Mathematics - Walton's Wizardswaltonswizards.weebly.com/uploads/1/2/0/2/12024199/grade... · 2020. 1. 31. · Metric and customary rulers can be found on the tear-out Mathematics

GRADE

TX00022123

A Student and Family GuideMathematics

Revised Based on TEKS Refinements

Revised 2008

Grade 5

Mathematics

A Student and Family Guide

Copyright © 2008, Texas Education Agency. All rights reserved. Reproduction of all or portions of this work is prohibited without express written permission from the Texas Education Agency.

Texas Assessment STUDY GUIDE

Texas Assessment of Knowledge and Skills

Cover photo credits: Top left © Gabe Palmer/CORBIS; Top right © Jim Craigmyle/CORBIS; Bottom right © Royalty-Free/CORBIS; Bottom left © Jim Craigmyle/CORBIS.

3

A Letter from the Deputy Associate Commissioner for Student Assessment

Dear Student and Parent:

The Texas Assessment of Knowledge and Skills (TAKS) is a comprehensive testingprogram for public school students in grades 3–11. TAKS, including TAKS(Accommodated) and Linguistically Accommodated Testing (LAT), is designed tomeasure to what extent a student has learned, understood, and is able to apply theimportant concepts and skills expected at each tested grade level. In addition, the testcan provide valuable feedback to students, parents, and schools about studentprogress from grade to grade.

Students are tested in mathematics in grades 3–11; reading in grades 3–9; writing ingrades 4 and 7; English language arts in grades 10 and 11; science in grades 5, 8, 10,and 11; and social studies in grades 8, 10, and 11. Every TAKS test is directly linkedto the Texas Essential Knowledge and Skills (TEKS) curriculum. The TEKS is thestate-mandated curriculum for Texas public school students. Essential knowledge and skills taught at each grade build upon the material learned in previous grades. By developing the academic skills specified in the TEKS, students can build a strongfoundation for future success.

The Texas Education Agency has developed this study guide to help studentsstrengthen the TEKS-based skills that are taught in class and tested on TAKS. Theguide is designed for students to use on their own or for students and families towork through together. Concepts are presented in a variety of ways that will helpstudents review the information and skills they need to be successful on TAKS. Everyguide includes explanations, practice questions, detailed answer keys, and studentactivities. At the end of this study guide is an evaluation form for you to complete andmail back when you have finished the guide. Your comments will help us improvefuture versions of this guide.

There are a number of resources available for students and families who would likemore information about the TAKS testing program. Information booklets are availablefor every TAKS subject and grade. Brochures are also available that explain the StudentSuccess Initiative promotion requirements and the graduation requirements for highschool students. To obtain copies of these resources or to learn more about the testingprogram, please contact your school or visit the Texas Education Agency website atwww.tea.state.tx.us/student.assessment.

Texas is proud of the progress our students have made as they strive to reach theiracademic goals. We hope the study guides will help foster student learning, growth,and success in all of the TAKS subject areas.

Sincerely,

Gloria ZyskowskiDeputy Associate Commissioner for Student AssessmentTexas Education Agency

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4

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Mathematics Chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Objective 1: Numbers, Operations, and

Quantitative Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Practice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Objective 2: Patterns, Relationships, and

Algebraic Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40


Objective 3: Geometry and Spatial Reasoning . . . . . . . . . . 53


Objective 4: Concepts and Uses of Measurement. . . . . . . . 70


Objective 5: Probability and Statistics . . . . . . . . . . . . . . . . 96

Practice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Objective 6: Mathematical Processes and Tools. . . . . . . . 120

Practice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

Mathematics Answer Key. . . . . . . . . . . . . . . . . . . . . . . . . . 139

Mathematics

Contents

MATHEMATICSMATHEMATICS

5

INTRODUCTION

What Is This Book?This is a study guide to help your childstrengthen the skills tested on the Grade 5 TexasAssessment of Knowledge and Skills (TAKS).TAKS is a state-developed test administered withno time limit. It is designed to provide anaccurate measure of learning in Texas schools.

By acquiring all the skills taught in fifth grade,your child will be better prepared to succeed onthe Grade 5 TAKS and during the next schoolyear.

What Are Objectives?Objectives are goals for the knowledge and skillsthat a student should achieve. The specific goalsfor instruction in Texas schools were providedby the Texas Essential Knowledge and Skills(TEKS). The objectives for TAKS were developedbased on the TEKS.

How Is This Book Organized?This study guide is divided into the sixobjectives tested on TAKS. A statement at thebeginning of each objective lists the mathematicsskills your child needs to acquire. The studyguide covers a large amount of material, whichyour child should not complete all at once. Itmay be best to help your child work throughone objective at a time.

Each objective is organized into review sectionsand a practice section. The review sectionspresent examples and explanations of themathematics skills for each objective. Thepractice sections feature mathematics problemsthat are similar to the ones used on the TAKStest.

How Can I Use This Book with My Child?First look at your child’s Confidential StudentReport. This is the report the school gave youthat shows your child’s TAKS scores. This reportwill tell you which TAKS subject-area test(s)your child passed and which one(s) he or shedid not pass. Use your child’s report todetermine which skills need improvement. Onceyou know which skills need to be improved, youcan guide your child through the instructionsand examples that support those skills. You mayalso choose to have your child work through allthe sections.

6

How Can I Help My Child Work on theStudy Guide?

● When possible, review each section of theguide before working with your child.This will give you a chance to plan howlong the study session should be.

● Sit with your child and work through thestudy guide with him or her.

● Pace your child through the questions inthe study guide. Work in short sessions. Ifyour child becomes frustrated, stop andstart again later.

● There are several words in this studyguide that are important for your child tounderstand. These words are boldfaced inthe text and are defined when they areintroduced. Help your child locate theboldfaced words and discuss thedefinitions.

What Are the Helpful Features of ThisStudy Guide?

● Examples are contained inside shadedboxes.

● Each objective has “Try It” problemsbased on the examples in the reviewsections.

● A Grade 5 Mathematics Chart is includedon pages 9–10 and also as a tear-out pagein the back of the book. This chartincludes useful mathematics information.The tear-out Mathematics Chart in theback of the book also provides both ametric and a customary ruler to helpsolve problems requiring measurement oflength.

● Look for the following features in themargin:

Ms. Mathematics provides importantinstructional information for a topic.

Detective Dataoffers a question thatwill help remind thestudent of theappropriate approachto a problem.

Do you see that . . .points to a significantsentence in theinstruction.

7

How Should the “Try It” Problems BeUsed? “Try It” problems are found throughout thereview sections of the mathematics study guide.These problems provide an opportunity for astudent to practice skills that have just beencovered in the instruction. Each “Try It”problem features lines for student responses.The answers to the “Try It” problems are foundimmediately following each problem.

While your child is completing a “Try It”problem, have him or her cover up the answerportion with a sheet of paper. Then have yourchild check the answer.

What Kinds of Practice Questions Are inthe Study Guide?The mathematics study guide contains questionssimilar to those found on the Grade 5 TAKS test.There are two types of questions in themathematics study guide.

● Multiple-Choice Questions: Most of thepractice questions are multiple choicewith four answer choices. These questionspresent a mathematics problem usingnumbers, symbols, words, a table, adiagram, or a combination of these. Readeach problem carefully. If there is a tableor diagram, study it. Your child shouldread each answer choice carefully beforechoosing the best answer.

● Griddable Questions: Some practicequestions use a four-column answer gridlike the one used on the Grade 5 TAKStest.

How Do You Use an Answer Grid?The answer grid contains four columns, the lastof which is a fixed decimal point. The answers toall the griddable questions will be wholenumbers.

Suppose the answer to a problem is 108. Firstwrite the number in the blank spaces. Be sure touse the correct place value. For example, 1 is inthe hundreds place, 0 is in the tens place, and 8is in the ones place.

Then fill in the correct bubble under each digit.Notice that if there is a zero in the answer, youneed to fill in the bubble for the zero. The gridbelow shows 108 correctly entered.

Where Can Correct Answers to thePractice Questions Be Found?The answers to the practice questions are in theanswer key at the back of the book (pages139–147). The answer key explains the correctanswer, and it also includes some explanationsfor incorrect answers. After your child answersthe practice questions, check the answers. Eachquestion includes a reference to the pagenumber in the answer key.

Even if your child chose the correct answer, it isa good idea to read the answer explanationbecause it may help your child betterunderstand why the answer is correct.

0

1

2

3

4

5

6

7

8

9

0

1

2

3

4

5

6

7

8

9

0

1

2

3

4

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6

7

8

9

0 81

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Metric and customary rulers can be found on the tear-out Mathematics Chartin the back of this book.

Grade 5Mathematics Chart

LENGTH

Metric Customary

1 kilometer = 1000 meters 1 mile = 1760 yards

1 meter = 100 centimeters 1 mile = 5280 feet

1 centimeter = 10 millimeters 1 yard = 3 feet

1 foot = 12 inches

CAPACITY AND VOLUME

Metric Customary

1 liter = 1000 milliliters 1 gallon = 4 quarts

1 gallon = 128 fluid ounces

1 quart = 2 pints

1 pint = 2 cups

1 cup = 8 fluid ounces

MASS AND WEIGHT

Metric Customary

1 kilogram = 1000 grams 1 ton = 2000 pounds

1 gram = 1000 milligrams 1 pound = 16 ounces

TIME

1 year = 365 days

1 year = 12 months

1 year = 52 weeks

1 week = 7 days

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds


10

Grade 5 Mathematics Chart

Perimeter square P = 4 × s

rectangle P = (2 × l) + (2 × w)

Area square A = s × s

rectangle A = l × w

Volume cube V = s × s × s

rectangular prism V = l × w × h

The student will demonstrate an understanding of numbers, operations, andquantitative reasoning.

Objective 1

For this objective you should be able to

● use place value to read, write, compare, and order wholenumbers and decimals;

● use fractions in problem-solving situations;

● add, subtract, multiply, and divide to solve problems; and

● estimate to determine reasonable results.

How Do You Read Large Numbers?When you read a whole number, start with the digits on the left. Use the commas to help you read the number.

11

A comma is used toseparate each group ofthree digits. Look at thenumber below:

2,167,986,450

Read the number 965,702,318,406. Look at the number in a place-value chart.

● Read the three-digit number to the left of the first comma. Then say what they represent. nine hundred sixty-five billion

● Read the three-digit number to the left of the second comma. Then say what they represent.seven hundred two million

● Read the three-digit number to the left of the third comma. Then say what they represent.three hundred eighteen thousand

● Read the last three-digit number.four hundred six

Read the number 965,702,318,406 as nine hundred sixty-five billion,seven hundred two million, three hundred eighteen thousand, four hundredsix.

Hundred TenBillions

Hundred Ten Millions Hundred Ten Thousands Hundreds Tens OnesBillions Billions Millions Millions Thousands Thousands

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

Objective 1

12

How Do You Compare and Order Whole Numbers?Look at the place values of the digits to help you compare and orderwhole numbers.

Look at these two numbers.

4,362,124,631 4,397,125,729

To determine which number is greater, look at them in a place-valuechart. Then compare the digits in each place value.

● Look at the digits in the billions place first. Both numbers have the digit 4 in the billions place.

● Look at the digits in the hundred millions place next. Bothnumbers have the digit 3 in the hundred millions place.

● Look at the digits in the ten millions place next. Since 9 � 6, the number with the digit 9 in the ten millions place is greater.

4,397,125,729 � 4,362,124,631

Try ItRead the number 2,309,758,011.

Write the number in the place-value chart below.

To read this number, say

_____________ billion, _____________________________________________________________________ million,

_________________________________________________________ thousand, _____________________________ .

Read the number 2,309,758,011 as two billion, three hundred nine million, seven hundred fifty-eight thousand,eleven.

BillionsHundred Ten Millions Hundred Ten Thousands Hundreds Tens OnesMillions Millions Thousands Thousands

4 3 6 2 1 2 4 6 3 1

4 3 9 7 1 2 5 7 2 9

BillionsHundred Ten Millions Hundred Ten Thousands Hundreds Tens OnesMillions Millions Thousands Thousands

You can use thesesymbols when youcompare numbers.

Symbol Meaning� is equal to> is greater than< is less than

Objective 1

13

Try ItUse a place-value chart to order these numbers from greatest to least.

6,490,781,004 63,758,902,449 6,837,200,312 67,554,309,377

● Write the numbers in the place-value chart. The first one has been done for you.

● Look at the digits in the ten billions place.

The numbers ____________________________ and ____________________________

both have a _______ in the ten billions place. They are the two greatest numbers.

For these two numbers, compare the digits in the billions place.

Since _______ � _______ , the number ____________________________ � ____________________________ .

The greatest number is ____________________________ .

The next-greatest number is ____________________________ .

● Look at the remaining two numbers. They both have a _______ in the billions place. So

compare the digits in the hundred millions place.

Since _______ � _______ , the number ____________________________ � ____________________________ .

The least number is ____________________________ .

The numbers in order from greatest to least are

_______________________ _______________________ _______________________ _______________________

The numbers 63,758,902,449 and 67,554,309,377 both have a 6 in the ten billions place. Since 7 � 3, the number 67,554,309,377 � 63,758,902,449. The greatest number is 67,554,309,377. The next-greatestnumber is 63,758,902,449. They both have a 6 in the billions place. Since 8 � 4, the number 6,837,200,312 � 6,490,781,004. The least number is 6,490,781,004. The numbers in order from greatest to least are 67,554,309,377 63,758,902,449 6,837,200,312 6,490,781,004

Hundred Ten BillionsHundred Ten Millions Hundred Ten Thousands Hundreds Tens Ones

Billions Billions Millions Millions Thousands Thousands

6 4 9 0 7 8 1 0 0 4

When a number with adecimal is written inwords, the -ths endingtells you that thosedigits belong on theright side of thedecimal point.

Objective 1

14

What Are Decimals?Decimals are another way to write fractions with denominators such as 10, 100, and 1,000. Decimals and fractions both name part of awhole. A decimal names part of a whole that has been divided into 10, 100, 1,000, or more parts.

The fraction �130� is written as the decimal 0.3.

The fraction �1

700� is written as the decimal 0.07.

The fraction �1,0

900� is written as the decimal 0.009.

Look at the decimal below:

1.47

The decimal point separates the whole part of the number from thefractional part of the number. There is a 1 to the left of the decimalpoint, so there is one whole. There is a 47 to the right of the decimalpoint. This means 47 out of 100 parts. The decimal point means and.The number 1.47 is read: one and forty-seven hundredths.

Looking at decimals in a place-value chart can help you read andunderstand them.

Read the decimal 12.34 in the place-value chart.

● Read the number to the left of the decimal point, twelve.

● Say the word and to represent the decimal point.

● Read the number to the right of the decimal point, thirty-four.

● Then say the place-value name of the last digit on the right,hundredths.

Read the number 12.34 as twelve and thirty-four hundredths.

Tens Ones . Tenths Hundredths

1 2 . 3 4

Decimalpoint

Objective 1

15

Read the number 5.826 in the place-value chart.

● Read the number to the left of the decimal point, five.

● Say the word and to represent the decimal point.

● Read the number to the right of the decimal point, eight hundred twenty-six.

● Then say the place-value name of the last digit on the right,thousandths.

Read the number 5.826 asfive and eight hundred twenty-six thousandths.

Here are 10 blocks put together to model thousandths. Each block isdivided into 100 small squares. There are a total of 1,000 smallsquares. The number 1,000 is the denominator of the fraction. Thenumerator of the fraction is the number of small squares that areshaded. The model shows 64 small squares shaded.

The model represents the fraction . The fraction is read as

sixty-four thousandths. The equivalent decimal should be written to

the thousandths place.

� 0.064

The decimal 0.064 is read as sixty-four thousandths. The decimal

0.064 represents the fraction . 641,000

641,000

641,000

641,000

Ones . Tenths Hundredths Thousandths

5 . 8 2 6

Placing zeros at the end of a decimal numeral does not change its value.

5.3 � 5.30

12.84 � 12.840

576.03 � 576.030

Objective 1

16

How Do You Compare and Order Decimals?Look at the values of the digits to help you compare and order decimals.

Compare these decimals.

2.9 2.925

To determine which decimal is greater, look at the numbers in aplace-value chart. You can write zeros at the end of 2.9 until it has the same number of digits to the right of the decimal point as 2.925.The number 2.9 � 2.900.

● Look at the ones place. Both numbers have a 2 in the onesplace.

● Look at the tenths place. Both numbers have a 9 in the tenthsplace.

● Look at the hundredths place. Since 2 � 0, then 2.925 �2.900.

Should you placezeros at the end of any of thesenumbers?

Try ItUse the place-value chart to order these decimals from greatestto least.

1.19 3.417 3.6 1.1

Write the numbers in the place-value chart. First look at the digitsin the ones place.

The numbers __________ and __________ both have a 3 inthe ones place. They are the two greatest numbers.

For these two numbers, compare the digits in the tenths place.

Since ______ � ______ , the number __________ � __________ .

The greatest number is __________ ; it should be written first.

The next-greatest number is __________; it should be written next.


2 . 9 0 02 . 9 2 5


.

.

.

.

Objective 1

17

How Do You Add or Subtract Decimals?To add or subtract decimals, vertically line up the decimal points of the numbers. If necessary, put zeros after the last digits so that eachnumber has the same number of digits to the right of the decimalpoint. This will not change the value of the number. Then add orsubtract as usual. Remember to regroup when necessary. Be sure toinclude the decimal point in the answer.

Find the sum of 3.24, 6.7, and 0.29.

Write the numbers in a column. Line up the decimal points.

1 13.246.70

�0.2910.23

The sum is 10.23.

● Put a zero at the end of 6.7 so that ithas the same number of digits.

● Add the hundredths.● Add the tenths.● Add the ones.● Bring the decimal point straight down

in the answer.

Look at the remaining two numbers. Compare the digits. Both

numbers have a _______ in the ones place and the tenths place. Look at the hundredths place.

Since ______ � ______ , the number __________ � __________ .

The least number is ___________ ; it should be written last.

Now, list the numbers in order from greatest to least.

_______________ _______________ _______________ _______________

The numbers 3.417 and 3.600 both have a 3 in the ones place. Since 6 � 4,the number 3.600 � 3.417. The greatest number is 3.6. The next-greatestnumber is 3.417. Both numbers have a 1 in the ones place and the tenthsplace. Since 9 � 0, the number 1.190 � 1.100. The least number is 1.1; itshould be written last. Listed from greatest to least, the numbers are: 3.6 3.417 1.19 1.1.

Objective 1

18

Hannah buys a magazine for $2.85. If she pays for it with a five-dollar bill, how much change should she receive? Use subtraction to find how much change Hannah should receive.

Write the numbers in a column and line up their decimal points. A five-dollar bill can be written as $5.00.

94 10 10

$5.00�2.85$2.15

Hannah should receive $2.15 in change.

● Subtract the hundredths. You need to regroup, butthere are no tenths.

● Regroup 5 ones as 4 ones and 10 tenths.● Regroup 10 tenths as 9 tenths and 10 hundredths.● Now subtract the hundredths.● Subtract the tenths.● Subtract the ones.● Be sure to place the decimal point in the answer.

In subtraction problems,remember to check youranswer by adding. Forexample,

1 1

2.85+2.15

5.00

Try ItTravis ran 1.5 kilometers on Monday, 2.25 kilometers onWednesday, and 0.9 kilometer on Friday. How many kilometers didhe run in all?

Use the operation of _____________________ to solve this problem. Use the space below to find the answer.

_______ . _______ _______

_______ . _______ _______

� _______ . _______ _______

_______ . _______ _______

The sum of the numbers is ____________ .

Travis ran a total of __________ kilometers.

Use the operation of addition to solve this problem. 1.50 � 2.25 � 0.90 � 4.65. The sum of the numbers is 4.65. Travis ran atotal of 4.65 kilometers.

Do you need to placezeros at the end of thedecimal numbers? Willyou need to regroup?

Objective 1

19

When Do You Use Multiplication and Division to Solve Problems?Use multiplication to combine groups of equal size. Use division toseparate a whole into groups of equal size.

A baker uses 325 pounds of flour each week to make pies and cakes.How many pounds of flour does the baker use in 26 weeks?

Multiply to find the total number of pounds of flour.

325 � 26 � 8,450

The baker uses 8,450 pounds of flour.

● Multiply the ones.

● Multiply the tens.

● Finally, add the products.

1 3

325� 261950

1

325� 2619506500

325� 261950

�65008450

The zero is aplace holder.

The principal needs 200 tacos for lunch on field day. The tacos come12 in a package. What is the least number of packages of tacos theprincipal will need for the lunch? Divide to find how many packagesof tacos the principal will need.

112��20�0�

– 128

1612��20�0�

– 1280

– 728

200 � 12 � 16 R8

There is a remainder of 8. If the principal buys 16 packages of tacos,she will not have enough. She will need 8 more tacos to have 200.The principal will have to buy one more package to have enoughtacos. She will need to buy 17 packages.

● Divide: 20 � 12● Multiply: 1 � 12● Subtract: 20 � 12

● Bring down the zero● Divide: 80 � 12● Multiply: 6 � 12● Subtract: 80 � 72

Do you seethat . . .

Objective 1

20

What Are Factors?Numbers multiplied together are called factors. For example, 6 and 5are factors of 30 because 6 � 5 � 30. Some other factors and theirproducts are shown below.

Factor � Factor � Product

3 � 7 � 21

8 � 6 � 48

9 � 7 � 63

5 � 12 � 60

Try ItThere are 178 baseball players who want to play in the summerleague. There can be no more than 15 players on each team. Whatis the least number of teams that can be formed for the summerleague?

Use the operation of _____________________ to find the number ofteams that can be formed.

_______ ��1�7�8

178 � _______ = _______ with a remainder of _______. Since there

is a remainder of 13, _______ more team can be formed.

_______ � 1 = _______. The least number of teams that can be

formed for the summer league is _______.

Use the operation of division to find the number of teams that can beformed.

1115��1�7�8

– 1528

– 1513

178 ÷ 15 � 11 with a remainder of 13. Since there is a remainder of 13,1 more team can be formed. 11 � 1 � 12. The least number of teams thatcan be formed for the summer league is 12.

What does theremainder tell you to do?

Objective 1

Find all the common factors of 30, 45, and 50.

● List the factors of each number.

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Factors of 45: 1, 3, 5, 9, 15, 45

Factors of 50: 1, 2, 5, 10, 25, 50

● Circle the factors that the three numbers have in common.

The common factors of 30, 45, and 50 are 1 and 5.

21

What Are Common Factors?Factors shared by two or more numbers are called common factors ofthose numbers. For example, 5 is a common factor of 10 and 25 because 5 is a factor of 10 and also a factor of 25.

To find all the factors of a number, write down all the factor pairs forthat number. For example, the factor pairs for 15 are 1 � 15 and 3 � 5. So the factors, listed in order, are 1, 3, 5, and 15.

Try ItFind all the common factors of 27 and 36.

The factors of 27 are: _______ , _______ , _______ , and _______ .

The factors of 36 are: _______ , _______ , _______ , _______ , _______ ,

_______ , _______ , _______ , and _______ .

The common factors of 27 and 36 are: _______ , _______ , and

_______ .

The factors of 27 are: 1, 3, 9, and 27. The factors of 36 are: 1, 2, 3, 4, 6, 9,12, 18, and 36. The common factors of 27 and 36 are: 1, 3, and 9.

Objective 1

22

How Are Decimals Related to Fractions?Decimals and fractions both name part of a whole or part of a group.A decimal shows part of a whole that has been divided into 10, 100,1,000, or more parts. A fraction shows part of a whole that has beendivided into any number of parts.

Models can represent both fractions anddecimals. Look at this model. The model isdivided into 100 equal parts, and 39 of theparts are shaded. You can represent theshaded part of the model in two ways.

● As a fraction: Use 100 as thedenominator. Use 39 as the numerator.

The fraction is �13090

�.

● As a decimal: Write the decimal to the hundredths place. Use39 as the number of hundredths. The decimal is 0.39.

Both the fraction �13090

� and the decimal 0.39 are read as

thirty-nine hundredths.

The fraction �13090

� and the decimal 0.39 are equivalent.

The denominator tellsthe number of equalparts into which thewhole has been divided.The numerator tells howmany of the equal partshave been selected.

Objective 1

23

Try ItEach large square in this model represents 1 whole.

What fraction does the model represent? What decimal does themodel represent?

The model shows _______ large squares completely shaded. In the

third large square, _______ out of _______ equal parts are shaded.

Write the number as a fraction: _____________

as a decimal: _____________

In words, you read this number as ________________________________

__________________________________________________________________ .

The model shows two large squares completely shaded. In the third largesquare, 71 out of 100 equal parts are shaded. Written as a fraction, the

number is 2�17010

� , and as a decimal, it is 2.71. The number is read as

two and seventy-one hundredths.

How Do You Find Equivalent Fractions?Equivalent fractions are fractions that have the same value but arewritten differently. Equivalent fractions name the same part of a wholein different ways.

Look at the circles below:

The fractions �12

�, �24

�, and �48

� all name the same part of a whole.

To find an equivalent fraction, multiply or divide the numerator andthe denominator by the same number. This is the same as multiplyingor dividing by a fraction that is equal to 1.

To find an equivalent fraction with a larger denominator, multiply by a

fraction equal to 1. Here are some fractions that are equivalent to �46

�.

To find an equivalent fraction with a smaller denominator, divide by afraction equal to 1. Look at these examples.

12

24

48

Any fraction with the same number in both its numerator and its denominator is equal to 1.

�33

� � 1

�22

� � 1

Original Fraction EquivalentFraction Equal to 1 Divide Fraction

Objective 1

24

37

37

��

12 � 428 � 4

44

1228

35

35

��

9 � 315 � 3

33

915

23

23

��

4 � 26 � 2

22

46

Original Fraction EquivalentFraction Equal to 1 Multiply Fraction

4060

4060

��

4 � 106 � 10

1010

46

1218

1218

��

4 � 36 � 3

33

46

812

812

��

4 � 26 � 2

22

46

Objective 1

25

Try It

Find two equivalent fractions for , one with a larger denominator

and one with a smaller denominator.

To find an equivalent fraction with a larger denominator,

____________ by a fraction equal to _______ . For example, use .

��

is a fraction equivalent to .

To find an equivalent fraction with a smaller denominator,

____________ by a fraction equal to _______ . For example, use

because 5 is a factor of both 5 and 15.

��

5 � 515 � 5

55

515

5 � 415 � 4

44

515

What are two equivalent fractions for ?

● To find an equivalent fraction with a denominator larger than

12, multiply by a fraction equal to 1. You could use , , , or

any other fraction equal to 1.

��

is a fraction equivalent to �162�.

● To find an equivalent fraction with a denominator smaller than

12, divide by a fraction equal to 1. You could use because 3

is a factor of both 6 and 12.


The fractions , , and are equivalent fractions. 24

1224

612

612

24

24

��

6 � 312 � 3

33

1224

1224

6 � 212 � 2

44

33

22

612

Compare the fractions �36

� and �56

�.

● Both fractions have the denominator 6.

● Compare the numerators to find how many parts are in eachfraction.

Since 3 5, then �36

� �56

� .

It is also true that 5 � 3. So you can also say that �56

� � �36

�.

Objective 1

26

How Do You Compare Fractions?To compare fractions that have the same denominator, compare theirnumerators.


The fractions , , and are _________________ fractions.

To find an equivalent fraction with a larger denominator, multiply by a fractionequal to 1.


To find an equivalent fraction with a smaller denominator, divide by a fractionequal to 1.


The fractions , , and are equivalent fractions.13

2060

515

515

13

13

��

5 � 515 � 5

515

2060

2060

��

5 � 415 � 4

515

515


Objective 1

27

To compare fractions that have different denominators:

● First find a common denominator for the two fractions. Acommon denominator is one that is the same in two or morefractions. To find a common denominator for two fractions, listthe multiples of each denominator, then find one multiple that isin both lists.

● Rewrite each fraction as an equivalent fraction with the commondenominator.

● Compare the numerators of the two rewritten fractions.

Compare the fractions �34

� and �56

�. Which fraction is greater?

● The denominators 4 and 6 are different. Find a commondenominator by listing the multiples of 4 and 6. A numberfound in both lists of multiples is a common multiple. It is alsoa common denominator for the two fractions.

Multiples of 4: 4, 8, 12, 16, . . .

Multiples of 6: 6, 12, 18, 24, . . .

A common multiple of 4 and 6 is 12. A common denominatoris 12.

● Rewrite �34

� and �56

� to have 12 as their denominators.

�34

� � �1?2�

��

�34

��

33

� �192� �

34

� � �192�

�56

� � �1?2�

��

�56

��

22

� �11

02� �

56

� � �1102�

● Now both fractions have a denominator of 12. Compare the

numerators. Since 10 � 9, then � .

Since � and � , then � . The fraction is greater

than the fraction .34

56

34

56

34

912

56

1012

912

1012

��

?12

5 � 226 � 22

��

?12

3 � 224 � 22

A multiple of a numberis the product of thatnumber and any otherfactor.

Try ItBart and Pablo had small pizzas for lunch. Bart ate �

56

� of his pizza.

Pablo ate �78

� of his pizza. Who ate more of his pizza?

Find a common denominator for �56

� and �78

�.

List the first four multiples of the two denominators.

Multiples of 6: ________ , _______ , _______ , _______

Multiples of 8: ________ , _______ , _______ , _______

A common multiple of 6 and 8 is _______ .

A common denominator is _______ .

Find fractions equivalent to �56

� and �78

� with _______ as their common denominator.

5 � �

6 � � 24

7 � �

8 � � 24

Since _______ � _______ , the fraction ______________ is greater.(circle one)

______________ ate more of his pizza.

The first four multiples of 6 are: 6, 12 ,18, and 24. The first four multiples

of 8 are: 8, 16, 24, and 32. A common multiple of 6 and 8 is 24. A

common denominator is 24. Find fractions equivalent to �56

� and �78

� with

24 as their common denominator.

�56

��

44

��

�78

��

33

��

Since 21 � 20, the fraction �78

� is greater. Pablo ate more of his pizza.

2124

2024

Sometimes it is necessaryto list more than thefirst four multiples.

Objective 1

28

�

�?

2478

?24

56

78

56

Objective 1

29

What Are Mixed Numbers and Improper Fractions?

Mixed numbers and improper fractions are two ways to name fractions

greater than 1. A mixed number includes a whole number and a

fraction. For example, 4 is a mixed number. The whole number is 4,

and the fraction is .

4

An improper fraction has a numerator that is greater than or equal to

its denominator. The fraction is an improper fraction because the

numerator 9 is greater than the denominator 4.

A mixed number and an improper fraction can both name the sameamount.

2 =14

94

94

94

13

13

13

The mixed number 4 can be written as an improper fraction.

● Multiply the denominator 3 by the whole number 4.

3 � 4 � 12

● Add the numerator to this product.

12 � 1 � 13

● 13 becomes the numerator of the improper fraction. Keep theoriginal denominator of 3.

The mixed number 4 is equivalent to the improper fraction .133

13

133

13

Whole numberNumerator

Denominator

Numerator

Denominator


Objective 1

30

Try ItWrite the improper fraction as a mixed number.

______________ the numerator _______ by the denominator _______.

��1�6�6�

The quotient _______ is a whole number in the mixed number.

The remainder 4 becomes the _________________ of the fraction.

The _________________ is 5.

The improper fraction is equivalent to the mixed number _______.

Divide the numerator 14 by the denominator 5. The quotient 2 is the whole

number in the mixed number. The remainder 4 becomes the numerator of

the fraction. The denominator is 5. The improper fraction is equivalent to

the mixed number 2 .45

145

145

145

The improper fraction can be written as a mixed number.

● Divide the numerator 22 by the denominator 7.

3 R17��22��

– 211

22 � 7 � 3 with a remainder of 1

● The 3 in the quotient becomes the whole number in the mixed number.

● The remainder can be written in fraction form using theremainder as the numerator and keeping the originaldenominator.

3

The improper fraction is equivalent to the mixed number 3 .17

227

17

227

Objective 1

How Do You Add or Subtract Fractions with Common Denominators?To add fractions with common denominators, add the numerators.Then write the sum over the common denominator.

�16

� � �26

� � �1�

62

� � �36

�

To subtract fractions with common denominators, subtract thenumerators. Then write the difference over the common denominator.

�172� � �

142� � �

71�24

� � �132�

712

412

312

– =

16

26

36+ =

31

Rasheed bought �18

� pound of green onions and �58

� pound of carrots.

How many pounds of vegetables did Rasheed buy altogether?

Find the sum of the two fractions. Since the denominators are thesame, add the numerators.

� �

Rasheed bought pound of vegetables.68

68

58

18

18

lb58

lb

Objective 1

32

When Should You Estimate an Answer?When you do not need an exact answer to a problem, you can estimateto find an answer that is close to the exact answer. For example, someproblems ask about how many or approximately how much. Useestimation when solving such problems.

One way to estimate is to round numbers in a problem before workingit out. You can round decimals in the same way you round wholenumbers. A number line or a set of rounding rules can help you. Forexample, to round a decimal to the nearest tenth, look at the digit inthe hundredths place.

● If the digit in the hundredths place is 0, 1, 2, 3, or 4, leave thedigit in the tenths place the same.

● If the digit in the hundredths place is 5, 6, 7, 8, or 9, round thedigit in the tenths place to the next-higher value.

Try ItA cook measures lemon juice and orange juice in two measuringcups. How much more lemon juice than orange juice does she have?

The drawing shows cup of lemon juice.

The drawing shows cup of orange juice.

The number sentence � � shows how much

more lemon juice than orange juice the cook has.

The drawing shows �34

� cup of lemon juice and �14

� cup of orange juice. The

number sentence �34

� � �14

� � �24

� shows how much more lemon juice than orange

juice the cook has.

Orange juice

14 cup

12 cup

34 cup

1 cup

14 cup

12 cup

34 cup

1 cup

Lemon juice

Objective 1

33

Jill and Simon are walking along a trail that is shaped like a triangle.The first side of the trail is 2.76 kilometers long. The second side of the trail is 2.39 kilometers long. The third side of the trail is 0.63 kilometer long. About how long is this trail?

Jill and Simon use different methods to round the numbers.

Jill’s method:

● Jill rounds the length of each side of the trail to the nearesttenth of a kilometer.

2.76 rounded to the nearest tenth is 2.8.2.39 rounded to the nearest tenth is 2.4.0.63 rounded to the nearest tenth is 0.6.

● Jill adds the rounded numbers to find the approximate lengthof the trail.

2.82.4

� 0.6 5.8

● Jill says the trail is about 5.8 kilometers long.

Simon’s method:

● Simon rounds the length of each side of the trail to the nearestkilometer. This is the same as rounding to the nearest wholenumber or ones place.

2.76 rounded to the nearest whole number is 3.2.39 rounded to the nearest whole number is 2.0.63 rounded to the nearest whole number is 1.

● Simon adds the rounded numbers to find the approximatelength of the trail.

3 � 2 � 1 � 6

● Simon says the trail is about 6 kilometers long.

Both methods show correct rounding. Even though Jill and Simonrounded the numbers to different places, both estimates arereasonable.


Objective 1

34

Another way to estimate is by using compatible numbers. Compatiblenumbers are numbers that are easy to add, subtract, multiply, or divide.Using compatible numbers makes the computation easier.

Walter is estimating the total number of marbles that he and five ofhis friends have. The number of marbles each person has is asfollows:

125 73 145 90 120 50

To estimate the sum, you can use compatible numbers. For thisexample, group together numbers that equal about 200.

● 125 � 73 is close to 200.

● 50 � 145 is close to 200.

● 90 � 120 is close to 200.

● 200 � 200 � 200 � 600.

Walter estimates that he and his friends have about 600 marblesaltogether.

When using compatible numbers to estimate a product or quotient,change the numbers to other numbers that form a basic fact. This canhelp you solve the problem in your head.

In the fall, 86 students played soccer. If there were 9 teams, abouthow many players were on each team?

To find about how many, estimate the answer. Use compatiblenumbers, or numbers that are easy to divide, to make the problemeasier. Use basic facts to help you.

● Find a number close to 86 that you can divide by 9 in yourhead.

86 is close to 90, and 90 divides easily by 9

● Divide to find about how many players were on each team.

90 ÷ 9 = 10

There were about 10 players on each team.

Objective 1

35

Now practice what you’ve learned.

Try ItSuzanne borrowed $358 from her mother to buy a computer. Inorder to pay back the entire $358, Suzanne gave her mother thesame amount of money each month for 1 year. About how muchmoney did Suzanne give her mother each month?

Use ____________ to find about how much money Suzanne will giveher mother each month.

There are ______ months in a year.

Find a number close to 358 that divides easily by 12. Use the basicfact 36 ÷ 12 = 3 to help.

$358 is close to __________.

360 � 12 � ______

Suzanne gave her mother about ________ each month.

Use division to find about how much money Suzanne will give her mothereach month. There are 12 months in a year. $358 is close to $360.360 � 12 � 30. Suzanne gave her mother about $30 each month.

Objective 1

36

Question 1Which numeral has the digit 8 in the millions place?

A 1,807,629

B 82,531,044

C 28,162,751

D 8,629,794,312

Question 2How is the number three hundred billion, seven hundred eighty thousand, four hundredthirty-nine written as a numeral?

A 3,780,000,439

B 300,000,780,439

C 3,780,439

D 300,780,439

Question 3Dylan wants to put the numbers below in order from greatest to least.

231,392,159 5,301,229,038 204,515,724 3,033,431,602

Which list shows the numbers in order from greatest to least?

A 204,515,724 231,392,159 3,033,431,602 5,301,229,038

B 5,301,229,038 231,392,159 204,515,724 3,033,431,602

C 5,301,229,038 3,033,431,602 231,392,159 204,515,724

D 3,033,431,602 231,392,159 5,301,229,038 204,515,724

Answer Key: page 139 Answer Key: page 139

Answer Key: page 139

Objective 1

37



Question 4Which list shows the numbers in order fromleast to greatest?

A 0.11 0.16 0.33 0.9

B 0.9 0.33 0.16 0.11

C 0.9 0.16 0.11 0.33

D 0.11 0.33 0.16 0.9

Question 5Which number is less than 7.424?

A 7.52

B 7.43

C 7.425

D 7.42

Question 6How is the numeral 1.035 written in words?

A One thousand thirty-five

B One and thirty-five hundredths

C One and thirty-five thousandths

D One thousand thirty-five hundredths

Question 7

Jackie is trying to write the improper fraction

in different ways. Which of the following is

equivalent to ?

A 1

B 2

C 3

D 1

Question 8Which fraction is NOT equivalent to ?

A

B

C

D

Question 9

Betty is ordering a cake for a party. She can cut

it into eighths or twelfths. Which of the following

correctly compares and ?

A �

B

C �

D Not here

112

18

112

18

112

18

112

18

512

618

1545

13

39

34

12

13

46

73

73





Objective 1

38

Question 10The model below shows shaded.

Which decimal represents the shaded part of this model?

A 0.50

B 0.050

C 0.015

D 0.150

1501,000

Question 11Bob bought a CD for $11.95. He gave the cashier$20.00. How much change did Bob receive?

A $7.95

B $8.05

C $8.15

D $8.25

Question 12Karen ordered 15 cases of cookies to sell for hersoccer team. Each case had 288 cookies in it.How many cookies did she order in all?

A 1,728

B 4,320

C 4,280

D Not here




Objective 1

39

Question 13A group of 12 friends spent a total of $156 at thecarnival. If each friend spent the same amountof money, how much did each friend spend?

Record your answer and fill in the bubbles. Be sure to use the correct place value.

Question 14Mr. Cohen is buying notepads for a school trip.There are 54 students going on the trip. Eachstudent needs 1 notepad. Notepads are sold inpackages of 5. How many packages of notepadsdoes Mr. Cohen need to buy?

A 10

B 7

C 11

D 9

Question 15Which list shows all the common factors of 12, 24, and 36?

A 1, 2, 3, 4, 6, 12

B 2, 6, 12

C 1, 2, 3

D 1, 3, 4, 6, 8

Question 16

Tristan has 4 yards of rope. He cuts off a piece

of rope 2 yards long. Which number sentence

can be used to find the length of rope, in yards,

Tristan will have left after he cuts off a piece

2 yards long?

A 4 � 2 �

B 4 � 2 � 2 �

C 4 � 2 �

D 4 � 2 � 2 �

Question 17Monica’s family went on a trip. The distancesthey drove each day are shown below.

59.6 miles, 79.5 miles, 89.8 miles, 70.3 miles

About how far did Monica’s family drivealtogether on their trip?

A 400 miles

B 280 miles

C 320 miles

D 300 miles

Question 18Tickets for a play cost $3.25 each. If 417 peoplebought tickets for the play, which is closest tothe total amount of money made in ticket sales?

A $1,200

B $1,000

C $800

D $400

14

14

34

14

34

14

14

34

14

34

14

14

34

0

1

2

3

4

5

6

7

8

9

0

1

2

3

4

5

6

7

8

9

0

1

2

3

4

5

6

7

8

9







40

The school library received boxes of new books. The table belowshows the number of books in each box.

New Books

Look at the relationship between the numbers.

There are 36 books in 2 boxes. 2 � � 36




The relationship shown in the table is:

The number of boxes times 18 equals the number of books.

The student will demonstrate an understanding of patterns, relationships, andalgebraic reasoning.

Objective 2


● make generalizations based on observed patterns andrelationships; and

● describe relationships mathematically.

How Can You Describe the Relationship Between Sets of Data?Sometimes you might need to know how sets of numbers are related.Looking at the data in a list, table, or chart can help you see arelationship.

Number of Number of Boxes Books

2 36 3 54 4 72 5 90

Objective 2

41

Rowan is saving money each week. The table below shows theamount of money he had saved after different numbers of weeks.

Rowan’s Savings

What is the relationship between the amount of money Rowan savedand the number of weeks he saved?

Look at the pairs of numbers in the table: 4 and $1005 and $1256 and $1507 and $175

How is the number of weeks related to the amount of money saved?

4 � � 100 4 � 25 = 100

5 � � 125 5 � 25 = 125

6 � � 150 6 � 25 = 150

7 � � 175 7 � 25 = 175

The amount of money saved is 25 times the number of weeks.

Week Amount of Money

4 $1005 $1256 $1507 $175

Objective 2

42

Try It The table below shows the total number of sheets of paper indifferent numbers of notebooks.

Paper in Notebooks

Describe the relationship between the number of notebooks and thenumber of sheets of paper in the notebooks.

Look at the pairs of numbers: 2 and 150

3 and 225

4 and 300

5 and 375

How is the number of sheets of paper related to the number ofnotebooks?

2 � _______ � 1503 � _______ � 2254 � _______ � 3005 � _______ � 375

The number of sheets of paper is _______ times the number ofnotebooks.

2 � 75 � 150

3 � 75 � 225

4 � 75 � 300

5 � 75 � 375

The number of sheets of paper is 75 times the number of notebooks.

Number of Number of Notebooks Sheets of Paper

2 1503 2254 3005 375

Objective 2

What Are Prime Numbers and Composite Numbers?A prime number is a number that has only 1 and itself as factors. For example, 17 is a prime number. The only factors of 17 are 1 and 17.

A composite number has 1, itself, and at least one other number as itsfactors. For example, 21 is a composite number. In addition to 1 and21, 21 also has 3 and 7 as factors. The factors of 21 are 1, 3, 7, and 21.

You do not need to know all the factors of a number to decide whetherit is a composite number. You need to know only that it has at least onefactor in addition to 1 and itself.

The number 1 is neitherprime nor composite.

43

Determine whether each number below is prime or composite.

List the factors of each number. If the only factors of a number are 1and itself, it is a prime number. If the number has other factors, it isa composite number.

The prime numbers from this list are 2, 3, 5, 7, 11, and 13.

The composite numbers from this list are 4, 6, 8, 9, 10, 12, 14, and15.

Number Factors Prime or Composite?2 1, 2 Prime (The only factors are 1 and 2.) 3 1, 3 Prime (The only factors are 1 and 3.)4 1, 2, 4 Composite5 1, 5 Prime (The only factors are 1 and 5.)6 1, 2, 3, 6 Composite7 1, 7 Prime (The only factors are 1 and 7.)8 1, 2, 4, 8 Composite9 1, 3, 9 Composite

10 1, 2, 5, 10 Composite11 1, 11 Prime (The only factors are 1 and 11.)12 1, 2, 3, 4, 6, 12 Composite13 1, 13 Prime (The only factors are 1 and 13.)14 1, 2, 7, 14 Composite15 1, 3, 5, 15 Composite


Objective 2

44

Try ItIs the number 28 a prime number or a composite number?

Think about all the factors of 28.

● 28 has 1 and itself as factors because 1 � ______ � ______.

● 28 is an even number, so another factor is ______.

2 � ______ � 28.

● Another factor pair of 28 is ______ and 7. _____ � 7 � 28.

Since the number 28 has factors besides 1 and 28, it is a

__________________ number.

28 has 1 and itself as factors because 1 � 28 � 28.

28 is an even number, so another factor is 2. 2 � 14 � 28.

Another factor pair of 28 is 4 and 7. 4 � 7 � 28.

Since the number 28 has factors besides 1 and 28, it is a compositenumber.

Objective 2

45

Arrays and area models can show prime numbers and compositenumbers.

2

2 � 1

1 � 2

7

7 � 1

1 � 7

8

8 � 1

1 � 8

4 � 2

2 � 4

This model shows 2 � 1 and1 � 2. The only factors of 2are 1 and 2. Therefore, 2 is aprime number.

This model shows 7 � 1 and1 � 7. The only factors of 7are 1 and 7. Therefore, 7 is aprime number.

This model shows 8 � 1, 1 � 8, 4 � 2, and 2 � 4. Thefactors of 8 are 1, 2, 4, and 8.Therefore, 8 is a compositenumber.

A factor pair shows 2 factors of a givenproduct. One factor pairof 18 is 3 and 6.

Factor trees can show whether a number is prime or composite.

Look at the factor trees for the numbers 16 and 17 below.

The number 16 has other factors besides 1 and itself. So it is not aprime number. It is a composite number.

The number 17 has no other factors besides 1 and itself. So it is aprime number.

x

x

16

2

8

4

2 x

17

171

2x2

Objective 2

46

How Can You Describe Relationships Mathematically?You can describe relationships mathematically by replacing words andsentences with numbers, symbols, and variables. Describing relationshipswith numbers, symbols, and variables can help you solve problems.

Follow these steps to help create number sentences or equations todescribe and solve problems.

● Read the whole problem carefully.

● Determine which numbers you know and which ones you needto find.

● Look for the relationship between these numbers.

● Write a number sentence or equation that represents therelationship.

An equation can consist of numbers,mathematical symbols,and variables.

Variables are letters suchas x or y that represent anumber.

For example, 4 � x � 7is an equation where x isthe variable.

Try ItUse factor pairs, arrays, or factor trees to determine whether thesenumbers are prime or composite.

18 23 31 27

The prime numbers are _______ and _______ .

The composite numbers are _______ and _______ .

The number 18 is a composite number. Its factors are 1, 2, 3, 6, 9, and 18.

The number 23 is a prime number; it has no other factors besides 1 and 23.

The number 31 is also prime; it has no other factors besides 1 and 31.

The number 27 is a composite number. Its factors are 1, 3, 9, and 27.

The prime numbers are 23 and 31. The composite numbers are 18 and 27.

Objective 2

In one middle school 250 students play school sports. Each studentplays only one sport. The graph shows the number of students whoparticipate in tennis, volleyball, or soccer. The remaining studentsplay basketball.

Read the whole problem. Look for what you know and what youneed to find.

● There are 250 students in all who play sports.

● The bar graph shows that 40 students play tennis,80 students play volleyball, and 100 students play soccer.

● Subtract these numbers from 250 to find the number ofstudents who play basketball.

Write an equation that can be used to represent b, the number ofstudents who play basketball.

The equation 250 � 40 � 80 � 100 � b represents the number ofstudents who play basketball.

Sports Participation

Numberof

Students

SportTennis Volleyball Soccer Basketball

120

100

80

60

40

20

0

47

Objective 2

48

Patrick bought 2 hats for $4 each and a video game for $45. Writean equation that represents the amount Patrick spent.

Read the whole problem. Look at what you know and what youneed to find.

● Patrick bought 2 hats for $4 each. The expression 4 � 4represents the total amount spent on hats.

● He spent $45 on a video game.

● Use addition to represent the amount he spent in all.

The equation 4 � 4 � 45 � represents the total amount of money Patrick spent.

Try ItGeorgia had a collection of 503 stickers. She bought 50 newstickers, and then her sister gave her 35 more stickers.

Write a number sentence that can be used to represent s, the totalnumber of stickers Georgia now has in her collection.

Georgia had a total of _________________ stickers in her collection.

She bought _______ new stickers.

Her sister gave her _______ more stickers.

The number sentence

s � _______ � _______ � _______

can be used to represent the total number of stickers Georgia now has.

Georgia had a total of 503 stickers. She bought 50 new stickers. Her sistergave her 35 more stickers. The number sentence s � 503 � 50 � 35 can beused to represent the total number of stickers Georgia now has.


Objective 2

49

Question 19The table below shows the ages of Jeannette and her brother Mark at different times.

Which statement is true about the relationship between Jeannette’s and Mark’s ages?

A Mark is 4 years older than Jeannette.

B Jeannette is 11 years younger than Mark.

C When Jeannette is 16 years old, Mark will be 24 years old.

D When Mark is 16 years old, Jeannette will be 6 years old.

Question 20Look at the pattern of numbers below.

1, 7, 8, 15, 23, 38, 61, 99

Which statement best describes the rule for determining the last 6 numbers shown in this pattern?

A Each number is 6 more than the number before it.

B Each number is the sum of the 2 numbers before it.

C Each number is 7 more than the number before it.

D Each number is the product of the 2 numbers before it.



Jeannette Mark 4 158 19

12 23

Age in Years

Objective 2

5050

Question 21The table shows the cost of different numbers ofzoo tickets.

Which equation can be used to find t, the cost of 8 tickets?

A t � 2 � 8

B t � 4 � 8

C t � 1 � 8

D t � 2 � 8

Question 22Some factor pairs for the composite number 24are shown below.

1 � 24

2 � 12

3 � 8

What factor pair is missing from this list?

A 4 � 5

B 4 � 6

C 4 � 7

D 4 � 9

Question 23Which of these is a prime number?

A 27

B 39

C 33

D 29




Number of Cost ofTickets Tickets

2 $44 $86 $12

10 $20

Zoo Tickets

51

Objective 2

51

Question 24Leah used tiles to show all the arrays for the numbers 3, 4, 5, and 6.

Which of these numbers are prime?

A 3 and 5

B 3 and 6

C 4 and 6

D 4 and 5


5

5 � 1

1 � 5

3

3 � 1

1 � 3

4

4 � 1 2 � 2

1 � 4

6

6 � 1

1 � 6

2 � 3

3 � 2

52

Objective 2

Question 25The table below shows the weight, in ounces, of different numbers of peanuts.

What is the relationship between the total number of peanuts and the weight of the peanuts inounces?

A The number of ounces is 117 less than the total number of peanuts.

B The total number of peanuts is 400 times the number of ounces.

C The total number of peanuts is 40 times the number of ounces.

D The number of ounces is 780 less than the total number of peanuts.

Question 26Last night Gianna did her homework. She spent 20 minutes on math, 15 minutes on reading, and 30 minutes on science. Which equation can be used to find m, the total number of minutes Giannaspent on her homework last night?

A 20 � 15 � 30 � m

B 20 � 15 � 30 � m

C 20 � 15 � 30 � m

D 20 � 15 � 30 � m



Peanuts

Weight (ounces)

Total Numberof Peanuts

3 5 10 20

120 200 400 800

53

Which two line segments in the figure below appear to be parallel?

Line segment WX and line segment ZY appear to be the samedistance apart at all points. Line segments WX and ZY appear to beparallel.

W X

Z Y

The student will demonstrate an understanding of geometry and spatial reasoning.

Objective 3


● identify essential attributes of two-dimensional and three-dimensional geometric figures;

● describe the results of transformations; and

● locate and name points on a coordinate grid.

What Are Parallel Lines?Parallel lines are lines that are the same distance apart at all points.Parallel lines never intersect. Several examples of parallel lines areshown below.

You can also look at a figure and identify line segments that areparallel. Line segments in figures are parallel if they are the samedistance apart at all points.

A

B

C

DR S

T V

J L

K M

Line AB can also benamed line BA.

Objective 3

54

A small is placed atthe vertex of an angle toshow that it is a rightangle.

What Are Perpendicular Lines?Perpendicular lines are lines that intersect to form right angles. Angle GXF is a right angle. Line EF is perpendicular to line GH.

You can also look at a figure and identify line segments that areperpendicular.

E F

G

H

X

A B

C

XT

S

X

Which line segments in the rectangle below are perpendicular?

The rectangle shows a right angle at each of the vertices: A, B, C, andD. The two line segments that meet at each vertex form a right angleand are perpendicular to each other.

● Line segments AB and BC are perpendicular.

● Line segments BC and CD are perpendicular.

● Line segments CD and AD are perpendicular.

● Line segments AD and AB are perpendicular.

A B

D C

Objective 3

55

Try ItLook at square KLMN below.

Which line segments are parallel?

Opposite sides of a square are parallel. Parallel lines never

_______________ or _______________.

Line segment _______ and line segment _______ are parallel.

Line segment _______ and line segment _______ are parallel.

Which line segments are perpendicular?

There is a ___________ angle at each vertex of a square. Perpendicular lines intersect at right angles.

Line segment _______ and line segment _______ are perpendicular.




Parallel lines never intersect or cross. Line segment KL and line segmentNM are parallel. Line segment KN and line segment LM are parallel. There isa right angle at each vertex of a square. Line segment KL and line segmentKN are perpendicular. Line segment KL and line segment LM areperpendicular. Line segment NM and line segment LM are perpendicular.Line segment NM and line segment KN are perpendicular.

K L

N M

Objective 3

56

How Can You Describe a Two-Dimensional Figure?You can describe a two-dimensional figure (or plane figure) bycounting the number of sides, vertices, and angles the figure has.

Polygons are closed two-dimensional figures with straight sides. Acircle is a closed two-dimensional figure, but it is not a polygonbecause it has no sides. You should be able to recognize and describethe following polygons.

A rectangle is aquadrilateral withopposite sides congruentand 4 right angles. Asquare is a rectangle withall sides congruent.

Polygons

Figure DescriptionCongruent Noncongruent

Sides Sides

● 3 sides● 3 vertices● 3 angles

All sides equalin length









Triangle

Quadrilateral

Pentagon

Hexagon

Octagon


Objective 3

5757

Try ItLook at the figures below. Count the number of sides, vertices, andangles. Then name the figure.

● Figure A has _______ sides, _______ vertices, and _______ angles.

Opposite sides appear to be ______________.

Figure A is a ______________.

● Figure B has _______ sides, _______ vertices, and _______ angles.

Figure B is a ______________.

● Figure C has _______ sides, _______ vertices, and _______ angles.

All sides appear to be ______________.

Figure C is a ______________.

● Figure D has _______ sides, _______ vertices, and _______ angles.

Figure D is a ______________.

Figure A has 4 sides, 4 vertices, and 4 angles. Opposite sides appear to becongruent. Figure A is a rectangle.

Figure B has 5 sides, 5 vertices, and 5 angles. Figure B is a pentagon.

Figure C has 4 sides, 4 vertices, and 4 angles. All sides appear to becongruent. Figure C is a square.

Figure D has 6 sides, 6 vertices, and 6 angles. Figure D is a hexagon.

A B C D

Objective 3

58

How Can You Describe a Three-Dimensional Figure?You can describe a three-dimensional figure (or solid figure) bycounting the number of vertices, edges, and faces the figure has.

● A face is a flat surface in the shape of a two-dimensionalfigure.

● An edge is a line segment where two faces meet.

● A vertex is a point where three or more edges meet. Theplural of vertex is vertices.

Here are some three-dimensional figures you should be able torecognize and describe.

A three-dimensionalfigure has length, width,and height.

Face

Vertex

Edge

Figure Example Description

Triangularprism

Rectangularprism

Cube

Square pyramid

Triangularpyramid

● 2 triangular faces● 3 rectangular faces● 9 edges● 6 vertices

● 6 rectangular faces● 12 edges● 8 vertices

● 6 square faces● 12 edges● 8 vertices

● 1 square face● 4 triangular faces● 8 edges● 5 vertices

● 4 triangular faces● 6 edges● 4 vertices

Three-Dimensional Figures

Objective 3

59

Try ItErnest gave his father a candy bar in a box shaped like the onebelow.

The box has _______ edges.

The box has _______ vertices.

The box has _______ rectangular faces.

The box has _______ triangular faces.

How many more edges than vertices does this box have?

_______ edges � _______ vertices � _______

This box has _______ more edges than vertices.

How many faces does this box have?

_______ rectangular faces � _______ triangular faces � _______

This box has _______ faces.

The box has 9 edges.

The box has 6 vertices.

The box has 3 rectangular faces.

The box has 2 triangular faces.

9 edges � 6 vertices � 3. This box has 3 more edges than vertices.

3 rectangular faces � 2 triangular faces � 5. This box has 5 faces.

chocolate

candy barchocolate

candy bar

Objective 3

60

Here are some three-dimensional figures with curved surfaces that youshould be able to recognize and describe.

Figure Example Description

Cylinder

Cone

Sphere

● 1 curved surface● 2 circular bases

● 1 curved surface● 1 circular base

● 1 curved surface

Three-Dimensional Figures

Some three-dimensional figures have a curved surface. Some of thesefigures also have one or two flat circular surfaces called bases.

Bases

Curvedsurface

Objective 3

What Are Transformations?Transformations are ways of moving a figure in a plane. Three kinds oftransformations are translations, reflections, and rotations. The result ofa translation, reflection, or rotation is a figure that is congruent to theoriginal figure.

● A translation is a sliding movement. A figure can be translatedup, down, left, right, or diagonally by sliding it.

● A reflection is a mirror image across a line.

● A rotation is a turning movement around a point. In a rotation,the figure moves in a circular path.

Rotatesaroundthis point

61


Objective 3

62

What transformation is represented in the diagram?

The figure has been moved down. This is a translation.

Try ItName the transformation in each diagram.

The figures in diagram A show a mirror image. This transformation

is a _________________.

The figures in diagram B show a sliding movement diagonally. This

transformation is a _________________.

The figures in diagram C show a turning movement around a point.

This transformation is a _________________.

The figures in diagram A show a mirror image. This transformation is a reflection.

The figures in diagram B show a sliding movement diagonally. Thistransformation is a translation.

The figures in diagram C show a turning movement around a point. Thistransformation is a rotation.

CBA

Objective 3

63

What Is a Coordinate Plane?A coordinate plane is a grid used to locate points. A point is located byusing an ordered pair of numbers. The two numbers that form theordered pair are called the point’s coordinates.

● Every coordinate plane has a special point called the origin.The coordinates of the origin are (0, 0).

● The horizontal line is called the x-axis. The first number of an ordered pair tells how many units the point is to the right ofthe origin. The first number goes right.

● The vertical line is called the y-axis. The second number of an ordered pair tells how many units the point is above theorigin. The second number goes up.

Look at the coordinate grid below. The coordinates of point P are (2, 5).

The first number of point P is 2. It is 2 units to the right of theorigin.The second number of point P is 5. It is 5 units above the origin.

(0, 0)Origin x

y

10 2 3 4 5 6

1

2

3

4

5

6P (2, 5)

Objective 3

64

Look at the coordinate grid.

What are the coordinates of points A, B, and C?

● Starting from the origin, point A is located 4 units to the rightand 2 units up. The ordered pair (4, 2) shows the location ofpoint A.

● Starting from the origin, point B is located 2 units to the rightand 4 units up. The ordered pair (2, 4) shows the location ofpoint B.

● Starting from the origin, point C is located 1 unit to the rightand 4 units up. The ordered pair (1, 4) shows the location ofpoint C.

x

y

10 2 3 4 5 6

1

2

3

4

5

6

BC

A

Objective 3

Try ItLook at the coordinate grid.

What are the coordinates of points R, S, and T?

Point R is _______ units to the right and _______ units up. The

ordered pair ( _______ , _______ ) shows the location of point R.

Point S is _______ units to the right and _______ units up. The

ordered pair ( _______ , _______ ) shows the location of point S.

Point T is _______ units to the right and _______ units up. The

ordered pair ( _______ , _______ ) shows the location of point T.

Point R is 6 units to the right and 4 units up. The ordered pair (6, 4) showsthe location of point R.

Point S is 3 units to the right and 0 units up. The ordered pair (3, 0) showsthe location of point S.

Point T is 0 units to the right and 2 units up. The ordered pair (0, 2) shows the location of point T.

x

y

10 2 3 4 5 6

1

2

3

4

5

6

S

T

R

What happens whena point is on thex-axis or y-axis?

65

Objective 3

66

Try ItThe grid below shows a map of a neighborhood.

The school is _______ units to the right of the origin and _______

unit above the origin. The school is located at ( _______ , _______ ).

The store is _______ units to the right of the origin and _______ units

above the origin. The store is located at (_______ , _______ ).

The library is _______ units to the right of the origin and _______

units above the origin. The library is located at (_______ , _______ ).

The school is 4 units to the right of the origin and 1 unit above the origin.The school is located at (4, 1).

The store is 6 units to the right of the origin and 3 units above the origin.The store is located at (6, 3).

The library is 5 units to the right of the origin and 8 units above the origin.The library is located at (5, 8).

0

1

2

3

4

5

6

7

8

9

1 2 3 4 5 6 7 8 9x

y

BOOKSTORE

Library

Store

School


Objective 3

67

Question 27Which figure appears to have exactly one pair ofparallel sides?

A

B

C

D

Question 28The figure below is a rectangle.

Which statement about the figure is true?

A Line segment WX is parallel to line segmentXY.

B Line segment YZ is parallel to line segmentXY.

C Line segment WX is perpendicular to linesegment XY.

D Line segment WX is perpendicular to linesegment YZ.

Question 29Which of the following figures has exactly twobases?

A Cylinder

B Cone

C Sphere

D Not here

Question 30Dennis has a bank shaped like the figure below.

Which statement is true about this figure?

A This figure has 8 more edges than vertices.

B This figure has 3 more vertices than faces.

C This figure has 5 more vertices than faces.

D This figure has 3 more edges than vertices.

W

Y

X

Z





Objective 3

68

Question 31Which of these shows only a rotation?

Question 32The pictures below show 3 pairs of figures that each represent a single transformation.

Which of the following correctly lists the transformations in order from 1 to 3?

A Reflection, rotation, reflection

B Translation, reflection, rotation

C Rotation, reflection, translation

D Translation, rotation, reflection



A C

B D

1 2 3

Objective 3

69

Question 33Look at the coordinate grid below.

Which ordered pair appears to be on line n?

A (3, 3)

B (3, 4)

C (4, 3)

D (4, 4)

Question 34The grid below represents a map of a playground.

Which ordered pair best represents the location of the sandbox?

A (4, 3)

B (1, 2)

C (2, 4)

D (5, 6)

x

y

10 2 3 4 5 6 7

1

2

3

4

5

6

7

Tree

Swing

Sandbox

Slide

x

y

10 2 3 4 5 6

1

2

3

4

5

6

n



70

The student will demonstrate an understanding of the concepts and usesof measurement.

Objective 4

For this objective you should be able to apply measurement conceptsinvolving conversions, length, perimeter, area, volume, time, andtemperature to solve problems.

When Do You Use Measurement?You can use measurement for many things. You can measure your legto find out how long it is. You can place a bag of peanuts on a scale tofind out how much it weighs. If you look at a clock to tell the time orat a thermometer to read the temperature, you are using measurement.

How Do You Convert Units of Measurement?In some problems you will need to convert one unit of measurement to another, such as pounds to ounces or centimeters to meters.

● To convert a smaller unit to a larger unit, divide by the numberof smaller units there are in one of the larger units.

● To convert a larger unit to a smaller unit, multiply by the numberof smaller units there are in one of the larger units.

Use the information from the Mathematics Chart to help convert unitsof measure.

Largeunits

Smallunits

Metric Customary


LENGTH

Metric Customary




1 foot = 12 inches

CAPACITY AND VOLUME

Metric Customary



1 quart = 2 pints

1 pint = 2 cups


MASS AND WEIGHT

Metric Customary




CAPACITY AND VOLUME

In the United Statesmost people use thecustomary system ofmeasurement. Scientistsand people in most other countries use the metric system.

Objective 4

71

Carlo has 6 gallons of water in a large container. He is using a one-quart bucket to empty the large container. How many timeswill he have to fill the bucket to empty the large container?

● Use the Mathematics Chart to compare gallons and quarts.

● 1 gallon � 4 quarts6 gallons � ? quarts

● A gallon is a larger unit than a quart. To convert a larger unit toa smaller unit, multiply.

● To convert 6 gallons to quarts, multiply 6 gallons by thenumber of quarts in one gallon.

6 gallons � 4 quarts per gallon � 24 quarts

Carlo will have to fill the one-quart bucket 24 times to empty thelarge container.

On a baseball field the distance from home plate to first base is 90 feet. How many yards is it from home plate to first base?

● Use the Mathematics Chart to compare feet and yards.

● 1 yard � 3 feet? yards � 90 feet

● A foot is a smaller unit than a yard. To convert a smaller unit toa larger unit, divide.

● To convert 90 feet to yards, divide 90 feet by the number of feetin one yard.

90 feet � 3 feet per yard � 30 yards

The distance from home plate to first base is 30 yards.

Objective 4

72

Try ItA cooler contains 20 liters of water. How many milliliters of waterdoes the cooler contain?

● 1 liter � _______ milliliters

● A ______________ is a larger unit than a ______________.

● To convert liters to milliliters, ______________ by the number of

milliliters in one liter.

● _______ liters � 1,000 milliliters per liter � _______ milliliters

The cooler contains _______ milliliters of water.

● 1 liter � 1,000 milliliters

● A liter is a larger unit than a milliliter.

● To convert liters to milliliters, multiply by the number of milliliters in one liter.

● 20 liters � 1,000 milliliters per liter � 20,000 milliliters

The cooler contains 20,000 milliliters of water.

Mario has 2 kilograms of pasta in a total of 4 boxes. Each box is thesame size. How many grams of pasta are in each box?

● Use the Mathematics Chart to compare kilograms and grams.

● 1 kilogram � 1,000 grams2 kilograms � ? grams

● A kilogram is a larger unit than a gram. To convert a larger unitto a smaller unit, multiply.

● To convert 2 kilograms to grams, multiply 2 kilograms by thenumber of grams in one kilogram.

2 kilograms � 1,000 grams per kilogram � 2,000 grams

Mario has 2,000 grams of pasta in a total of 4 boxes. Now find howmany grams of pasta are in each box.

● Divide 2,000 grams by 4 boxes to find the number of grams ineach box.

2,000 grams � 4 boxes � 500 grams per box

Each box of pasta contains 500 grams.

Pasta

Objective 4

73

Try ItPaul is making signs for the school dance. He has a roll of paper 5 feet 3 inches long. If Paul divides the paper into 3 equal pieces to make the signs, how long will each sign be in feet and inches?

First convert the measurement 5 feet 3 inches to inches.

1 foot � _______ inches

5 feet � 12 inches per foot � _______ inches

_______ inches � _______ inches � _______ inches

To find the length of each sign, divide by 3.

_______ � 3 equal pieces � _______

Each sign will be _______ inches long.

Since _______ inches is greater than 1 foot, convert this measurement

to feet and inches.

_______ � 12 � 1 R _______

Each sign will be 1 _______ 9 _______ long.

1 foot � 12 inches. 5 feet � 12 inches per foot � 60 inches.60 inches � 3 inches � 63 inches. 63 � 3 equal pieces � 21. Each sign will be 21 inches long. Since 21 inches is greater than 1 foot, convert this measurement to feet and inches. 21 � 12 � 1 R9. Each sign will be1 foot 9 inches long.

Objective 4

74

Use the ruler below to measure this screw to the nearest inch.

● The 0-inch mark on the ruler is placed at the left end of thescrew.

● The right end of the screw aligns with the mark on the rulerthat is about halfway between 3 inches and 4 inches.

The length of the screw is about 3 inches. 12

0 1 2 3 4Inches

12

Use the ruler on the Mathematics Chart to measure the line segmentnext to the paper clip to the nearest millimeter.

● Place the 0-centimeter mark on the ruler at one end of thepaper clip.

● Read the mark on the ruler that aligns with the other end ofthe paper clip.

● The paper clip is between 4 and 5 centimeters long. This is thesame as between 40 and 50 millimeters long.

● The end of the paper clip aligns with the mark on the ruler thatis 9 marks past the 4.

The paper clip is about 49 millimeters long.

How Do You Measure Length?To find the length of an object, use a ruler. There are two rulers on theMathematics Chart in the back of this book.

Objective 4

75

Try ItMai rode a bus to school. After school she rode a bus to the library,and then she rode another bus home. Use the inch ruler on theMathematics Chart and the map below to find the total distance Mai rode.

What is the total distance Mai rode in miles?

The distance from Mai’s house to the school on the map is

_______ inches.

The distance from the school to the library on the map is

_______ inch.

The distance from the library to Mai’s house on the map is

_______ inches.

_______ � _______ � _______ � _______

The map’s scale shows that _______ inch represents _______ miles.

The total distance equals _______ inches � _______ miles per inch.

Mai rode a total of _______ miles.

The distance from Mai’s house to the school on the map is 2 inches. Thedistance from the school to the library on the map is 1 inch. The distancefrom the library to Mai’s house on the map is 2 inches. The total distance is2 � 1 � 2 � 5 inches. The map’s scale shows that 1 inch represents2 miles. The total distance equals 5 inches � 2 miles per inch. Mai rode atotal of 10 miles.

Mai’shouse

School

Library

Scale1 inch � 2 miles

75

Objective 4

76

How Do You Find the Perimeter of a Figure Using a Formula?Perimeter is the distance around a figure. To find the perimeter of afigure, add the lengths of all its sides. Some figures have certainattributes that let you find the perimeter in a different way.

Look at the square below. The side length is shown in centimeters.What is the perimeter of the square in centimeters?

Remember what you know about a square.

● All sides of a square are congruent.

● So each side of this square is 8 cm long.

Find the perimeter of the square.

● You could add the lengths of all the sides:8 � 8 � 8 � 8 � 32

● Since all four sides are the same length, you could multiply thelength of one side by the number of sides:4 sides � 8 cm � 32 cm

Both strategies show that the perimeter of the square is 32 cm.

8 cm

Objective 4

77

A rectangular garden has a length of 12 yards and a width of 8 yards.What is the perimeter of the garden?

Remember what you know about a rectangle and use it to find theperimeter of the rectangular garden.

● Opposite sides of a rectangle are congruent.

● The length of the rectangular garden is 12 yards. There are 2 sides that are 12 yards long. 2 � 12 yards � 24 yards.

● The width of the rectangular garden is 8 yards. There are 2 sidesthat are 8 yards wide. 2 � 8 yards � 16 yards.

● Add 24 and 16 to find the perimeter: 24 yards � 16 yards � 40 yards

The perimeter of the rectangular garden is 40 yards.

12 yd

8 yd

Objective 4

78

For squares and rectangles, you can use a formula to find the perimeter.A formula is an equation that uses numbers, mathematical symbols, andletters to help solve a problem. The formulas for finding the perimeter ofa square and a rectangle can be found on the back of the MathematicsChart.



rectangle P = (2 × l) + (2 × w)



Look at the rectangle below.

Find the perimeter using a formula.

● The formula for the perimeter of a rectangle is P � (2 � l) � (2 � w). The letter P stands for the perimeter,the letter l stands for the length, and the letter w stands for thewidth.

● Substitute the values for the length and width of the rectangleinto the formula. The length (l) is 5 ft, and the width (w) is 2 ft. Then solve for the perimeter.

P � (2 � l) � (2 � w)

P � (2 � 5) � (2 � 2)

P � 10 � 4

P � 14

The perimeter of the rectangle is 14 feet.

2 feet

5 feet

Multiply 2 � 5 and 2 � 2

Add 10 and 4

The formula for theperimeter of a rectangle is P � (2 � l)� (2 � w).Read this as Perimeterequals two times thelength plus two times thewidth.

Objective 4

79

A square mirror has a side length of 16 inches. Find the perimeter ofthe square mirror using a formula.

● The formula for the perimeter of a square is P � 4 � s. Theletter P stands for the perimeter, and the letter s stands for theside length.

● Substitute the value for the side length of the square into theformula. Each side (s) is 16 inches. Then solve for theperimeter.

P � 4 � s

P � 4 � 16

P � 64

The perimeter of the square mirror is 64 inches.

The formula for theperimeter of a square is P � 4 � s. Read this asPerimeter equals fourtimes the length of theside.

Objective 4

80

Try ItThe picture frame below is 24 centimeters long and 16 centimeterswide. What is the perimeter of the picture frame?

Use the formula to find the perimeter of the rectangle.

P � (_______ � _______) � (_______ � _______)

P � (2 � _______ ) � (2 � _______ )

P � _______ � _______

P � _______

The perimeter of the picture frame is _______ centimeters.

P � (2 � l) � (2 � w)

P � (2 � 24) � (2 � 16)

P � 48 � 32

P � 80

The perimeter of the picture frame is 80 centimeters.

16 cm

24 cm

Objective 4

81

How Do You Find the Area of a Figure Using a Formula?Area is the measure of how many square units a figure covers. To findthe area of a figure, you could count the number of square units thefigure covers. Some figures have certain attributes that let you find thearea in other ways.

In the rectangle below, there are 5 columns and 3 rows.

The number of columns and the number of rows represent thedimensions of the rectangle. You could multiply the number of columnsby the number of rows to find the total number of square units. This isthe same as multiplying the length by the width. In this rectangle, thelength is 5 units and the width is 3 units. If you multiply the length bythe width, the area is 5 � 3 � 15 square units.

For squares and rectangles, you can use a formula to find the area. Aformula is an equation that uses numbers, mathematical symbols, andletters to help solve a problem. The formulas for finding the area of asquare and a rectangle can be found on the back of the MathematicsChart.

q

rectangle P = (2 × l) + (2 × w)





Area is measured insquare units, such assquare feet or squaremeters.

Objective 4

82

Bonita drew a rectangle 7 centimeters long and 3 centimeters wide.

Use a formula to find the area of the rectangle.

● The formula for the area of a rectangle is A � l � w. The letterA stands for the area, the letter l stands for the length, and theletter w stands for the width.

● Substitute the values for the length and width of the rectangleinto the formula. The length (l) is 7 cm, and the width (w) is3 cm. Then solve for the area.

A � l � w

A � 7 � 3

A � 21

The area of Bonita’s rectangle is 21 square centimeters.

3 cm

7 cm

The formula for thearea of a rectangle isA � l � w. Read thisas Area equals lengthtimes width.

Objective 4

83

A square is a special kind of rectangle. All the sides of a square are thesame length. Each side can be represented by the letter s.

Find the area of a square with a side that is 6 inches long.

Use the formula for the area of a square.

● The formula for the area of a square is A � s � s. The letter Astands for the area, and the letter s stands for the side length.

● Substitute the value for the side length into the formula. Eachside (s) is 6 inches. Then solve for the area.

A � s � s

A � 6 � 6

A � 36

The area of the square is 36 square inches.

6 in.

The formula for the area of a square is A � s � s. Read this asArea equals side timesside.

Objective 4

84

Try ItCarolyn measured the front cover of her photo album and found thatit was 9 inches wide and 12 inches long. What is the area of the frontcover?

The length of the front cover is _______ inches.

The width of the front cover is _______ inches.

Use the formula A � _______ � _______ to find the area of a

rectangle.

A � _______ � _______

A � _______

The area of the front cover is _______ square inches.

The length of the front cover is 12 inches.

The width of the front cover is 9 inches.

A � l � w

A � 12 � 9

A � 108

The area of the front cover is 108 square inches.

12 inches

9 inches

Objective 4

85

How Do You Find the Volume of a Figure Using a Formula?The volume of an object is the number of cubic units it takes to fill the object. One way to find the volume of an object is to count thenumber of cubes it takes to fill it.

The cube below has edges that each measure 1 unit long. It has avolume of 1 cubic unit.

1 unit

1 unit

1 cubic unit

1 unit

Try ItTy is using square tiles for an art project. The side of each tilemeasures 5 centimeters. What is the area of each tile?

5 cm

Use the formula A � _______ � _______ to find the area of a square.

A � _______ � _______

A � _______

The area of each tile is _______ square centimeters.

A � s � s

A � 5 � 5

A � 25

The area of each tile is 25 square centimeters.

Volume is measured incubic units, such ascubic inches or cubiccentimeters.

Objective 4

86

A rectangular prism has three dimensions: length, width, and height. Ina model of a rectangular prism, the number of columns, the number ofrows, and the number of layers represent the dimensions of the prism.Multiplying the number of columns by the number of rows and thenmultiplying by the number of layers is the same as multiplying thelength by the width by the height.

For cubes and rectangular prisms, you can use a formula to find thevolume. A formula is an equation that uses numbers, mathematicalsymbols, and letters to help solve a problem. The formulas for findingthe volume of a cube and a rectangular prism can be found on the backof the Mathematics Chart.




The rectangular prism shown below is made of 1-unit cubes. What isits volume?

The prism has two layers. Find the number of cubic units in eachlayer.

● The top layer has a width of 3 units and a length of 4 units.The top layer is made up of 3 � 4 � 12 cubic units.

● The bottom layer also has 12 cubic units, even though youcannot see them all in the original figure.

● Since there are 2 layers, multiply the number of cubic units inone layer by 2.

12 � 2 � 24

The volume of the rectangular prism is 24 cubic units.

Bottom layerTop layer

Objective 4

87

Lance uses a box shaped like a cube for storing his toys. Each side ofthe box is 20 inches. What is the volume of Lance’s toy box?

Use a formula to find the volume of the cube.

● The formula for the volume of a cube is V � s � s � s. Theletter V stands for the volume, and the letter s stands for theside length.

● Substitute the value for the side length into the formula. Eachside (s) is 20 inches. Then solve for the volume.

V � s � s � s

V � 20 � 20 � 20

V � 400 � 20

V � 8,000

The volume of Lance’s toy box is 8,000 cubic inches.

Look again at this rectangular prism.

Use the formula to find the volume of the rectangular prism.

● The formula for the volume of a rectangular prism isV � l � w � h. The letter V stands for the volume, the letter lstands for the length, the letter w stands for the width, and theletter h stands for the height.

● Substitute the values for the length, width, and height of therectangular prism into the formula. The length (l) is 4 units,the width (w) is 3 units, and the height (h) is 2 units. Thensolve for volume.

V � l � w � h

V � 4 � 3 � 2

Multiply 4 � 3 V � 12 � 2

Multiply 12 � 2 V � 24

The volume of the rectangular prism is 24 cubic units.

2

43

Multiply 20 � 20

Multiply 400 � 20

The formula for the volume of a rectangularprism is V � l � w � h.Read this as Volumeequals length times widthtimes height.

The formula for the volume of a cube isV � s � s � s. Readthis as Volume equalsside times side timesside.

A cube is a special kind of prism. All the dimensions of a cube are thesame. Each side length can be represented by the letter s.

Objective 4

88

Try ItThe rectangular prism below is made of 1-centimeter cubes.

What is the volume of this prism?

The length is _______ cm.

The width is _______ cm.

The height is _______ cm.

Use the formula V � _______ � _______ � _______ to find the volume

of this rectangular prism.

V � _______ � _______ � _______

V � _______ � _______

V � _______

The prism has a volume of _______ cubic centimeters.

The length is 5 cm. The width is 4 cm. The height is 3 cm.

V � l � w � h

V � 5 � 4 � 3

V � 20 � 3

V � 60

The prism has a volume of 60 cubic centimeters.

5 cm

4 cm

3 cm

Objective 4

Emilio and his friends went to a movie. The movie started at 4:30and lasted 2 hours 20 minutes. What time was the movie over?

● Start at 4:30 and add 2 hours: 4:30 � 2 hours is 6:30.

● Add 20 minutes to 6:30: 6:30 � 20 minutes is 6:50.

The movie was over at 6:50.

How Do You Solve Problems Involving Elapsed Time?Time can be measured in several ways. Daily activities are measured inseconds, minutes, and hours. Longer periods of time are measured indays, weeks, months, and years.

Some problems require you to calculate the amount of time that haspassed between one event and another.

Gene got a new watch for his birthday. He used the watch to findhow many minutes he walked his dog. Gene and his dog left thehouse at 10:30 A.M. They returned at 11:13 that morning. For howmany minutes did Gene walk his dog?

● From 10:30 to 11:00 is 30 minutes.


● 30 minutes � 13 minutes � 43 minutes

Gene walked his dog for 43 minutes.

121110

9

87 6 5

4

32

1

121110

9

87 6 5

4

32

1

89

Objective 4

9090

Try ItSam and his family went to visit his grandmother. They left theirhouse at 8:15 A.M. They arrived at his grandmother’s house at 11:05 A.M. How long did it take Sam and his family to get to hisgrandmother’s house?

The family started out at 8:15 A.M.

8:15 to 10:15 is _______ hours.

10:15 to 11:05 is _______ minutes.

It took _______ hours _______ minutes for Sam and his family to get

to his grandmother’s house.

8:15 to 10:15 is 2 hours.

10:15 to 11:05 is 50 minutes.

It took 2 hours 50 minutes for Sam and his family to get to hisgrandmother’s house.

Jamie was at the dentist’s office from 9:25 until 10:40. How manyhours and minutes was Jamie at the dentist?

● From 9:25 to 10:25 is 1 hour.

● Count by fives from 10:25 to 10:40.

10:25 10:30 10:35 10:40


Jamie was at the dentist’s office for 1 hour 15 minutes.

5 5 5� � � 15

Objective 4

91

How Do You Solve Problems Involving Changes in Temperature?Temperature is a measure of how hot or cold something is.Temperature is measured with a thermometer.

Temperature is measured in degrees Fahrenheit (°F) in the customarysystem and in degrees Celsius (°C) in the metric system.

The thermometers below show some common temperatures measuredin the customary system and in the metric system.

The temperature at 8:00 A.M. was 50°F. By 10:00 A.M. thetemperature had increased 7°F. From 10:00 A.M. to 2:00 P.M., thetemperature increased 3°F per hour. What was the temperature at2:00 P.M.?

First find the temperature at 10:00 A.M.

● At 8:00 A.M. the temperature was 50°F.

● By 10:00 A.M. the temperature was 7°F higher than it was at 8:00 A.M.

● 50 � 7 � 57


Then find the number of degrees the temperature increased from 10:00 A.M. to 2:00 P.M.

● The temperature increased 3°F per hour from 10:00 A.M.to 2:00 P.M.

200

180

160

140

120

100

80

60

40

Boiling point of water

Temperature ona summer day

Freezing point of water

95°F

212°F

32°F

100

0

35°C

100°C

0°C

20

40

60

80

220

°F °C

What do the markson the thermometerrepresent?

Objective 4

92

● From 10:00 A.M. to 2:00 P.M. is 4 hours.

● Use multiplication to find the number of degrees the temperature increased.

● 4 hours � 3°F per hour � 12°F

Next find the temperature at 2:00 P.M.


● At 2:00 P.M. the temperature was 12°F higher than it was at 10:00 A.M.

● 57 � 12 � 69

At 2:00 P.M. the temperature was 69°F.


Objective 4

93

Question 35A rectangular prism is shown below.

What is the volume of the prism?

A 10 cubic centimeters

B 25 cubic centimeters

C 21 cubic centimeters

D 30 cubic centimeters

Question 36At 8:00 A.M. the temperature is 45°F. If thetemperature increases 5°F each hour, what willthe temperature be at 2:00 P.M.?

A 51°F

B 50°F

C 75°F

D 70°F

Question 37A rectangular playground has a length of 110 yards and a width of 70 yards.

What is the perimeter of the playground inyards?

Record your answer and fill in the bubbles. Be sure to use the correct place value.

0

1

2

3

4

5

6

7

8

9

0

1

2

3

4

5

6

7

8

9

0

1

2

3

4

5

6

7

8

9

110 yd

70 yd5 cm

3 cm

2 cm



Objective 4

94

Question 38Harry takes a bus to visit his cousin. The bus leaves at 10:40 A.M. The bus trip takes 3 hours 45 minutes. What time is it when thebus arrives at Harry’s destination?

A 2:25 P.M.

B 1:45 P.M.

C 3:45 P.M.

D 1:25 P.M.

Question 39A cell phone has the dimensions shown below.

Which of the following equations can be used tofind V, the volume of the cell phone in cubiccentimeters?

A V � 8 � 3 � 1

B V � 8 � 3 � 1

C V � 8 � 3 � 1

D V � 8 � 3 � 1

Question 40Band practice started at 1:30 P.M. and was overat 3:25 P.M. How long was band practice?

A 2 hours 5 minutes

B 2 hours 55 minutes

C 1 hour 55 minutes

D 1 hour 5 minutes

Question 41How many meters are equal to 50 kilometers?

A 5,000 m

B 500 m

C 5 m

D 50,000 m

12ABC 3DEF

4GHI 5JKL 6MNO

7PQRS 8TUV 9WXYZ

*0OPER #

TALKBACK

END

3 cm8 cm

1 cm




Objective 4

95

Question 43The area of a rectangular sidewalk is 856 square feet. The width of the sidewalk is 8 feet. What is the length of the sidewalk?

A 420 feet

B 6,848 feet

C 107 feet

D 17 feet

Question 44Jesse’s father is 6 feet 2 inches tall. How manyinches tall is Jesse’s father?

A 74 inches

B 62 inches

C 72 inches

D 68 inches



Question 42The drawing below represents a rectangular patio floor. Use the ruler on the Mathematics Chart tomeasure the dimensions of the drawing to the nearest centimeter.

If each centimeter on the drawing represents 1 meter, which of the following is closest to theperimeter of the actual patio floor?

A 16 meters

B 18 meters

C 20 meters

D 25 meters

96

The student will demonstrate an understanding of probability and statistics.

Objective 5


● describe and predict the results of a probability experiment; and

● solve problems by collecting, organizing, displaying, andinterpreting sets of data.

What Is Probability?Probability is a way of describing how likely it is that a particularoutcome, or result, will occur. A fraction can be used to describe theresults of a probability experiment.

● The numerator of the fraction is the number of favorableoutcomes for the experiment.

● The denominator of the fraction is the number of all possibleoutcomes for the experiment.

number of favorable outcomes��

number of possible outcomes

The spinner below is divided into 4 equal sections. Each section is adifferent color. If the spinner is spun one time, what is theprobability of the spinner landing on the color yellow?

You can use a fraction to describe the results of this probabilityexperiment.

● The favorable outcome for this experiment is landing on thecolor yellow. There is only one section of the spinner labeledyellow. There is only one favorable outcome. The numerator ofthe fraction is 1.

● There are 4 sections on the spinner: red, blue, yellow, andgreen. The number of possible outcomes is 4. The denominatorof the fraction is 4.

�

The probability of the spinner landing on the color yellow is 1 out of 4, or .1

4

14



Red Blue

Yellow Green


Objective 5

97

A random event occurswhen a selection is madewithout looking.

Mike has several coins in his pocket: 3 dimes, 2 nickels, 1 quarter,and 2 pennies. Mike reaches into his pocket and takes out one coinat random. What is the probability that Mike will pick a dime?

● A favorable outcome for this experiment is to pick a dime. There are 3 dimes in his pocket. There are 3 favorableoutcomes.

● There are a total of 3 � 2 � 1 � 2 coins in his pocket. Thereare 8 coins in all in his pocket. There are 8 possible outcomes.

The probability that Mike will pick a dime is the fraction:

� �38

�

The probability that Mike will pick a dime is 3 out of 8, or �38

�.



Objective 5

98

Try ItJoel has a bag with colored cubes in it. There are 5 red cubes, 2 white cubes, and 4 blue cubes. Joel will take a cube out of the bagat random. What is the probability that he will take out a red cube?

A favorable outcome for this experiment is to take a _______ cubeout of the bag.

There are _______ red cubes in the bag.

There are _______ favorable outcomes.

The expression _______ � _______ � _______ represents the totalnumber of cubes in the bag.

There are _______ cubes in the bag.

There are _______ possible outcomes.

The probability that Joel will pick a red cube is .

A favorable outcome for this experiment is to take a red cube out of the

bag. There are 5 red cubes in the bag. There are 5 favorable outcomes.

There are a total of 5 � 2 � 4 cubes in the bag. There are 11 cubes in the

bag. There are 11 possible outcomes. The probability that Joel will pick a

red cube is �151�.

Objective 5

99

How Can You Use Experimental Results to Make Predictions?Sometimes you need to predict the probability of an event based on theresults of an experiment. If you know the probability of an event, youcan use it to predict the probability of that event occurring in the future.

John plays baseball. This season he has been at bat 36 times. He gota hit 6 of those times.

Based on this information, how many times can John expect to get ahit in his next 12 times at bat?

● Find the fraction that describes the number of hits John got outof 36 times at bat.

� �366�

● The probability that John got a hit is .

● Use what you know about equivalent fractions to find thenumber of hits John can expect to get in his next 12 times atbat.

�

John can expect to get 2 hits in his next 12 times at bat.

212

��

6 � 336 � 3

126

36

636

number of favorable outcomes (getting a hit)��number of possible outcomes (number of times at bat)

©P

hoto

dis

c

Objective 5

100

Marta has a bag of blue marbles, red marbles, and white marbles.She reaches into the bag and removes a marble at random. Sherecords the marble’s color and puts the marble back in the bag.Marta does this 20 times. The table shows the data she collects.

Marble Experiment

Based on this information, what is the probability that Marta willremove a blue marble from the bag?

● In this experiment a favorable outcome is to remove a bluemarble. Marta removed a blue marble 11 times. The number offavorable outcomes is 11.

● In this experiment the number of possible outcomes is the totalnumber of times a marble is removed. Marta removed a marblefrom the bag 11 � 5 � 4 � 20 times.

● The probability of removing a blue marble is the number offavorable outcomes over the number of possible outcomes.

The probability is �12

10�.

Based on this probability, what is a reasonable prediction of thenumber of times Marta will remove a blue marble on her next 80tries?

It is reasonable to predict that Marta will remove a blue marble fromthe bag on 44 out of her next 80 tries.

4480

��

11 � 420 � 4

80��

1120

ColorNumber of Times

RemovedBlue 11 Red 5 White 4

Objective 5

101

Try ItThe table below shows the number of free throws each player madeat basketball practice.

Based on these results, how many free throws will Lian make out ofher next 20 tries?

Lian made _______ of her 10 free throws.

The probability of Lian making a free throw is .

Use this probability to predict how many free throws Lian will makein her next 20 tries.

7 2 �

10 2 � 20

Based on the results in the table, Lian will make _______ free throwsout of her next 20 tries.

Lian made 7 of her 10 free throws.

The probability of Lian making a free throw is .

Use this probability to predict how many free throws Lian will make in hernext 20 tries.

Based on the results in the table, Lian will make 14 free throws out of hernext 20 tries.

1420

��

7 � 210 � 2

710

PlayerNumber of Number of

Free Throws Made TriesDashiell 8 10Lian 7 10Nadia 5 10Darin 9 10

Should you multiplyor divide to find anequivalent fractionwith a largerdenominator?

Objective 5

102

How Can You List All Possible Outcomes of a Probability Experiment?Sometimes it is important to see all the results that might happen in aprobability experiment. Making an organized list of all possible outcomes isone way to do this.

Karly is having cereal and fruit for breakfast. She has several kinds ofcereal and several kinds of fruit to choose from.

What are all the possible outcomes of one kind of cereal and one kind offruit that Karly can choose from?

● Start with the first cereal, Corn Flakies. List Corn Flakies with each kind of fruit.

● Then list Oat Nuggets with each kind of fruit.

● Finally list Rice Crunchies with each kind of fruit.

The list shows all the possible outcomes of one kind of cereal and onekind of fruit that Karly can have for breakfast.

Corn Flakies and banana Corn Flakies and raisinsCorn Flakies and strawberries

Oat Nuggets and bananaOat Nuggets and raisinsOat Nuggets and strawberries

Rice Crunchies and bananaRice Crunchies and raisinsRice Crunchies and strawberries

CerealCorn FlakiesOat Nuggets

Rice Crunchies

Fruit BananaRaisins

Strawberries

Objective 5

103

Look at the table below. It shows the number of students from eachfifth-grade class who sing in the school choir.

You could represent the data in the table with a pictograph. Becausethe number of students in the table are all multiples of 3, the key for

the pictograph could show that each means 3 students.

How Can You Represent Data in a Graph?There are many ways to represent data in a graph. A bar graph useseither vertical or horizontal bars of different heights or lengths todisplay data. Bar graphs are useful for comparing data by looking at thelengths or heights of the bars.

A line graph consists of points graphed on a coordinate grid. Thepoints represent numbers taken from the data. Line graphs are usefulfor showing changes in data over a period of time.

A pictograph uses small pictures or symbols to represent pieces of a setof data. A key tells how many objects each picture or symbol standsfor.

Class Number of Students

Smith 12Jones 21Hsu 15Ramos 18

Students in Choir

Smith

Jones

Hsu

Ramos

Students in Choir

Each means 3 students.

How do you use thepictograph’s key tofind the actualnumber of students?

Objective 5

104

Color Number of Butterflies

Orange 6Yellow 8Blue 2

Orange

Yellow

Blue

Each means _______ butterflies.

Try ItThe table below shows butterflies of different colors Mia saw oneafternoon.

Butterflies Mia Saw

Mia wants to make a pictograph and a bar graph to represent thedata. Complete the graphs below.

Butterflies Mia Saw

The data in the table can also be shown as a horizontal bar graph.The scale is numbered by threes.

0 3 6 9 12 15 18 21

Ramos

Hsu

Jones

Smith

Cla

ssNumber of Students

Students in ChoirDo you seethat . . .

Objective 5

105

Butterflies Mia Saw

0Orange Yellow BlueN

umb

er o

f But

terf

lies

Color

Butterflies Mia Saw

2

4

6

8

0Orange Yellow BlueN

um

ber

of

Bu

tter

flie

s

Color

Butterflies Mia Saw

Orange

Yellow

Blue

Each means 2 butterflies.

Objective 5

106

A coordinate plane is a grid used to locatepoints. A point is locatedby using an ordered pairof numbers. The twonumbers that form theordered pair are calledthe point’s coordinates(x, y).

Here is a table of related number pairs. The pairs of numbers areused to graph a line on a coordinate grid.

The two numbers (x, y) form an ordered pair. They are also calledthe point’s coordinates. You can use the number pairs in the table tograph points on a coordinate grid.

Point M is 2 units to the right of the origin. The first number ofpoint M’s ordered pair is 2.

Point M is 3 units above the origin. The second number of point M’sordered pair is 3.

Point M has the coordinates (2, 3).

Point N has the coordinates (5, 7).

Point P has the coordinates (8, 6).

y

x0

123456789

1 2 3 4 5 6 7 8 9

M

NP

Point x y

M 2 3

N 5 7

P 8 6

How Can You Represent Pairs of Related Numbers?Pairs of numbers can be related in different ways. For example, a tableof related numbers might include distances and the amount of time ittakes to travel those distances. You can use a line graph to representpairs of related numbers.

A line graph consists of points graphed on a coordinate grid. Linegraphs are often used to show changes in data over a period of time.

Objective 5

107

The table below shows the temperature in degrees Fahrenheit on aday in March from 8:00 in the morning until 2:00 in the afternoon.

Temperature on a Day in March

The data in the table can be used to create a line graph.

● The title of the graph is “Temperature on a Day in March.”

● The time information is at the bottom, labeled “Time.”

● The temperature information is on the left side, labeled“Temperature (°F).”

● Points representing the temperature at each time are plotted.

● The points are connected to show the change in temperatureover time.

0

10

20

30

40

50

8:00

A.M

.

9:00

A.M

.

10:0

0 A.M

.

11:0

0 A.M

.

12:0

0 P.M

.

1:00

P.M

.

2:00

P.M

.

Tem

pera

ture

(°F

)

Time

Temperature on a Day in March

TimeTemperature

(°F) 8:00 A.M. 35 9:00 A.M. 30 10:00 A.M. 39 11:00 A.M. 40 12:00 P.M. 42 1:00 P.M. 462:00 P.M. 49

Objective 5

108

Use the graph to answer the following questions:

1. At what time was the temperature the lowest?

2. Between which times did the temperature increase the most?

Look at the graph.

1. The lowest temperature on the line graph is 30°F. Thistemperature occurred at 9:00 A.M.

2. The line between 9:00 A.M. and 10:00 A.M. is the steepest. Thetemperature changed the most between the times of 9:00 A.M.and 10:00 A.M.

Try ItThe graph shows a line segment with 3 points labeled.

Fill in the table to show the coordinates of these three points.

The coordinates of point A are (2, 3). The coordinates of point B are (4, 5).The coordinates of point C are (6, 7).

y

x0

123456789

1 2 3 4 5 6 7 8 9

C

A

B

Point x y

A

B

C

Objective 5

109

How Can You Describe Data? Data can be described using range, median, and mode.

● The range of a set of data is the difference between the largestnumber and the smallest number in the data. Subtract to find thedifference.

Suppose you have a set of data that represents the ages of severalfamily members: 34, 23, 12, 54, 47, 14, 47.

The largest number is 54.

The smallest number is 12.

The range for this data set is 54 � 12, or 42.

● The median of a set of data is the middle value. To find themiddle value, list all the data in order from least to greatest.Then cross out one number on each end of the list until youreach the middle.

Look at the data set of ages of family members: 34, 23, 12, 54, 47, 14, 47.

The data written in numerical order are:12, 14, 23, 34, 47, 47, 54.

Cross out one number from each end until you reach themiddle: 12, 14, 23, 34, 47, 47, 54.

The number in the middle is 34.

The median for this data set is 34.

● The mode of a set of data is the value (or values) that appearsmore frequently than any other value. If all the values in a set ofdata appear the same number of times, the set does not have amode.

Look again at the data set of ages of family members:

34, 23, 12, 54, 47, 14, 47.

The value 47 appears two times.

No other value appears more than once.

The mode for this data set is 47.

Objective 5

110

The table shows the number of minutes used on a cell phone for 7 days.

Minutes Used on a Cell Phone

What is the range of this data set?

● The range of a set of data is the difference between the largestnumber and the smallest number in the set. Subtract to find the difference.

78 � 12 � 66

The range is 66.

What is the median number of minutes used?

● To find the median of this data set, list the numbers in orderfrom least to greatest. Cross out numbers from each end untilyou reach the middle. Then find the number that is in themiddle.

12 12 20 26 40 63 78

The median is 26.

What is the mode of this data set?

● To find the mode of this data set, look for the number ofminutes that appears most frequently. The value 12 appearstwice. No other value appears more than once.

The mode is 12.

Day Su M Tu W Th F SaNumber of Minutes Used 20 12 12 26 40 63 78

Objective 5

111

Sometimes a data set has an even number of values. To determine themedian when there is not a single middle value, find the number that isexactly halfway between the two middle values of the data set.

Jennifer is comparing prices of shorts at different stores. She writesdown the different prices in a table.

What is the median price?

● Write the prices of the shorts in numerical order.

25 28 28 30 33 40

● Since this data set does not have one middle number, find thetwo numbers in the middle.

$25 $28 $28 $30 $33 $40

● Find the number that is halfway between 28 and 30.

28 29 30

The number 29 is halfway between 28 and 30.

The median price is $29.

What is the range of the prices of shorts?

● The range is the difference between the highest price and thelowest price. Subtract to find the difference.

40 � 25 � 15

The range is $15.

What is the mode?

● The mode is the price that appears most frequently. The priceof $28 appears twice. No other price appears more than once.

The mode is $28.

Store Price A $40B $25C $28D $30E $28F $33

Prices of Shorts

Objective 5

112

The bar graph below shows the number of CDs purchased at a storeone week.

Use the graph to find the range, median, and mode of the data.

● Find the range of this data set by looking at the heights of thebars. Find the value that the tallest and the shortest barsrepresent and then subtract.

60 � 15 � 45

The range of the data is 45.

● Find the median of the data by listing the values of the bars in numerical order and then locating the middle value:

15 25 30 40 45 50 60

The median of the data is 40.

● Find the mode of the data by looking for the value that appearsmost frequently. In this data set, every value appears only once.

There is no mode.

Num

ber

of C

Ds

CDs Purchased

Mon

day

Tues

day

Wed

nesd

ay

Thur

sday

Friday

30

40

50

60

0

10

20

Satur

day

Sunday

Day


Objective 5

113

Try ItThe bar graph below shows the number of cars parked in theparking lot at a school each day last week.

Look at the length of each bar to find the number of cars parkedthere each day.

Mon.: _______ Tues.: _______ Wed.: _______ Thurs.: _______

Fri.: _______

List the data in order from least to greatest.

__________ __________ __________ __________ __________

The median number of cars parked in the parking lot last week was

_______ .

The range of this set of data is _______ � _______ � _______ .

The mode is _______.

Mon.: 40, Tues.: 40, Wed.: 100, Thurs.: 70, Fri.: 50. To find the median of thedata set, list the data in order from least to greatest: 40, 40, 50, 70, 100. Themedian number of cars parked in the parking lot last week was 50. Therange is 100 � 40 � 60. The mode is 40.

Cars Parked in Lot

Day Wed.

Tues.

Mon.

0 10 20 30 40 50 60 70 80 90 100

Fri.

Thurs.

Number


Objective 5

114

Question 45Roxy has different-colored shirts in her closet.The table below shows how many shirts of eachcolor she has.

Roxy’s Shirts

If Roxy selects a shirt from her closet at random,what is the probability that the shirt will bewhite?

A

B

C

D

Question 46A box of art supplies contains 12 colored pencils,30 markers, and 28 crayons. If Roberto selectsone item from the box at random, what is theprobability that he will select a crayon?

A

B

C

D1270

2870

1228

2842

110

610

410

14


Color Number of Shirts

Red 3Blue 2Pink 1White 4

Objective 5

115

Question 47Alaine is passing out different flavors of candy toher friends at random. The table below showsthe flavors and numbers of candy that she has ina bag.

Candy

According to this information, which flavor ofcandy is Alaine least likely to pick from her bag?

A Peppermint

B Lemon

C Grape

D Cherry

Question 48Mark is the goalkeeper for a soccer team. So farhe has blocked 48 out of 100 shots on goal. Basedon this information, which is the mostreasonable prediction of the number of shotsMark will block out of the next 50 shots on goal?

A 48

B 12

C 50

D 24

Question 49Jake is cooking hot dogs and hamburgers for aparty. His guests have a choice of either a hot dogor a hamburger and one condiment. The tablebelow shows these choices.

Which list shows all the possible outcomes of onetype of meat and one condiment?

A Hot dog with ketchupHot dog with mustardHot dog with relishHamburger with ketchupHamburger with mustardHamburger with relish

B Hot dog with ketchupHamburger with ketchupHot dog with mustardHamburger with mustard

C Hot dog with hamburgerHot dog with ketchupHot dog with relishHamburger with mustardHamburger with hot dogHamburger with relish

D Hot dog with hamburgerKetchup with mustardHamburger with hot dogMustard with relish




Flavor Number of Pieces

Cherry 13Grape 15Peppermint 7Lemon 10

Type of Meat

Hot DogHamburger

Condiment

KetchupMustardRelish

Objective 5

116

Question 50There are 3 points labeled on the line graph below.

Which table best represents the coordinates of points L, M, and N?

A C

B D

y

x0

123456789

101112

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

M

N

L

Point x y L 3 4 M 2 6 N 11 9

Point x y L 3 4 M 6 2 N 10 8

Point x y L 4 5 M 7 3 N 11 9

Point x y L 4 3 M 2 6 N 8 10


Objective 5

117

Question 51The table below shows the number of inches ofrain that fell in 6 months.

Rainfall

What is the mode of this set of data?

A 6

B 5

C 3

D 1

Question 52The graph shows the price of a Stunt-Pro bicycleat four different stores.

Based on the graph, which of the following best represents the range of the prices for aStunt-Pro bicycle at these stores?

A $10

B $20

C $30

D $40

Bicycle Prices

Sto

re

$0 $20 $40 $60 $80 $100 $120

Cost

BikeMart

Mike’sBikes

BestBikes

BikePlanet

Answer Key: page 145Answer Key: page 145

Month Inches of Rain

January 4February 3March 6April 2May 3June 1

Objective 5

118

Question 53The table shows the outdoor temperature at each hour from 9:00 A.M. to 2:00 P.M. Whatwas the median temperature for the time period recorded?

Outdoor Temperatures

A 51°F

B 52°F

C 47°F

D 50°F


Time Temperature 9:00 A.M. 47°F 10:00 A.M. 50°F 11:00 A.M. 53°F 12:00 P.M. 58°F 1:00 P.M. 52°F 2:00 P.M. 50°F

Objective 5

119

Question 54The table shows the number of books checked out of the school library for 5 days.

School Library Books Checked Out

Which graph most accurately represents the data shown in the table?


Day NumberMonday 20 Tuesday 10 Wednesday 25 Thursday 35 Friday 15

A C

B D

Num

ber

of B

ooks

Mon

day

Tues

day

Wed

nesd

ayTh

ursd

ayFr

iday

25

30

35

40

5

0

10

15

20

Day

School Library BooksChecked Out

Number of Books


Mon

day

Tuesd

ay

Wed

nesd

ay

Thurs

day

Friday

3520 2510 30 400 5 15

Day

Num

ber

of B

ooks


Mon

day

Tuesd

ay

Wed

nesd

ay

Thurs

day

Friday

25

30

35

40

5

0

10

15

20

Day


Wednesday

Tuesday

Monday

Friday

Thursday

Each represents 5 books.

120

The student will demonstrate an understanding of the mathematical processesand tools used in problem solving.

Objective 6


● apply mathematics to everyday problem situations;

● communicate about mathematics using everyday language; and

● use logical reasoning.

What Is Problem Solving?Problem solving includes understanding a problem, making a plan tosolve it, carrying out that plan, and checking the answer to see whetherit is reasonable. A reasonable answer is an answer that makes sense. Ananswer makes sense if it is not too big or too small for the question.

Louisa plans to serve fruit juice to her guests at lunch. Louisa, 1 ofher friends, and her 2 parents will all have juice. Each juice glassholds 10 fluid ounces. If each person will have a full glass of juice,how many cups of juice will Louisa need?

Understand the problem.

● Identify the question you need to answer. How many cups of juice will Louisa need?

● Identify the information you know.One glass holds 10 fluid ounces of juice.Louisa, 1 friend, and her 2 parents will all have juice.The Mathematics Chart has the information necessary toconvert fluid ounces to cups.

1 cup � 8 fluid ounces

Make a plan.

● Add to find the total number of glasses of juice needed.

● Multiply the number of glasses by the number of fluid ounces each glass holds.

● Divide by 8 to convert fluid ounces to cups.

Carry out the plan.

● Add: Louisa (1) � 1 friend � 2 parents � 4 glasses of juice

● Multiply: 4 glasses � 10 fluid ounces per glass � 40 fluidounces of juice

● Divide: 40 fluid ounces � 8 fluid ounces per cup � 5 cups

Louisa will need 5 cups of juice.

Objective 6

121

Alexa studied for 1 hour 45 minutes on Tuesday, 1 hour 20 minutes on Wednesday, and 2 hours 30 minutes on Thursday.How long did Alexa study during these three days?


● Identify the question you need to answer.How long did Alexa study during these three days?

● Identify the information you know. She studied 1 hour 45 minutes on Tuesday.She studied 1 hour 20 minutes on Wednesday.She studied 2 hours 30 minutes on Thursday.The Mathematics Chart has the information needed to convertminutes to hours.

1 hour � 60 minutes

Make a plan.

● Add to find the total number of hours and minutes Alexastudied.

● Convert minutes to hours and minutes.

Carry out the plan.

1 hour 45 minutes1 hour 20 minutes

� 2 hours 30 minutes

4 hours 95 minutes

● Since 95 minutes is greater than 1 hour, convert 95 minutes to hours and minutes. Subtract 1 hour (60 minutes) from 95 minutes.

95 minutes � 60 minutes � 35 minutes

95 minutes � 1 hour 35 minutes

Check for reasonableness.

● Is 5 cups of juice a reasonable answer? Is it enough juice for 4 people or too much juice for 4 people?

● One glass holds 10 fluid ounces, which is a little more than 1 cup. So 4 people would need more than 4 cups of juice.

● 10 fluid ounces is not close to 2 cups. So 4 people � 2 cups �8 cups of juice, which would be too much juice.

● A reasonable answer is an amount between 4 and 8 cups. Thenumber 5 is between 4 and 8.

5 cups of juice is a reasonable answer. Do you seethat . . .

Objective 6

122

● Now add this to 4 hours.

4 hours � 1 hour 35 minutes � 5 hours 35 minutes

Alexa studied a total of 5 hours 35 minutes during these threedays.


● Alexa studied more than 1 hour on Tuesday, more than 1 hour on Wednesday, and more than 2 hours on Thursday.

1 hour � 1 hour � 2 hours � 4 hours

Alexa studied more than 4 hours.

● Alexa studied less than 2 hours on Tuesday, less than 2 hourson Wednesday, and less than 3 hours on Thursday.

2 hours � 2 hours � 3 hours � 7 hours

Alexa studied less than 7 hours.

● Alexa studied more than 4 hours but less than 7 hours duringthese three days. A reasonable answer is an amount of timebetween 4 and 7 hours.

5 hours 35 minutes is a reasonable answer.

Objective 6

123

Try ItShalika is buying hamburger buns for a picnic. She needs at least 60 buns. Each package of hamburger buns contains 8 buns andcosts $2. If Shalika buys enough packages to have at least 60 buns,what will she pay for the buns?


What do you know?

Shalika needs to buy at least ______ buns.

Hamburger buns come in packages of ______ buns.

A package of buns costs $________.

Make a plan.

Use the operation of _________________ to find the number of

packages of hamburger buns she needs to buy.

Use the operation of _________________ to find the total cost of

the buns.

Carry out the plan.

______ buns � ______ per package � ______.

The remainder means that Shalika needs to buy an extra package.

Shalika needs to buy ______ packages of hamburger buns.

______ packages � $________ per package � $________

Shalika will pay $________ for the hamburger buns.

Objective 6

124124

What Is a Problem-Solving Strategy?A problem-solving strategy is a plan for solving a problem. The strategy you choose depends on the type of problem you are solving. Sometimes you can use more than one strategy to solve a problem. Some problem-solving strategies include:

● drawing a picture;

● looking for a pattern;

● guessing and checking;

● acting it out;

● making a table;

● working a simpler problem; and

● working backward.


If Shalika buys 5 packages of buns, she will have ______ buns and

spend $________. Five packages of buns is enough not enough .(circle one)

If Shalika buys 10 packages of buns, she will have _____ buns and

spend $________. Ten packages of buns is too many not enough .(circle one)

Shalika will spend more than $________ but less than $________ in

order to have 60 buns. Therefore, $16 is a _______________________

answer.

Shalika needs to buy at least 60 buns. Hamburger buns come in packages of8 buns. A package of buns costs $2. Use the operation of division to find thenumber of packages she needs to buy. Use the operation of multiplication tofind the total cost of the buns. 60 buns � 8 per package � 7 R4. Shalikaneeds to buy 8 packages. 8 packages � $2 per package � $16. Shalika willpay $16 for the hamburger buns. If Shalika buys 5 packages of buns, shewill have 40 buns and spend $10. Five packages of buns is not enough. IfShalika buys 10 packages of buns, she will have 80 buns and spend $20.Ten packages of buns is too many. Shalika will spend more than $10 butless than $20 in order to have 60 buns. Therefore, $16 is a reasonableanswer.

Objective 6

125

Sometimes the numbers in a problem can make it seem difficult. Youcan change the numbers in the problem so that you can solve a simplerproblem. Then use the same steps to solve the original problem.

An unopened box of cereal weighs a total of 1 pound 9 ounces, andthis includes 2 ounces of raisins. What fractional part of this totalweight is raisins?

The numbers in this problem represent two different units of weight.This could make it complicated to solve. Change the numbers sothey are easier to work with.

● Suppose the box of cereal weighed 10 ounces and the raisins weighed 2 ounces.

● Ask yourself: What fractional part of 10 is 2?

● 2 is part of the total weight and is the numerator of thefraction.10 is the total weight and is the denominator of the fraction.

The answer for this easier problem would be �120�.

Use the same method to help you find the answer to the originalproblem.

● The box of cereal weighs 1 pound 9 ounces.

● You need the weight of the box of cereal in ounces if you aregoing to compare it to the weight of the raisins.

● Use the Mathematics Chart to convert 1 pound 9 ounces toounces.

1 pound � 16 ounces

● 1 pound 9 ounces � 16 ounces � 9 ounces � 25 ounces

● The box of cereal weighs 25 ounces.

● The raisins weigh 2 ounces.

● What fractional part of 25 is 2?

● 2 is part of the total weight and is the numerator of thefraction.25 is the total weight and is the denominator of the fraction.

The weight of the raisins is the weight of the box of cereal.225

Objective 6

126

Another way to solve a problem is to work backward. When workingbackward, you can start with the information that is given last.

Some fifth-grade students volunteered to clean up a park. Theyworked one morning for 2 hours. Then they took a 30-minute lunchbreak. After lunch they worked for 1 hour 35 minutes. The studentsleft the park at 2:00 P.M. At what time did the students start cleaningthe park?

To find the time the students started cleaning the park, use theinformation that is given last.

● The students left the park at 2:00 P.M.

● The students worked for 1 hour 35 minutes after lunch. What is 1 hour 35 minutes before 2:00? From 2:00 count back1 hour. Then count back 35 minutes.

1 hour before 2:00 is 1:00 (Think: 2 � 1 � 1)

35 minutes before 1:00 is 12:25(Think: 60 minutes � 35 minutes � 25 minutes)

The students finished lunch at 12:25 P.M.

● The lunch break lasted 30 minutes. What time did the lunchbreak start? From 12:25 count back 30 minutes.

12:25 � 25 minutes � 12:00

12:00 � 5 minutes � 11:55(Think: 25 minutes � 5 minutes � 30 minutes)

The students started lunch at 11:55 A.M.

● The students worked for 2 hours before lunch. What is 2 hoursbefore 11:55?

2 hours before 11:55 is 9:55 (Think: 11 � 2 � 9)

The students started cleaning the park at 9:55 A.M.

121110

9

87 6 5

4

32

1

Objective 6

127

Try ItTwo cans of fruit weigh 4 pounds. Four cans weigh 8 pounds. Sixcans weigh 12 pounds. If each can weighs the same, how muchwould 7 cans of fruit weigh?

One way to solve this problem is to make a table to help youorganize the data. Then look for a pattern in the data. Write themissing numbers in the table below.

Look for a pattern in the table.

The pattern is to multiply the number of cans by _______ .

To find the weight of 7 cans, multiply _______ � _______ .

Seven cans of fruit weigh _______ pounds.

The pattern is to multiply the number of cans by 2. To find the weight of 7 cans, multiply 7 � 2. Seven cans of fruit weigh 14 pounds.

Number Weightof Cans (pounds)

2 4

4 8

6 12

7 14

Cans of Fruit

Number Weightof Cans (pounds)

2 4

4

6

7

Cans of Fruit

Objective 6

128

Try ItThe perimeter of a gym floor is 180 feet. The floor is shaped like a rectangle. If the width of the gym floor is 40 feet, what is itslength?

One way to solve this problem is to draw a picture.

The floor is ________ feet wide.

The opposite sides of a rectangle are _______________ .

Therefore, the gym floor has two sides that are ________ feet wide.

The sum of the two widths of the gym floor is ________ feet.

Subtract ________ from ________ to find the sum of the two lengths of the gym floor.

________ � ________ � ________

The sum of the two lengths of the gym floor is _______________ feet.

Divide ________ by ________ to find the floor’s length.

________ � ________ � ________

The length of the gym floor is ________ feet.

The floor is 40 feet wide. The opposite sides of a rectangle are congruent.Therefore, the gym floor has two sides that are 40 feet wide. The sum of the two widths of the gym floor is 80 feet.Subtract 80 from 180 to find the sum of the two lengths of the gym floor: 180 – 80 = 100. The sum of the twolengths of the gym floor is 100 feet.Divide 100 by 2 to find the floor’s length:100 ÷ 2 = 50. The length of the gym flooris 50 feet.

Gym floorP � 180 ft40 ft

?

What dimensionsdo you need tofind the perimeterof a rectangle?

Objective 6

129

Try ItMatthew is 5 years older than his sister Janet. The sum of their ages is 37.How old are Matthew and Janet?

Use the guess-and-check strategy.

1st guess: Suppose Janet is 12 years old.

Then Matthew is 12 � _______ years old. Matthew is _______ years old.

The sum of their ages can be represented by: 12 � _______ � _______

This guess is too large small .(circle one)

Try a larger smaller number for Janet’s age.(circle one)

2nd guess: Suppose Janet is 20 years old.


The sum of their ages can be represented by: ______ � ______ � ______

This guess is too large small .(circle one)

Try a number for Janet’s age that is between _______ and _______ .

3rd guess: Suppose Janet is 16 years old.


The sum of their ages can be represented by: ______ � ______ � ______

This guess is ____________________________ .

Janet is _______ years old, and Matthew is _______ years old.

If Janet is 12, then Matthew is 12 � 5, or 17. The sum of their ages is 12 � 17 � 29.This guess is too small. Try a larger number for Janet’s age. If Janet is 20, thenMatthew is 20 � 5, or 25. The sum of their ages is 20 � 25 � 45. This guess is toolarge. Try a number for Janet’s age that is between 12 and 20. If Janet is 16, thenMatthew is 16 � 5, or 21. The sum of their ages is 16 � 21 � 37. This guess iscorrect. Janet is 16 years old, and Matthew is 21 years old.

Objective 6

130

Jim bought 6 sandwiches for $5 each. He gave the cashier two $20 bills. What steps will show how much change Jim should receive from the cashier?

The question doesn’t ask for the amount of change Jim shouldreceive. It asks about the steps to find the solution. Think about themath that needs to be done to find the solution.

● First use multiplication to find the total cost of the sandwiches.Find the product of 6 and $5.

● Then use multiplication to find the total amount he gave thecashier. Find the product of 2 and $20.

● Then use subtraction to find the difference between the amountJim gave the cashier and the total cost of the sandwiches.

In order to know how much change Jim should receive from thecashier, subtract the product of 6 and 5 from the product of 2 and 20.

How Do You Change Words into Math Language and Symbols?An important part of solving story problems is to rewrite the problemusing math language and symbols. The words in the problem will giveyou clues about what operations to use.

Sometimes you will not be asked to solve a problem. Instead, you willbe asked what math needs to be done to solve the problem.

The sum is the answer toan addition problem. Thedifference is the answerto a subtraction problem.The product is the answerto a multiplicationproblem. The quotient isthe answer to a divisionproblem.

Objective 6

131

Try ItA store had a sale on backpacks. On Monday the store sold 65 backpacks. For the next 4 days, the store sold 25 backpacks aday. How can you find how many backpacks the store sold in these5 days?

Think about the math that needs to be done to find a solution.

On Monday the store sold _________ backpacks.

The store sold _________ backpacks a day for the next 4 days.

Use the operation of __________________ to find how many

backpacks were sold during the 4 days.

To find how many backpacks were sold during these 5 days,

_________ 65 to the _________ of 25 and 4.

On Monday the store sold 65 backpacks. The store sold 25 backpacks a dayfor the next 4 days. Use the operation of multiplication to find how manybackpacks were sold during the 4 days. To find how many backpacks weresold during these 5 days, add 65 to the product of 25 and 4.

Objective 6

132

Which statement about this group of numbers is true?

3, 4, 6, 12, 24

1. All the numbers are multiples of 2.

2. All the numbers are factors of 24.

3. All the numbers are divisible by 3.

● The first statement is about multiples. The multiples of 2 are2, 4, 6, 8, 10, … The number 3 is not a multiple of 2. The firststatement is not true.

● The second statement is about factors. The factors of 24 are1, 2, 3, 4, 6, 8, 12, 24. All the numbers listed in the problemare factors of 24. This statement is true.

● The third statement is about the numbers being divisible by 3.A number is divisible by another number if there is noremainder when you divide.

3 � 3 � 1 There is no remainder, so 3 is divisible by 3.

4 � 3 � 1 R1 There is a remainder, so 4 is not divisible by 3.The third statement is not true.

The second statement is true. All the numbers in the group arefactors of 24.

What Is Logical Reasoning?Logical reasoning is thinking about something in a way that makessense. Being logical can mean looking for a pattern or looking for whata group has in common.

Sometimes you will need to apply what you know about certain mathconcepts to determine what characteristics a set of numbers have incommon.

Objective 6

133

Another way to use logical reasoning is to look for a commoncharacteristic in a set of figures or objects.

Mary drew the figures below and named them quisks.

Notice that each of Mary’s quisks is made up of two shapes: one onthe outside and one on the inside. Count the number of sides oneach shape.

● Figure A is a square with a triangle inside of it. The square has4 sides, and the triangle has 3 sides.

● Figure B is a pentagon with a rectangle inside of it. Thepentagon has 5 sides, and the rectangle has 4 sides.

● Figure C is an octagon with a 7-sided figure inside of it. Theoctagon has 8 sides, and the inner figure has 7 sides.

In Mary’s quisks, the shape on the outside has one more side thanthe shape on the inside.

Now look at Figures D and E. Which of these could be a quisk?

● Figure D is a trapezoid with a pentagon inside of it. Thetrapezoid has 4 sides, and the pentagon has 5 sides. The shapeon the outside has one fewer side than the shape on the inside.Figure D is not a quisk.

● Figure E is a hexagon with a pentagon inside of it. Thehexagon has 6 sides, and the pentagon has 5 sides. The shapeon the outside has one more side than the shape on the inside.Figure E is a quisk.

D E

A B C

Special made-up words,such as quisks, may beused to name a set ofexamples.

Objective 6

134


Try ItMrs. Cole sells eggs from her farm. She separates her eggs into threegroups: small, medium, and large. The size of the egg is determinedby its mass as measured in grams.

This list shows the masses of some medium-size eggs.

Medium-size eggs: 52.3 grams 49.6 grams 56.2 grams

This list shows the masses of some eggs that were not put into themedium-size group.

Not medium-size eggs: 47.3 grams 58.1 grams 48.0 grams

Put the masses of the medium-size eggs in order from least togreatest.

__________ __________ __________

A medium-size egg has a mass between __________ grams and__________ grams.

The eggs that were not put into the medium-size group were either__________ or __________ than the medium-size eggs.

Which eggs shown below could be medium-size eggs?

Look at the pictures of the eggs. According to the rule, which eggcould be a medium-size egg?

Egg X is is not a medium-size egg. Its mass is too __________.(circle one)

Egg Y is is not a medium-size egg. Its mass is too __________.(circle one)

Egg Z is is not a medium-size egg. Its mass is between(circle one)

__________ and __________ grams.

The masses of medium-size eggs from least to greatest are: 49.6, 52.3, and56.2. A medium-size egg has a mass between 49.6 grams and 56.2 grams.The eggs that were not put into the medium-size group were either smalleror larger than the medium-size eggs. Egg X is not a medium-size egg. Itsmass is too large. Egg Y is not a medium-size egg. Its mass is too small.Egg Z is a medium-size egg. Its mass is between 49.6 and 56.2 grams.

58.3 grams

Egg X

45.9 grams

Egg Y

54.2 grams

Egg Z

Objective 6

135

Question 55Tim needs to buy the following items at the store.The table shows the lowest and highest prices ofeach item.

Tim’s mother gave him $10.00 to buy the items.What could Tim do to determine whether he hasenough money to buy these items?

A Add all the lowest prices together

B Subtract the lowest-priced bread from thehighest-priced bread

C Add all the highest prices together

D Subtract the sum of the highest-priced milkand bread from the sum of the highest-pricedcheese and peanut butter

Question 56There were 375 customers served at a restaurantlast week. If each customer paid between $6 and$10, which of the following could be the totalamount of money paid by these customers lastweek?

A $4,000

B $3,000

C $391

D $6,000

Question 57The students at Dayton Elementary Schoolcollected cans to recycle. The table below showsthe weight in pounds of the cans that Mr. Gómez’s class collected.

Mr. Gómez’s Class

Ms. Miller’s class collected twice as many pounds of cans as Mr. Gómez’s class did. Ms.Warren’s class collected 10 pounds more thanMs. Miller’s class collected. What is the totalweight of cans collected by the three classes?

A 594 pounds

B 95 pounds

C 64 pounds

D 145 pounds

Question 58There are four children in the Smith family.Only one of the children is older than Pete.Sarah is younger than Brad. Kevin is older thanBrad. Which lists the children in order fromyoungest to oldest?

A Brad, Sarah, Kevin, Pete

B Sarah, Brad, Pete, Kevin

C Pete, Sarah, Brad, Kevin

D Sarah, Kevin, Pete, Brad

Day Weight of Cans(pounds)

Monday 6 pounds Tuesday 8 pounds Wednesday 4 pounds Thursday 5 pounds Friday 4 pounds





Items Needed

Item LowestPrice

$1.39Milk

$1.99Orange juice

$1.29Bread

$2.50Cheese

$1.99Peanut butter

HighestPrice

$1.59

$2.50

$2.50

$2.99

$2.39

Objective 6

136

Question 59Tickets to a county fair cost $6.75 each for adultsand $3.25 each for children. Which of thefollowing could be used to determine the cost for1 adult and 2 children to go to the fair?

A Add $6.75, $3.25, and $3.25

B Add $6.75, $6.75, and $3.25

C Subtract $3.25 from $6.75

D Subtract $6.75 from $3.25

Question 60Lin’s father is covering the floor in his office with carpet. The carpet sells for $12 a squareyard. Which of the following will help Lin’sfather find the total cost of the carpet for hisoffice?

A The height of the office

B The perimeter of the floor

C The volume of the office

D The area of the floor

Question 61Two adults and 13 children are going on acamping trip. They need to buy one sleeping bagfor each person. Each sleeping bag costs $30.What is one way to find the total cost of thesleeping bags?

A Multiply the sum of 13 and 2 by 30

B Add 30 to the sum of 13 and 2

C Divide 30 by the sum of 13 and 2

D Subtract the sum of 13 and 2 from 30

Question 62Which statement about the shapes belowappears to be true?

A They all have at least 1 right angle.

B They all have at least 2 lines of symmetry.

C They all have at least 1 acute angle.

D They all have at least 1 pair of parallel sides.

Question 63The group of numbers below have something incommon.

20, 8, 16, 24

Which of the following describes the numbers inthis group?

A Multiples of 8

B Factors of 24

C Numbers that are divisible by 4

D Multiples of 6




Answer Key: page 147Answer Key: page 147

W X

Y Z

Objective 6

137


Question 64The sign below shows the prices at a hot-dog stand.

Kendra bought 12 hot dogs. How much did she save by purchasing the hot dogs with a coupon ratherthan buying 12 hot dogs at the regular price?

A $24

B $36

C $3

D $4

$2 eachor

3 for $5 with a coupon

Hot Dogs

Objective 6

138


School Supplies

Item Price

Pack of pens

Pack of pencils

Pack of erasers

Notebook

Folder

$1.50

$1.00

$0.50

$2.00

$1.00

Question 65Niko bought his school supplies at the store. The table below shows the prices, including tax.

Niko spent $10.00 at the store. He bought 3 notebooks and 2 folders. Which additional items couldNOT have been purchased by Niko?

A 1 pack of pens and 1 pack of erasers

B 1 pack of pens and 1 pack of pencils

C 2 packs of pencils

D 1 pack of pencils and 2 packs of erasers

139

Question 1 (page 36)

C Correct. Look at this number in the place-valuechart.

The numeral 28,162,751 has the digit 8 in themillions place.


B Correct. Write the number in a place-value chart.Look at how the commas separate the numberinto groups of three digits each.Write three hundred billion in the chart.Write seven hundred eighty thousand in the chart.Write four hundred thirty-nine in the chart.Notice that there are no ten billions, billions,hundred millions, ten millions, or millions in thenumber. There are no thousands in the number,either. Write zeros in these places in the chart.

The number is written as 300,000,780,439.


C Correct. Two numbers have a digit in the billionsplace, 5,301,229,038 and 3,033,431,602. Since 5 � 3, then 5,301,229,038 is the greaternumber and should be listed first. Then3,033,431,602 should be listed second.The two remaining numbers, 231,392,159 and204,515,724, have a 2 in the hundred millionsplace, but different digits in the ten millionsplace. Since 3 � 0, then 231,392,159 is greaterthan 204,515,724. The correct order is as follows:

5,301,229,0383,033,431,602231,392,159204,515,724.


A Correct. First, compare the digits in the placewith the greatest value, the ones place. All the

numbers have a 0 in the ones place. Look at thenext place value to the right, the tenths place.Compare the digits in the tenths place.Since 1 is less than 3 or 9, the two numbers with1 in the tenths place are the smallest. Look atthe hundredths place of 0.11 and 0.16. Since1 6, then 0.11 is less than 0.16. List 0.11 first,followed by 0.16.Look at the tenths place of the two remainingnumbers, 0.33 and 0.9. Since 3 9, then 0.33 isless than 0.9. The number 0.33 should be listedthird, and 0.9 should be listed last. The correctorder is as follows:

0.11 0.16 0.33 0.9


A Incorrect. To compare 7.424 to 7.52, line up thedecimal places in the numbers.

7.4247.52

The numbers are the same in the ones place. Tocompare the numbers, look at the digits in thetenths place.Since 5 � 4, the number 7.52 � 7.424.

B Incorrect. To compare 7.424 to 7.43, line up thedecimal places in the numbers.

7.4247.43

The digits in the ones place and the tenths placeare the same. To compare the numbers, look atthe digits in the hundredths place.Since 3 � 2, the number 7.43 � 7.424.

C Incorrect. To compare 7.424 to 7.425, line up thedecimal places in the numbers.

7.4247.425

The digits in the ones place, the tenths place,and the hundredths place are the same. Comparethe digits in the thousandths place.Since 5 � 4, the number 7.425 � 7.424.

D Correct. To compare 7.424 to 7.42, line up thedecimal places in the numbers.

7.4247.42

The digits in the ones place, the tenths place,and the hundredths place are the same. Comparethe digits in the thousandths place. The number7.42 does not have a digit in the thousandthsplace.

Objective 1

Mathematics Answer Key

BillionsHundred Ten

MillionsHundred Ten

Thousands Hundreds Tens OnesMillions Millions Thousands Thousands

2 8 1 6 2 7 5 1

Hundred TenBillions

Hundred Ten Millions

Hundred TenThousands Hundreds Tens Ones

Billions Billions Millions Millions Thousands Thousands

3 0 0 0 0 0 7 8 0 4 3 9


140

Place a 0 in the thousandths place of the number7.42 to show that the value in the thousandthsplace is 0. The number 7.42 and the number7.420 are equal. Now compare the digits in thethousandths place.

7.4247.420

Since 0 4, the number 7.42 7.424.


C Correct. Look at the number in the place-valuechart below.

First, read the number to the left of the decimalpoint: one. Next, say the word and to representthe decimal point. Read the number to the rightof the decimal point: thirty-five. Then say theplace-value name of the last digit on the right:thousandths. Read the number 1.035 as one andthirty-five thousandths.


B Correct. The improper fraction can be writtenas a mixed number. First divide the numeratorby the denominator.

7 � 3 � 2 R1The quotient becomes the whole number, theremainder becomes the numerator, and thedenominator is 3. The improper fraction isequivalent to the mixed number 2 .


A Incorrect. Divide both the numerator and thedenominator by 3.

is equivalent to .

B Incorrect. Multiply both the numerator anddenominator by 5.

is equivalent to .

C Incorrect. Multiply both the numerator anddenominator by 2.

is equivalent to .

D Correct. There is not a fraction equal to 1 that

you can multiply or divide by to get .

is not equivalent to .


A Correct. To compare fractions with differentdenominators, first find a common denominator.List some of the multiples of each denominator.

Multiples of 8: 8, 16, 24, 32, 40Multiples of 12: 12, 24, 36, 48

A number that is in both lists is 24.

A common denominator for and is 24.

Rewrite and to have a common denominator

of 24.

Now look at the numerators of both fractions. The number 3 is greater than the number 2, so

� . This means that � .


D Correct. The model shows thousandths. 150 ofthe thousand equal parts are shaded. Use aplace-value chart to write the fraction as adecimal.

There are no ones. Put a 0 in the ones place, andthen write the 150 to the right of the decimalpoint. The fraction can be written as 0.150.


B Correct. Bob spent $11.95. He gave the cashier$20.00. To find Bob’s change, subtract.Remember to regroup when necessary.

9 91 10 10 10

$2/0/.0/0/– 11.95

$8.05Bob received $8.05.

1501,000

112

18

224

324

224

��

1 � 212 � 2

324

��

1 � 38 � 3

112

18

112

18

39

512

512

39

39

618

618

��

3 � 29 � 2

39

1545

1545

��

3 � 59 � 5

39

13

13

��

3 � 39 � 3

13

73

73

Hundreds Tens Ones . Tenths Hundredths Thousandths

1 . 0 3 5


0 . 1 5 0


141


B Correct. Since all the cases have the samenumber of cookies, you can multiply.

Karen ordered 4,320 cookies.


The correct answer is $13. To find how mucheach person spent, divide $156 equally among 12 friends.

Each friend spent $13.


C Correct. Use division to separate 54 into groupsof 5.

The quotient shows that Mr. Cohen needs 10 packages of notepads. The remainder showsthat 4 students will not have a notepad. He willneed to buy another package. Mr. Cohen needs to buy 11 packages of notepads.


A Correct. A factor of a number divides into thenumber with no remainder. Look at the list offactors of each number.Factors of 12: 1, 2, 3, 4, 6, 12Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36Only the numbers 1, 2, 3, 4, 6, and 12 appear ineach list of factors. They are the common factorsof the three numbers.


C Correct. To find the number of yards of rope Tristan has left, subtract 2 from 4 .

The number sentence 4 � 2 � can be used to find how many yards of rope Tristan hasleft.


D Correct. The question asks about how farMonica’s family traveled altogether. Round thenumbers and add them to find a reasonableestimate.

59.6 rounds to 6079.5 rounds to 8089.8 rounds to 9070.3 rounds to 70

Add: 60 � 80 � 90 � 70 � 300. Monica’s familytraveled about 300 miles on their trip.


A Correct. The question asks which is closest to theamount of money made on the tickets. Round 417to 400 and round $3.25 to $3.00. Multiply 400 by3 to find a reasonable estimate.

400 � 3 � 1,200About $1,200 was made in ticket sales.


B Correct. Look at the pairs of numbers in thetable.

4 and 158 and 1912 and 23

The difference in the numbers is 11.15 � 4 � 1119 � 8 � 1123 � 12 � 11

Jeanette is 11 years younger than Mark.

Objective 2

14

34

34

14

10 R45�5��4�

� 5 04

� 0 4

0

1

2

3

4

5

6

7

8

9

0

1

2

3

4

5

6

7

8

9

0

1

2

3

4

5

6

7

8

9

1 3

1312�1�5�6�� 12

36� 36

0

4 4

288� 15_____1440

� 2880______4,320


142


B Correct. Look at the first two numbers in thepattern: 1 and 7. The sum of 1 and 7 is 8. Look at the second and third numbers in the pattern:7 and 8. The sum of 7 and 8 is 15. Now look atthe pattern of all the numbers.

1, 7, 8, 15, 23, 38, 61, 991 � 7 � 87 � 8 � 158 � 15 � 2315 � 23 � 3823 � 38 � 6138 � 61 � 99

Each number is the sum of the 2 numbers before it.


D Correct. Look for a rule. The cost of tickets isequal to $2 multiplied by the number of tickets.

$2 � 2 � $4$2 � 4 � $8$2 � 6 � $12$2 � 10 � $20

The equation t � 2 � 8 can be used to find thecost of 8 tickets.


B Correct. Each of the factor pairs multiply toequal 24.

1 � 24 � 242 � 12 � 243 � 8 � 24

The factor pair missing from the list is 4 � 6because 4 � 6 � 24.


A Incorrect. A prime number is a number with onlyitself and 1 as factors. The factors of 27 are 1, 3,9, and 27. The number 27 is not prime.

B Incorrect. A prime number is a number with onlyitself and 1 as factors. The factors of 39 are 1, 3,13, and 39. The number 39 is not prime.

C Incorrect. A prime number is a number with onlyitself and 1 as factors. The factors of 33 are 1, 3,11, and 33. The number 33 is not prime.

D Correct. A prime number is a number with onlyitself and 1 as factors. The only factors of 29 are1 and 29. The number 29 is prime.


A Correct. A prime number is a number that hasonly 1 and itself as factors. The only factors ofthe number 3 are 1 and 3. The only factors of thenumber 5 are 1 and 5. The numbers 4 and 6 havemore factors. They are not prime numbers. Theyare composite numbers.


C Correct. The table shows that the total numberof peanuts is 40 times the number of ounces ofpeanuts.

3 times 40 equals 1205 times 40 equals 20010 times 40 equals 40020 times 40 equals 800


A Correct. Add the number of minutes Giannaspends on each subject to find the total numberof minutes she spends on her homework eachnight. The equation 20 � 15 � 30 � mrepresents the total number of minutes Giannaspent on her homework.


A Incorrect. This figure has no sides.B Correct. Parallel sides are sides that are always

the same distance apart. Exactly two oppositesides in this figure appear to be parallel. Theother two opposite sides do not appear to beparallel.

C Incorrect. This figure appears to have no parallelsides.

D Incorrect. This figure appears to have two pairsof parallel sides. The question asks for the figurewith exactly one pair of parallel sides.


C Correct. Since WXYZ is a rectangle, it has fourright angles. Line segments WX and XY intersectto form a right angle. Two line segments are

Objective 3


143

perpendicular if they intersect to form a rightangle. Therefore, line segment WX isperpendicular to line segment XY.


A Correct. The cylinder is the only figure with two bases.


D Correct. The bank is a square pyramid. A squarepyramid has 5 vertices, 8 edges, and 5 faces. Sothis figure has 3 more edges than vertices.


A Incorrect. This drawing shows a slidingmovement diagonally. It is a translation.

B Incorrect. This drawing shows a flippingmovement across a vertical line. It is a reflection.

C Incorrect. This drawing shows a slidingmovement diagonally. It is a translation.

D Correct. This drawing shows a turningmovement around a point. It is a rotation.


B Correct. The first picture shows a translation(sliding movement), the second picture shows areflection (flipping movement), and the thirdpicture shows a rotation (turning movement)around a point outside the figure.


B Correct. The point (3, 4) appears to be on line n.The other ordered pairs are not on line n.


A Incorrect. The point (4, 3) is 4 units to the rightof the origin and 3 units above the origin. This isthe location of the slide.

B Incorrect. The point (1, 2) is 1 unit to the right ofthe origin and 2 units above the origin. This isthe location of the tree.

C Correct. The point (2, 4) is 2 units to the right ofthe origin and 4 units above the origin. This isthe location of the sandbox.

D Incorrect. The point (5, 6) is 5 units to the rightof the origin and 6 units above the origin. This isthe location of the swing.


D Correct. To find the volume of the prism, use theformula for the volume of a rectangular prismfrom the Mathematics Chart.

V � l � w � hV � 5 � 2 � 3

V � 30The volume of the prism is 30 cubic centimeters.


C Correct. One way to solve this is to show thetimes and temperatures in a table. Thetemperature increases 5°F each hour.

The temperature at 2:00 P.M. will be 75°F.


The correct answer is 360. Use the perimeterformula on the Mathematics Chart: P � (2 � l) � (2 � w).

Objective 4

Bases

TimeTemperature

(°F) 8:00 A.M. 45

9:00 A.M. 50

10:00 A.M. 55

11:00 A.M. 60

12:00 P.M. 65

1:00 P.M. 70

2:00 P.M. 75


144

Substitute the numbers representing length andwidth for the letters l and w in the formula.

P � (2 � 110) � (2 � 70)P � 220 � 140

P � 360The perimeter of the playground is 360 yards.


A Correct. The start time is 10:40 A.M. The triptakes 3 hours 45 minutes.First find the time when 3 hours have passed. From 10:40 A.M. to 11:40 A.M. is 1 hour. From 11:40 A.M. to 12:40 P.M. is 1 hour.From 12:40 P.M. to 1:40 P.M. is 1 hour.From 10:40 A.M. to 1:40 P.M., 3 hours have passed. Next find the time when 45 more minutes havepassed. Look at the clock below.

The bus arrives at Harry’s destination at 2:25 P.M.


B Correct. The cell phone has the shape of arectangular prism. The formula for the volume ofa rectangular prism is V � l � w � h. Theequation V � 8 � 3 � 1 can be used to find thevolume of the cell phone.


C Correct. From 1:30 to 2:30 is 1 hour. From 2:30 to 3:00 is 30 minutes. From 3:00 to 3:25 is

25 minutes. Add the minutes: 30 minutes � 25 minutes � 55 minutes. Band practice was 1 hour 55 minutes.


D Correct. According to the Mathematics Chart,1 kilometer � 1,000 meters. To convert a largerunit to a smaller unit, multiply:50 kilometers � 1,000 meters per kilometer �50,000 meters.There are 50,000 meters in 50 kilometers.


B Correct. The length of the drawing is about5 centimeters. The width of the drawing is about4 centimeters. Use the formula for the perimeterof a rectangle to find the perimeter of thedrawing.

P � (2 � l) � (2 � w)P � (2 � 5) � (2 � 4)

P � 10 � 8P � 18

The perimeter of the drawing is 18 centimeters.Each centimeter in the drawing represents 1 meter. The perimeter of the actual patio is 18 meters.


C Correct. Use the formula for the area of arectangle to find the length of the sidewalk.

A � l � w856 � l � 8856 � 8 � l

107 � lThe length of the sidewalk is 107 feet.


A Correct. Convert feet and inches to inches. Thereare 12 inches in a foot. Multiply 6 feet by 12 inches: 6 � 12 � 72. There are 72 inches in 6 feet. Jesse’s father is 6 feet 2 inches. Add 2 inches to 72 inches: 72 � 2 � 74.Jesse’s father is 74 inches tall.

121110

9

87 6 5

4

32

1

0

1

2

3

4

5

6

7

8

9

0

1

2

3

4

5

6

7

8

9

0

1

2

3

4

5

6

7

8

9

63 0


145


B Correct. The probability of an event occurring isequal to the fraction:

Add to find the total number of shirts Roxy hasin her closet.

3 � 2 � 1 � 4 � 10 Roxy has 10 shirts in her closet. Use 10 as thedenominator of the fraction. The favorableoutcome is selecting a white shirt. Roxy has 4 white shirts in her closet. Use 4 as thenumerator of the fraction. The probability thatRoxy will select a white shirt is .


C Correct. The probability that Roberto will selecta crayon is shown by the following fraction:

The favorable outcome is selecting a crayon.There are 28 crayons. The numerator is 28.There are a total of 12 � 30 � 28 � 70 suppliesin the box. The denominator is 70. Theprobability that Roberto will select a crayonis 28 out of 70, or .


A Correct. Alaine has 7 peppermint candies in herbag. She has fewer peppermint candies than anyother flavor of candy in the bag. So she is leastlikely to pick a peppermint candy.


D Correct. Use the data of the shots alreadyblocked to predict the number of shots Mark willblock. The probability of an event occurring isequal to the fraction:

In this experiment a favorable outcome isblocking a shot. Mark has blocked 48 shots. In this experiment the number of possibleoutcomes is the total number of shots on goal.There have been 100 shots on goal.

So the probability that Mark will block a shotis . How many times out of 50 does this represent?Find an equivalent fraction with a denominatorof 50.

You can predict that Mark will block 24 out ofthe next 50 shots on goal.


A Correct. To show all the possible outcomes of onetype of meat and one condiment, make a list. Listeach type of meat with each condiment.


B Correct. Point L is 3 units to the right of theorigin and 4 units above the origin. Thecoordinates of point L are (3, 4).Point M is 6 units to the right of the origin and2 units above the origin. The coordinates of point M are (6, 2).Point N is 10 units to the right of the origin and8 units above the origin. The coordinates of point N are (10, 8).The table in answer choice B shows thesecoordinates.


C Correct. The mode of a set of data is the valuethat appears most frequently. Only the number 3 appears more than once. The mode of this setof data is 3.


C Correct. The range is the difference between thehighest price and the lowest price. The highestprice for the bike is $110. The lowest price for thebike is $80. Subtract to find the difference.

$110 � $80 � $30The range of the prices for a Stunt-Pro bicycle is $30.


A Correct. The median of a set of data is the middlevalue when the data are listed in order fromleast to greatest.

2450

��

48 � 2100 � 2

48100

number of favorable outcomes��number of possible outcomes

2870


410


Objective 5


146

List the temperatures in order from least togreatest.

47°F 50°F 50°F 52°F 53°F 58°F To find the middle value, cross out one value oneach end until you reach the middle.

47 50 50 52 53 58The numbers in the middle are 50 and 52. Findthe number halfway between 50 and 52.

50 51 52The median temperature for the time period is51°F.


A Incorrect. The data represented in the line graphdo not match the data in the table. This linegraph shows 35 books checked out of the libraryon Wednesday. The table shows 25 books werechecked out on Wednesday.

B Correct. This bar graph correctly represents thedata in the table. Compare the length of each barto the data given in the table. The graph and thetable agree.

C Incorrect. The data represented in this bar graphdo not match the data in the table. The graphdoes not have bars of the correct lengths forWednesday, Thursday, or Friday.

D Incorrect. The data represented in the pictographdo not match the data in the table. Thepictograph does not show the correct informationfor Thursday or Friday.


A Correct. Before Tim can determine whether hehas enough money to buy the items, he must findout the least amount of money he will need forall the items. To do this, Tim could add all thelowest prices together. Then he will knowwhether $10.00 will be enough to buy all theitems.


B Correct. If each customer paid the lowestamount, $6, the total amount of money paidwould be $6 � 375. Multiply to find the product: 6 � 375 � 2,250.

The least amount of money the customers wouldhave paid is $2,250. But not all customers paid$6 each.If each customer paid the highest amount, $10,the total amount of money paid would be $10 � 375. Multiply to find the product: 10 � 375 � 3,750. The highest amount of money the customerswould have paid is $3,750.An amount of money between $2,250 and $3,750would be reasonable. Only $3,000 is between$2,250 and $3,750.


D Correct. First add the numbers in the table tofind the weight in pounds of the cans Mr.Gómez’s class collected.

6 � 8 � 4 � 5 � 4 � 27Mr. Gómez’s class collected 27 pounds of cans.Ms. Miller’s class collected twice as many poundsas Mr. Gómez’s class did. Multiply by 2 to find aweight that is twice as large.

2 � 27 � 54Ms. Miller’s class collected 54 pounds of cans.Ms. Warren’s class collected 10 pounds more thanMs. Miller’s class did. Add 10 to the weight ofcans collected by Ms. Miller’s class.

54 � 10 � 64Ms. Warren’s class collected 64 pounds of cans.Add to find the total weight of cans collected bythe three classes.

27 � 54 � 64 � 145 The classes collected 145 pounds of cans in all.


B Correct. One way to answer this question is towork backward.Start with the last piece of information: Kevin isolder than Brad. List the children from youngestto oldest. Write Kevin’s name to the right ofBrad’s.

Brad, KevinUse the next piece of information: Sarah isyounger than Brad. Write Sarah’s name to theleft of Brad’s.

Sarah, Brad, Kevin

Objective 6


147

Use the next piece of information: only one of thechildren is older than Pete. This means Kevin isthe oldest. Write Pete’s name to the left ofKevin’s.

Sarah, Brad, Pete, Kevin


A Correct. Add $6.75, $3.25, and $3.25 to find thetotal cost for one adult and two children to go tothe fair.


D Correct. The total cost of the carpet is equal tothe area of the floor in square yards multipliedby the cost of the carpet per square yard. Lin’sfather needs to know the area of the floor to findthe total cost of the carpet.


A Correct. First find the total number of people.There are 2 adults and 13 children going on thetrip. The sum of 13 and 2 can be used torepresent the total number of people.Each sleeping bag costs $30. The cost of thesleeping bags is $30 times the number of people.Multiply the sum of 13 and 2 by 30 to find thetotal cost of the sleeping bags.


A Incorrect. A right angle is formed byperpendicular lines. Figures W and Z do not have perpendicular lines.

B Incorrect. Only Figure W has at least two lines ofsymmetry.

C Correct. An acute angle is smaller than a rightangle. Each figure has at least one acute angle.

D Incorrect. Figure W does not have a pair ofparallel sides.


C Correct. A number is divisible by 4 if there is noremainder when you divide it by 4. Each of thenumbers in the group can be divided by 4 withno remainder.

20 � 4 � 58 � 4 � 2

16 � 4 � 424 � 4 � 6


D Correct. Hot dogs cost $2 each without a coupon.If Kendra bought 12 hot dogs without a coupon,the cost would be 12 � $2, or $24.To find how much Kendra paid for 12 hot dogswith a coupon, draw a picture of 12 hot dogs andcircle groups of 3. Each group costs $5.

Kendra needed to buy 4 groups of 3 hot dogs.Multiply to find how much 4 groups cost:5 � 4 � 20. The 12 hot dogs cost $20 with acoupon. Subtract to find the difference between buying12 hot dogs without a coupon and buying 12 hotdogs with a coupon.

24 � 20 � 4Kendra saved $4 by purchasing the hot dogs witha coupon.


B Correct. First find the amount that Niko spenton 3 notebooks and 2 folders.

3 notebooks 3 � $2 � $62 folders 2 � $1 � $2

Add to find the total: $6 � $2 � $8. Niko spent$8 on 3 notebooks and 2 folders. Niko spent $10at the store. Subtract the amount he spent from$10 in order to find how much he spent onadditional items.

$10 – $8 � $2Niko spent $2 more on additional items. Onepack of pens costs $1.50, and 1 pack of pencilscosts $1. The total for 1 pack of pens and 1 pack of pencils is $2.50. Niko only spent $2 more. Hecould not have purchased 1 pack of pens and 1 pack of pencils because they cost more than $2.

$5 $5 $5 $5

10

23

45

67

89

1011

1213

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1617

1819

20

Cen

timet

ers

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0Inches

Continued on the next side


LENGTH

Metric Customary




1 foot = 12 inches

CAPACITY AND VOLUME

Metric Customary



1 quart = 2 pints

1 pint = 2 cups


MASS AND WEIGHT

Metric Customary



TIME

1 year = 365 days

1 year = 12 months

1 year = 52 weeks

1 week = 7 days

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds




rectangle P = (2 × l) + (2 × w)





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Mathematics - Walton's Wizardswaltonswizards.weebly.com/uploads/1/2/0/2/12024199/grade... · 2020. 1. 31. · Metric and customary rulers can be found on the tear-out Mathematics