19, 57; composite

D C


Number PatternsFind a rule. Then find the next two numbers in your pattern.

1. 108, 99, 90, 81, ,

2. 2, 4, 6, 8, ,

3. 2, 4, 8, 16, ,

4. 85, 88, 82, 85, 79, 82, ,

ALGEBRA Find a rule. Then find the missing numbers in your pattern.

5. 2, 6, 10, , 18, 22, 26,

6. 545, 540, 535, , 525,

7. 600, 590, 592, 582, 584,

8. 400, 410, 409, , 418,

Use the rule to make a number pattern. Write the first four numbers in the pattern.

9. Rule: Add 7. Start with 14.

10. Rule: Subtract 6.Start with 72.

11. Rule: Add 2, subtract 5.

Start with 98.

12. Rule: Multiply by 2, subtract 1.Start with 2.

Problem Solving and Test Prep13. Look at the number pattern below.

What is the next number if the rule is multiply by 2?

3, 6, 12,

14. Use the pattern 6, 9, 18, 21. What is a rule for the pattern if the next number is 24?

15. Which of the following describes a

rule for this pattern? 3, 8, 5, 10, 7, 12

A Add 3, subtract 5.

B Add 5, subtract 3.

C Add 5, subtract 2.

D Add 5, subtract 3.

16. What might the next two numbers in this pattern be? 192, 96, 48, 24, ,

Name Lesson 14.4

Rule: subtract 9 Rule: add 2

Rule: multiply by 2 Rule: add 3, subtract 6

Rule: add 4 Rule: subtract 5

Rule: subtract 10, add 2 Rule: add 10, subtract 1

14, 21, 28, 35

98, 100, 95, 97 2, 4, 3, 6

Add 3



72, 66, 60, 54

Possible answers: 12, 6

B


24

72 63 10 12

530 520

419 428574

14 30

797632 64




2solve problems using the find a pattern strategy





2write fractional parts of a whole using models

5 draw fractional parts

9write a fraction for its word name

11write a fraction for its word name

12problem solving; write a fractional part of a whole

14multiple choice; write a fractional part of a whole

15problem solving; write fractional parts of a whole


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

1. A 3 by 3 array of blocks is painted so that every other row, starting with row 1, begins with a red block, and the alternate rows begin with a black block. Does the 12th row begin with red or black?

2. What will be the next three shapes in the pattern?

3. The first day on a March calendar is Saturday. The month of March has 31 days. On which day of the week is the last day of March?

4. How many blocks are needed to build a stair step pattern that has a base of 10, a height of 10, and where each step is one block high and one block deep?

Mixed Strategy Practice 5. USE DATA If the pattern continues,

how much would each 5-inch spike cost if you buy 10,000?

6. Jules bought 5 pet turtles for $2 each. How much money did Jules spend on turtles in all?

7. Dorothy bought gloves with a $20 dollar bill. The gloves cost $6. How much change did Dorothy receive?

Ralph’s Hardware Builder’s Sale

Spike 10 100 1,000

5-inch 10 cents ea. 8 cents ea. 6 cents ea.



Name Lesson 14.5


black 3 lightning bolts

Monday 55 blocks

4 cents each

$10 $14


Read and Write FractionsWrite a fraction for the shaded part. Write a fraction for the unshaded part.

1.

2.

3.

Draw a picture and shade part of it to show the fraction. Write a fraction in word form for the unshaded part.

4. 5 __ 6 5. 4 ___

10 6. 3 __

7 7. 3 __

5

Write the fraction for each.

8. one eighth

9. seven tenths

10. four out of five

11. two divided by three

Problem Solving and Test Prep12. Angela has 5 dollars to spend on

lunch. She spends 1 dollar on a drink, 3 dollars on a hot dog, and 1 dollar on a bag of pretzels. What fraction of Angela’s money does she spend on a hot dog?

13. There are 9 houses on Zack’s block. Four of them are red brick and the rest are gray brick. What fraction of the houses on Zack’s block are gray brick?

14. Niko cuts a pizza into eight equal parts. He eats 3 slices of pizza. What fraction of Niko’s pizza is left?

A 1 __ 8 C 3 __ 5

B 3 __ 8 D 5 __

8

15. Melissa buys 9 pieces of fruit. Of the fruit, 3 _ 9 are apples, 2 _ 9 are bananas and the rest are pears. What fraction of Melissa’s fruit are pears? Explain.

Name Lesson 15.1

4 _ 6 ; 2 _

6 7 _

8 ; 1 _

8 3 _

5 ; 2 _

5

1 _ 8 7 __

10 4 _

5 2 _

3

5 _ 9 3 _

5

4 __ 9 ; I can count the fruit that

isn’t apples or bananas.

Check students’ drawings.


four sevenths

one sixth

six tenths

two fifths

D





2writing equivalent fractions for a model

6 writing equivalent fractions

9 identify equivalent fractions

14identify if a fraction is in simplest form

20problem solving; write a fraction in simplest form

22multiple choice; identify equivalent fractions


1compare fractions using a model



7 order fractions

10 order fractions

15multiple choice; write equivalent fractions

16problem solving; compare two fractions


Model Equivalent FractionsWrite two equivalent fractions for each model.

1.

2.

3.

Write two equivalent fractions for each.

4. 1 __ 5 5. 2 __

3 6. 3 ___

12 7. 6 __

8

Tell whether the fractions are equivalent. Write � or �.

8. 2 __ 9 , 4 ___ 16

9. 2 __ 6 , 8 ___ 24

10. 1 __ 7 , 2 ___ 14

11. 6 ___ 12

, 2 __ 3

Tell whether the fraction is in simplest form. If not, write it in simplest form.

12. 12 ___ 16

13. 5 __ 9 14. 18 ___

20 15. 3 ___

14

ALGEBRA Find the missing numerator or denominator.

16. 2 __ 8 � ____

24 17. 6 ___

16 � ____

8 18. 7 __

9 � 28 ____ 19. 2 __

5 � 20 ____

Problem Solving and Test Prep 20. Sheryl’s cat had a litter of kittens. Of the

kittens, 3 are white and 6 are gray. What fraction of the kittens are white? Write the fraction in simplest form.

21. Mario ate 4 hot dogs. One of them had mustard on it and the rest were plain. What fraction of Mario’s hot dogs were plain? Write an equivalent fraction for Mario’s plain hot dogs.

22. Which fraction is equivalent to 2 __ 5 ?

A 3 __ 6 C 4 ___

10

B 2 __ 8 D 5 ___

15

23. Explain why 15 __ 45 is not equivalent to 5 _ 8 ?

Name Lesson 15.2

2 3 4 5 6 7 88 8 8 8 8 8 8 81

3 _ 5 , 9 __

15 3 _

4 , 9 __

12 1 _

2 , 3 _

6

2 __ 10

; 3 ____ 15

4 _ 6 ; 6 _

9 1 _

4 ; 6 ____

24 3 _

4 ; 12 __

16

� ��

no; 3 _ 4 yes no; 9 ____

10 yes

3 _ 9 ; 1 _

3 3 _

4 ; 6 _

8




C

15 ____ 45

in simplest form is 1 _ 3 ;

1 _ 3 � 5 _

8 .

6 336 50

PracticePW96© Harcourt · Grade 4

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

1. 4 __ 5 2 __

3 2. 1 __

5 1 __

8

3. 2 __ 6 1 __

3 4. 3 __

8 5 __

8

Order the fractions from least to greatest.

5. 1 __ 3 , 1 __

8 , 1 __

6

6. 2 __ 5 , 5 ___

10 , 3 __

9

7. 5 __ 6 , 11 ___

12 , 2 __

4

8. 3 __ 8 , 4 ___

12 , 1 __

9

Order the fractions from greatest to least.

9. 1 __ 5 , 1 __

4 , 1 __

8

10. 2 __ 6 , 3 ___

10 , 5 __

8

11. 2 __ 3 , 1 __

5 , 4 __

9

12. 1 __ 2 , 2 ___

12 , 2 ___

10

Problem Solving and Test Prep13. Trisha has 8 stamps from the United

States, 4 stamps from Mexico, and 3 stamps from Canada. What fraction of stamps does Trisha have from each country?

14. Pete has 12 stamps from the United States, twice that many from Mexico, and 3 from Canada. What fraction of stamps does Pete have from each country?

15. Which number makes this statement true?

1 __ 4 � ___

16

A 1 C 4

B 2 D 16

16. In Billy’s collection, 1 _ 4 of his stamps are from the United States and 3 __ 12 of his stamps are from Mexico. From which country does Billy have more stamps? Explain.

Name Lesson 15.3

15

18

0 1 2 3

1 3

15

25

35

450 1

.

,�

1 _ 8 , 1 _

6 , 1 _

3 3 _

9 , 2 _

5 , 5 __

10 2 _

4 , 5 _

6 , 11 __

12 1 _

9 , 4 __

12 , 3 _

8

1 _ 2 , 2 __

10 , 2 __

12 2 _

3 , 4 _

9 , 1 _

5 5 _

8 , 2 _

6 , 3 __

10 1 _

4 , 1 _

5 , 1 _

8

U.S. 8 ____ 15 ; Mexico 4 ____ 15 ; Canada 3 ____ 15 , or 1 __ 5

U.S. 4 ____ 13 ; Mexico 8 ____ 13 ; Canada 1 ____ 13

They are equal 1 __ 4 = 3 ____ 12 .


C

.





1write a mixed number from a picture

6identify a fraction on a number line

10write a mixed number as a fraction

12write a fraction as a mixed number

14locate a fraction on a number line

16multiple choice; write a mixed number as a fraction


2use fraction bars to compare mixed numbers

4use a number line to compare mixed numbers

6 order three mixed numbers

8use a table to compare mixed numbers

10multiple choice; compare mixed numbers


Read and Write Mixed NumbersWrite a mixed number for each picture in standard form and word form.

1. 2. 3.

Use the number line to write the letter each mixed number or fraction represents.

4. 14 ___ 6 5. 3 4 __

6 6. 11 ___

6 7. 3 3 __

6 8. 7 __

6

Rename each fraction as a mixed number and each mixed number as a fraction.

9. 5 3 __ 4

10. 3 2 ___ 10

11. 38 ___ 6

12. 23 ___ 3

13. 2 3 __ 8

Problem Solving and Test Prep14. Ned cuts a board that is 5 1 _ 4 inches

long. Draw a number line and locate and label 5 1 _ 4 inches.

15. Julia goes for a bike ride for 1 2 _ 3 hours. Draw a number line to represent the length of the bike ride.

16. Denzel makes a cake with 2 2 _ 3 cups of flour. Which shows 2 2 _ 3 as a fraction?

A 4 __ 3 C 6 __

3

B 8 __ 3 D 10 ___

3

17. Ashley serves 3 5 _ 8 trays of muffins. Explan how you would draw a picture to show the mixed number.

Name Lesson 15.4

41 1 1 2 2 3 3 3

A B C

56

26

36

46

16

D E

3 1 _ 4 ; three and one fourth

2 3 _ 5 ; two and three fifths

4 5 _ 6 ; four and five sixths

C E B D A

23 __ 4 32 __

10 6 2 _

6 7 2 _

3 19 __

8





B

PracticePW98

Compare and Order Mixed NumbersCompare the mixed numbers. Write ,, ., or � for each .

1. 2.

1 3 __ 5 1 3 __ 4 1 1 __

3 1 5 __

8

3. 43 1

2

3 414

24

34

4. 6 71

626

36

46

56

3 1 __ 2 3 2 __

4 6 5 __

6 6 2 __

6

Order the mixed numbers from least to greatest.

5. 2 1 __ 4 , 4 3 __

8 , 2 3 __

4

6. 5 4 __ 9 , 5 2 __

3 , 5 1 __

8

7. 3 4 __ 5 , 3 2 ___

10 , 3 5 ___

12


8. Which ingredient shows the largest amount?

9. Which ingredient requires 5_3 cups?

10. The lengths of four activities are listed below. Which activity is the longest?

A 12__5 hours C 22__

5 hours

B 32__5 hours D 32__

3hours

11. Eddie is at an amusement park and wants to find the ride with the shortest wait time. The wait times for four rides are shown. Which wait time is the shortest?

A 14__5 hours C 11__

2hours

B 1 1 __ 5 hours D 1 2 __ 3 hours

Name Lesson 15.5

Recipe for Trail Mix

Ingredient Amount

Corn chips 2 cups

Peanuts 1 1 _ 3 cups

Raisins 1 2 _ 3 cups

1

131

18

18

18

18

18


�

2 1 _ 4 , 2 3 _

4 , 4 3 _

8

corn chips

raisins

5 1 _ 8 , 5 4 _

9 , 5 2 _

3 3 2 __

10 , 3 5 __

12 , 3 4 _

5


� �

�

B

D




2use sequencing to order mixed numbers

3use sequencing to compare fractions

6change the information in a problem to write a new problem


2use a model to add like fractions

8add like fractions in horizontal form




PracticePW99© Harcourt · Grade 4

Problem Solving Workshop Skill: Sequence InformationProblem Solving Skill PracticeSequence the information to solve.

1. Ben practices piano for 1 2 _ 3 hours. Charlene practices flute for 3 _ 4 hours. Walter practices drums for 1 1 _ 2 hours. Who practices for the most time? the least?

2. Sara cuts 3 lengths of ribbon. The first piece is 4 5 _ 8 inches long. The second piece is 3 1 _ 4 inches long. The third piece is 4 1 _ 2 inches long. Which piece of ribbon is the longest? the shortest?

3. Joyce naps for 8 _ 5 hours. Rex naps for 5 _ 3 hours. Maya naps for 5 _ 4 hours. Who takes the longest nap? the shortest?

4. Betsy, Latisha, and Ramon eat a pizza pie. Betsy eats 2 _ 8 of the pie. Latisha eats 1 _ 4 of the pie. Ramon eats 3 _ 8 of the pie. Which two children eat the same amount of pie?

Mixed Applications 5. Raul and Marty bake 12 muffins.

Raul brings home 5 __ 12 of the muffins. Marty brings home 1 _ 3 of the muffins. Draw number lines to show who brought home more muffins?

6. Suppose that the number of muffins Marty brought home, in Exercise 5, was changed to 1 _ 2 . Write a new word problem using this information.

7. Zach makes this number line:

Between which two fractions would you place 3 _ 8 ?

8. Rina makes this number line:

Between which two numbers would you place 2 5 __ 6 ?

Name Lesson 15.6

0 114

24

34

32 13

2 23

2

0 1512

0 113

Rex; Maya

Longest 4 5 _ 8 ; Shortest 3 1 _

4

Raul

Betsy and Latisha


between 1 _ 4 and 2 _ 4 between 2 2 _ 3 and 3

Ben; Charlene

Answers will vary.


Model AdditionFind the sum.

1.

1 __ 3 � 2 __

3 �

2.

2 __ 6 � 2 __

6 �

3.

1 __ 2 � 1 __

2 �

4.

3 __ 8 � 2 __

8 �

5.

2 __ 4 � 1 __

4 �

6.

3 __ 6 � 3 __

6 �

Model the sum. Record your answer.

7. 3 __ 8 � 1 __

8 � 8. 4 __

9 � 2 __

9 � 9. 2 ___

10 � 4 ___

10 �

10. 3 __ 6 � 1 __

6 � 11. 4 ___

12 � 5 ___

12 � 12. 1 __

4 � 1 __

4 �

13. 1 __ 8 � 5 __

8 � 14. 3 __

6 � 2 __

6 � 15. 5 ___

10 � 2 ___

10 �

16. 2 __ 9 � 3 __

9 � 17. 6 ___

12 � 2 ___

12 � 18. 1 __

4 � 3 __

4 �

19. 2 __ 3 � 1 __

3 � 20. 6 __

9 � 4 __

9 � 21. 1 __

8 � 6 __

8 �

0 118

28

38

48

58

68

78

0 116

26

36

46

56

0 114

24

34

Name Lesson 16.1

3 _ 3 , or 1 4 _

6 2 _

2 , or 1

5 _ 8 3 _

4 6 _

6 ; or 1

4 _ 8 6 _

9 6 __

10

4 _ 6 9 __

12 2 _

4

6 _ 8 5 _

6 7 __

10

5 _ 9 8 __

12 4 _

4 , or 1

3 _ 3 , or 1 10 __

9 , or 1 1 _

9



7 _ 8





2subtracting fractions using a model

9 subtracting in horizontal form





2 subtract in vertical form

5 add in horizontal form

7 add in horizontal form

9 compare equivalent fractions

11 solve for a variable

15problem solving; use a bar graph to subtract fractions

17 multiple choice; add fractions


Model SubtractionFind the difference.

1.

5 __ 6 � 2 __

6 �

2.

2 __ 6 � 1 __

6 �

3.

1 __ 2 � 1 __

2 �

4.

3 __ 4 � 2 __

4 �

5.

2 __ 3 � 1 __

3 �

6.

3 __ 5 � 1 __ 5 �

Model the difference. Record your answer.

7. 8 ___ 10

� 3 ___ 10

� 8. 7 __ 9 � 2 __

9 � 9. 10 ___

12 � 5 ___

12 �

10. 5 __ 6 � 1 __

6 � 11. 6 __

8 � 1 __

8 � 12. 8 __

9 � 5 __

9 �

13. 7 __ 8 � 5 __

8 � 14. 3 __

4 � 1 __

4 � 15. 4 __

6 � 1 __

6 �

16. 8 __ 9 � 3 __

9 � 17. 8 ___

12 � 2 ___

12 � 18. 6 ___

10 � 1 ___

10 �

19. 2 __ 3 � 1 __

3 � 20. 6 __

9 � 4 __

9 � 21. 7 __

9 � 6 __

9 �

Name Lesson 16.2

140 12

434

130 12

325

35

15

450 1

3 _ 6 1 _

6 0 _

2 , or 0

2 _ 5

5 __ 12

3 _ 9

5 _ 9

5 _ 8

5 __ 10

4 _ 6

1 _ 4 1 _

3

2 _ 8 2 _

4 3 _

6

5 _ 9

2 _ 9 1 _

3

5 __ 10

6 __ 12



1 _ 9


Record Addition and SubtractionFind and record the sum or difference.

1. 7 __ 8

� 3 __ 8

_

2. 5 __ 6

� 3 __ 6

_

3. 3 ___ 12

� 4 ___ 12

_

4. 8 __ 9

� 1 __ 9

_

5. 7 ___ 10

� 3 ___ 10

� 6. 7 __ 9 � 4 __

9 � 7. 4 ___

12 � 7 ___

12 �

Compare. Write ,, ., or � for each .

8. 5 __ 6 � 1 __

6 1 9. 4 __

9 � 1 __

9 1 __

3 10. 10 ___

12 � 2 ___

12 7 ___

12

ALGEBRA Find the value of x.

11. 2 __ 7 � x __ 7 � 6 __

7

x �

12. x __ 3 � 1 __

3 � 1 __

3

x �

13. 4 __ 5 � 3 __

5 � 1 __ x

x �

14. 4 __ x � 6 __ x � 1

x �

Problem Solving and Test PrepUSE DATA For 15–16, use the graph.

15. How much more time does Sara study than Brian studies?

16. How much more time does Malik study than Sara and Brian together?

17. Sue buys 2 _ 8 pound of walnuts and 5 _ 8 pound of peanuts. How many pounds of nuts does Sue buy in all?

A 3 __ 8 C 7 __

8

B 2 ___ 16

D 7 ___ 16

18. Juan’s garden is divided into eighths. Of the garden, 3 _ 8 is tomato plants and 1 _ 8 is cucumber plants. What part of the garden is planted with tomato and cucumber plants?

Name Lesson 16.3

1-21-4

1

3-42-41-4

0

1

1

Sara Malik Brian

Time Spent Studying

Frac

tions

of a

n Ho

ur

10__8

, or 1 2_8 , or 1 1_

4 2 _ 6 , or 1 _

3 7__

12 7 _ 9

10 __ 10

, or 1 3_9 , or 1_

3 11 __ 12

< >�

4 2 5 10

1 _ 2 hour

1 _ 4 hour

4 __ 8 , or 1 __

2


C




2 write a subtraction equation

3 write an addition equation

6 use a table to add fractions


2 add with mixed numbers

5add mixed numbers with a sum of a whole number

7subtract with mixed numbers; answer written in simplest form

11add a mixed number and a fraction

13find the value for n in the numerator to make an equation true

15use a table to subtract mixed numbers

18problem solving; subtract mixed numbers


Problem Solving Workshop Strategy: Write an EquationProblem Solving Strategy PracticeWrite an equation to solve.

1. Jasmine takes dance class for tap and modern dance. The class lasts for 5 _ 6 hour. The modern dance part lasts for 2 _ 6 hour. How long does the tap class last?

2. Martin buys 5 _ 8 yard of fabric for a project. He has 2 _ 8 yard of fabric left over after completing the project. How much fabric did Martin use for his project?

3. Robert goes to soccer practice on Saturdays. This week, 2 _ 5 of the children at practice are girls. What fraction of the children at practice are boys?

4. Harley and Belinda share a bag of crackers. Harley eats 7 __ 12 of the crackers. Belinda eats 4 __ 12 of the crackers. What fraction of the crackers do they eat in all?

Mixed Strategy PracticeUSE DATA For 5–6, use the table.

5. Nicky walks dogs to earn money. How much more time does Nicky spend walking Binky than Pugg?

6. How much time does Nicky spend walking Rusty and Pugg together?

7. Michel practices piano for 75 minutes each day. Write a mixed number to show the number of hours Michel practices.

8. Linda plays 90 minutes of softball a day. Write a mixed number to show the number of hours Linda plays softball.

Name Lesson 16.4

Dog Walking Hours

Dog Names Time Spent

Pugg 2 _ 8 hour

Rusty 3 _ 8 hour

Binky 5 _ 8 hour


2 __ 6 � d � 5 __

6 ; 3 __

6 5 __

8 � f � 2 __

8 ; 3 __

8

2 __ 5 � b � 5 __

5 ; 3 __

5 7 ____

12 � 4 ____

12 � c; 11 ____

12

3 __ 8 hour

5 __ 8 hour

1 1 __ 4 hours 1 1 __

2 hours

Equations and variables may vary.


Add and Subtract Mixed NumbersModel and record the sum or difference.

1. 2 1 __ 8

� 1 3 __ 8

_

2. 1 3 __ 5

� 3 1 __ 5

_

3. 5 7 ___ 10

� 1 2 ___ 10

__

4. 3 7 __ 9

� 3 __ 9

_

5. 2 1 __ 3

� 1 2 __ 3

_

6. 3 3 ___ 12

� 1 4 ___ 12

__

7. 2 5 __ 6

� 1 3 __ 6

_

8. 4 8 ___ 12

� 1 3 ___ 12

__

9. 1 7 __ 9 � 1 4 __

9 � 10. 2 3 __

4 � 2 1 __

4 � 11. 4 4 ___

10 � 7 ___

10 �


12. 2 4 __ 6 � 1 n __

9 � 3 5 __

6

n �

13. 3 n __ 8 � 2 3 __

8 � 1 2 __

8

n �

14. 5 9 ___ 10

� 5 n ___ 10

� 2 ___ 10

n �


15. How many more inches are there of green ribbon than blue ribbon?

16. Tim adds another 2 2 _ 8 inches of red ribbon. How many inches are there now of both red and green ribbon?

17. Sonya drives 2 3 __ 10 miles to the store and 4 4 __ 10 miles to the library. How far does Sonya drive in all?

A 2 7 __ 10 miles

B 6 7 __ 10 miles

C 6 6 __ 10 miles

D 6 7 __ 20 miles

18. Ira uses 4 3 _ 8 cups of almonds, 2 1 _ 8 cups of raisins, and 1 2 _ 8 cups of peanuts to make trail mix. How much more almonds does Ira use than peanuts? Explain.

Name Lesson 16.5

Ribbons Used for Puppets

Red 3 4 _ 8 inches

Blue 4 1 _ 4 inches

Green 5 1 _ 8 inches

3 4 __ 8 , or 3 1 __

2 4 4 __

5 4 5 ____

10 , or 4 1 __

2 3 4 __

9

3 3 __ 3 , or 4 4 7 ____

12 1 2 __

6 , or 1 1 __

3 3 5 ____

12

3 __ 9 , or 1 __

3 4 4 __

4 , or 5

1 5 7

7 __ 8 inches

10 7 __ 8

4 11 __ 10

, or 5 1 __ 10

Possible explanation:4 3 __ 8 � 1 2 __ 8 � 3 1 __ 8.

B





2 model the sum less than 1

3 change both denominators

5 model the difference

9 model the sum greater than 1

11 sum greater than 1

13 subtract

18change both denominators and subtract


2find equivalent decimal and fraction of a model

4find equivalent decimal and fraction of a model

7 write a fraction as a decimal


12write the equivalent fractions, decimals, and money amounts

13write the decimal for the expanded form

14write the missing number in the expanded form

17multiple choice; write a decimal in fraction form


Model Addition and Subtraction of Unlike FractionsModel the sum or difference. Draw a picture of your model.

1. 1 __ 2 � 1 __

4 � 2. 3 __

8 � 1 __

4 � 3. 1 __

2 � 1 __

5 �

4. 2 __ 3 � 2 __

6 � 5. 3 __

8 � 1 __

4 � 6. 8 ___

12 � 1 __

2 �

7. 1 __ 2 � 2 __

6 � 8. 7 __

9 � 1 __

3 � 9. 7 ___

10 � 3 __

5 �

Find the sum or difference.

10. 1 __ 8 � 1 __

4 � 11. 3 __

4 � 1 __

2 � 12. 4 ___

10 � 4 __

5 �

13. 3 __ 4 � 3 __

8 � 14. 2 __

3 � 3 ___

12 � 15. 5 __

6 � 1 __

3 �

16. 4 __ 9 � 1 __

3 � 17. 3 __

4 � 5 __

8 � 18. 1 __

3 � 1 __

4 �

Name Lesson 16.6

3 _ 4 5 _

8 7 __

10

2 _ 6 , or 1 _

3 1 _

8 2 ____

12 , or 1 _

6

5 _ 6 4 _

9 13 __

10 , or 1 3 __

10

3 _ 8 5 _

4 , or 1 1 _

4

12 __ 10

, or 1 2 __ 10

,or 1 1 __

5

3 _ 8 5 ____

12 3 _

6 , or 1 _

2

7 _ 9 1 _

8 1 ____

12



Relate Fractions and DecimalsWrite the fraction and decimal shown by each model.

1.

2.

3.

4.

Write each fraction as a decimal. You may draw a picture.

5. 6 ___ 10

6. 2 ____ 100

7. 1 ___ 10

8. 63 ____ 100

Write the amount as a fraction of a dollar, a decimal, and as a money amount.

9. 6 dimes

10. 2 nickels 7 pennies

11. 4 dimes 9 pennies

12. 8 dimes 12 pennies

ALEGBRA Find the missing number.

13. 9 tenths � 7 hundredths � 14. 6 tenths � hundredths � 0.66

Problem Solving and Test Prep15. Write five cents in decimal form.

16. Write one and thirty-four hundredths in decimal form.

17. Which shows the decimal 0.06 in

fraction form?

A 8 ____ 100

B 6 ____ 100

C 8 ___ 10

D 6 ___ 10

18. Abby and Bridget each get $1 a week in allowance. So far this week, Abby has spent $0.40 of her allowance and Bridget has spent 8 __ 10 of her allowance. Abby says that she has spent more than Bridget. Explain how to determine if Abby is correct.

Name Lesson 17.1

3 __ 10

; 0.3 9 __ 10

; 0.9 45 ______ 100

; 0.45 75 ___ 100

; 0.75

0.6 0.02 0.1 0.63

6 ____ 10

, or 3 __ 5 ;

0.6; $0.60 17 ______ 100

; 0.17; $0.17

92 ______ 100

; 0.92; $0.92

0.97 6

0.05 1.34

Possible answer: Abby is incorrect because $0.40 � 4 ____

10 and 4 ____

10 , 8 ____

10 .


49 ______ 100

; 0.49; $0.49

B





2 write a decimal as a fraction



9write words in decimal and fraction form

14write words in decimal and fraction form


20multiple choice; write a decimal as a fraction


4reinforce decimal equivalents with models

7recognize decimals that are not equivalent

10write a fraction as an equivalent decimal

11 write equivalent decimals

15write a fraction as an equivalent decimal

17use models to write equivalent decimals




Decimals to ThousandthsWrite each decimal as a fraction.

1. 0.423

2. 0.003

3. 0.091

4. 0.202

Write each fraction as a decimal.

5. 776 _____ 1,000

6. 103 _____ 1,000

7. 45 _____ 1,000

8. 6 _____ 1,000

Write the decimal in two other ways.

9. ten thousandths

10. 0.063

11. forty-one thousandths

12. 0.189

13. 0.2 � 0.022

14. five hundred thousandths

15. 0.33 � 0.303

16. two thousandths

Problem Solving and Test Prep 17. A millisecond is 1 _____ 1,000 of a second. How

would you write 115 milliseconds in decimal form?

18. The length of 1 thief ant is 0.079 cm. What is the length of one thief ant written as a faction?

19. Which decimal is equivalent to 300 _____ 1,000 ?

A 3 C 0.0300

B 0.300 D 0.003

20. Which fraction is equivalent to 0.007?

A 7 ___ 10

C 7 _____ 1,000

B 7 ____ 100

D 70 ____ 100

Name Lesson 17.2

423 _____ 1,000

3 __________ 1,000

91 __________ 1,000

202 __________ 1,000

0.776 0.103 0.045 0.006

63 __________ 1,000

,

sixty-three thousandths

41 __________ 1,000

,

0.041

189 __________ 1,000

,

one-hundredeighty-nine thousandths

0.222, two-hundred twenty-two thousandths

500 __________ 1,000

,

0.500

633 __________ 1,000

, six-hundred thirty-three thousandths

2 __________ 1,000

,

0.002

0.115 79 __________ 1,000


10 __________ 1,000

,

0.010

B C



Equivalent DecimalsUse a tenths model and a hundredths model. Are the two decimals equivalent? Write � or �.

1. 0.1 and 0.10

2. 0.23 and 0.32

3. 0.65 and 0.56

4. 0.3 and 0.30

5. 0.22 and 0.23

6. 0.9 and 0.09

7. 0.76 and 0.67

8. 0.50 and 0.5

Write an equivalent decimal for each. You may use decimal models.

9. 0.70

10. 1 __ 4

11. 0.2

12. 3 __ 4

13. 0.3

14. 0.50

15. 7 ___ 10

16. 0.90

ALGEBRA Write an equivalent decimal. Use the models to help.

17.

0.3 � 0.04 �

18.

� � 0.75

19.

� � 0.93

Name Lesson 17.3

� �

� �

� �

� � � �

0.7 0.25 0.20 0.75

0.90.70.50.30

0.34

0.9

0.7

��


0.05

0.03





1use model to write an equivalent decimal and mixed number

2use a number line to write an equivalent decimal and mixed number

4write a mixed number in other forms

7 write a decimal in other forms

9 write the missing addend

10 write the missing addend

12write the word form as the decimal form

13multiple choice; write a decimal as a mixed number


3 find equivalent decimals

6 compare unlike decimals

8 compare unlike decimals

11 order decimals

13 order money amounts

16recognize if an equation is true

17recognize if an equation is true

19 place value of decimals

21multiple choice; recognize if an equation is true

PracticePW109

Name Lesson 17.4


Relate Mixed Numbers and DecimalsWrite an equivalent mixed number and a decimal for each model.

1.

2.

Write an equivalent mixed number and a decimal for each. Then write the word form. You may use a model.

3. 6.6

4. 3 90 ____ 100

5. 4.75

6. 5 1 __ 4

7. 2.09

ALGEBRA Write the missing number for each .

8. 2.4 � 2 � 9. 3.80 � 3 � 0.8 � 10. 5.06 � 5 � � 0.00

Problem Solving and Test Prep11. Harriet is thinking of a decimal

that is equivalent to eight and one-fifth. What is that decimal?

12. A CD case measures four and four-fifths inches by five and three-fifths inches. What is the decimal form of the measurements?

13. Which mixed number is equivalent to 3.25?

A 3 1 __ 4

B 3 2 __ 5

C 3 2 __ 3

D 2 9 ____ 100

14. In simplest form, what is an equivalent fraction for the decimal 2.36?

A 2 4 ___ 50

B 2 3 ___ 10

C 2 9 ___ 25

D 2 6 ____ 100

3010

3510

4010

4.03.0

3.4, 3 4 ____ 10

3.5, 3 5 __ 10

6 3 __ 5 , six

and three-fifths

3.9, three and 9 tenths

4 3 __ 4 , four

and three-fourths

5.25, five and twenty-five hundredths

2 9 ______ 100

, two and nine-hundredths

0.4 0.0 0.06

8.2 4.8 by 5.6 inches


A C


PracticePW110

Name Lesson 17.5


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

1. 4.2 4.01 2. $6.03 $6.33 3. 2.30 2.3 4. $7.75 $7.57

5. 3.5 3.50 6. 8.08 8.80 7. $5.51 $5.15 8. 9.94 9.59

Use a number line to order the decimals from least to greatest.

9. 1.01, 1.02, 1.0, 1.05 10. 3.33, 3.03, 3.34, 3.04 11. 0.01, 1.02, 1.01, 1.05

Order the decimals from greatest to least.

12. 5.4, 5.04, 5.44, 5.43 13. $26.67, $26.76, $26.07 14. 2.77, 2.76, 2.70, 2.66

ALGEBRA Tell whether each number sentence is true or false. If the sentence is false, write the correct number sentence.

15. 4.20 � 4.2

16. 7.67 � 7.76

17. 6.6 � 6.60

18. 8.06 � 8.05

Problem Solving and Test Prep19. Which of the following numbers has

the same value as the digit 6 in the number 2.06? 6.6, 6.06, 6.60, 6.206

20. Order the following numbers from greatest to least.7.07, 7 1 __

2 , 7.05, 7 60 ____

100

21. Which number sentence is correct?

A 5.2 � 5.20 C 3.43 � 3.34

B 6.007 � 6.07 D 4.22 � 4.21

22. Order the decimals from least to greatest. 0.5, 0.9, 0.09, 0.05

. , � .

� ., .

1.0, 1.01, 1.02, 1.05

3.03, 3.04, 3.33, 3.34

1.05, 1.02, 1.01, 0.01

5.44, 5.43, 5.4, 5.04

$26.76, $26.67, $26.07

2.77, 2.76, 2.70, 2.66

true true false; 6.6 � 6.60

false; 8.06 . 8.05

6.06 7 60 ___ 100

, 7 1 _ 2 , 7.07, 7.05

0.05, 0.09, 0.5, 0.9


C





1 compare to find the best value

4problem solving; compare decimals

5problem solving; estimate or exact answer


4 practice rounding to tenths

5practice rounding money to the nearest dollar

8practice rounding money to the nearest dollar

9practice rounding to the nearest hundredth




17 round data shown on a map

19multiple choice; round a decimal to the nearest tenth

20multiple choice; round a decimal to the nearest tenth

PracticePW111

Name Lesson 17.6


Problem Solving Workshop Skill: Draw ConclusionsProblem Solving Skill PracticeUse the information on the chart to draw a conclusion.

1. Jane looks at the ads to the right and wants the best value for her money. Jane wants to buy playing cards. Which game store has the best price for the playing cards?

2. Which store has the better price for checkers?

Mixed ApplicationsUSE DATA For 3–4, use the map.

3. Sal lives 4.08 miles from Discount Games. Who lives closer: Amy or Sal?

4. Sal lives 6.33 miles from Great Games. List Amy, Sal, and Zelda in the order they live from each store from the least to greatest distance.

5. Patty paid for 8 Tshirts with five $20-dollar bills. If the shirts each cost $12.35, about how much change did Patty receive? Do you need an estimate or an exact answer?

GREAT GAMES

DISCOUNT GAMES

Amy’s house

Zelda’s house

6.3 miles

4.8 m

iles

2.5 m

iles

8.3 miles

Discount Games

Discount Games

Sal

Great Games: Zelda, Amy, Sal; Discount Games: Sal, Amy, Zelda

estimate; about $4



Round DecimalsRound each number to the nearest tenth and each money amount to the nearest dollar.

1. 7.38

2. 43.56

3. 199.62

4. 76.04

5. $22.51

6. $8.87

7. $255.02

8. $655.78

Round each number to the nearest hundredth.

9. 7.236

10. 5.499

11. 51.511

12. 388.901

13. 299.454

14. 49.995

15. 87.468

16. 6.666

Problem Solving and Test PrepUSE DATA For 17–18, use the map.

17. Round each weight per fleece to the nearest whole number. Which states now show equal weight per fleece?

18. Order the states shown according to the heaviest weight per fleece to the lightest.

19. Mr. Scott gets 29.57 miles per gallon in his van. Which shows the miles per gallon rounded to the nearest tenth?

A 29.5 miles

B 29.4 miles

C 29.6 miles

D 29.7 miles

20. Paul is 5.89 feet tall. Which shows Paul’s height to the nearest tenth?

A 5.2 feet

B 5.9 feet

C 5.6 feet

D 5.8 feet

Name Lesson 18.1

NY6.7 lb

PA6.5 lb

MD6.9 lb

WI7.1 lb

IL6.8 lb

MI5.8 lb

Average Weight per Fleece for Six Selected States

7.4 43.6 199.6 76.0

$23 $9 $255 $656

7.24 5.50 51.51 388.90

299.45 50.00 6.67 87.47

IL, NY, MD, PA, WI

WI, MD, IL, NY, PA, MI


CB




2 practice estimating the sum

5use money to practice estimating the difference

7practice estimating the difference

8use money to practice estimating the sum

10compare estimates of sums and differences

12compare estimates of sums and differences

14use data in a table to practice estimating the difference

15 estimate the difference

16 estimate the difference


1 use a model to find the sum





9use a model to find the missing addend

10use a model to find the missing addend


Estimate Decimal Sums and DifferencesEstimate the sum or difference.

1. 6.42 � 8.55 2. 12.88 � 9.52

3. $12.24 � $8.27 4. 53.514 � 48.661

5. $44.03 � $15.97 6. 3.034 � 5.807

7. 502.229 � 497.536 8. $71.04 � $8.49

Estimate to compare. Write �, �, or � for each .

9. 43.22 � 15.67 81.77 � 22.14 10. 52.48 � 12.02 15.65 � 23.99

11. 76.993 � 47.225 15.425 � 12.601 12. 21.88 � 16.02 75.61 � 40.65


Name Lesson 18.2

Month Snowfall (in inches)

Average SnowfallBuffalo, New York

December

January

February

March

24.3

24.0

17.7

12.5

13. About how much less snow falls in Buffalo in March than in December?

14. In December 2001, Buffalo reported 82.1 inches of snowfall. About how much more is this than the average?

15. David drove 99.15 miles in January and 88.98 miles in February. About how many more miles did David drive in January than in February? Show your work.

16. Mr. Frances drives 35.62 miles to work. Mrs. Frances drives 27.25 miles to work. About how many more miles does Mr. Frances drive to work than Mrs. Frances? Show your work.


15 23 $4 5

4 $799$28

, �

..

about 11 in. less

about 58 in. more

about 10 miles more; 99 � 89 � 10

about 9 miles more; 36 � 27 � 9



Model AdditionUse models to find the sum.

1. 0.56 �0.45

__

2. 0.4 �0.7

_

3. 0.25 �0.07

__

4. 1.05 � 0.78

5. 0.2 � 1.6

6. 0.44 � 1.08

7. 1.06 �0.67

__

8. 0.38 �1.9

__

ALGEBRA Use the models to find the missing addend.

9.

0.7 � � 0.9

10.

0.34 � � 0.59

Name Lesson 18.3

1.01 1.1 0.32

1.83 1.8 1.52

1.73 2.28

0.2 0.25






2use a model to find the difference





9use a model to find the missing number

10use a model to find the missing number


3practice estimating and subtracting money amounts

6practice estimating and adding decimals

8practice estimating and subtracting decimals

9practice comparing sums of money

10practice comparing decimal sums and differences

11 practice adding decimals

13practice finding missing addends

16 practice adding decimals

17 practice subtracting decimals

18multiple choice; subtract money


Model SubtractionUse models to find the difference.

1. 0.57 �0.18

__

2. 0.7 �0.3

_

3. 1.07 �0.42

__

4. 1.09 �0.90

__

5. 1.9 �1.2

_

6. 1.00 �0.63

__

7. 2.73 � 1.79

8. 2.9 � 2.07

ALGEBRA Use the models to find the missing number.

9.

0.80 � � 0.56

10.

� 0.73 � 0.95

Name Lesson 18.4


0.39 0.4 0.65

0.370.70.19

0.830.94

0.24 1.68


Name Lesson 18.5


Record Addition and SubtractionEstimate. Then record the sum or difference.

1. 5.43 �2.54

__

2. 2.89 �1.22

__

3. $41.32 �37.44

__

4. 2.29 � 1.53

__

5. $21.82 � $13.09

6. 42.14 � 24.36

7. $94.23 � $65.44

8. 57.22 � 53.88

Compare. Write ,, �, or � for each .

9. $5.15 � $0.10 $4.84 � $0.35 10. 3.78 � 2.51 9.54 � 3.30

ALGEBRA Find the missing decimals. The sums are given at the end of each row and bottom of each column.

11. 13.06 4.12 22.77

12. 67.77 15.14 83.64

13. 0.98 73.22 80.78

14. 78.07 44.49 204.37

Problem Solving and Test Prep15. Sierra had 8.25 feet of plastic wrap.

She used 3.75 feet. How much plastic wrap does Sierra have left?

16. Lyle spent $2.47 on peanut butter, $3.56 on jelly, and $2.37 on a loaf of bread. How much did Lyle spend in all?

17. Lauren saved $9.25 of her allowance. Chloe saved $2.45 less than what Lauren saved. How much did Chloe save?

18. Jason bought pants on sale for $25.89. The original price was $33.98. How much did Jason save?

A $8.25

B $8.19

C $8.11

D $8.09

2; 2.89 4; 4.11 $4; $3.88 4; 3.82

$35; $34.91 66; 66.5 or 66.50

$29; $28.79 3; 3.34

39.95

0.73

6.58

81.81

..

4.5 or 4.50 feet $8.40



D

$6.80




1find the amount of change due



7use a table to find the amount of change due

9multiple choice; find the amount of change due

10multiple choice; find the amount of money paid with


2predict and test the different ways of making change

3predict and test the different ways of making change

4predict and test the different ways to find the coins needed to pay for an item

6use a table to find the amount of money spent

8 subtract money


Make ChangeMake change. List the bills and coins.

1. Cost: $0.38 Paid with:







7. Babs bought 4 sandwiches and 3 salads. If she paid with a $20 bill, how much change should Babs receive?

8. Faith bought one of each item on the menu. How much change should Faith receive if she paid with a $10 bill?

9. Lila bought 10 yogurts. How much change did Lila receive if she paid with a $10 bill?

A Four quarters

B One $1 bill

C One $5 bill

D One dime

10. Jay paid for a $14.05 baseball cap and received $1 in change. Which of the following amounts did Jay give the cashier for the baseball cap?

A One $10 bill

B One $10 bill and four $1 bills

C One $10 bill, one $5 bill, and 1 nickel

D One $20 bill

Name Lesson 18.6

Food Item Price

Beach Snack Bar

Salad

Sandwich

Yogurt

Fruit Cup

$1.75

$3.29

$0.99

$1.45

2 quarters, 1 dime, 2 pennies; $0.62

1 quarter; $0.25 1 $10 bill, 4 $1, 1 dime,1 nickel; $14.15

2 $1 bills, 1 quarter, 2 dimes, 3 pennies; $2.48

3 quarters, 1 dime, 2 pennies; $0.87

1 $20 bill, 1 $10 bill, 1 $5 bill, 1 $1 bill, 3 quarters; $36.75

$1.59

$2.52

Possible coins and bills are given.


DC


Problem Solving Workshop Strategy: Compare Strategies

Problem Solving Strategy PracticePredict and test or make a table to solve.

1. Dana will buy a sandwich from the vending machine. The sandwich costs $2.45. Dana has two $1 bills, 3 quarters, 3 dimes, and 4 nickels. What are two different ways Dana can make exactly $2.45 with the bills and coins she has?

2. Victor has a $1 bill, 4 quarters, and 2 dimes. He will borrow some money from a friend to buy a sandwich for $2.45. What coin or coins must he borrow in order to pay for the sandwich?

3. A bag of pretzels costs $1.00 in a vending machine. How many different ways can you pay the exact amount in coins if only one of your coins is a quarter?

4. Sugar-free gum costs $0.85 in a vending machine. If you have only one quarter, how many dimes would you need to buy a pack of sugar-free gum?


5. Tanya spent $9.80 at the pool. What did Tanya pay for ?

6. Libby paid for herself and two sisters to go to the pool. She also bought 3 towels and a bathing cap. How much money did Libby spend?

7. Henry had the exact change to pay for a $0.50 pencil. He paid with 6 coins. What could those coins be?

8. In Exercise 1, how much money will Dana have left over after she buys the sandwich?

Name Lesson 18.7

Item Prices

Community Center Pool

Entrance Fee

Bathing Cap

Towel

$1.50

$2.75

$5.55

Answers will vary; must equal $2.45

6



Entrance fee, bathing cap, and a towel

$23.90

4 dimes and 2 nickels $0.80Circled problems are suggested homework problems.





3 recognize a ray

4 recognize a point

7identify a line segment in real life situations

8identify a plane in real life situations

9 draw an example of a plane

11 draw an example of a ray

13identify a line segment in real life situations

15multiple choice; recognize a ray in real life situations

16multiple choice; recognize a point in real life situations


2 measure a straight angle

5 draw an acute angle

7 draw a right angle

8identify a right angle in real life situations

10identify an obtuse angle in real life situations

11 identify acute angles

13multiple choice; identify the number of degrees in a straight angle

14multiple choice; estimate the number of degrees in an obtuse angle


Points, Lines, and RaysName a geometric term that represents the object.

1. top of a desk

2. chalk tray

3. a point from Earth into space

4. point of a pencil

Name an everyday object that represents the term.

5. point

6. ray

7. line segment

8. plane

Draw and label an example of each.

9. plane ABC 10. line segment DE 11. ray FG 12. point H

Problem Solving and Test PrepUSE DATA For 13–16, use the picture.

13. What geometric term describes the place where the ceiling meets a wall?

14. What feature in the hallway shows planes?

15. What geometric term best describes the arrow on the ceiling?

A Line C Point

B Line segment D Ray

16. Which geometric term best describes the black dot on the window?

A Line C Point

B Line segment D Ray

Name Lesson 19.1

plane ray point

Answers will vary.

line segment


line segment

Possible answer: tile on floor


D C



Measure and Classify AnglesTrace each angle. Use a protractor to measure the angle. Then write acute, right, straight, or obtuse.

1.

2.

3.

4.

Draw and label an example of each angle. Identify and name the points and rays of each angle.

5. acute angle PQR 6. straight angle STU 7. right angle XYZ

Classify each angle. Write acute, right, straight, or obtuse.

8.

9.

10.

Problem Solving and Test PrepUSE DATA For 11–12, use the angles shown at the right.

11. Which angles appear to be acute?

12. What type of angle does angle HJM appear to be?

13. Which word describes an angle that has a measure of 180�?A acute B right C straightD obtuse

14. What is the best estimate of the measure of the angle below?A between 15� and 45�

B between 90� and 135�

C between 45� and 90�

D between 180� and 270�

A

CB E

D

F

K

JL

M

ON

GK

L

M

J

H

Name Lesson 19.2

135�; obtuse 180�; straight 90�;right 45�;acute

Check students’ angles.

right acute

obtuse

KJM; KJL; KJG; LJM

obtuse


C B




1 identify perpendicular lines

4 identify intersecting lines

8identify parallel lines in real life situations

9use a map to identify parallel streets

11multiple choice; describe intersecting lines

12multiple choice; describe parallel lines


3identify a polygon that is not regular

4 identify a regular polygon

7identify a figure that is not a polygon

9distinguish between polygons and figures that are not polygons

10 identify polygons in a pattern

12multiple choice; name a six-sided polygon


Line RelationshipsName any line relationships you see in each figure. Write intersecting, parallel, or perpendicular.

1.

2.

3.

4.

5.

6.

7.

8.

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

9. Name a street that appears to be parallel to E Broadway Street.

10. Name a street that intersects Madison Street NE and appears to be parallel to 15th Avenue NE.

11. Which best describes intersecting lines?

A They never meet.

B They form four angles.

C They form only obtuse angles.

D They form only acute angles.

12. Which best describes parallel lines?

A They never meet.

B They form four angles.

C They form only obtuse angles.

D They form only acute angles.

E Broadway St

12th Ave NE

13th Ave NE5t

h St

NE

6th

St N

E

14th Ave NE

16th Ave NE

17th Ave NE

15th Ave NE

Ada

ms

St N

E

Jeff

erso

n St

NE

Mad

ison

St

NE

Name Lesson 19.3

perpendicular,

intersectingparallel intersecting intersecting

Possible answer: 13th Ave NE

Possible answer: 17th Ave NE


parallelparallel intersecting intersecting,

perpendicular

B A



PolygonsName the polygon. Tell if it appears to be regular or not regular.

1.

2.

3.

4.

Tell if each figure is a polygon. Write yes or no. Explain.

5.

6.

7.

8.

9. Choose the figure below that does not belong. Explain.

Problem Solving and Test PrepUSE DATA For 10–11, use the pattern at the right.

10. What is the name of the shaded polygon?

11. What other polygon do you see?

12. Which is a six-sided polygon?

A Triangle

B Pentagon

C Octagon

D Hexagon

13. A yield sign has three sides of equal length and three angles of equal measure. What is the name of the shape of a yield sign?

B C D

Name Lesson 19.4

A

triangle

no; sides are not connected

yes; 8 straight line segments

no; curved side

yes; 7 straight line segments

pentagon, not regular

triangle, regular

quadrilateral, not regular

quadrilateral, regular

hexagon

trapezoid or quadrilateral


B; sides of the figure are curved

D




1

distinguish among isosceles, scalene, and equilateral and right, acute, and obtuse triangles

3

distinguish among isosceles, scalene, and equilateral and right, acute, and obtuse triangles

6distinguish among isosceles, scalene, and equilateral triangles

7identify an equilateral triangle in real life situations

8determine whether a triangle is right, acute, or obtuse

10multiple choice; identify a scalene triangle by its properties


1 classify a four sided figure

4 classify a four sided figure

5draw quadrilateral from a description

7draw quadrilateral from a description

8draw a quadrilateral from a description

9classify a four sided figure in a real life situation

10classify a four sided figure in a real life situation

12multiple choice; choose the best description of four sided figures


Classify TrianglesClassify each triangle. Write isosceles, scalene, or equilateral. Then write right, acute, or obtuse.

1.

2.

3.

Classify each triangle by the lengths of its sides.

4.

5.

6.


7. Classify the triangle made by the gray patch by the length of its sides. Write isosceles, scalene, or equilateral.

8. Classify the triangle made by the gray patch by its angles. Write right, acute, or obtuse.

9. Which kind of triangle has only 2 equal sides?

A Right

B Equilateral

C Isosceles

D Scalene

10. Which kind of triangle has no equal sides?

A Right

B Equilateral

C Isosceles

D Scalene

Name Lesson 19.5

5 cm

5 cm 3 cm

8 m

5 m5 m

6 m

6 m 6 m

4 ft

4 ft 6 ft

25 mm

20mm 15 mm

9 in.

7 in. 12 in.

isosceles, acute scalene, obtuse isosceles, right

equilateral isosceles scalene

equilateral

acute


C D


Classify QuadrilateralsClassify each figure in as many of the following ways as possible. Write quadrilateral, parallelogram, rhombus, rectangle, square, or trapezoid.

1.

2.

3.

4.

Draw an example of each quadrilateral.

5. It has exactly two pairs of parallel sides and opposite sides that are equal.

6. It has 4 equal sides with 4 right angles.

7. It has 4 equal sides with 2 pairs of parallel sides.

8. It has no pairs of parallel sides.

Problem Solving and Test PrepUSE DATA For 9–10, use the picture of the dollhouse.

9. Describe and classify the roof of the dollhouse.

10. What are the different ways to classify the shape of the windows?

11. Which is the best description for the

figures?

A Parallelograms C Rectangles

B Squares D Trapezoids

12. Which is the best description for the figures?

A Circles C Rectangles

B Squares D Trapezoids

Name Lesson 19.6

quadrilateral, parallelogram, rectangle

quadrilateral, trapezoid

quadrilateral, parallelogram, rectangle, square, rhombus

quadrilateral, rhombus, parallelogram


quadrilateral, trapezoid

quadrilateral, parallelogram, rectangle, square


CA





1 draw a chord on a circle

2 draw a diameter on a circle

3 draw a radius on a circle

5 draw a chord on a circle

6identify and measure a radius on a circle

8identify and measure a chord on a circle

9identify and measure a diameter on a circle

10use a table to determine the measure of a diameter

12multiple choice; determine the diameter of a given circle


1use figures to compare and choose a table or Venn diagram to solve a problem

3use figures to compare and choose a table or Venn diagram to solve a problem

4count money to solve a problem

6classify a square in as many ways as possible


CirclesIn the box at the right, construct circle M with a 3-centimeter radius. Label each of the following.

1. chord: ___

AB

2. diameter: ___

CD

3. radius: ___

ME

4. radius: ___

MF

5. chord: ___

GH

For 6–9, use the drawing of circle R and a centimeter ruler to complete the table.

Problem Solving and Test PrepUSE DATA For 10–11, use the diagram.

10. What is the diameter of hurricane A in miles?

11. What is the radius of hurricane B in miles?

12. What is the length of the diameter of a circle with a radius of 6 feet?

A 3 feet C 9 feet

B 6 feet D 12 feet

13. What is the length of the radius of a circle with a diameter of 48 inches?

A 2 inches C 14 inches

B 24 inches D 26 inches

Name Lesson 19.7

Name Part of Circle Length in cm

6. ___

RE

7. ___

CD

8. ___

AB

9. ___

GH

HurricaneA

HurricaneB

0 100 200 300

Radius of Tropical Storm-Force Winds (in miles)

A

B

G H

C

D

E

R


diameter2 cm

chord

200 miles

200 miles


radius4 cm

answers will vary diameter 4 cm

D B



Problem Solving Workshop Strategy: Compare StrategiesProblem Solving Strategy PracticeFor 1–3, use the figures at the right. Make a table or Venn diagram to solve.

1. Lenny’s parents put a barbeque area in their backyard. All the sides of the barbeque area are of equal length and none of the angles are acute or right. Identify the figure shown that appears to be like Lenny’s parents’ barbeque area.

A B C D E

2. Cyd is designing a garden that has no parallel sides and all obtuse angles. Identify the figure shown that appears to be like Cyd’s design.

3. The shape of Holly’s backyard has two parallel sides, two sides that are not parallel, and two acute angles. Identify the figure shown that appears to be like Holly’s backyard.

Mixed Strategy Practice4. Willa and her two brothers have the money amounts shown below.

How much money does each person have?

5. After Della tossed coins into a pool, James dove in to pick up the quarter. Then, Della dove in to pick up her remaining 30 cents. How much money did Della toss into the pool?

6. Han’s backyard was shaped like a square with all right angles. Classify the design in as many ways as possible.

Name Lesson 19.8

Willa Bob Jon


C

E B

Willa: $5.21; Bob: $8.33; Jon: $6.45

55 cents

quadrilateral, parallelogram, rectangle, square, rhombus





1identify as similar or congruent figures

3Identify figures that are similar

6identify figures that are similar and congruent

8 identify similar figures

9identify figures on a grid that are congruent

12use figures on a grid to make two congruent triangles

15multiple choice; identify figures that appear to be congruent


2identify symmetry in a real life situation

5draw llines of symmetry in a figure

8draw llines of symmetry in a figure

10 identify turns made on a circle

11 identify turns made on a circle

14multiple choice; describe symmetry in real life situations

15describe the turn made on a circle


Congruent and Similar FiguresTell whether the two figures are congruent and similar, similar or neither.

1.

2.

3.

4.

5.

6.

7.

8.

For 9–11, use the coordinate grid.

9. Which pair of rectangles are congruent?

10. Which rectangle is not congruent to the others?

11. Use the coordinate gird at the right to draw a figure that is congruent to figure B.

Problem Solving and Test PrepUSE DATA For 12–13, use the coordinate grid above.

12. Draw a diagonal line through figure B to make two triangles. Are the triangles congruent?

13. On the coordinate grid above, draw a figure that is congruent to figure D.

14. Draw a triangle that is similar to the one in Exercise 2. Then explain why your triangle is similar.

15. Which two figures below appear to be congruent?

A

B

C

D

Name Lesson 20.1

A

x-axis

y-ax

is

1

1 2 3 4 5 6 7 8 9

10 11

0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

B C D

neithercongruent and similar neither

similarcongruent and similar neither similar

A and C

B


similar



yes


C


Turns and SymmetryTell whether the figure appears to have line symmetry, rotational symmetry, both, or neither.

1.

2.

3.

4.

Draw the line or lines of symmetry.

5.

6.

7.

8.

Tell whether the rays on the circle show a 1 _ 4 , 1 _ 2 , 3 _ 4 , or full turn.

9.

10.

11.

12.

Problem Solving and Test Prep 13. Which letters in the STOP sign at the

right appear to have no lines of symmetry?

14. Which best describes the symmetry of the letter A?

A Line C Both

B Rotational D None

15. The rays on the circle show the turn Todd made. Describe the turn.

Name Lesson 20.2

STOP


both line symmetry both line symmetry


S, P

1/2 turn clockwise

full turn 1 _ 2 turn 3 _ 4 turn 1 _ 2 turn

A




1 identify a rotation

4 identify a reflection

6draw a translation, a rotation, and a reflection

7draw a translation, a rotation, and a reflection

8identify multiple moves of a figure

10multiple choice; define reflection


1use the act it out strategy to solve a problem

2use the act it out strategy to solve a problem

4draw a diagram or picture to solve a problem

5use predict and test to solve a problem

6use the work backward strategy to solve a problem

7make an organized list to solve a problem

PracticePW129

Name Lesson 20.3

TransformationsTell how each figure was moved. Write translation, rotation, or reflection.

1.

2.

3.

4.

Draw figures to show a translation, a rotation, and a reflection of each.

5. Translation Rotation Reflection



Problem Solving and Test Prep 8. Tell what moves were made to

transform each figure into its next position.

9. What type of transformation describes the change of position in the figure below?

10. Which describes a reflection?

A Slide along a straight line

B Transformation

C A flip over a line

D A turn around a point

11. If you rotate the equilateral triangle shown 180º will it look like a reflection? Explain.

G G


1 2 3


rotation reflection translation reflection

translation; rotation reflection

yes; Explanations will vary.


C


Name Lesson 20.4

Problem Solving Workshop Strategy: Act It OutProblem Solving Strategy Practice Act it out to solve.

1. Don used pattern blocks to make the rocketship at the right. Does the rocketship have line symmetry?

2. Jen, Bea, Sara, and Jon are in a math contest. Before it starts, each contestant gives one score card to each of the other contestants. How many scorecards are there in all?

3. Here is the pattern Craig made.

What will be the 20th figure in the pattern?

Mixed Strategy Practice 4. Starting at a base, Don flies his model

airplane 50 feet south, 20 feet east, 10 feet north, and 20 feet west. How far is Don’s plane from a flagpole that is 15 feet north of the base?

5. Fred uses 3 red, 2 blue, and 4 green squares to make one design for the border in his room. If he uses 108 squares in all, how many of each color will Fred use?

6. Lara spent $44 on supplies to make a curtain. She bought fabric for $25, backing for $8, hem tape for $8, and thread. How much did the thread cost?

7. Dianna is making a list of the 120 seashells in her collection. What are some of the ways Dianna might organize her list if she has 7 different colors, the shells came from 12 different beaches, and she has 3 display shelves?


yes

12 scorecards

55 feet 36 red, 24 blue, 48 green

$3

Answers will vary.




1use cutouts to determine whether a figure tessellates







1 extend a pattern of reflections

3 extend a pattern of flips

5find the missing item in a pattern

7find the missing item in a pattern

9 extend a pattern

10multiple choice; extend a pattern

11multiple choice; extend a pattern


Name Lesson 20.5

TessellationsTrace and cut out several of each figure. Tell whether the figure will tessellate. Write yes or no.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

yes no yes

no yes yes

no no yes

yes no no



Name Lesson 20.6

Geometric PatternsFind a possible pattern. Then draw the next two figures in your pattern.

1.

2.

3.

4.

Write a possible pattern. Then draw the missing figure in your pattern.

5.

6.

7.

Problem Solving and Test PrepUSE DATA For 8–9, use the quilt.

8. Does a rule for the pattern appear to include shading? Explain.

9. If you remove the border and add a row at the bottom, will that row start with a square or triangles?

10. Look at Exercise 6. What will be the tenth figure in the pattern?

A C

B D

11. Look at Exercise 2. What will be the fifteenth figure in the pattern?

A C

B D

color: white, black; shape: original, reflection, repeat

2 black arrows, 1 white arrow, repeat flipping white arrow horizontally:

original, flip vertically, repeat

2 black brackets, 2 white brackets, repeat

1, 2, 3, 2, 1 circles, repeat

rotate original 90° clockwise, repeat

original, reflection, repeat

yes, pattern repeats gray-stripe and white stripe

a block



B D

Check students’ figures.





1recognize attributes of a cylinder

3recognize attributes of a rectangular pyramid

6recognize solid shapes in real life situations

9recognize attributes of a rectangular prism

11recognize attributes of a rectangular prism and a triangular prism

13multiple choice; identify triangular faces on shapes


4practice drawing 2-dimensional figure

5practice drawing a 3-dimensional figure fom a 2-dimensional figure

6practice drawing a 3-dimensional figure

7practice drawing a 3-dimensional figure

8practice identifying parallel line segments in3-dimensional shapes

9practice identifying perpendicular line segments in 3-dimensional shapes


Faces, Edges, and VerticesName a solid figure that is described.

1. two circular bases

2. six square faces

3. 1 rectangular and 4 triangular faces

4. one circular base

Which solid figure do you see in each?

5.

6.

7.

8.

Problem Solving and Test PrepFor 9–10, look at the edges of the prism.

9. Name a pair of parallel line segments.

10. Name a pair of perpendicular line segments.

11. Which solid figure has more edges: a rectangular prism or a triangular prism? How many more?

12. What is the relationship between the number of edges and the number of faces of a cube?

13. Which of the following figures has all triangular faces?

A Triangular pyramid

B Sphere

C Cylinder

D Triangular prism

A

E H

GF

B C

D

Name Lesson 21.1


cylinder square prism or cube

rectangular pyramid cone

cylinder sphere triangular prism

rectangular prism

Possible answer: AB and EF

Possible answer: AB and BC

Rectangular prism, 3 more

There are half as many faces as edges.

A




Name Lesson 21.2

Draw FiguresDraw the missing line segments so that each figure matches its label.

1. triangle 2. octagon 3. right triangle

For 4–7, use the dot paper on the right to draw each figure.Label the vertices.

4. a square with sides 2 units long

5. a square pyramid rising from the square in Exercise 4

6. a rectangular prism with one edge 3 units long

7. a cube with sides 2 units long

Problem Solving and Test Prep 8. Identify a set of parallel line segments in

each of the three figures you drew above.

9. Identify one perpendicular line segment in each of the three figures you drew above.

10. Use the dot paper above to draw 6 triangles that form a hexagon. Label the vertices.

11. How many line segments do you need to draw a cube?

A 12 C 9

B 10 D 6



Answers will vary.

A

Answers will vary.






1draw a net of a 3-dimensional figure

2draw a net of a 3-dimensional figure

5recognize a net of a rectangular prism

7 recognize similarities in nets

9recognize how to change a net to make a different solid figure

10recognize a net for a solid figure

12recognize a net of a square pyramid


1recognize a solid shape from its different views

2recognize a solid shape from its different views

8draw different views of a cylinder

9recognize attributes of a solid figure

12multiple choice; recognize shapes that make the different views of a cone


Patterns for Solid FiguresDraw a net that can be cut to make a model of each solid figure.

1. 2.

Would the net make a rectangular prism? Write yes or no.

3. 4.

5. 6.

For 7–8, use the nets.

7. Do nets B and C make figures with the same number of sides?

8. Do nets A and C make figures with the same number of edges? Explain.

Problem Solving and Test Prep 9. How would you change the figure in

Exercise 3 to make a solid figure?

10. Can the net in Exercise 6 make a solid figure?

11. What solid figure can you make from net A?

12. What solid figure can you make from net B?

C

A

Name Lesson 21.3

B


yes

no no

no

no

yes, a rectangular prism has 12 edges, and so does a cube.

move one square to other side of the rectangle no

square pyramidcubeCircled problems are suggested homework problems.

PW136© Harcourt • Grade 4Practice

Different Views of Solid FiguresName the solid figure that has the following views.

1.

2.

3.

4.

Draw the top, front, and side views of each solid figure.

5. 6.

7. 8.

Problem Solving and Test Prep 9. What solid figures have a circle on

two views?

10. What solid figures have a triangle on at least one of its views?

11. Which figure is the top view of a

cube?

A Square C Point

B Cylinder D Triangle

12. Which figure is the front view of a cone?

A Square C Point

B Rectangle D Triangle

top view front view side view top view front view side view

top view front view side view top view front view side view

Name Lesson 21.4

triangular prism cone

sphere triangular pyramidCheck students’ drawings.

cylinder or sphere triangular prism, triangular pyramid, rectangular pyramid


A D




3practice solving problems using the make a model strategy



6solve problems using the work backward strategy

8solve problems using the make an organized list strategy


1practice dividing a quadrilateral into four triangles

3practice combining right triangles to make a square

6practice identifying figures on real life objects

9find shapes within another shape

10

multiple choice; recognize new shapes that can be formed when you change a shape


Problem Solving Workshop Strategy: Make a ModelProblem Solving Strategy PracticeMake a model to solve.

1. Paula has 36 cubes to build a wall that is a repeating pattern of 1, 2, and 3 cubes high. How many cubes long can Paula make the wall?

2. What if Paula used a repeating pattern of 1, 3, and 5 blocks high? How many blocks would Paula need to build a wall 9 blocks long?

3. John has 66 cubes. He gives 21 to Mark and then builds a staircase beginning with 1 cube, then 2, and so on. How tall will John’s staircase be?

4. How many cubes would John need to build the next step of his staircase?

Mixed Strategy Practice 5. Jan has 88 cubes. She uses half of them

to build a bridge. She gives Sandra half of what is not used so she can build a bridge. If Sandra uses 16 cubes to build her bridge, how many of the 88 cubes are still not used?

6. Mrs. Lutie left home and went to the bank. Then she drove 18 miles to the dentist, 9 miles for groceries, 8 miles to pick up her kids, and 3 miles back home. If Mrs. Lutie drove a total of 45 miles, how far was it from home to the bank?

7. Change the numbers in Exercise 6. Make a new problem about Mrs. Lutie’s errands.

8. How many ways can you arrange 12 cubes in more than one row? Name the ways.

Name Lesson 21.5

18 cubes 27 blocks

9 cubes 10 cubes

6 cubes 7 miles

Check students’ problems. 4 ways: 2 by 6, 6 by 2,

3 by 4, and 4 by 3



Combine and Divide FiguresDraw a picture to show the new figure.

1. Divide a quadrilateral to make four triangles.

2. Combine a triangle and a trapezoid to make a triangle.

3. Combine two right triangles to make a square.

4. Combine a triangle and a square to make a pentagon.

What figures do you see in each?

5.

6.

7.

Problem Solving and Test PrepFor 8–9, use the picture at the right.

8. Without the dashed line, how many triangles are in the picture?

9. How many triangles are in the picture when you add the

dashed line?

10. If the parallelogram is divided on the dashed line, what arethe new figures?

A Hexagons C Squares

B Pentagons D Triangles

11. Combine 6 equilateral triangles. What is the new polygon?

Name Lesson 21.6


Answers will vary.

4

hexagonCircled problems are suggested homework problems.

D

10




2recognize the most reasonable unit of measurement for real life situations

5practice measuring to the nearest 1 _ 8 inch

7practice measuring to the nearest 1 _ 8 inch

8use a bar graph to recognize the most accurate measurement

10multiple choice; practice measuring to the nearest 1 _ 8 inch


2 change miles to yards

4 change feet to inches

8 compare lengths

12write and solve an equation to complete a function table

13use a table to subtract mixed numbers

14use a table to change yards to inches

15 change inches to feet


Name Lesson 22.1

Measure Fractional PartsChoose the most reasonable unit to measure. Write in., ft, yd, or mi. 1. the width of a car

2. the length of a lawn

3. the length of your foot

Estimate to the nearest 1 _ 2 inch. Then measure to the nearest 1 _ 8 inch.

4.

5.

6.

7.

Problem Solving and Test PrepFor 8–9, use the bar graph.

8. Grace measured the Hibiscus in yards. Which is more accurate: Grace’s measurement or the measurement given?

9. For which plant would it be the most

reasonable to measure the height in inches?

10. What is the length of the string to the

nearest 1 _ 8 inch?

A 1 1 _ 8 in. C 1 3 _ 8 in.

B 1 1 _ 4 in. D 1 1 _ 2 in.

11. Haley painted a picture using paintbrushes that were 1 1 _ 8 in. wide, 1 1 _ 4 in. wide, 1 3 _ 8 in. wide, and 1 1 _ 2 in. wide. Order the width of the paintbrushes from greatest to least.

12 11 10 9 8 7 6 5 4 3 2 1 0

Thyme Coneflower Plant

Plant Height

Heig

ht (i

n fe

et)

Dogwood Hibiscus


ft yd in.

Thyme

1 1 _ 2 in., 1 3 _ 8 in., 1 1 _ 4 in., 1 1 _ 8 in.

1 1 _ 2 in.; 1 3 _ 8 in. 2 in.; 2 in.


A

1 _ 2 in. or 1 in.; 6 _ 8 in. 1 in.; 1 1 _ 8 in. or 1 2 _ 8 in.

measurement given



Name Lesson 22.2

Algebra: Change Customary Linear UnitsComplete. Tell whether you multiply or divide.

1. 8 yd � � in.

2. � yd � 4 mi

3. 15 ft � � yd

4. � in. � 7 ft

5. 144 in. � � ft

6. � yd � 288 in.

Compare. Write �, �, or � in each .

7. 60 in. 5 ft 8. 36 ft 11 yd 9. 98 in. 5 yd 10. 3,520 yd 1 mi

Write a rule you can use to complete each table. Then complete each table.

11.

12.

Problem Solving and Test PrepFor 13–14, use the Fabric Requirements table.

13. Sara has 8 yards of fabric. How many yards of fabric will Sara have left over if she makes 3 small dog costumes?

14. How many inches of fabric are needed to make one costume for a large dog?

15. George is 72 inches tall. How many feet tall is he?

16. Barbara is 5 feet tall. How many inches tall is she?

Inches, n 48 60 72 84 96

Feet, f 4 5

Miles, m 1 2 3 4 5

Yards, Y 1,760 3,520

Fabric Requirements

Dog Costume

Size Yards

Small 2 5 _ 8

Medium 2 7 _ 8

Large 3 1 _ 8

288; multiply 5; divide7,040; multiply

84; multiply 12; divide 8; divide

� � � �

f � n � � 12; 6, 7, 8y � 1,760 � m; 5,280; 7,040; 8,800

7 __ 8 yd

112 1 __ 2 in.

6 ft 60 in.






2change weight from pounds to ounces

3change weight from tons to pounds

7identify reasonable measurements

11identify reasonable measurements

13 change pounds to ounces

15multiple choice; change pounds to ounces


1change units of capacity to complete a function table



7identify reasonable capacity in real life situations

10identify reasonable capacity in real life situations

13compute by changing units in real life situations

15compute by changing units in real life situations


Name Lesson 22.3

Adult Animal Daily Food Consumption

Animal Diet Amount

Crow Corn, meat 11 oz

Tiger Meat 14 Ib

Panda Bamboo 26 Ib

WeightComplete. Tell whether you multiply or divide.

1. 176 oz � � lb 2. � oz � 5 lb 3. 7 T � � lb

4. � oz � 12 lb 5. 320 oz � � lb 6. � T � 8,000 lb

Choose the more reasonable measurement.

7. 8. 9.

10. 11. 12.


13. How many ounces of bamboo does a panda eat dailly?

14. How many more ounces of food does a tiger eat in 2 days than a crow eats 30 days?

15. Cara bought five 4-lb bags of cat food. How many ounces is that?

A 64 ounces

B 320 ounces

C 20 ounces

D 160 ounces

16. Two Goliath toads can together weigh up to 208 ounces. How many pounds can the toads weigh?

A 9 lb

B 11 lb

C 13 lb

D 15 lb

4 oz or 4 lb 6 oz or 6 lb 16 Ib or 16 T

7 Ib or 7 T 100 oz or 100 lb 5 oz or 5 lb

11; divide 80; multiply 14,000; multiply

192; multiply 20; divide 4; divide

416 ounces

118 ounces


4 oz 6 lb 16 T

7 lb 100 lb 5 oz

CB


Name Lesson 22.4

Customary CapacityComplete each table. Change the units.

1. Quarts, q 5 10 15

Cups, c

2. Pints, p 14 16

Quarts, q 3

3. Gallons, g 4

Pints, p 16 48

4. Teaspoon, t

Tablespoon, b 5 10 15

5. Cups, c 20

Pints, p 8 12

6. Gallons, g

Quarts, q 16 24 36

Choose the more reasonable unit of capacity.

7.

quart or gallon

8.

teaspoon or pint

9.

tablespoon or quart

10.

teaspoon or cup

11.

teaspoon or quart

12.

pint or gallon

Problem Solving and Test PrepUSE DATA For 13–15, use the recipe.

13. How many total fluid ounces are used in the recipe?

14. How many ounces are in one serving

of the Green Tea Punch?

15. Sandy makes 4 gallons of Green Tea Punch for a meeting. How many pints of Green Tea Punch does Sandy make?

16. Randy filled 48 pint jars to the top with jelly. How many gallons of jelly did Randy make? Explain.

Makes twelve 1-cup servings

20

8 ounces

gal


60406

87

102416

3262

15 4530 4 96

galqttsp

pt tbsp

97 fluid ounces

32 pints6 gallons; 8 pints to a gallon 8 � 6 � 48




1choose one strategy from among several to solve a problem

4choose one strategy from among several to solve a problem

5use a table to change pounds to ounces and solve a problem

6add whole numbers and mixed numbers to solve a problem

8choose a strategy and explain the choice


1recognize the most reasonable unit of measurement

5measure to the nearest half centimeter

6measure to the nearest millimeter

9multiple choice; recognize the most reasonable unit of measurement


Name Lesson 22.5

Problem Solving Workshop Strategy: Compare StrategiesProblem Solving Strategy PracticeChoose a strategy to solve. Explain your choice.

1. Karen visited an aquarium. She saw a tank for small fish that was 8 feet long. How many inches long was the tank?

2. Bea baked 36 four-ounce servings of catfish. How many pounds of fish did Bea bake in all?

3. Lyle made 7 quarts of tartar sauce for a club outing. How many 1 _ 2 pint jars will Lyle need to store all the tartar sauce?

4. Mitch gave a mile of fishing line to each of 4 competitors in a fishing tournament. How many feet of fishing line did Mitch give away in all?


5. If the next largest Searobin caught weighed 80 ounces, how many ounces did the two largest Searobins weigh together?

Scout Deep Sea Fishing TripLargest Fish Caught

Fish Weight (lb) Length (ft)

Cod 85 6

Flounder 15 2

Striped bass 45 4

Bluefi sh 12 3

Searobin 7 1 1 _ 4

6. Suppose one of each of the largest fish caught were laid end-to-end. How long would the line of fish be?

7. How many more ounces did the flounder weigh than the bluefish?

8. What strategy would you use to find out the weight in ounces of the entire catch? Explain your choice.


192 oz

195 in.

48 ozStrategies and explanations will vary.

96 in. 9 lb

21,120 ft28 pint jars



Name Lesson 22.6

Metric LengthChoose the most reasonable unit of measure. Write mm, cm, dm, m, or km.

1. 2.

3.

Estimate the nearest centimeter. Then measure to the nearest half centimeter. Write the answer as a decimal.

4.

5.

Estimate to the nearest half centimeter. Then measure to the nearest millimeter.

6.

7.

Problem Solving and Test Prep 8. In Exercise 1, what is the length of the

ant to the nearest millimeter?

9. What is the most reasonable unit of measure that can be used to measure the length of this workbook?

A Millimeters C Meters

B Centimeters D Kilometers

mm cm cm

6 cm, 5.7 cm 4 cm, 4.0 cm

3 cm, 32 mm 3 cm, 32 mm

18 mm

Possible estimate are given.


B




3change centimeters to millimeters

9change millimeters to decimeters

10 change centimeters to meters

13 compare metric linear units

18 compare metric linear units

19change millimeters to centimeters

22multiple choice; change kilometers to meters


2choose reasonable metric unit to measure real life situations

5choose reasonable metric unit to measure real life situations

7 change grams to kilograms



14compare mass of real life objects

16multiple choice; change kg to grams and divide


Name Lesson 22.7

Algebra: Change Metric Linear UnitsComplete. Tell whether you multiply or divide.

1. � cm � 40 mm

2. 5,000 m � � km

3. 50 cm � � mm

4. 62,000 mm � � cm

5. � m � 1,200 cm

6. � cm � 25 m

Write the correct unit.

7. 25 � � 25,000 mm

8. 50 dm � 500 �

9. 2 � � 200 mm

10. 600 � � 60,000 cm

11. 340 mm � 34 �

12. 300 m � 300,000 �

ALGEBRA Compare. Write �, �, or � for each .

13. 300 m 0.03 km 14. 4,000 mm 40 cm 15. 5,000 cm 6 dm

16. 1.2 km 130,000 cm 17. 120 mm 1.1 dm 18. 3,460 m 3.47 km


19. A river otter is about 1,000 mm long. How many centimeters long is a river otter?

20. A giant garter snake can reach 1,600 mm in length. How many decimeters long is a giant garter snake?

21. A river otter’s tail may reach 457 mm in length. How many meters long is a river otter’s tail?

A 0.457 C 45.7

B 4.57 D 457

22. Felicia walked 1.205 km. How many meters did Felicia walk?

A 1,205 m C 12.05 m

B 120.5 m D 1.205 m

m cm dm

m mm

. . .

, . ,

cm

100 cm 16 dm


AA

4; divide 5; divide 500; multiply

620; divide 120; divide 250; divide


Name Lesson 22.8

MassChoose the more reasonable measurement.

1.

20 g or 20 kg

2.

14,500 kg or 14,500 g

3.

5,220 g or 1.22 kg

4.

8,000 g or 1 kg

5.

300 g or 300 kg

6.

23 g or 23 kg

Complete. Tell whether you multiply or divide.

7. 6,000 g � � kg

8. 2,000 g � � kg

9. � g � 4 kg

10. 8 kg � � g

11. 25,000 g � � kg

12. � kg � 4,000 g


13. What is the total mass in grams of one each of the sports balls?

14. Which has the greater mass: 1 basketball or 11 tennis balls?

15. Wanda needs a kilogram of peanut butter. How many 510-gram jars will Wanda need to buy?

A 2 C 4

B 3 D 5

16. Ed bought a 1-kg box of instant noodles. There are 10 packs in each box. What is the mass of each pack?

A 0.1 grams C 10 grams

B 1.0 grams D 100 grams

Basket ball616 grams

Table tennis ball2.5 grams

Bowling ball6 kilograms

Tennis ball57 grams

Mass of Sports Balls

6; divide

6,675.5 g or 6.68 kg

11 tennis balls


20g 14,500 kg 1.22 kg

1 kg 300 g 23 kg

2; divide 4,000; multiply

8,000; multiply 25; divide 4; divide

AD



Lesson 22.10Item

1make a table to solve a problem

3make a table to order metric length found in a table

4subtract units of metric length to solve a problem

5change centimeters to millimeters and divide to solve a problem


1 change liters and milliliters

5 change milliliters to liters

7determine a reasonable capacity of real life objects

12compare the capacity of an object with a liter

14problem solving; multistep problem using metric capacity

15multiple choice; change liters to milliliters


Metric CapacityComplete. Tell whether you multiply or divide.

1. 500 L � � mL

2. 4,000 mL � � L

3. 1.4 L � � mL

4. � L � 12,000 mL

5. � L � 6,500 mL

6. � mL � 4.5 L

Choose the most reasonable measurement. Write a, b, or c.

7. a. 8 L

b. 8 mL

c. 20 mL

8. a. 4 L

b. 1 L

c. 10 mL

9. a. 2 L

b. 3 mL

c. 6 L

Estimate and tell whether each object had a capacity of about a liter, less than a liter, or more than a liter.

10.

11.

12.

Problem Solving and Test Prep 13. Kyle gets 12 km per liter of gas. How

far will 500 mL take him?

14. Patti uses 2 L of sauce for every 4 servings of spaghetti. How many liters does Patti need to make 12 servings?

15. Jane put 3 L of gas in her car. How many mL is this?

A 3 mL C 300 mL

B 30 mL D 3,000 mL

16. Hal put 7,000 mL of an additive in his gas tank. How many liters is this?

A 7 L C 700 L

B 70 L D 7,000 L

Name Lesson 22.9


500,000; multiply 4; divide 1,400; multiply

12; divide 6.5; divide 4,500; multiply

more than a liter about a liter less than a liter

6 km 6 L

D A

a c a

PracticePW148

Name Lesson 22.10


Problem Solving Workshop Strategy: Make a TableProblem Solving Strategy PracticeMake a table to solve each problem.

1. Sam wants to know how tall his 2-year-old brother might be as an adult. He went to the library and found that a boy who is 87 cm tall at age two will be about 174 cm tall as an adult, a boy who is 90 cm tall at age two will be about 180 cm tall as an adult, and a boy who is about 92 cm tall at age two will be 184 cm tall as an adult. Sam knows that his brother is 91 cm tall now. About how tall will Sam’s brother be as an adult?

2. A pattern of mosaic tiles is lined up in this order: 8 cm, 5 cm, 8 cm, and 12 cm. How many meters long will be pattern be if it repeats 50 times?


3. Draw a table to show the heights of History’s Tallest and Shortest People in order from greatest height to least height. Include your height in the table.

4. How many decimeters difference is there between the height of the tallest woman and that of the shortest man?

5. Elijah is buying a plant that will grow 10.4 cm in 2 days. How many millimeters will it grow per day?

Tallest man

Shortest man

Tallest woman

Shortest woman

Person

2.720 m

57 cm

2.48 m

61 cm

Height

History’s Tallest and

Shortest People


History’s Tallest and Shortest PeopleTallest man 2.720 mTallest woman 2.48 mStudent Student’s heightShortest woman 61 cmShortest man 57 cm

19.1 dm 52 mm

16.5 m

182 cm




1use string to estimate and measure perimeter of real life objects

3use string to estimate and measure perimeter of a real life object

5 compute perimeter

7 compute perimeter

8 compute perimeter

11draw a rectangle with a given perimeter

13draw a rectangle with a given perimeter


1find the perimeter of a triangle

5find the perimeter of a regular hexagon

6find the perimeter of an irregular figure

7find the perimeter of a regular pentagon

8find the perimeter of a rectangle

10find the length of two sides when the perimeter is given

12multiple choice; find the perimeter of an equilateral triangle


Estimate and Measure PerimeterUse string to estimate and measure the perimeter of each object.

1. this workbook 2. the doorway to your bedroom

3. the face of a TV

4. the door of your refrigerator

Find the perimeter of each figure.

5. 6. 7.

8. 9. 10.

Use dot paper to draw a rectangle with the given perimeter.Then record the lengths of the sides.

11. 8 units 12. 10 units 13. 14 units

Name Lesson 23.1

38 in.

6 units 6 units 12 units

12 units 14 units



220 in. 90 in. 184 in.

16 units

Check students’ drawings and measurements.


Name Lesson 23.2

Algebra: Find PerimeterFind the perimeter.

1.

2.

3.

4.

5.

6.

Use a formula to find each perimeter.

7.

8.

9.

Problem Solving and Test Prep10. The perimeter of an isosceles triangle

is 30 inches. Its base is 8 inches. How long are each of the other two sides?

11. The perimeter of a rectangle is 46 feet. The width of the rectangle is 10 feet. What is the length?

12. What is the perimeter of this figure?

A 18 in.

B 27 in.

C 36 in.

D 45 in.

13. What is the perimeter of an equilateral hexagon with sides 6 centimeters long? Explain.

9 m

10 m

12 m

4 m

16 cm

16 cm16 cm 16 cm

16 cm 16 cm

7 cm 7 cm

7 cm

7 cm 7 cm

9 in. 9 in.

9 in.

15 mm15 mm

5 mm

5 in.

4 in.7 in.

9 in.

11 in.

5 ft4 ft

3 ft

6 yd 6 yd

9 yd

12 yd

2 yd

7 yd

15 yd5 in.

5 in.

35 mm 36 in. 12 ft

35 m 96 cm 35 yd

35 cm 44 yd 20 in.

11 inches 13 feet

36 cm; 6 � 6 � 6 � 6 � 6 � 6 � 36.


B




1estimate the area of an irregular figure on grid paper

3estimate the area of a triangle on grid paper

5draw a right triangle on grid paper and estimate its area

6draw a figure on grid paper with straight lines and estimate its area

9use a drawing to estimate area of an irregular figure

10multiple choice; estimate area of an irregular figure on grid paper


2practice finding the area of a rectangle

5

practice measuring with a centimeter ruler and finding the area and perimeter of a rectangle

7practice finding the area and perimeter of an irregular figure

8practice finding the difference in the area of two different figures

9multiple choice; practice finding area of a rectangle


Area of Plane FiguresEstimate the area of each figure. Each unit is 1 sq in.

1.

2.

3.

Draw each figure on the grid paper at the right. Then estimate its area in square units.

4. hexagon

5. right triangle

6. figure with only straight lines

7. figure with curved and straight lines

Problem Solving and Test PrepUSE DATA For 8–9, use the diagram.

8. About how many square yards is the area of the hallway?

9. About how many square yards is the area of the closet?

10. In the figure below, each square is 1 square meter. What is the best estimate of the area of the figure?A 12 sq mB 17 sq mC 20 sq mD 14 sq m

11. In the figure below, each square stands for 1 square foot. What is the best estimate of the area of the figure?

A 30 sq ftB 20 sq ftC 35 sq ftD 25 sq ft

Name Lesson 23.3

Floor Plan

1 square unit = 1 square yard

Familyroom

LivingroomKitchen

Closet

about 28 sq in.about 30 sq in.about 75 sq in.

Check students’ drawings and answers.

about 25 1 _ 2 sq yd

about 7 1 _ 2 sq yd



BD



Name Lesson 23.4

Algebra: Find AreaFind the area.

1.

2.

3.

Use a centimeter ruler to measure each figure. Find the area and perimeter.

4.

5.

6.

Problem Solving and Test PrepFor 7–8, use the diagram.

7. What is the perimeter and area of the entire patio?

8. How much smaller is the area of the patio than the area of the lawn?

9. What is the area of this figure?

A 152 sq ft

B 162 sq ft

C 180 sq ft

D 200 sq ft

10. Use a formula to find the area of a rectangle that is 7 cm wide and 35 cm long. Explain.

5 mm

15 mm

9 in.

36 in.

5 cm

18 cm

45 ft

15 ft

30 ft30 ft

Lawn

Patio

Patio

7 ft

8 ft

18 ft

9 ft

75 sq mm 324 sq in. 90 sq cm

P � 12 cmA � 9 sq cm

P � 90 ft; A � 330 sq ft

690 sq feet

245 sq cm ; A � l � w

A � 7 � 35 � 245


B







1use a diagram and the formula to find a perimeter

3use a diagram and the formula to find the area

4problem solving; multistep; use a table to find the area

5problem solving; multistep; use a table to find the cost

6use a diagram to subtract customary length


1find and draw pictures of figures with related perimeters and areas

2find and draw pictures of figures with related perimeters and areas

4distinguish between figures with equal areas and different perimeters

5distinguish between figures with equal perimeters and different areas

7multiple choice; distinguish between figures with equal perimeters and different areas


Name Lesson 23.5

Problem Solving Workshop Skill: Use a FormulaProblem Solving Skill PracticeUse a formula to solve.

For 1–3, use the diagram.

1. Stacy’s backyard is 50 ft wide and 95 ft long. She wants to put in a privacy fence. How many feet of fencing will Stacy need for the perimeter of her backyard?

2. In Stacy’s yard, the floors of the dog

run, sandbox, and Zen garden are covered with outdoor carpeting. How many square feet of carpeting do these areas use in all?

3. The area not covered by the dog run, sandbox, and Zen garden is grass in Stacy’s yard. How many square feet of grass are in Stacy’s yard?

Mixed ApplicationsUSE DATA For 4–6, use the table.

4. Mr. Daley spent $195 for 3 how-to books and fencing. How many yards of fencing did Mr. Daley buy?

5. Bethany bought a how-to book and an 8-foot-by-10-foot piece of carpet. How much did Bethany spend?

6. Use the diagram above. How much more fencing does Stacy need to fence the sandbox than the Zen garden?

Bart’s Building Supplies

Supply Cost

How-To Book $15

Outdoor Carpet $8/square foot

Fencing $15/yard

Dog Run

Sand boxZen

garden

15 ft

25 ft13 ft50 ft

50 ft80 ft

10 ft

95 ft

290 ft


1,825 sq feet 2,925 sq feet

46 more feet$655

10 yards


Name Lesson 23.6

Relate Perimeter and AreaFind the perimeter and area of each figure. Then draw another figure that has the same perimeter but a different area.

1.

2.

3.

Problem Solving and Test PrepFor 4–5, use figures a–c.

4. Which figures have the same area but different perimeters?

5. Which figures have the same perimeter but different areas?

6. The rectangles below have the same

area. Which has the greatest perimeter?

A C

B D

7. The rectangles below have the same perimeter. Which has the greatest area?

A C

B D

3 yd

7 yd4 cm

5 cm 6 ft

10 ft

a.

b. c.

P � 18 cm

A � 20 sq cm

P � 20 yd

A � 21 sq yd

P � 32 ft

A � 60 sq ft

a and b

none





D A





3use cubes to find the volume of a rectangular prism



8find the height of a rectangular prism when the volume is given

10find the length and width of a rectangular prism when the volume and height are given


1determine the number of outcomes from spinning a 5-color spinner

2determine the number of outcomes from tossing two coins

4determine the number of outcomes from tossing one coin and spinning a spinner

5use a table to identify a specific outcome


Name Lesson 23.7

Estimate and Find Volume of PrismsCount or multiply to find the volume.

1.

2.

3.

4.

5.

6.

Problem Solving and Test Prep 7. Which has the greater volume, a blue

rectangular prism that is 4 cm by 1 cm by 3 cm or a red rectangular prism that is 2 cm by 2 cm by 4 cm?

8. The volume of a rectangular prism is 200 cubic cm. If the length and width are each 5 cm, what is the height?

9. Jamal built the prism below using centimeter cubes. What is the volume of the figure?

A 288 cu cm

B 72 cu cm

C 48 cu cm

D 24 cu cm

10. The volume of a rectangular prism is 60 cubic inches. The height is 4 inches. What could the length and width of the rectangular prism be? Explain how you know.

4 cm

12 c

m

6 cm


120 cu units 100 cu units 84 cu units

red rectangular prism 8 cm

3 in. and 5 in. or 1 in. and 15 in. Explanations may vary.

A

30 cu units 15 cu units 180 cu units


Name Lesson 24.1


List All Possible OutcomesUSE DATA For 1–4, use the picture. List all the possible outcomes of each experiment.

1. spinning the pointer

2. tossing the quarter and the nickel

3. tossing the number cube and spinning the pointer

4. tossing the nickel and spinning the pointer

USE DATA For 5–8, use the table.

5. How many times did the outcome Green, 5 occur?

6. How many times did the outcome Yellow, 4 occur?

7. List all the possible outcomes of the experiment.

8. How many possible outcomes are there?

Ahmed’s ExperimentSpin the Pointer and Toss a Number Cube

Colors

Red Blue Green Yellow Purple

1

23

456

NumberCube

red

green

bluepurple

yello

w

62 3

red, blue, green,

yellow, purple

4

0

Q heads, N heads:

Q tails N tails: Q heads

N tails: Q tails N heads


30

R1, R2, R3, R4, R5, R6, B1, B2, B3, B4, B5, B6, G1, G2, G3, G4, G5, G6, Y1, Y2, Y3, Y4, Y5, Y6,P1, P2, P3, P4, P5, P6

RH, RT,BH, BT,GH, GT,YH, YT, PH, PT

R1, R2, R3, R4, R5, R6, B1, B2, B3, B4, B5, B6, G1, G2, G3, G4, G5, G6, Y1, Y2, Y3, Y4, Y5, Y6,P1, P2, P3, P4, P5, P6

MXENL08ASE4X_PW_C24_L1.indd PW156 7/2/07 10:12:58 AM




1make an organized list of possible outcomes to solve a problem

3make an organized list of possible outcomes to solve a problem

4make an organized list to solve a problem

6subtract whole numbers to the hundred thousands place

7draw a diagram to solve a problem


1 identify an impossible event

4 identify a certain event

5 identify equally likely events

6identify events that are not equally likely

7use a spinner to identify equally likely events

10multiple choice; use a spinner to determine which event is least likely

Name Lesson 24.2


Problem Solving Workshop Strategy: Make an Organized ListProblem Solving Strategy PracticeUSE DATA For 1–3, use the spinners. Make an organized list to solve.

1. Franco made these spinners for a school carnival game. If each player must spin both pointers, what are the possible outcomes?

2. To win, Gloria must spin both pointers for a total of more than 6. Name the outcomes that allow Gloria to win.

3. Patty can win if she spins both pointers for a total of more than 5. Name the outcomes that allow Patty to win.

Mixed Strategy Practice4. Pedro is making cards for a game.

Each type of card will be a different color. The suits will be hearts and flags. In each suit, there will be 3 sets: numbers, letters, and symbols. How many colors will there be?

5. You probably made an organized list to solve Exercise 4. What is another strategy you could use to solve it? Explain.

6. Jorge’s father has driven his car 103,240 miles. His mother has driven hers 69,879. How much further has Jorge’s father driven than his mother?

7. There are 110 students in fourth grade. Thirty-two take only music, 25 take only art, and 12 take both. How many students do not take art or music?

1

2

31

2

3

4

5

1, 1; 1, 2; 1, 3; 1, 4; 1, 5;

2, 1; 2, 2; 2, 3; 2, 4; 2, 5;

3, 1; 3, 2; 3, 3; 3, 4; 3, 5


2, 5; 3, 4: 3, 5 1, 5; 2, 4: 2, 5; 3, 3; 3, 4; 3, 5

6 colors

Possible answer: act it

out; explanations will

vary.

33,361 miles 41 students

Name Lesson 24.3


Predict Outcomes of ExperimentsTell whether the event is likely, unlikely, certain, or impossible.

1. spinning blue on a spinner with equal sections of red, yellow, and green

2. tossing the number 2 on a cube labeled 1 to 6

3. pulling a red tile from a bag that contains 6 red, 2 white, and 1 blue tiles

4. spinning red on a spinner that is all red

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.

5. Experiment: Toss a cube numbered 1�6.Event A: tossing an odd numberEvent B: tossing an even number

6. Experiment: Spin the pointer Event A: blue Event B: yellow

Problem Solving and Test PrepUSE DATA For 7–10, use the spinner. The spinner has equal sections.

7. Which two events are equally likely?

8. Which event is most likely?

9. Which event is impossible?

A brown C purple

B blue D green

10. Which event is least likely?

A red C purple

B blue D green

BlueBlue

Yellow

YellowYellowYellow

Blue

GreenBlue

Pur

ple

Yellow

White

Whi

teWhi

te

Gre

en

impossible

likely

unlikely

yellow


certain

equally likely

blue and green

not equally likely; blue

CA




1use a diagram to identify the probability of an event

4use a diagram to identify the probability of an event

6use a diagram to determine the likelihood and identify the probability of an event

7determine the probability of an event

9multiple choice; use a diagram to determine the probability of an event


2use a diagram to determine if a prediction is accurate

3

conduct a probability experiment using two coins and record the outcomes in a tally table

5use a spinner to find the experimental and mathematical probability

6use a spinner and tally table to find the experimental and mathematical probability

Name Lesson 24.4

PracticePW159

Probability as a FractionUSE DATA For 1–4, use the equal-sized marbles. Write the probability as a fraction.

1. pulling a white marble

2. pulling an orange marble

3. pulling a red or a yellow marble

4. pulling a color that is not green

USE DATA For 5–6, use the equal-sized cards. Write the probability as a fraction. Then, tell whether each event is certain, impossible, likely, or unlikely.

P R O B A B I L I T Y

5. pulling an L 6. pulling a B or an I

Problem Solving and Test PrepUSE DATA For 7–8, use the equal-sized cards above.

7. What is the probability of pulling a C, F, or E?

8. What is the probability of pulling an A, P, R, O, L, or T?

9. What is the probability of pulling a green marble?

A 1 ___ 12

B 1 __ 4

C 1 __ 2

D 3 __ 4

10. What is the likelihood that you will pull a pink tile from a bag of pink tiles? Explain.


Y Y

GG

GG

G

G

Y

Y R

R

BR

R

YY

WW

W

W WG

GG


5 _ 13

0 _ 13

2 _ 13

10 _ 13

unlikely; 1 _ 11

impossible; 0 _ 11

likely; 6 _ 11

Certain; possible explanation:

because there aren’t any

other colors in the bag that I

could draw.

unlikely; 4 _ 11

C

MXENL08ASE4X_PW_C24_L4.indd PW159 7/2/07 10:13:26 AM

Name Lesson 24.5


Experimental Probability 1. Toss a coin 20 times. Record the

outcomes in the tally table. Write the experimental probability of heads.

2. Grant pulls a marble from the bag, returns it, and then chooses another one. He does this 30 times. Grant predicts that he will pull a yellow marble 5 times. Do you agree with Grant’s Prediction? Why or why not?

3. Toss two coins thirty times. Use the tally table to record the outcomes. How close do you think your experimental probability is to the mathematical probability?

USE DATA For 4–6, use the spinner and the table. The spinner has equal sections.

4. What is the experimental probability of the pointer stopping on blue? What is the mathematical probability?

5. What is the experimental probability of the pointer not stopping on blue? What is the mathematical probability?

6. What is the experimental probability of the pointer stopping on green or yellow? What is the mathematical probability?

Tally Table

Outcomes Heads Tails

Tally

Tally Table

Outcomes Coin 1Heads

Coin 1Tails

Coin 2Heads

Coin 2Tails

Tally

R

R RR

Y

YYYY

Y

Y

Y

BR

BR

B L

B L

B L

p p

G

G

G

R

R

Green

YellowBlue

Red

Maryellen’s Results

Outcomes Blue Red Green Yellow

Tally

Check students’ work.

no; mathematical probability is 1 _ 4 _

Check students’ work.

10 ____ 40 or 1 _ 4 ; 1 _ 4

30 ____ 40 or 3 _ 4 ; 3 _ 4

22 ____ 40 or 11 ____ 20 ; 1 _ 2





2make a tree diagram to determine the number of possible combinations

3make an organized list to determine the number of possible arrangements

4make an organized list to determine the number of possible arrangements

6determine the number of possible arrangements

8determine the number of different combinations that are possible

Name Lesson 24.6


Combinations and ArrangementsMake a tree diagram in the space provided to list and find the number of possible combinations.

1. Dinner choicesSauce: marinara, cheese, meatPasta: spaghetti, linguine, macaroni

2. Hamburger choicesCheese: American, cheddar, Swiss, proveloneCondiments: ketchup, mustard,

mayonnaise, horseradish

Make an organized list to find the number of possible arrangements.

3. apple, orange, plum 4. ballpoint pen, fountain pen, flair pen, roller ball pen

Problem Solving and Test Prep 5. How many possible arrangements can

be made with the pastas in Exercise 1?

6. How many possible arrangements can be made with the cheeses in Exercise 2?

7. How many different combinations of salads are possible?

8. Spinach is added as a fourth choice of greens to Exercise 7. How many different combinations are now possible?

Salad ChoicesGreens Dressings

Mixed greens Oil and vinegar

Romaine Caesar

Red loose leaf Ranch

Honey mustard


Check students’ diagrams.

6 arrangements 24 arrangements

16 combinations12 combinations

9 Combinations

16 Combinations

6 arrangements 24 arrangements

Check students’ lists.

PW161© Harcourt · Grade 4

MXENL08AWK4X_PHTE_Rat.indd PW161MXENL08AWK4X_PHTE_Rat.indd PW161 6/19/07 3:24:48 PM6/19/07 3:24:48 PM

SPIRALREVIEW

To the TeacherSpiral Review Worksheets

Reviewing skills and concepts are important in your students’ learning.

These weekly worksheets are provided for the student to review the skills and concepts previously learned.

Each weekly worksheet is divided into four sections. Each section reviews the standards from the strand identified by the icon.

Number, Operation, and Quantitative Reasoning

Patterns, Relationships, and Algebraic Reasoning

Geometry and Spatial Reasoning

Measurement

Probability and Statistics

The weekly worksheets are designed for you to give your students the entire page if you want them to review all the strands, or one of the four sections if you only want them to review one strand.


MXENL08AWX4X_SR-TeachLetter.indd iiMXENL08AWX4X_SR-TeachLetter.indd ii 6/20/07 1:52:45 PM6/20/07 1:52:45 PM

Spira

l Rev

iew

Nam

eW

eek

1

Spir

al R

evie

w©

Har

cour

t • G

rade

4S

R1

For

1–4,

co

mp

are

the

num

be

rs.

Wri

te <

, >, o

r =

fo

r e

ach

.

1.

29

3 1

93

2.

32

4 4

23

3.

9,

120

9,0

12

4.

2,

003

2,0

03

For

9–11

, use

the

dat

a in

the

g

rap

h.

9.

H

ow m

any

peop

le v

oted

fo

r th

e be

ach?

10.

How

man

y pe

ople

vot

ed

for

the

amus

emen

t pa

rk?

11.

Whi

ch v

acat

ion

spot

rec

eive

d th

e le

ast

num

ber

of v

otes

?

For

12–1

3, w

rite

the

fac

t fa

mily

fo

r e

ach

set

of

num

be

rs.

12.

2, 3

, 5

13.

2, 7

, 9

For

5–8,

wri

te t

he t

ime

. Wri

te o

ne

way

yo

u ca

n re

ad t

he t

ime

.

5.

891011

12

76

5432

1

6.

7.

8

.

891011

12

76

5432

1

Beach

Amusem

ent Park

Campin

g Visit R

elativ

es

Number of Votes024681012

Favo

rite

Vaca

tio

n S

po

ts

Plac

es

5:15

;P

oss

ible

A

nsw

er:

five

fif

teen

� �

� �

4:40

;P

oss

ible

A

nsw

er:

fou

r fo

rty

7 p

eop

le

10 p

eop

le

visi

t re

lati

ves 2

� 7

� 9

;

7 �

2 �

9;

9 �

2 �

7;

9 �

7 �

2

2 �

3 �

5;

3 �

2 �

5;

5 �

2 �

3;

5 �

3 �

2

12:3

0;

Po

ssib

le

An

swer

:tw

elve

th

rity

10:4

5;P

oss

ible

A

nsw

er:

ten

fo

rty-

five

MX

EN

L08A

WK

4X_S

R_W

K01

.indd

S

R01

7/2/

07

10:4

4:17

AM

Spira

l Rev

iew

Nam

eW

eek

2

Spir

al R

evie

w©

Har

cour

t • G

rade

4S

R2

For

1–2,

use

pre

dic

t an

d t

est

to

so

lve

.

1.

D

urin

g a

socc

er g

ame,

the

Dra

gons

sc

ored

3 m

ore

poin

ts tha

n th

e Ea

gles

. A tot

al o

f 7 p

oint

s w

ere

scor

ed b

y bo

th tea

ms.

How

man

y po

ints

did

eac

h te

am s

core

?

2.

A

t th

e sc

hool

car

niva

l, a

tota

l of

300

bottle

s of

app

le ju

ice

and

grap

e ju

ice

wer

e so

ld. T

here

wer

e 80

mor

e bo

ttle

s of

app

le ju

ice

sold

tha

n gr

ape

juic

e. H

ow m

any

bottle

s of

eac

h ty

pe

of ju

ice

wer

e so

ld?

For

6–8,

use

the

dat

a in

th

e t

able

.

Mrs

. Yin

’s c

lass

vot

ed fo

r th

eir

favo

rite

colo

r.

6.

W

hich

col

or

had

the

mos

t vo

tes?

7.

H

ow m

any

vote

s w

ere

ther

e in

all?

8.

H

ow m

any

mor

e st

uden

ts v

oted

for

red

than

vot

ed fo

r ye

llow

?

For

9–11

, nam

e e

ach

figur

e.

Wri

te li

ne, r

ay, o

r lin

e se

gmen

t.

9.

10.

11.

For

3–5,

cho

ose

the

be

tte

r un

it o

f m

eas

ure

.

3.

Th

e le

ngth

of a

sch

ool b

us:

9 fe

et o

r 9

yard

s?

4.

Th

e di

stan

ce b

etw

een

New

Yor

k C

ity a

nd L

os A

ngel

es:

2,50

0 ya

rds

or 2

,500

mile

s?

5.

Th

e am

ount

of c

offe

e in

a m

ug:

2 cu

ps o

r 2

quar

ts?

Favo

rite

Co

lor

Colo

rVo

tes

Blac

k2

Blue

8

Gree

n5

Red

7

Yello

w4

Dra

go

ns:

5 p

oin

ts;

Eag

les:

2 p

oin

ts

app

le:

190

bo

ttle

s;

gra

pe:

110

bo

ttle

s

9 ya

rds

2,50

0 m

iles

2 cu

ps

blu

e

26 v

ote

s

3 m

ore

stu

den

ts

line

seg

men

t

line

ray

© Harcourt • Grade 4SR1-SR2

MXENL08AWK4XSR_PHTE_2UP.indd SR1MXENL08AWK4XSR_PHTE_2UP.indd SR1 7/2/07 11:38:53 AM7/2/07 11:38:53 AM

Spira

l Rev

iew

Nam

eW

eek

3

Spir

al R

evie

w©

Har

cour

t • G

rade

4S

R3

For

que

stio

ns 1

–4, c

om

par

e u

sing

<

, >, o

r =

fo

r e

ach

.

1.

5,

327

5,3

41

2.

3.

3,30

0 3

,460

4.

4,0

39

4,0

39

For

9–11

, use

the

tab

le b

elo

w

to t

ell

whe

the

r e

ach

eve

nt is

lik

ely,

unl

ikel

y, o

r im

poss

ible

fo

r o

ne p

ull,

cons

ide

ring

the

m

arb

les

are

the

sam

e s

ize

.

Warr

en

’s B

ag

of

Marb

les

Colo

rNu

mbe

r

Blue

2

Gree

n7

Red

12

9.

War

ren

will

pul

l a r

ed m

arbl

e.

10.

War

ren

will

pul

l a y

ello

w m

arbl

e.

11.

War

ren

will

pul

l a b

lue

mar

ble.

For

12–1

5, w

rite

a r

ela

ted

fac

t.U

se it

to

co

mp

lete

the

nu

mb

er

sent

enc

e.

12.

7 �

�

9

13.

� 3

� 9

14.

4 �

�

6

15.

8 �

�

5

For

5–8 ,

cho

ose

the

uni

t yo

u w

oul

d u

se t

o m

eas

ure

eac

h. W

rite

cu

p, p

int,

quar

t, o

r ga

llon.

5.

6.

7.

8.

likel

y

� �

imp

oss

ible

un

likel

y

9 �

3 �

12

9 �

7 �

2

6 �

4 �

2

8 �

5 �

3

cup

cup

qu

art

pin

t, q

uar

t,

or

gal

lon

2

12

2 3

�

�

Spira

l Rev

iew

Nam

eW

eek

4

Spir

al R

evie

wS

R4

© H

arco

urt •

Gra

de 4

For

1–2,

te

ll w

heth

er

to e

stim

ate

o

r fin

d a

n e

xact

ans

we

r. Th

en

solv

e.

1.

K

etan

nee

ds to

buy

a no

tebo

ok, a

pe

ncil,

and

a p

en. A

not

eboo

k co

sts

$ 4.7

5, a

pen

cil c

osts

$1.

29, a

nd a

pe

n co

sts

$ 1.6

9. A

bout

how

muc

h m

oney

doe

s K

etan

nee

d?

2.

A

sch

ool b

us h

as 3

2 ro

ws

of s

eats

. Tw

o st

uden

ts c

an s

it in

eac

h se

at.

How

man

y st

uden

ts c

an the

sch

ool

bus

carr

y?

For

6–9,

list

the

po

ssib

le

out

com

es

for

eac

h.

6.

El

ena

flips

a

7.

G

ene

rolls

a d

ie.

quar

ter.

8.

Lynn

e sp

ins

9.

H

aley

pul

ls a

a

spin

ner.

m

arbl

e.

oran

ge

gree

n

For

10–1

2, u

se t

he f

igur

es

be

low

.

10.

Whi

ch fi

gure

s ha

ve fo

ur s

ides

?

11.

Whi

ch fi

gure

s ha

ve thr

ee s

ides

?

12.

Whi

ch fi

gure

s ar

e po

lygo

ns?

For

3–5 ,

cho

ose

the

be

st e

stim

ate

.

3.

D

iam

eter

of a

pen

ny:

2 cm

or

2 dm

or

2 m

4.

Leng

th o

f a s

choo

l boo

k:30

0 cm

or

3 dm

or

3 m

5.

Le

ngth

of a

hai

rbru

sh:

15 c

m o

r 15

dm

or

15 m

esti

mat

e; p

oss

ible

answ

er:

abo

ut

$8

exac

t an

swer

;

64 s

tud

ents

2 cm

3 d

m

15 c

m

hea

ds,

ta

ils

A, B

, C, a

nd

D

gre

en,

ora

ng

e

1, 2

, 3, 4

, 5,

or

6

gra

y,b

lack

A a

nd

B

C a

nd

D


MXENL08AWK4XSR_PHTE_2UP.indd SR3-SR4MXENL08AWK4XSR_PHTE_2UP.indd SR3-SR4 6/19/07 3:54:28 PM6/19/07 3:54:28 PM

Spira

l Rev

iew

Nam

eW

eek

5

Spir

al R

evie

w©

Har

cour

t • G

rade

4SR

5For

9–12

, pre

dic

t th

e n

ext

tw

o

num

be

rs o

r sh

ape

s in

eac

h p

atte

rn.

9.

10.

2, 2

, 2, 5

, 2, 2

, 2, 5

, 2,

,

11.

9, 5

, 5, 9

, 9, 5

, 5, 9

, 9, 5

, ,

12.

For

1–4,

est

imat

e. T

hen

find

the

su

m o

r d

iffe

renc

e.

1.

2,34

5 �

1,1

79

2.

4,84

5 �

2,9

54

3.

9,67

8 �

928

4.

6,42

9 �

3,2

18

For

7–8,

use

the

gra

ph

be

low

.

7.

Kim

eiko

is g

oing

to

spin

the

spi

nner

. O

n w

hich

col

or w

ill the

spi

nner

m

ost lik

ely

land

?

8.

Is th

e nu

mbe

r of

tim

es th

e sp

inne

r la

nded

on

red

grea

ter

than

or

less

than

th

e nu

mbe

r of

tim

es it

land

ed o

n gr

een?

For

5–6 ,

use

cub

es

to m

ake

e

ach

solid

. The

n w

rite

the

vo

lum

e in

cub

ic u

nits

.

5.

6.

015 10 525 2035 3040

Red

Blue

Gree

nYe

llow

OccurrenceCo

lor

Po

ssib

le e

stim

ate:

3,

500

; 3,

524

Po

ssib

le e

stim

ate:

9,

000

; 8,

750

Po

ssib

le e

stim

ate:

2,

000

; 1,

891

Po

ssib

le e

stim

ate:

9,

000

; 9,

647

45 c

ub

ic u

nit

s

12 c

ub

ic u

nit

s

red

gre

ater

th

an

22

59

Spira

l Rev

iew

Nam

eW

eek

6

Spir

al R

evie

w©

Har

cour

t • G

rade

4SR

6

For

1–2,

te

ll w

heth

er

to e

stim

ate

o

r fin

d a

n e

xact

ans

we

r. Th

en

solv

e.

1.

The

scho

ol a

udito

rium

has

300

sea

ts.

For

the

sprin

g pl

ay, t

he s

choo

l pre

-so

ld 1

87 tic

kets

. On

the

nigh

t of

the

sh

ow, t

hey

sold

109

mor

e tic

kets

at

the

door

. How

man

y tic

kets

wer

e le

ft un

sold

?

2.

Cae

sar’s

tra

ck c

oach

wan

ts h

im to

run

abou

t 15

mile

s a

wee

k. If

Cae

sar

runs

4 m

iles

on M

onda

y, 7

mile

s on

W

edne

sday

, and

3 m

iles

on F

riday

, w

ill h

e ha

ve r

un a

bout

15

mile

s?

For

4–6,

use

the

Fav

ori

te F

ruit

p

icto

gra

ph.

4.

Use

the

dat

a in

the

pic

togr

aph

to

mak

e a

bar

grap

h.

5.

Whi

ch fr

uit re

ceiv

ed the

mos

t vo

tes?

6.

How

man

y m

ore

vote

s di

d ba

nana

re

ceiv

e th

an o

rang

e re

ceiv

ed?

For

7–9,

fin

d t

he a

rea

of

eac

h fig

ure

. Wri

te t

he a

nsw

er

in s

qua

re u

nits

.

7.

8.

9.

Use

a m

od

el t

o s

olv

e.

3.

Ian

fille

d a

box

with

blo

cks.

The

re

wer

e 4

laye

rs. E

ach

laye

r ha

d 2

row

s of

4 b

lock

s. W

hat w

as the

vol

ume

of

the

box?

Key:

= 2

vot

es

Oran

ge

Bana

na

Appl

e

Favo

rite

Fru

it

exac

t an

swer

; 4

tick

ets

esti

mat

e; y

es

32 c

ub

ic u

nit

s

app

le

4 m

ore

vo

tes

10 s

qu

are

un

its

16 s

qu

are

un

its

10 s

qu

are

un

its

Po

ssib

le g

rap

h:

Ch

eck

stu

den

ts’

mo

del

s.

Type

s of

Fru

it

Favo

rite

Fru

it

20 16 12 8 4 0

Number of Votes

Apple

Bana

nas

Oran

ges


MXENL08AWK4XSR_PHTE_2UP.indd SR5MXENL08AWK4XSR_PHTE_2UP.indd SR5 6/19/07 3:54:38 PM6/19/07 3:54:38 PM

Spira

l Rev

iew

Nam

eW

eek

7

Spir

al R

evie

wS

R7

© H

arco

urt •

Gra

de 4

For

1–4,

fin

d t

he p

rod

uct.

1.

4

� 3

�

2.

8

� 4

�

3.

5

�

4

4.

4

�

4

For

10–1

3, f

ind

the

val

ue o

f th

e v

aria

ble

. The

n w

rite

a

rela

ted

num

be

r se

nte

nce

.

10.

36 �

t �

6

11.

a �

3 �

21

12.

y �

3 �

6

13.

9 �

m �

63

For

5–6,

wri

te t

he t

ime

. Wri

te o

ne

way

yo

u ca

n re

ad t

he t

ime

.

5.

891011

12

76

5432

1

6.

891011

12

76

5432

1

For

7–9,

use

the

tab

le b

elo

w.

Stu

den

t’s

Favo

rite

C

olo

rCo

lor

Num

ber

Blac

k6

Blon

de5

Brow

n8

Red

2

7.

W

hat co

lor

was

pre

ferr

ed b

y m

ost?

8.

H

ow m

any

stud

ents

wer

e su

rvey

ed?

9.

W

hat is

the

titl

e of

thi

s su

rvey

?

21 s

tud

ents

12 32

20 16 5:45

; P

oss

ible

An

swer

: fiv

e fo

rty-

five

2:26

; Pos

sibl

e A

nsw

er:

two

twen

ty-s

ix

bro

wn

Stu

den

t’s F

avo

rite

C

olo

r

t �

6, 6

� 6

� 3

6

a �

7;

21 �

3 �

7

y �

18,

3 �

6 �

18

m �

7, 6

3 �

9 �

7

Po

ssib

le a

nsw

ers

are

giv

en.

Spira

l Rev

iew

Nam

eW

eek

8

Spir

al R

evie

wS

R8

© H

arco

urt •

Gra

de 4

For

1–4,

fin

d t

he p

rod

uct

or

quo

tie

nt.

1.

8

� 8

�

2.

8

� �

48

3.

11

� 7

_

4.

90

� 9

�

For

9–11

, use

the

pic

tog

rap

h b

elo

w.

9.

How

man

y to

uchd

owns

did

Rya

n sc

ore?

10.

Whi

ch p

laye

rs s

core

d th

e sa

me

num

ber

of tou

chdo

wns

?

11.

How

man

y to

uchd

owns

wer

e sc

ored

in

all?

For

12–1

4, t

race

and

cut

out

e

ach

pai

r o

f fig

ure

s. T

ell

if th

e

figur

es

are

co

ngru

ent

. Wri

te y

es o

r no

.

12.

13.

14.

For

5–8 ,

wri

te e

ach

tem

pe

ratu

re

in �

F.

5.

6.

7.

8.

Roy

Eric

RyanTo

uchd

owns

Sco

red

in a

Sea

son

Each

2 to

uchd

owns

.

90 70

80

°F°F

80 60

70

°F

50 30

40

90 70

80

°F

Eri

c an

d R

oy

16 t

ou

chd

ow

ns

64

6

7710

85�F

8 to

uch

do

wn

s

no

40�F

65�F

80�F

yes

no



Spira

l Rev

iew

Nam

eW

eek

9

Spir

al R

evie

wS

R9

© H

arco

urt •

Gra

de 4

For

1–5,

fin

d t

he p

rod

uct

or

quo

tie

nt.

1.

10 �

3 �

2.

3 �

8 �

3.

32 �

4 �

4.

18 �

3 �

5.

50 �

5 �

For

10–1

2, u

se t

he t

able

be

low

.

Siz

es

Wo

rn B

y B

oys

an

d G

irls

Shirt

Siz

eBo

ysGi

rls

Smal

l8

7

Med

ium

69

Larg

e4

2

10.

How

man

y bo

ys w

ear

med

ium

?

11.

How

man

y st

uden

ts w

ere

surv

eyed

in

all?

12.

How

man

y m

ore

girls

wea

r m

ediu

m

than

boy

s?

For

13–1

6, w

rite

a r

ela

ted

fac

t.U

se it

to

co

mp

lete

the

nu

mb

er

sent

enc

e.

13.

12 �

�

16

14.

8 �

�

2

15.

6 �

�

7

16.

10 �

�

3

For

6–9,

use

a r

ule

r. D

raw

a li

ne

for

eac

h le

ngth

.

6.

1 in

ch

7.

2 1 4

inch

es

8.

1 1 2

inch

es

9.

1 1 8

inch

es

30 8

24

6 b

oys

36 s

tud

ents

3 m

ore

gir

ls

Fo

r 6

–9, c

hec

k st

ud

ents

’ dra

win

gs.

6 10

16 �

12

� 4

8 �

2 �

6

7 �

6 �

1

10 �

3 �

7

Po

ssib

le

rela

ted

fac

ts

are

giv

en.

4 6 1 7

Spira

l Rev

iew

Nam

eW

eek

10

Spir

al R

evie

wS

R10

© H

arco

urt •

Gra

de 4

For

1–4,

use

a b

asic

fac

t an

d

pat

tern

s to

fin

d t

he p

rod

ucts

.

1.

4

� 2

� 8

4 �

20

�

4 �

200

�

4 �

2,0

00 �

2.

6 �

8 �

48

6 �

80

�

6 �

800

�

6 �

8,0

00 �

3.

8 �

3 �

24

8 �

30

�

8 �

300

�

8 �

3,0

00 �

4.

5 �

7 �

35

5 �

70

�

5 �

700

�

5 �

7,0

00 �

For

9–11

, use

the

gra

ph

be

low

to

ans

we

r th

e q

uest

ions

.

0Ja

n.Fe

b.M

ar.

Apr.

123456789Num

ber o

f Boo

ks R

ead

by M

r. He

rn’s

Clas

s

Number

Mon

th

9.

How

man

y bo

oks

wer

e re

ad in

all?

10.

In w

hich

mon

ths

wer

e th

e sa

me

num

ber

of b

ooks

rea

d?

11.

How

man

y m

ore

book

s w

ere

read

in

Janu

ary

than

in A

pril?

For

12–1

4, t

ell

if th

e li

ne is

a

line

of

sym

me

try.

Wri

te y

es o

r no

.

12.

13. B

14

.

For

5–8,

co

mp

are

. Wri

te <

, >, o

r =

fo

r e

ach

.

5.

19

oun

ces

1 p

ound

6.

32

oun

ces

2 p

ound

s

7.

23

oun

ces

3 p

ound

s

8.

8

ounc

es

1 p

ound

80

27 b

oo

ks

Febr

uary

and

Apr

il

2 m

ore

bo

oks

800

8,00

0

480

4,80

048

,000

240

2,40

024

,000

350

3,50

035

,000

�n

o

no

yes

� � �



Spira

l Rev

iew

Nam

eW

eek

11

Spir

al R

evie

wS

R11

© H

arco

urt •

Gra

de 4

For

1–2,

so

lve

the

pro

ble

m.

1.

In 199

6, p

eopl

e in

the

Uni

ted

Stat

es

ate 10

0 ac

res

of p

izza

eve

ry d

ay.

Wou

ld it

be

reas

onab

le to

say

that

pe

ople

eat

1,000

acr

es o

f piz

za e

very

w

eek?

Exp

lain

.

2.

Th

e Pa

ine

fam

ily is

hav

ing

a pi

zza

part

y. T

hey

need

9 p

izza

s. If

eac

h pi

zza

cost

s $1

7, is

$15

0 a

reas

onab

le

estim

ate

for

the

tota

l? E

xpla

in.

For

5–7,

use

the

sp

inne

r b

elo

w.

5.

Whi

ch o

utco

me

is m

ost lik

ely?

6.

Whi

ch o

utco

me

is le

ast lik

ely?

7.

Whi

ch o

utco

mes

are

equ

ally

like

ly?

For

8–11

, fin

d t

he v

alue

of

the

va

riab

le. T

hen

wri

te a

re

late

d

num

be

r se

nte

nce

.

8.

36

� t

� 6

9.

a

� 3

� 21

10.

y �

3 �

6

11. 9

� m

� 63

For

3–4,

wri

te e

ach

tem

pe

ratu

rein

�F.

3.

4.

°F

50 30

40

°F

100

70

80

no; P

ossi

ble

Ans

wer

: 7

� 1

00 �

700

, so

1,00

0 ac

res

is to

o la

rge.

t �

6;

6 �

6 �

36

a �

7;

21 �

7 �

3

y �

18;

6 �

3 �

18

m �

7;

63 �

7 �

9

Sen

tenc

es m

ay v

ary.

37 �

F

yes;

Pos

sibl

e A

nsw

er:

$17

� 9

� $

153

1

2 an

d 4

3

99 �

F

Spira

l Rev

iew

Nam

eW

eek

12

Spir

al R

evie

wS

R12

© H

arco

urt •

Gra

de 4

For

1–5,

est

imat

e t

he p

rod

uct.

1.

78

� 34

�

2.

91

� 46

�

3.

22

� 33

�

4.

61

� 359

�

5.

20

� 119

�

For

10–1

1, u

se t

he g

rap

h b

elo

w.

Go

als

Sco

red

in

a H

ock

ey S

easo

n

Andy

Dwig

ht

Mia

10

23

46

5

Goal

s

Name

10.

How

man

y ho

ckey

goa

ls w

ere

scor

ed

for

the

entir

e se

ason

?

11.

How

man

y m

ore

goal

s di

d M

ia s

core

th

an A

ndy

scor

ed?

For

12–1

4, n

ame

eac

h tr

iang

le b

y its

sid

es.

12.

13.

14.

For

6–9,

cho

ose

the

uni

t yo

u w

oul

d u

se t

o m

eas

ure

eac

h.

Wri

te c

entim

eter

, met

er, o

r ki

lom

eter

.

6.

heig

ht o

f a s

choo

l des

k

7.

leng

th o

f a p

enci

l

8.

four

city

blo

cks

9.

leng

th o

f the

hal

lway

in y

our

scho

ol

4 cm

4 cm

4 cm

12 c

m12

cm

15 c

m

8 cm

2 cm

11 c

m

2,40

0

Est

imat

es w

ill v

ary.

4,50

0

600

24,0

00

2,00

0

met

er

cen

tim

eter

kilo

met

er

12 g

oal

s

2 g

oal

s equ

ilate

ral

iso

scel

es

scal

ene

met

er



Spira

l Rev

iew

Nam

eW

eek

13

Spir

al R

evie

wS

R13

© H

arco

urt •

Gra

de 4

For

1–5,

ro

und

eac

h nu

mb

er

to t

he p

lace

val

ue o

f th

e

und

erl

ine

d d

igit

.

1.

1,

754

2.

45

,981

3.

71

3,40

2

4.

3,

922,

703

5.

9,

779,

911

For

9–11

, use

the

dat

a in

the

p

icto

gra

ph.

9.

Who

cau

ght th

e m

ost fis

h?

10.

Who

cau

ght th

e le

ast fis

h?

11.

How

man

y fis

h w

ere

caug

ht in

all?

12.

Mr.

Hei

nze

wro

te a

num

ber

patter

n on

the

boa

rd. I

f he

cont

inue

s th

e pa

tter

n, w

hat

will

the

nex

t tw

o nu

mbe

rs b

e?50

, 55,

60,

65,

70,

75

13.

Che

lsea

is d

esig

ning

a b

orde

r ar

ound

he

r be

droo

m. T

he p

atte

rn is

tw

o st

ars

and

one

circ

le. F

or h

er p

atte

rn, s

he

pain

ted

12 fi

gure

s. W

hat is

the

sha

pe

of the

9th

figu

re in

her

pat

tern

?

For

6–8,

cho

ose

the

uni

t yo

uw

oul

d u

se t

o m

eas

ure

eac

h.W

rite

cup

, pin

t, qu

art,

or

gallo

n.

6.

7.

8.

Trac

y

Key:

Eac

h

= 2

fish

Stev

e

Aida

n

Fish

Cau

gh

t

1,80

0

80, 8

5

Aid

an

a ci

rcle

50,0

00

9,80

0,00

0

4,00

0,00

0

710,

000

pin

t; q

uar

t o

r g

allo

n

Ste

ve

24 f

ish

gal

lon

; q

uar

t

cup

; p

int

Spira

l Rev

iew

Nam

eW

eek

14

Spir

al R

evie

wS

R14

© H

arco

urt •

Gra

de 4

For

1–2,

wri

te a

fra

ctio

n in

nu

mb

ers

and

in w

ord

s th

at

nam

es

the

sha

de

d p

art.

1.

2.

For

7–8,

use

the

pic

tog

rap

h b

elo

w.

7.

Ex

plai

n ho

w y

ou w

ould

dis

play

the

da

ta in

the

pic

togr

aph

if 3

pinw

heel

s w

ere

won

.

8.

W

hich

priz

e w

as w

on the

mo

st?

Whi

ch p

rize

was

won

the

leas

t?

For

9–12

, nam

e e

ach

qua

dri

late

ral.

9.

10

.

11.

12

.

For

3–6,

cho

ose

the

uni

t yo

u w

oul

d u

se t

o m

eas

ure

eac

h.W

rite

inch

, fo

ot,

yard

, or

mile

.

3.

a

foot

ball

field

4.

a

high

way

5.

a

pen

6.

a

car

yard

Po

ssib

le a

nsw

er: I

wo

uld

ad

d t

he

cate

go

ry

“pin

wh

eels

” an

d p

ut

3 st

ars

afte

r it

.th

ree

fou

rth

s

two

fo

urt

hs

mile

inch

free

gam

e; g

old

fish

squ

are;

re

ctan

gle

rect

ang

le;

par

alle

log

ram

rho

mb

us

rho

mb

us

foo

t

2 _ 4 3 _ 4



Spira

l Rev

iew

Nam

eW

eek

15

Spir

al R

evie

wS

R15

© H

arco

urt •

Gra

de 4

For

1–5,

div

ide

and

che

ck.

1.

49

8 �

7 �

2.

18

6 �

5 �

3.

30

4 �

6 �

4.

10

1 �

7 �

5.

$1

98 �

3 �

For

8, u

se t

he li

ne p

lot.

8.

M

rs. R

ober

ts’s

cla

ss r

ecor

ded

the

num

bers

spu

n du

ring

15 s

pins

. Pr

edic

t w

hat nu

mbe

r w

ill m

ost lik

ely

be s

pun

on the

nex

t sp

in.

For

9–12

, use

me

ntal

mat

h an

d p

atte

rns

to f

ind

th

e p

rod

uct.

9.

7 �

30

�

10.

5 �

600

�

11.

4 �

3,0

00 �

12.

8 �

8,0

00 �

For

6–7,

wri

te t

he v

olu

me

in

cub

ic u

nits

.

6.

7.

71 R

1

24 c

ub

ic u

nit

s

12 c

ub

ic u

nit

s

$66

37 R

1

14 R

3

50 R

6

210 3,00

0

12,0

00

64,0

00

6

Spira

l Rev

iew

Nam

eW

eek

16

Spir

al R

evie

wS

R16

© H

arco

urt •

Gra

de 4

For

1–4,

div

ide

and

che

ck.

1.

189

� 3

�

2.

564

� 7

�

3.

898

� 9

�

4.

732

� 8

�

For

8–10

, use

the

tab

le

be

low

.

Marb

les

Red

Blue

Gree

n

Larg

e3

41

Med

ium

62

2

Smal

l1

60

8.

How

man

y sm

all b

lue

mar

bles

are

th

ere?

9.

How

man

y la

rge

red

mar

bles

are

th

ere?

10.

How

man

y gr

een

mar

bles

are

the

re

in a

ll?

For

11–1

2, w

rite

a m

ulti

plic

atio

n se

nte

nce

fo

r e

ach

arra

y.

11.

12.

For

5–7,

cho

ose

the

uni

t yo

u w

oul

d u

se t

o m

eas

ure

eac

h.W

rite

mL

or

L.

5.

6.

7.

63

80 R

4

91 R

4

99 R

7

3 g

reen

mar

ble

s

3 la

rge

red

mar

ble

s

6 sm

all b

lue

mar

ble

s

2 �

3 �

6 a

nd

3

� 2

� 6

5 �

4 �

20

and

4

� 5

� 2

0

L mL L



Spira

l Rev

iew

Nam

eW

eek

17

Spir

al R

evie

wS

R17

© H

arco

urt •

Gra

de 4

For

1–4,

ord

er

the

fra

ctio

ns f

rom

le

ast t

o g

reat

est.

1.

2

, 1 ,

43

2

5

2.

2 , 5

, 3

5 8

7

3.

1

, 1 ,

13

2

4

4.

3 , 5

, 3

4 6

8

For

8–10

, use

the

sp

inne

r b

elo

w.

Tell

whe

the

r e

ach

eve

nt is

lik

ely,

unl

ikel

y, o

r im

poss

ible

fo

r o

ne s

pin

.

8.

The

poi

nter

will

land

on

1.

9.

The

poi

nter

will

land

on

3.

10.

The

poi

nter

will

land

on

4.

For

11–1

4, d

esc

rib

e t

he li

nes.

W

rite

inte

rsec

ting,

per

pend

icul

ar,

or

para

llel.

11.

12

.

13.

14

.

For

5–7,

se

lect

the

fig

ure

wit

hth

e g

reat

er

are

a.

5.

A

B

6.

A

B

7.

A

B

likel

y

un

likel

y

par

alle

l

par

alle

lin

ters

ecti

ng

per

pen

dic

ula

r

imp

oss

ible

B B A

1 _ 2 , 2 _ 3 , 4 _ 5 3 _ 7 ,

2 _ 5 , 5 _ 8

1 _ 4 , 1 _ 3 , 1 _ 2 3 _ 8 , 3 _ 4 , 5 _ 6

Spira

l Rev

iew

Nam

eW

eek

18

Spir

al R

evie

wS

R18

© H

arco

urt •

Gra

de 4

For

1–4,

re

nam

e e

ach

frac

tio

n as

a

mix

ed

num

be

r an

d e

ach

mix

ed

nu

mb

er

as a

fra

ctio

n.

1.

23 5

2.

8 3

3.

41 5

4.

15 7

For

7–9,

list

the

po

ssib

le

out

com

es

for

eac

h.

7.

Jam

es fl

ips

the

penn

y.

8.

Xoc

hi p

ulls

a c

oin.

9.

Ella

spi

ns the

spi

nner

.

For

10–1

3, t

ell

if e

ach

figur

e is

a

po

lyg

on.

Wri

te y

es o

r no

.

10.

11.

12.

13.

For

5–6,

est

imat

e. T

hen

use

a

cent

ime

ter

rule

r to

fin

d t

he

pe

rim

ete

r.

5.

6.

hea

ds,

tai

ls

Po

ssib

le e

stim

ate:

5

cm;

6 cm

nic

kel,

dim

e

1 , 2

, 3

, 4

no

yes

no

yes

Po

ssib

le e

stim

ate:

3

cm;

3 cm

13 _ 5

2 2 _ 3

21 _ 5

2 1 _ 7

MX

EN

L08A

WK

4X_S

R_W

K18

.indd

S

R18

7/2/

07

10:4

5:12

AM



Spira

l Rev

iew

Nam

eW

eek

19

Spir

al R

evie

wS

R19

© H

arco

urt •

Gra

de 4

For

1–4,

est

imat

e t

he s

um o

rd

iffe

renc

e.

1.

5.9

� 2

.1

2.

5.39

� 9

.77

3.

$79.

23 �

$18

.18

4.

$10.

09 �

$1.

00 �

$6.

97

For

9–11

, use

the

fre

que

ncy

tab

le b

elo

w. Fa

vo

rite

Fo

od

Food

Freq

uenc

y

Pizz

a10

Sal

ad7

Chic

ken

Nugg

ets

6

9.

Mor

e st

uden

ts c

hose

sal

ad tha

n pi

zza.

Tru

e or

fals

e?

10.

How

man

y st

uden

ts v

oted

for

chic

ken

nugg

ets?

11.

Whi

ch fo

od r

ecei

ved

the

mos

t vo

tes?

For

12–1

3, u

se lo

gic

al

reas

oni

ng t

o s

olv

e t

he

pro

ble

ms.

Mel

inda

invi

tes

Alic

ia, B

onni

e, C

arlo

s, a

nd

Dan

to

her

part

y. A

licia

arr

ives

at th

e pa

rty

afte

r D

an. C

arlo

s ar

rives

at th

e pa

rty

afte

r A

licia

. Bon

nie

arriv

es a

t th

e pa

rty

befo

re

Dan

.

12.

Whi

ch g

uest

arr

ives

firs

t to

the

par

ty?

13.

Whi

ch g

uest

arr

ives

last

?

For

5–8,

wri

te t

he t

ime

as

it w

oul

d

be

sho

wn

on

a d

igit

al c

lock

.

5.

25 m

inut

es b

efor

e se

ven

6.

38 m

inut

es a

fter

nine

7.

10 m

inut

es b

efor

e th

ree

8.

29 m

inut

es a

fter

six

6:35

9:3

8

fals

e

6 st

ud

ents

piz

za

Bo

nn

ie

Car

los

Po

ssib

le

esti

mat

esar

e g

iven

. 4 15 $1

00

$2

2:5

0

6:29

Spira

l Rev

iew

Nam

eW

eek

20

Spir

al R

evie

wS

R20

© H

arco

urt •

Gra

de 4

For

1–4,

wri

te e

ach

frac

tio

n as

a

de

cim

al.

1.

2 10

2.

38 100

3.

90 100

4.

5 10

For

9–10

, use

the

bar

gra

ph

be

low

.

Favo

rite

Co

okie

Oatm

eal

Choc

olat

eCh

ip

Pean

utBu

tter

24

68

1412

10

Vote

s

Cookie

9.

Whi

ch c

ooki

e w

as c

hose

n by

the

fe

wes

t nu

mbe

r of

peo

ple?

10.

How

man

y pe

ople

cho

se o

atm

eal a

s th

eir

favo

rite

cook

ie?

For

11–1

3, w

rite

a r

ela

ted

fac

t.

Use

it t

o c

om

ple

te t

he n

umb

er

sent

enc

e.

11.

7 �

�

10

12.

7 �

�

7

13.

7 �

�

4

For

5–8,

fin

d t

he e

lap

sed

tim

e.

5.

star

t: 6:

15 A

.M.

end:

5:4

5 P.

M.

6.

star

t: 7:

45 A

.M.

end:

11:

55 A

.M.

7.

star

t: 8:

08 P

.M.

end:

11:

45 P

.M.

8.

star

t: 12

:00

A.M

.

en

d: 1

:27

P.M

.

0.2

10 �

3 �

7

0.38

0.90

0.5

7 �

0 �

7

3 �

4 �

7

pea

nu

t b

utt

er

8 p

eop

le

Po

ssib

le r

elat

ed

fact

s ar

e g

iven

.11

hr

30 m

in

4 h

r 10

min

3 h

r 37

min

13 h

r 27

min

3 0 3



Spira

l Rev

iew

Nam

eW

eek

21

Spir

al R

evie

wS

R21

© H

arco

urt •

Gra

de 4

For

1–4,

wri

te t

wo

eq

uiva

lent

fr

acti

ons

fo

r e

ach.

1.

1 2

2.

8 10

3.

4 6

4.

3 4

For

9–10

, use

the

Ve

nn D

iag

ram

.

1530

A

36

95

1015

B

9.

How

wou

ld y

ou la

bel o

vals

A a

nd B

?

10.

Why

are

the

num

bers

15

and

30 s

orte

d in

the

over

lap

sect

ion

of th

e di

agra

m?

For

11–1

3, w

rite

inte

rsec

ting,

para

llel,

or

perp

endi

cula

r.

11.

12.

13.

For

5–8,

use

the

the

rmo

me

ter

to

find

the

te

mp

era

ture

in º

F.

5.

°F

90 70

80

6.

°F

60 40

50

7.

°F

40 20

30

8.

°F

80 60

70

90�F

55�F

30�F

75�F

par

alle

l

inte

rsec

tin

g, o

rp

erp

end

icu

lar

per

pen

dic

ula

r

Po

ssib

le

equ

ival

ent

frac

tio

ns

are

giv

en.

A:

Mu

ltip

les

of

3 an

d 5

;

B:

Mu

ltip

les

of

5

15 a

nd

30

are

mu

ltip

les

of

bo

th 3

an

d 5

2 _ 4 , 3 _ 6

4 _ 5 , 16 _ 20

2 _ 3 , 3 _ 6

6 _ 8 , 9 _ 12

MX

EN

L08A

WK

4X_S

R_W

K21

.indd

S

R21

7/2/

07

10:4

5:54

AM

Nam

e

Spira

l Rev

iew

Wee

k 22

Spir

al R

evie

wS

R22

© H

arco

urt •

Gra

de 4

For

1–3,

ord

er

the

de

cim

als

fro

m

leas

t to

gre

ate

st.

1.

1.3,

1.0

3, 1

.13,

1.3

1

2.

1.9,

1.1

9, 1

.09,

1.9

6

3.

1.11

, 1.0

1, 1

.08,

1.1

For

9, p

red

ict

and

te

st t

o s

olv

e.

9.

Mar

ge is

thi

nkin

g of

tw

o nu

mbe

rs.

The

sum

of t

he tw

o nu

mbe

rs is

15,

an

d th

e pr

oduc

t is

56.

Wha

t tw

o nu

mbe

rs is

Mar

ge thi

nkin

g of

?

Pred

ict

Test

Sum

Test

Pro

duct

Does

it

Chec

k?

For

10–1

2, t

ell

how

eac

h fig

ure

was

mo

ved

. Wri

te s

lide,

flip

, or

turn

.

10.

11.

12.

For

4–8,

so

lve

the

eq

uati

on.

4.

45 �

x �

9

5.

y �

6 �

18

6.

a �

4 �

9

7.

9 �

c �

18

8.

r �

7 �

6

1.03

, 1.1

3, 1

.3, 1

.31

1.09

, 1.1

9, 1

.9, 1

.96

1.01

, 1.0

8, 1

.1, 1

.11

x �

5

y �

3

a �

36

c �

2

r �

42

7 an

d 8

turn

slid

e

flip



Spira

l Rev

iew

Nam

eW

eek

23

Spir

al R

evie

wS

R23

© H

arco

urt •

Gra

de 4

For

1–5,

wri

te a

n e

qui

vale

nt

de

cim

al f

or

eac

h. Y

ou

may

use

d

eci

mal

mo

de

ls.

1.

0.5

2.

0.80

3.

0.3

4.

2 10

5.

0.90

For

8–9,

use

the

do

uble

b

ar g

rap

h.

8.

Whi

ch s

port

was

leas

t po

pula

r w

ith

the

boys

?

9.

Whi

ch s

port

was

equ

ally

pop

ular

with

th

e bo

ys a

nd the

girl

s?

For

10–1

3, c

om

ple

te. T

ell

whe

the

r yo

u m

ultip

ly o

r di

vide

.Fo

r 6–

7, u

se t

he c

ale

ndar

be

low

.

July

Sun

Mon

Tue

Wed

Thu

Fri

Sat

12

34

56

78

910

1112

1314

1516

1718

1920

2122

2324

2526

2728

2930

31

6.

Ale

x ce

lebr

ated

Inde

pend

ence

Day

on

Jul

y 4.

If tod

ay is

Jul

y 19

, how

m

any

days

has

it b

een

sinc

e he

ce

lebr

ated

?

7.

Am

y’s

sum

mer

rea

ding

cla

ss s

tart

s on

Jul

y 9.

If h

er c

lass

is 1

4 da

ys lo

ng,

whe

n w

ill it

end

?

Metr

ic U

nit

s o

f Le

ng

th1

cent

imet

er (c

m) �

10

mill

imet

ers

(mm

)1

deci

met

er (d

m) �

10

cent

imet

ers

(cm

)1

met

er (m

) � 1

,000

mill

imet

ers

1 ki

lom

eter

(km

) � 1

,000

met

ers

10.

10 c

m �

m

m

11.

m �

2,0

00 m

m

12.

km

� 1

8,00

0 m

13.

cm

� 2

dm

Favo

rite

Spor

t

Favo

rite

Sp

ort

s

Boys

Girls

10 8 6 4 2 0

Number of Votes

Base

ball

Foot

ball

Socc

er

bas

ebal

l

socc

er

15 d

ays

July

23

0.50 0.8

0.30 0.2

0.9

Pos

sibl

e an

swer

s ar

e gi

ven.

mul

tiply

divi

de

divi

de

mul

tiply

100

2 18 20

Spira

l Rev

iew

Nam

eW

eek

24

Spir

al R

evie

w©

Har

cour

t • G

rade

4

SR

24Fo

r 12

–13,

nam

e t

he s

olid

fig

ure

that

has

the

fo

llow

ing

vie

ws.

12.

top

view

fron

t vi

ewsi

de v

iew

13.

top

view

fron

t vi

ewsi

de v

iew

For

1–4,

use

ob

ject

s o

r p

ictu

res

to f

ind

the

sum

or

diff

ere

nce

.

1.

5.

4

2.

12.6

7�

1.7

�

10.2

3

3.

89

.45

4.

$3.2

5�

21.9

6

�$0

.89

For

9–11

, lis

t th

e p

oss

ible

o

utco

me

s o

f e

ach.

9.

gre

en gre

en

red

10.

11.

For

5–8,

co

mp

lete

. Te

llw

heth

er

you

mul

tiply

or

divi

de.

Cu

sto

mary

Un

its

of

Weig

ht

1 po

und

(lb) �

16

ounc

es (o

z)

1 to

n (T

) � 2

,000

pou

nds

(lbs)

5.

oz

� 1

3 lb

6.

lb �

12

T

7.

lb �

224

oz

8.

T �

32,

000

lb

7.1

mu

ltip

lytr

ian

gu

lar

pyra

mid

2.44

67.4

9$4

.14

mu

ltip

ly

div

ide

div

ide

gree

n, r

ed

squ

are

pyr

amid

7, 8

, 9

blac

k, w

hite

, gr

ay

208

24,0

00

14 16



Spira

l Rev

iew

Nam

eW

eek

25

Spir

al R

evie

wS

R25

© H

arco

urt •

Gra

de 4

For

1–3,

find

the

sum

. You

m

ay w

ish

to u

se m

odel

s.

1.

0.67

� 0

.36

2.

0.8

� 0

.5

3.

1.75

� 1

.08

For

7–8,

use

the

tab

le. M

ake

a

ge

nera

lizat

ion.

The

n so

lve

the

p

rob

lem

.

70 60 50 40 30 20 10 022

yea

rs8

year

s12

Mon

ths

28 d

ays

Age

Bre

ath

Rate

Breaths Per Minute

7.

Jeff

take

s 20

bre

aths

per

min

ute.

G

ary

take

s 50

bre

aths

per

min

ute.

W

ho is

old

er?

8.

If Je

nny

brea

thes

40

brea

ths

per

min

ute,

who

is the

you

nges

t of

the

th

ree

peop

le?

For

9–11

, fin

d a

rule

. W

rite

the

rule

as

an e

quat

ion.

Use

th

e eq

uatio

n to

com

plet

e th

e ta

ble.

9.

x2

48

y1

57

9

10.

x12

119

y15

1413

11

11.

x1

24

y10

2030

50

For

4–6,

cho

ose

the

mo

st

reas

ona

ble

uni

t o

f m

eas

ure

.W

rite

mm

, cm

, dm

, m, o

r km

.

4.

5.

6.

Jeff

Gar

y

m cmsu

btr

act

1; y

� x

� 1

add

3;

y �

x �

3

mu

ltip

ly b

y 10

; y

� 1

0x

63

10

108

12

35

40

1.03 1.3

2.83

dm

Spira

l Rev

iew

Nam

eW

eek

26

Spir

al R

evie

wS

R26

© H

arco

urt •

Gra

de 4

For

1–3,

mak

e c

hang

e. L

ist

the

b

ills

and

co

ins.

1.

Cos

t: $3

.86;

Pai

d w

ith:

2.

Cos

t: $7

.15;

Pai

d w

ith:

3.

Cos

t: $1

.39;

Pai

d w

ith:

For

5–6,

use

the

fo

llow

ing

sc

ene

rio

. Th

e s

cho

ol c

afe

teri

a ha

s tw

o p

late

ch

oic

es:

che

ese

piz

za o

r ch

icke

n nu

gg

ets

. Eac

h p

late

co

me

s w

ith

the

ch

oic

e o

f e

ithe

r a

frui

t cu

p o

r sa

lad

.

5.

Dra

w a

tre

e di

agra

m to

show

all

poss

ible

com

bina

tions

.

6.

List

all

the

poss

ible

com

bina

tions

.

For

7–9,

dra

w e

ach

of

the

fo

llow

ing

in t

he c

ircl

e b

elo

w.

7.

Rad

ius

AB

8.

Dia

met

er A

C

9.

Cho

rd D

E

Find

the

are

a an

d p

eri

me

ter

of

the

fig

ure

. The

n d

raw

ano

the

r fig

ure

tha

t ha

s th

e s

ame

pe

rim

ete

r b

ut a

diff

ere

nt a

rea.

4.

6

ft

4 ft

fru

it c

up

chee

se p

izza

sa

lad

chic

ken

nu

gg

ets

fru

it c

up

sala

d

Ch

eck

stu

den

ts’

dra

win

gs.

P

oss

ible

d

raw

ing

:

chee

se p

izza

, fru

it c

up

;

On

e $1

bill

, 1 d

ime,

4

pen

nie

s

Two

$1

bill

s, 3

qu

arte

rs,

1 d

ime

Th

ree

$5

bill

s, t

hre

e $1

bill

s, 2

qu

arte

rs,

1 d

ime,

1 p

enny

Ch

eck

stu

den

ts’

dra

win

gs.

An

swer

s w

ill v

ary.

Po

ssib

le

answ

ers

are

giv

en.

A �

24

sq f

t; P

� 2

0 ft

.

chee

se p

izza

, sal

ad;

chic

ken

nu

gg

ets,

fru

it c

up

;ch

icke

n n

ug

get

s, s

alad

MX

EN

L09A

WK

4X_S

R_W

K26

.indd

S

R26

7/2/

07

10:4

7:29

AM



Nam

eW

eek

27

Spira

l Rev

iew

Spir

al R

evie

wS

R27

© H

arco

urt •

Gra

de 4

For

1–4,

te

ll w

heth

er

the

fra

ctio

ns

are

eq

uiva

lent

. Wri

te y

es o

r no

.

1.

2 __

4 ,

1 __

2

2.

3 __

8 ,

1 __

4

3.

3 __

4 ,

6 __

8

4.

3 __

9 ,

1 __

3

8.

Aud

rey

is a

ski

inst

ruct

or. F

or

her

unifo

rm, s

he is

giv

en a

re

d sk

i jac

ket an

d a

gree

n ja

cket

. She

is a

lso

give

n a

red

ski c

ap a

nd a

gre

en s

ki c

ap.

Mak

e an

org

aniz

ed li

st o

f the

po

ssib

le c

loth

ing

com

bina

tions

.

Colo

r of S

ki J

acke

tsCo

lor o

f Ski

Cap

s

9.

Acc

ordi

ng to

the

orga

nize

d lis

t yo

u m

ade,

how

man

y po

ssib

le c

loth

ing

com

bina

tions

doe

s A

udre

y ha

ve?

For

10–1

3, c

om

ple

te. T

ell

whe

the

r yo

u m

ultip

ly o

r di

vide

.

Cu

sto

mary

Un

its

of

Len

gth

1 fo

ot (f

t) =

12 in

ches

(in.

)

1 ya

rd (y

d) =

3 fe

et, o

r 36

inch

es

1 m

ile (m

i) =

5,28

0 fe

et, o

r 1,7

60 y

ards

10.

yd

� 3

24 in

.

11.

ft �

108

in.

12.

ft �

10

yd

13.

mi �

10,

560

yd

For

5–7,

fin

d t

he p

eri

me

ter

of

eac

h fig

ure

.

5.

6.

7.

no

yes

yes

yes

4 co

mb

inat

ion

s

divi

de

mul

tiply

divi

de

divi

de

Red

Red

Gre

enG

reen

Gre

enR

ed

12 u

nit

s

12 u

nit

s

16 u

nit

s

9 9 30 6

Spira

l Rev

iew

Nam

eW

eek

28

Spir

al R

evie

wS

R28

© H

arco

urt •

Gra

de 4

For

1–5,

co

mp

are

. Wri

te <

, >,

or

= f

or

eac

h .

1.

1 3

2 3

2.

4 5

2 5

3.

1 8

2 9

4.

6 12

1 2

5.

3 7

8 9

For

8–11

, te

ll w

heth

er

the

dat

a is

num

eric

al o

r ca

tego

rical

.

8.

colo

r of

hai

r

9.

num

ber

of h

its in

a b

aseb

all i

nnin

g

10.

vote

s fo

r cl

ass

pres

iden

t

11.

favo

rite

pets

For

12–1

5, n

ame

the

ge

om

etr

ic

term

tha

t b

est

re

pre

sent

sth

e o

bje

ct.

12.

a hi

ghw

ay

13.

the

cent

er o

f a c

lock

14.

the

hand

of a

clo

ck

15.

a pa

rkin

g lin

e

For

6–7,

fin

d t

he a

rea

and

pe

rim

ete

r o

f e

ach

figur

e. T

hen

dra

w

ano

the

r fig

ure

tha

t ha

s th

e s

ame

p

eri

me

ter

but

a d

iffe

rent

are

a.

6.

7.

4 ft

4 ft

4 ft

4 ft

2 ft

2 ft

9 ft

9 ft

cate

go

rica

l

nu

mer

ical

nu

mer

ical

cate

go

rica

l

line;

lin

e se

gm

ent

po

int

ray;

lin

e se

gm

ent

line

seg

men

t

16 s

q f

t; 1

6 ft

18 s

q f

t; 2

2 ft

� � � � � Ch

eck

stu

den

ts’

dra

win

gs

Ch

eck

stu

den

ts’

dra

win

gs



Spira

l Rev

iew

Nam

eW

eek

29

Spir

al R

evie

wS

R29

© H

arco

urt •

Gra

de 4

For

1–3,

wri

te a

mix

ed

nu

mb

er

for

eac

h m

od

el.

1.

2.

3.

For

7–8,

use

the

Ve

nn

dia

gra

m b

elo

w.

7.

W

hat la

bels

sho

uld

you

use

for

sect

ion

B a

nd s

ectio

n C

?

8.

In

whi

ch s

ectio

n w

ould

you

put

27?

For

9–12

, co

mp

lete

. Te

ll w

heth

er

you

mul

tiply

or

divi

de.

Cu

sto

mary

Un

its

of

Measu

rem

en

t1

poun

d (lb

) = 1

6 ou

nces

(oz)

1 to

n (T

) = 2

,000

pou

nds

(lb)

1 pi

nt (p

t) =

2 cu

ps (c

)

1 qu

art (

qt) =

2 p

ints

(pt)

1 ga

llon

(gal

) = 4

qua

rts (q

t)

9.

o

z �

10

lb

10.

T �

10,

000

lb

11.

qt

� 2

00 c

12.

qt

� 2

0 ga

l

For

4–6,

co

unt

or

mul

tip

ly t

o

find

the

vo

lum

e.

4.

5.

6.

9 12

15 30

25 20

3 6

5 10

B?

A M

ulti

ple

s o

f 3

C?

B:

Mu

ltip

les

of

3 an

d 5

;

sect

ion

A

C:

Mu

ltip

les

of

5

160 5 50 80

mu

ltip

ly

div

ide

div

ide

mu

ltip

ly

45 c

ub

ic u

nit

s

8 cu

bic

un

its

36 c

ub

ic u

nit

s

2 4 _ 6

2 3 _ 4

2 1 _ 2

Spira

l Rev

iew

Nam

eW

eek

30

Spir

al R

evie

wSR

30

© H

arco

urt •

Gra

de 4

For

1–3,

co

mp

are

the

mix

ed

nu

mb

ers

. Use

<, >

, or

= f

or

eac

h

.

1.

22 8

26 8

2.

32 5

31 5

3.

41 3

41 3

For

7–9,

te

ll w

heth

er

the

eve

nt

is li

kely

, unl

ikel

y, c

erta

in, o

r im

poss

ible

.

7.

Rol

ling

a 9

on a

num

ber

cube

labe

led

1 to

8.

8.

Pulli

ng a

red

mar

ble

out of

a b

ag tha

t co

ntai

ns 1

0 re

d, 4

gre

en, a

nd 2

blu

e m

arbl

es e

ach

of e

qual

siz

e.

9.

Spin

ning

a n

umbe

r le

ss tha

n 5

on a

sp

inne

r w

ith 4

equ

al p

arts

labe

led

1, 2

, 3, a

nd 4

.

For

10–1

2, f

ind

a r

ule

. The

n fin

d t

he n

ext

tw

o n

umb

ers

in

the

pat

tern

.

10.

39, 4

2, 4

5, 4

8, 5

1, 5

4

11.

110,

105

, 100

, 95,

90

12.

23, 3

3, 3

0, 4

0, 3

7, 4

7, 4

4

For

4–6,

est

imat

e t

he a

rea

of

eac

h fig

ure

. Eac

h un

it s

tand

s fo

r 1

sq f

t. 4

.

5

.

6

.

� � �

imp

oss

ible

likel

y

cert

ain

add

3;

57, 6

0

sub

trac

t 5;

85,

80

add

10,

su

btr

act

3;

54, 5

1

16 s

q f

t

20 s

q f

t

24 s

q f

t



Spira

l Rev

iew

Nam

eW

eek

31

Spir

al R

evie

wS

R31

© H

arco

urt •

Gra

de 4

For

1–4,

wri

te e

ach

frac

tio

n as

a

de

cim

al.

1.

1 __

2

2.

90

____

100

3.

7

____

100

4.

65

____

100

For

9–13

, cho

ose

5, 1

0, o

r 10

0 as

the

mo

st r

eas

ona

ble

inte

rval

to

sho

w e

ach

set

of

dat

a o

n a

bar

gra

ph.

9.

256,

387

, 491

, 502

, 630

10.

10, 2

9, 8

0, 9

9, 1

00

11.

10, 1

29, 1

80, 1

99, 3

10

12.

1, 4

, 7, 9

, 10,

12

13.

8, 1

6, 1

9, 3

1, 4

4

For

14–1

5, c

lass

ify e

ach

ang

le.

Wri

te a

cute

, rig

ht, o

r o

btus

e.

14.

15.

For

5–8,

co

mp

lete

. Te

ll w

heth

er

you

mul

tiply

or

divi

de.

Un

its

of

Mass

1 ki

logr

am (k

g) �

1,0

00 g

ram

(g)

5.

9 kg

�

g

6.

11,0

00 g

�

kg

7.

13 k

g �

g

8.

kg

� 2

,000

g0.5

0.90

or

0.9

0.07

0.65

9,00

0;

mu

ltip

ly

100

10 100 5 10

acu

te

ob

tuse

11;

div

ide

13,0

00;

mu

ltip

ly

2;

div

ide

MX

EN

L09A

WK

4X_S

R_W

K31

.indd

S

R31

8/8/

07

8:48

:02

AM

Spira

l Rev

iew

Nam

eW

eek

32

Spir

al R

evie

wS

R32

© H

arco

urt •

Gra

de 4

For

1–4,

wri

te e

ach

frac

tio

n as

a d

eci

mal

.

1.

79

__

__

100

2.

45

__

__

100

3.

3 __

_ 10

4.

49

__

__

100

For

9–11

, use

the

bar

gra

ph

be

low

. Turr

i Fa

mil

y B

ud

get

For

July

Utili

ties

FoodCa

r

Hous

e $0$1

00$2

00$3

00$7

00$5

00$6

00$4

00Ex

pens

e

Item

9.

H

ow m

uch

did

the

Turr

i fam

ily s

pend

on

food

in J

uly?

10.

On

wha

t di

d th

e Tu

rri f

amily

spe

nd

the

mos

t m

oney

?

11.

Estim

ate

the

Turr

i’s tot

al e

xpen

ses

for

the

mon

th.

For

12–1

5, u

se t

he p

ictu

re

be

low

.

12.

Iden

tify

ZX

13.

Iden

tify

Y

14.

Iden

tify

YW

15.

Iden

tify

UV

For

5–8,

co

mp

lete

. Te

ll w

heth

er

you

mul

tiply

or

divi

de.

Un

its

of

Cap

aci

ty1

liter

(L) �

1,0

00 m

illili

ters

(mL)

5.

16

L �

m

L

6.

m

L �

9 L

7.

20

L �

m

L

8.

L

� 19

,000

mL

0.79

0.45

0.3

0.49

dia

met

er

cen

ter

rad

ius

cho

rd

$40

0

16,0

00;

mu

ltip

ly

ho

use

[est

imat

es w

ill v

ary]

ab

ou

t $1

,600

9,00

0;

mu

ltip

ly

20,0

00;

mu

ltip

ly

19;

div

ide


MXENL08AWK4XSR_PHTE_2UP.indd SR31-SR32MXENL08AWK4XSR_PHTE_2UP.indd SR31-SR32 8/8/07 8:56:37 AM8/8/07 8:56:37 AM

Spira

l Rev

iew

Nam

eW

eek

33

Spir

al R

evie

wS

R33

© H

arco

urt •

Gra

de 4

For

1–4,

ord

er

the

de

cim

als

fro

m

grea

test

to

leas

t.

1.

0.7,

1.7

1, 0

.07

2.

0.05

, 5, 0

.5

3.

0.02

, 0.0

4, 0

.6

4.

5.01

, 6.9

9, 6

.8

For

7–8,

use

the

do

uble

-bar

g

rap

h b

elo

w.

Cam

ps3r

d Gr

ade

4th

Grad

e

35 30 25 20 15 10 5 0

Number of Votes

Spor

ts Ca

mp

Dram

a Cam

pSp

ace C

amp

7.

Whi

ch c

amp

was

leas

t po

pula

r w

ith

the

3rd

grad

ers?

8.

How

man

y m

ore

3rd

grad

ers

than

4th

grad

ers

vote

d fo

r sp

ace

cam

p?

For

9–11

, fin

d t

he a

rea

usin

g

the

fo

rmul

a A

� l

� w

.

9.

10.

11.

For

5–6,

fin

d t

he p

eri

me

ter

of

eac

h fig

ure

.

5.

6.

1.71

, 0.7

, 0.0

7

5, 0

.5, 0

.05

0.6,

0.0

4, 0

.02

6.99

, 6.8

, 5.0

1

14 u

nit

s

16 u

nit

s

dra

ma

cam

p

7 m

ore

th

ird

gra

der

s

50 s

q f

t

25 s

q in

.

9 sq

cm

MX

EN

L09A

WK

4X_S

R_W

K33

.indd

S

R33

7/2/

07

10:4

6:40

AM

Spira

l Rev

iew

Nam

eW

eek

34

Spir

al R

evie

wS

R3

4©

Har

cour

t • G

rade

4

For

1–2,

dra

w c

onc

lusi

ons

to

solv

e t

he p

rob

lem

.

1.

Jill

lives

3.6

mile

s fr

om s

choo

l. G

retc

hen

lives

3.1

mile

s fr

om s

choo

l. H

enry

live

s 3.

7 m

iles

from

sch

ool.

Who

live

s cl

oses

t to

sch

ool?

2.

Penc

ils E

tc. s

ells

bac

kpac

ks a

t 2

for

$ 24.

00. O

ffice

Box

sel

ls the

sam

e ba

ckpa

cks

for

$ 14.

00 e

ach

. Whi

ch

stor

e of

fers

the

bet

ter

pric

e?

For

6–7,

use

the

box

of

lett

ers

. Te

ll w

heth

er

eac

h e

vent

is c

erta

in, i

mpo

ssib

le,

likel

y o

r un

likel

y. T

hen,

fin

d t

he

pro

bab

ility

of

the

eve

nt.

6.

pulli

ng a

B, A

, or

L in

one

pul

l

7.

pulli

ng a

n E

in o

ne p

ull

For

8–11

, nam

e t

he p

oly

go

n.

Tell

whe

the

r it

ap

pe

ars

regu

lar

or

not r

egul

ar.

8.

9.

10.

11.

For

3–5,

fin

d t

he e

lap

sed

tim

e.

Each

clo

ck is

sho

win

g a

P.M

. tim

e.

3.

St

art

F

inis

h

891011

12

76

5432

1

891011

12

76

5432

1

4.

St

art

F

inis

h

891011

12

76

5432

1

891011

12

76

5432

1

5.

St

art

F

inis

h

891011

12

76

5432

1

891011

12

76

5432

1

BA

SE

BA

LL

Gre

tch

en

Pen

cils

Etc

.

1 h

ou

r an

d 1

5 m

inu

tes

1 h

ou

r

1 h

ou

r an

d 4

5 m

inu

tes

tria

ng

le;

reg

ula

r

oct

ago

n,

reg

ula

r

qu

adri

late

ral,

no

t re

gu

lar

squ

are

(or

rect

ang

le);

re

gu

lar

likel

y; 6 _ 8 , o

r 3 _ 4

un

likel

y; 1 _ 8



Wee

k 35

Spira

l Rev

iew

Nam

e

SR

35Sp

iral

Rev

iew

© H

arco

urt •

Gra

de 4

For

1–5,

est

imat

e t

he p

rod

uct.

C

hoo

se t

he m

eth

od

.

1.

45

� 2

1 �

2.

23

� 1

1 �

3.

30

� 2

9 �

4.

91

� 1

9 �

5.

13

� 1

3 �

For

10–1

1, u

se t

he s

pin

ner

and

the

tab

le. Jo

hn

’s R

esu

lts

Outc

omes

AB

C

Tally

IIII I

IIIII

I IIII

I IIII

I

10.

How

man

y tim

es d

id J

ohn

spin

the

po

inte

r?

11.

Wha

t is

the

exp

erim

enta

l pro

babi

lity

of s

pinn

ing

C?

For

12–1

6, u

se m

ent

al m

ath

and

pat

tern

s to

fin

d t

he

pro

duc

t.

12.

9 �

40

�

13.

4 �

400

�

14.

7 �

3,0

00 �

15.

5 �

6,0

00 �

16.

10 �

100

�

For

6–9,

use

the

the

rmo

me

ter

to f

ind

the

te

mp

era

ture

in �

F.

6.

10 10

0

°F

7.

10

0

80

90

°F

8.

60 40

50

°F

9.

30 10

20

°F

AB

C

–5�

F90

�F

100

200

900

1,80

0

100

360

1,60

0

21,0

00

30,0

00

1,00

0

Pos

sibl

e es

timat

es a

re g

iven

. Met

hods

w

ill v

ary.

25

55�F

25�F

11

__

25

Spira

l Rev

iew

Nam

eW

eek

36

Spir

al R

evie

wS

R36

© H

arco

urt •

Gra

de 4

For

1–4,

est

imat

e. T

hen

find

the

pro

duc

t.

1.

31

� 3

�

2.

91

� 5

�

3.

59

� 2

�

4.

22

� 7

�

For

9–12

, cho

ose

5, 1

0, o

r 10

0 as

the

mo

st r

eas

ona

ble

in

terv

al t

o s

how

eac

h se

t o

f d

ata

on

a b

ar g

rap

h.

9.

41

, 73,

31,

88,

24

10.

70, 3

90, 7

20, 4

50, 1

00

11.

20, 3

5, 4

0, 1

0, 5

12.

250,

300

, 100

, 200

, 500

For

13–1

5, c

lass

ify e

ach

tria

ngle

. Wri

te is

osc

eles

, sc

alen

e, o

r eq

uila

tera

l. Th

en

wri

te r

ight

, acu

te, o

r o

btus

e.

13.

14.

15.

For

5–8,

fin

d t

he e

lap

sed

tim

e.

5.

st

art:

6:15

P.M

.en

d: 9:

00 P

.M.

6.

star

t: 4:

45 P

.M.

end:

5:

15 P

.M.

7.

st

art:

11:2

8 P.

M.

end:

2:

36 A

.M.

8.

star

t: 2:

00 A

.M.

end:

5:

59 P

.M.

90;

93

450

; 45

5

120

; 11

8

140

; 15

4

10 100 5 100

Est

imat

es m

ay v

ary.

equ

ilate

ral,

acu

te

scal

ene,

rig

ht

scal

ene,

ob

tuse

2 h

r 45

min

30 m

in

3 h

r 8

min

15 h

r 59

min



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