Chapter 3 Resource · PDF fileCourse 2 Chapter 3 Resource Masters. ... ISBN: 0-07-860110-X...

Course 1

Chapter XResource Masters

Course 2

Chapter 3Resource Masters

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce thematerial contained herein on the condition that such material be reproduced only forclassroom use; be provided to students, teacher, and families without charge; andbe used solely in conjunction with Glencoe Mathematics: Applications andConcepts, Course 2. Any other reproduction, for use or sale, is prohibited withoutprior written permission of the publisher.

Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240

Mathematics: Applications and Concepts, Course 2ISBN: 0-07-860110-X Chapter 3 Resource Masters

1 2 3 4 5 6 7 8 9 10 024 12 11 10 09 08 07 06 05 04 03

Consumable Workbooks

Many of the worksheets contained in the Chapter Resource Mastersbooklets are available as consumable workbooks in both English andSpanish.

Study Guide and Intervention Workbook 0-07-860128-2

Study Guide and Intervention Workbook (Spanish) 0-07-860134-7

Practice: Skills Workbook 0-07-860129-0

Practice: Skills Workbook (Spanish) 0-07-860135-5

Practice: Word Problems Workbook 0-07-860130-4

Practice: Word Problems Workbook (Spanish) 0-07-860136-3

Reading to Learn Mathematics Workbook 0-07-861058-3

Answers for Workbooks The answers for Chapter 3 of theseworkbooks can be found in the back of this Chapter Resource Mastersbooklet.

Spanish Assessment Masters Spanish versions of forms 2A and 2C ofthe Chapter 3 Test are available in the Glencoe Mathematics: Applicationsand Concepts Spanish Assessment Masters, Course 2 (0-07-860138-X).

iii

Vocabulary Builder .............................vii

Family Letter............................................ix

Family Activity ........................................x

Lesson 3-1Study Guide and Intervention ........................129Practice: Skills ................................................130Practice: Word Problems................................131Reading to Learn Mathematics......................132Enrichment .....................................................133







Chapter 3 AssessmentChapter 3 Test, Form 1 ...........................165-166Chapter 3 Test, Form 2A.........................167-168Chapter 3 Test, Form 2B.........................169-170Chapter 3 Test, Form 2C ........................171-172Chapter 3 Test, Form 2D ........................173-174Chapter 3 Test, Form 3 ...........................175-176Chapter 3 Extended Response Assessment .177Chapter 3 Vocabulary Test/Review.................178Chapter 3 Quizzes 1 & 2................................179Chapter 3 Quizzes 3 & 4................................180Chapter 3 Mid-Chapter Test ...........................181Chapter 3 Cumulative Review........................182Chapter 3 Standardized Test Practice ....183-184

Standardized Test Practice Student Recording Sheet ..............................A1

Standardized Test Practice Rubric...................A2ANSWERS ..............................................A3-A30

CONTENTS

iv

Teacher’s Guide to Using the Chapter 3 Resource Masters

The Fast File Chapter Resource system allows you to conveniently file the resources youuse most often. The Chapter 3 Resource Masters includes the core materials needed forChapter 3. These materials include worksheets, extensions, and assessment options. Theanswers for these pages appear at the back of this booklet.

All of the materials found in this booklet are included for viewing and printing in theGlencoe Mathematics: Applications and Concepts, Course 2, TeacherWorks CD-ROM.

Vocabulary Builder Pages vii-viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.

When to Use Give these pages to studentsbefore beginning Lesson 3-1. Encouragethem to add these pages to theirmathematics study notebook. Remind themto add definitions and examples as theycomplete each lesson.

Family Letter and Family ActivityPage ix is a letter to inform your students’families of the requirements of the chapter.The family activity on page x helps themunderstand how the mathematics studentsare learning is applicable to real life.

When to Use Give these pages to studentsto take home before beginning the chapter.

Study Guide and InterventionThere is one Study Guide and Interventionmaster for each lesson in Chapter 3.

When to Use Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.

Practice: Skills There is one master foreach lesson. These provide practice thatmore closely follows the structure of thePractice and Applications section of theStudent Edition exercises.

When to Use These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.

Practice: Word Problems There is onemaster for each lesson. These providepractice in solving word problems that applythe concepts of the lesson.

When to Use These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.

Reading to Learn Mathematics Onemaster is included for each lesson. The firstsection of each master asks questions aboutthe opening paragraph of the lesson in theStudent Edition. Additional questions askstudents to interpret the context of andrelationships among terms in the lesson.Finally, students are asked to summarizewhat they have learned using variousrepresentation techniques.

When to Use This master can be used as astudy tool when presenting the lesson or asan informal reading assessment afterpresenting the lesson. It is also a helpful toolfor ELL (English Language Learner)students.

v

Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.

When to Use These may be used as extracredit, short-term projects, or as activitiesfor days when class periods are shortened.

Assessment OptionsThe assessment masters in the Chapter 3Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.

Chapter AssessmentChapter Tests

• Form 1 contains multiple-choice questionsand is intended for use with basic levelstudents.

• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.

• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.

• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.

All of the above tests include a free-responseBonus question.

• The Extended-Response Assessmentincludes performance assessment tasksthat are suitable for all students. Ascoring rubric is included for evaluationguidelines. Sample answers are providedfor assessment.

• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used inconjunction with one of the chapter testsor as a review worksheet.

Intermediate Assessment• Four free-response quizzes are included

to offer assessment at appropriateintervals in the chapter.

• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice and free-response questions.

Continuing Assessment• The Cumulative Review provides

students an opportunity to reinforce andretain skills as they proceed through theirstudy of Glencoe Mathematics:Applications and Concepts, Course 2. Itcan also be used as a test. This masterincludes free-response questions.

• The Standardized Test Practice offerscontinuing review of pre-algebra conceptsin various formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, short response, grid-in, andextended response questions. Bubble-inand grid-in answer sections are providedon the master.

Answers• Page A1 is an answer sheet for the

Standardized Test Practice questions thatappear in the Student Edition on pages 146–147. This improves students’familiarity with the answer formats theymay encounter in test taking.

• Detailed rubrics for assessing theextended response questions on page 147are provided on page A2.

• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.

• Full-size answer keys are provided for theassessment masters in this booklet.

This is an alphabetical list of new vocabulary terms you will learn inChapter 3. As you study the chapter, complete each term’s definitionor description. Remember to add the page number where you foundthe term. Add this page to your math study notebook to reviewvocabulary at the end of the chapter.

Vo

cab

ula

ry B

uild

er

© Glencoe/McGraw-Hill vii Mathematics: Applications and Concepts, Course 2

NAME ________________________________________ DATE ______________ PERIOD _____

Vocabulary TermFound

Definition/Description/Exampleon Page

absolute value

additive inverse

coordinate grid

coordinate plane

graph

integer [IHN-tih-juhr]

negative integer

opposite

Reading to Learn MathematicsVocabulary Builder

Vo

cab

ula

ry B

uild

er

© Glencoe/McGraw-Hill viii Mathematics: Applications and Concepts, Course 2

Vocabulary TermFound

Definition/Description/Exampleon Page

ordered pair

origin

positive integer

quadrant

x-axis

x-coordinate

y-axis

y-coordinate

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn MathematicsVocabulary Builder (continued)

Family LetterNAME ________________________________________ DATE ______________ PERIOD _____

© Glencoe/McGraw-Hill ix Mathematics: Applications and Concepts, Course 2

Dear Parent or Guardian:

“When am I ever going to use this stuff?” Students in math

classes often ask this question. Integers are everywhere. We use

them for golf scores. We use them when finding elevation, bal-

ancing a checkbook, or talking about temperature. There are

many practical uses of integers.

In Chapter 3, Algebra: Integers, your child will learn how to

order, add, subtract, multiply, divide, and find the absolute value

of integers. Your child will also learn about the coordinate sys-

tem and how to graph points. In the study of this chapter,

your child will complete a variety of daily classroom assign-

ments and activities and possibly produce a chapter project.

By signing this letter and returning it with your child, you

agree to encourage your child by getting involved. Enclosed is

an activity you can do with your child that also relates the

math we will be learning in Chapter 3 to the real world. You

may also wish to log on to the Online Study Tools for self-

check quizzes, Parent and Student Study Guide pages, and

other study help at www.msmath2.net. If you have any ques-

tions or comments, feel free to contact me at school.

Sincerely,

Fam

ily L

ette

r

Signature of Parent or Guardian ______________________________________ Date ________

Family ActivityNAME ________________________________________ DATE ______________ PERIOD _____

© Glencoe/McGraw-Hill x Mathematics: Applications and Concepts, Course 2

Ordering IntegersConsult a newspaper, watch the news, surf the Internet, or watch theweather channel with a family member. Find the high and lowtemperatures on the same day for eight cities: Buenos Aires, Moscow,Zurich, Tokyo, New York, Denver, Los Angeles, and your community.Record the date and the temperatures in the table.

High and Low Temperatures on _____________

1. Which city has the highest high temperature?

2. Which city has the lowest low temperature?

3. List the cities in order from lowest high temperature to highest hightemperature.

4. List the cities in order from lowest low temperature to highest lowtemperature.

5. Were the cities in the same order in the answers for Questions 3 and 4?Why or why not?

City

Buenos Aires

Low Temperature (�F)

Moscow

High Temperature (�F)

Zurich

Tokyo

New York

Denver

Los Angeles

Less

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© Glencoe/McGraw-Hill 129 Mathematics: Applications and Concepts, Course 2

Write an integer that represents 160 feet below sea level.

Because it represents below sea level, the integer is �160.

Evaluate |�2|.

On the number line, the graph of �2 is

2 units away from 0. So, �2 � 2.

Write an integer for each situation.

1. 12°C above 0 2. a loss of $24

3. a gain of 20 pounds 4. falling 6 feet

Evaluate each expression.

5. 12 6. �150

7. �8 8. 75

9. �19 10. 84

�2 �1 0 2 3�3�4 1 4

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionIntegers and Absolute Value

Integers less than zero are negative integers. Integers greater than zero are positive integers.

The absolute value of an integer is the distance the number is from zero on a number line. Twovertical bars are used to represent absolute value. The symbol for absolute value of 3 is 3.

8�7�6�5�4 6 754321�3�2�1 0

negative integers positive integers

zero is neitherpositive nor negative



1. 15�C below 0 2. a profit of $27

3. 2010 A.D. 4. average attendance is down 38 people

5. 376 feet above sea level 6. a withdrawal of $200

7. 3 points lost 8. a bonus of $150

9. a deposit of $41 10. 240 B.C.

11. a wage increase of $120 12. 60 feet below sea level


13. |�1| 14. |9|

15. |23| 16. |�107|

17. |�45| 18. |19|

19. |0| 20. |6|�|�2|

21. �8�4 22. |�12|�|12|

Graph each set of integers on a number line.

23. {0, 2, �3} 24. {�4, �1, 3}

�2 �1 0 2 3�3�4 1 4�2 �1 0 2 3�3�4 1 4

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: SkillsIntegers and Absolute Value


Practice: Word ProblemsIntegers and Absolute Value

NAME ________________________________________ DATE ______________ PERIOD _____

1. DEATH VALLEY The lowest point in theUnited States is Death Valley inCalifornia. Its altitude is 282 feet belowsea level. Write an integer to representthe altitude of Death Valley.

2. RAIN A meteorologist reported that inthe month of April there were 3 inchesmore rainfall than normal. Write aninteger to represent the amount ofrainfall above normal in April.

3. ARCHIMEDES A famous mathematicianand physicist named Archimedes wasborn in 287 B.C. Write an integer toexpress the year of his birth.

4. TEMPERATURE In our world’s tropicalrain forests, the average temperature ofevery month is 64 degrees above zeroor higher. Write an integer to expressthis temperature.

5. STOCK MARKET A certain stock gained5 points in one day and lost 4 pointsthe next day. Write integers torepresent the stock’s gains and lossesfor the two days.

6. ALTITUDE An airplane pilot changed hisaltitude by 100 meters. Describe whatthis could mean.

Less

on

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Pre-Activity Read the introduction at the top of page 106 in your textbook.Write your answers below.

1. What does a value of �2 represent?

2. On which down did they lose the most yards?

3. How can you represent a gain of 9 yards?

Reading the Lesson4. Express each of the following in words.

5. On the following number line, draw a circle around the negative integersand label them negative. Draw a rectangle around the positive integersand label them positive.

Helping You Remember6. Show a classmate how a number line can be used to show negative and

positive integers. Explain the difference between some integers and theabsolute values of those integers. Draw a number line to show what youmean.

�2 �1 0 2 3 4�3�4 1

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn MathematicsIntegers and Absolute Value

Symbols

�7

�7

|7|

Words


Jaime EscalanteJaime Escalante (1930– ) was born in La Paz, Bolivia,and came to the United States in 1963. For ten years,he worked at odd jobs to support himself and his family while pursuing his dream—becoming certified to teach high school mathematics in California. As a mathematicsteacher, he has become well known for his ability to inspire students to succeed in mathematics at levels they never thought possible. In 1988, the story ofMr. Escalante and a group of his students was the subject of the popular motion picture Stand and Deliver.

Mr. Escalante teaches concepts students must master if they are to succeed in high school and college mathematics.One of these is the concept of absolute value. For instance,a student should be able to solve an equation like y � 6quickly using mental math. Here’s how.

You know that 6 � 6 and �6 � 6.

So, the equation y � 6 has two solutions: 6 and �6.

Solve each equation. (Hint: One equation has no solution.)

1. a � 8 2. r � 0 3. j � �3

4. t � 1 � 15 5. 10 � m� 3 6. c � 4 � 16

7. 5z � 60 8. 12 � g � 4 9. 48 � 8x

10. 2d � 3 � 5 11. 4p � 9 � 59 12. 7z � 12 � 12

13. Suppose that the value of x can be selected from the set {�2, �1, 0, 1, 2}.Find all of the solutions of the equation x � x.

14. One of these statements is false. Which one is it? Explain.

a. The absolute value of every integer is positive.

b. There is at least one integer whose absolute value is zero.

c. The absolute value of an integer is never negative.

EnrichmentNAME ________________________________________ DATE ______________ PERIOD _____

Less

on

3–1


Replace the � with � or � to make �1 � �6 a true sentence.

Graph each integer on a number line.

Since �1 is to the right of �6, �1 � �6.

Order the integers 2, �3, 0, �5 from least to greatest.

To order the integers, graph them on a number line.

Order the integers by reading from left to right: �5, �3, 0, 2.

1. Replace the � with < or > to make �5 � �10 a true sentence.

2. Order �1, 5, �3, and 2 from least to greatest.

3. Order 0, �4, �2, and 7 from greatest to least.

4. Order �3, �2, 4, 0, and �5 from greatest to least.

�2 �1 0 2 3�3 1 4 5�5 �4�6

�2 �1 0 2 3�3�7 1 4�5 �4�6

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionComparing and Ordering Integers

When two numbers are graphed on a number line, the number to the left is always less than (<) thenumber to the right. The number to the right is always greater than (>) the number to the left.

�2 �1 0 2 3�3�4 1 4Model

WordsSymbols

�3 is less than �1. �1 is greater than �1.

The symbol points to the lesser number.

�3 � �1 �1 � �3

Less

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Practice: SkillsComparing and Ordering Integers


Replace each � with < or > to make a true sentence.

1. �15 � �16 2. �8 � �7

3. 0 � �2 4. �2 � �5

5. �25 � 3 6. �14 � �20

7. �4 � 3 8. �6 � �7

9. �7 � 2 10. �8 � �9

Determine whether each sentence is true or false. If false, change onenumber to make the sentence true.

11. �7 � 3

12. 2 � 0

13. �20 � �22

14. 12 � 15

15. 3 ��5

16. �2� �3

17. 8��10

18. �11� 11

19. �4 � 4

20. �9 � �10

Order the integers from least to greatest.

21. 12, �6, 20, �47, �11 22. 9, �6, 0, �4, 17, �11

Order the integers from greatest to least.

23. �40, 65, �7, 24, �6, 15 24. �13, 0, 7, �8, �5, 2

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word ProblemsComparing and Ordering Integers


NAME ________________________________________ DATE ______________ PERIOD _____

HISTORY OF WRITING For Exercises 1 and 2,use the table below. It shows importantevents in the history of writing.

EXTREME TEMPERATURES For Exercises 3–5,use the table below. It shows the extremetemperatures for four states. Temperaturesare in degrees Fahrenheit.

Extreme Temperatures (�F)Event

The Iliad and the Odyssey arecomposed by Homer. 700 BC

Aprox.Year

T’sai Lun invents paper. 105 AD

Date of oldest existing papyrus 2200 BC

Ovid wrote Metamorphosis. 5 AD

Torah is compiled. 450 BC

Metal type developed in Korea 1241 AD

State

Nebraska

Alabama

�47

Maine

3

�30

Lowest

Florida �2

Highest

118

104

101

109

1. Write each year as an integer. 2. Order the integers from Exercise 1from least to greatest. Write a sentencedescribing the earliest and most recentevents in the table.

3. Arrange the highest temperatures from greatest to least.

4. What is the median low temperaturefor these four states?

5. Nebraska’s lowest temperature was�47�F, and Maine’s lowest temperaturewas �30�F. Write a true statementusing the two temperatures with thesymbol � or �.

6. MONEY Mr. Firewalks pays closeattention to how much money is in hischecking account. One week hedeposited $230, spent $15 on a lunch,and loaned $25 to a friend. Write eachtransaction as an integer, and list themfrom least to greatest.


1. What is the wind chill if there is a wind at 20 miles per hour and thetemperature is 5�?

2. Which is colder, a temperature of 15� with a 20 mile-per-hour wind or a temperature of 10� with a 10 mile-per-hour wind?

3. Graph both wind chills found in Exercise 2 on a number line.

Reading the LessonFor Exercises 4 and 5, express each of the following in words. Thengraph the numbers on a number line.

4. �1 � 0

5. 3 � �2

6. When two numbers are graphed on a number line, what can you tellabout the number to the left? the number to the right?

Helping You Remember7. Write a set of six numbers, some positive and some negative. Explain how

you can use a number line to order the numbers from least to greatest.

�2 �1 0 2 3 4�3�4 1

�2 �1 0 2 3 4�3�4 1

�2 �1 0 2 3�3�4�5 1

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Reading to Learn MathematicsComparing and Ordering Integers


NAME ________________________________________ DATE ______________ PERIOD _____


Quantitative ComparisonsAn unusual type of problem is found on some standardized multiple-choicetests. This problem type is called the quantitative comparison.

In each quantitative comparison question, you are given two quantities, one inColumn A and one in Column B. You are to compare the two quantities andshade one of four circles on an answer sheet.

Shade circle A if the quantity in Column A is greater;

Shade circle B if the quantity in Column B is greater;

Shade circle C if the two quantities are equal;

Shade circle D if the relationship cannot be determined from theinformation given.

Shade the correct oval to the left of each problem number.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.DCBA

DCBA

DCBA

DCBA

DCBA

DCBA

DCBA

DCBA

DCBA

DCBA

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment

Column A

ten billion dollars

0.006 � 2

1,000 million dollars

20 inches

0.002 � 6

the perimeter of a squarewith an area of 25 squareinches

Column B

half of one third one fifth

the greatest possibleproduct of two oddpositive numbers lessthan 20

the greatest possibleproduct of two evenpositive numbers lessthan 20

0.000000001 �x is x if greater than 0

|x| |x � 1|

|y| |�y|

2|x| if x 0 |x| if x 0

�x if x is less than 0 |x| if x is less than 0

Less

on

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Name the ordered pair for point P. Then identify the quadrant inwhich P lies.

• Start at the origin.• Move 4 units left along the x-axis.• Move 3 units up on the y-axis.

The ordered pair for point P is (�4, 3).P is in the upper left quadrant or quadrant II.

Graph and label the point M(0, �4).

• Start at the origin.• Move 0 units along the x-axis.• Move 4 units down on the y-axis.• Draw a dot and label it M(0, �4).

Name the ordered pair for each point graphed at the right. Then identify the quadrant in which each point lies.

1. P 2. Q

3. R 4. S

Graph and label each point on the coordinate plane.

5. A(�1, 1) 6. B(0, �3)

7. C(3, 2) 8. D(�3, �1)

9. E(1, �2) 10. F(1, 3)

y

xO

�2�3�4

�2�3�4 21 43

1234

y

xO

�2�3�4

�2�3�4 21 43

1234

SR

Q P

y

xO

�2�3�4

�2�3�4 21 43

1234

(0, �4)M

P

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionThe Coordinate Plane

The coordinate plane is used to locate points. The horizontal number line is the x-axis. The verticalnumber line is the y-axis. Their intersection is the origin.

Points are located using ordered pairs. The first number in an ordered pair is the x-coordinate; thesecond number is the y-coordinate.

The coordinate plane is separated into four sections called quadrants.


Name the ordered pair for each point graphed at the right.Then identify the quadrant in which each point lies.

1. A 2. B

3. C 4. D

5. E 6. F

7. G 8. H

9. I 10. J

Graph and label each point on the coordinate plane.

11. N(�1, 3) 12. V(2, �4)

13. C(4, 0) 14. P(�6, 2)

15. M(�5, 0) 16. K(�1, 5)

17. I(�3, �3) 18. A(5, �3)

19. D(0, �5)

Name the ordered pair for each point on the city map at the right.

20. City Hall

21. Theater

22. Gas Station

23. Grocery

y

xO

�2�3�4�5

21 4 5 6 73

12345

�2�3�4�5�6�7

Grocery

Theater

City Hall

Gas Station

�2�3�4�5�6

y

xO�2�3�4�5�6 21 4 5 63

123456

y

xO

�2�3�4�5

�2�3�4�5 21 4 53

12345

F

I

A

B

E

DH

C GJ

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: SkillsThe Coordinate Plane


SCHOOL For Exercises 1–4, use the coordinate plane at the right. It shows a map of the rooms in a junior high school.

�2�3�4�5

�2�3�4�5 21 4 53

Art Entrance

Library

Science

y

xO

12345

Computer Lab

Special Services

English

HistoryCounselor

Athletic Dept.

Music

Exit

Math

Nurse

Practice: Word ProblemsThe Coordinate Plane

NAME ________________________________________ DATE ______________ PERIOD _____

1. Thalia is in the room located at (�2, 1).What room is she in? Describe in wordshow to get from the origin to this point.

2. Thalia’s next class is 8 units to theright and 5 units down on the mapfrom where she is now. In what room isThalia’s next class? Find the orderedpair that represents the location of thatroom.

3. Tyrone is in the Art room, but his nextclass is in the History room. GiveTyrone directions on how to get to theHistory room.

4. On the map, which classrooms arelocated in the third quadrant? Describethe coordinates of all points in the thirdquadrant.

5. NEIGHBORHOOD Delsin made a map ofhis neighborhood in such a way thateach intersection is a point on acoordinate plane. Right now, Delsinstands at point (�4, �3). Give theordered pair of where he will be ifmoves 5 units to the right and 7 unitsup on the map.

6. NEIGHBORHOOD Refer to Exercise 5. Inwhich quadrant is Delsin when he isdone walking? Describe this quadrant.

Less

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1. Suppose Terrell starts at the corner of Russel and Main and walks 1 block north and 2 blocks east. Name the intersection of his location.

2. Using the words north, south, west, and east, write directions to go from the corner of School and Highland to the corner of Main and Oak.

Reading the Lesson3. The word coordinate comes from two Latin words that mean “to arrange

together.” How are coordinates used together to locate a point in acoordinate plane?

4. Look at the coordinate plane at the right. Name the ordered pair for each point graphed.

5. In the coordinate plane in Exercise 4, tell whichquadrant each of the points is in.

Helping You Remember6. Write a way to remember the names of the four quadrants of the

coordinate plane.

y

xO

�2�3�4

�2�3�4 21 43

1234A

B

C

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn MathematicsThe Coordinate Plane


Latitude and LongitudeThis world map shows some of the latitude and longitude lines. Latitude ismeasured in degrees north and south of the equator. Longitude is measured indegrees east and west of the prime meridian, a line passing throughGreenwich, England. (Greenwich is a suburb of London.)

The latitude is usually given first. For example, the location of 30�S, 60�W islower South America.

Name a place near each location. Use an atlas or other referencesource to check your answers.

1. 30�N, 30�W 2. 30�S, 30�E 3. 60�N, 120�W

4. 15�N, 150�W 5. 30�S, 140�E 6. 25�N, 100�W

7. 40�N, 120�W 8. 45�N, 90�W 9. 40�N, 5�W

10. 60�N, 45�W 11. 35�N, 140�E 12. 0�, 60�E

EquatorP

rime

Mer

idia

n

60˚N

30˚N

30˚S, 60˚W

30˚N

0˚

0˚

0˚

30˚S 30˚S

60˚S 60˚S

60˚N

30˚E

30˚ W

60˚E

90˚E

120̊

E

150̊

E

180̊

E

60˚ W

90˚ W

120˚ W

150W̊


Less

on

3–3


Find 4 � (�6).

Method 1 Use counters. Method 2 Use a number line.Combine a set of 4 positive counters • Start at 0.and a set of 6 negative counters on a mat. • Move 4 units right.

• Then move 6 units left.

Add.

1. �5 � (�2) 2. 8 � 1 3. �7 � 10

4. 16 � (�11) 5. �22 � (�7) 6. �50 � 50

7. �10 � (�10) 8. 100 � (�25) 9. �35 � �20

Evaluate each expression if a � 8, b � �8, and c � 4.

10. a � 15 11. b � (�9) 12. a � b

13. b � c 14. �10 � c 15. 12 � b

�1 0 1 3 4�2�3

�6�4

2 54 � (�6) ��2

4 � (�6) 4 � (�6) ��2

�1

� �

��

�

�

�

� �

� �

�

�

�

�

� �

�

�

�

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionAdding Integers

For integers with the same sign:• the sum of two positive integers is positive.• the sum of two negative integers is negative.

For integers with different signs, subtract their absolute values. The sum is:• positive if the positive integer has the greater absolute value.• negative if the negative integer has the greater absolute value.

To add integers, it is helpful to use counters or a number line.

Less

on

3–4


NAME ________________________________________ DATE ______________ PERIOD _____

Tell whether each sum is positive, negative, or zero without adding.

Add.

1. 5 � (�8) 2. �3 � 3

3. �3 � (�8) 4. �7 � (�7)

5. �8 � 10 6. �7 � 13

7. 15 � (�10) 8. �11 � (�12)

9. 25 � (�12) 10. �14 � (�13)

11. 14 � (�27) 12. �28 � 16

Evaluate each expression if a � �8, b � 12, and c � �4.

13. 5 � a 14. b � (�9)

15. c � (�5) 16. a � b

17. a � 0 18. b � c

19. �12 � b 20. a � (�7)

21. 21 � c 22. a � c

Practice: SkillsAdding Integers


NAME ________________________________________ DATE ______________ PERIOD _____

Write an addition expression to describe each situation. Then find each sum.

Practice: Word ProblemsAdding Integers

1. FOOTBALL A team gains 20 yards. Thenthey lose 7 yards.

2. MONEY Roger owes his mom $5. Heborrows another $6 from her.

3. GOLF Juanita’s score was 5 over par onthe first 9 holes. Her score was 4 underpar on the second 9 holes.

4. HOT AIR BALLOON A balloon rises340 feet into the air. Then it descends130 feet.

5. CYCLING A cyclist travels downhill for125 feet. Then she travels up a hill50 feet.

6. AIRPLANE A plane descends 1,200 feet.Then it descends another 500 feet.


NAME ________________________________________ DATE ______________ PERIOD _____


1. What is the charge at the top of a cloud where there are more protonsthan electrons?

2. What is the charge at the bottom of a cloud where there are moreelectrons than protons?

Reading the LessonFor Exercises 3 and 4, tell how you would solve each of the followingon a number line. Then solve.

3. �7 � (�9)

4. �7 � 9

5. When you use counters to add integers, what property are you applyingwhen you remove zero pairs?

6. How many units away from 0 is the number 17? How many units awayfrom 0 is the number �17? What are 17 and �17 called?

Helping You Remember7. Work with a partner. Tell your partner how to use absolute values to add

integers with different signs when the positive integer has the greaterabsolute value. Then have your partner explain to you how to useabsolute values to add integers with different signs when the negativeinteger has the greater absolute value.

Reading to Learn MathematicsAdding Integers

Less

on

3–4


Dartboard Puzzles

Three darts are thrown. Each dart must land on a different space inorder to count. Find the highest and the lowest possible scores.

1. 2. 3.

highest score: highest score: highest score:lowest score: lowest score: lowest score:

In these problems, five darts are thrown. Each dart must land on adifferent space in order to count. Solve each puzzle.

4. Find three ways to make the score �5. 5. Find three ways to make the score 0.

�5

�5

�5

�5

�5

�5

�5

�50

�5

�10

�10

�10�10

�15

�15

�10

�20

�20

�20

�25

0

0

10

10

10

10

105

55

55

5

5

50

35

25

25

20

20 2015

1515

15

15

15

20

50

�10

�10

�1

�3

�3

�3

�2

�2

�8

�7

�7

�9�8

�9

�5

�5

�6

�6

�4

�4

�1

�1

0

0

0

0

5

5

8

8

2

22

9

10

10

3

3

3

7

7

6

6

4

4

1

1

1

9

100

�75�50

�50

25

25

�150

�150

75

75

�10

�10�75

10

10

200

200

0

�1

�4�1

�4

�3

�3

�8

�8

�7

�7�2

�2

�6�6�5

�5

�8

�1 �4

�6�7

�2

26

3

5

4

3

170

�6

�5

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment

Less

on

3–5


Find 6 � 9.

6 � 9 � 6 � (�9) To subtract 9, add �9.� �3 Simplify.

Find �10 � (�12).

�10 � (�12) � �10 � 12 To subtract �12, add 12.� 2 Simplify.

Evaluate a � b if a � �3 and b � 7.

a � b � �3 � 7 Replace a with �3 and b with 7.� �3 � (�7) To subtract 7, add �7.� �10 Simplify.

Subtract.

1. 7 � 9 2. 20 � (�6)

3. �10 � 4 4. 0 � 12

5. �7 � 8 6. 13 � 18

7. �20 � (�5) 8. �8 � (�6)

9. 25 � (�14) 10. �75 � 50

11. 15 � 65 12. 19 � (�10)

Evaluate each expression if m � �2, n � 10, and p � 5.

13. m � 6 14. 9 � n

15. p � (�8) 16. p � m

17. m � n 18. �25 � p

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionSubtracting Integers

To subtract an integer, add its opposite.


Subtract.

1. 5 � 2 2. 6 � (�7)

3. �3 � 2 4. 8 � 13

5. �7 � (�7) 6. 6 � 12

7. 15 � (�7) 8. �15 � 6

9. �3 � 8 10. �10 � 12

11. 13 � (�12) 12. 14 � (�22)

13. 10 � (�20) 14. �16 � 14

15. �25 � 25 16. 6 � (�31)

17. �18 � (�40) 18. 15 � (�61)

Evaluate each expression if r � �4, s � 10, and t � �7.

19. r � 7 20. t � s

21. s � (�8) 22. t � r

23. s � t 24. r � s

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: SkillsSubtracting Integers


Subtract.

Practice: Word ProblemsSubtracting Integers

NAME ________________________________________ DATE ______________ PERIOD _____

1. FOOTBALL A team gained 5 yards ontheir first play of the game. Then theylost 6 yards. Find the total change inyardage.

2. CHECKING Your checking account isoverdrawn by $50. You write a checkfor $20. What is the balance in youraccount?

3. TEMPERATURE The average temperaturein Calgary, Canada, is 22�C in July and�11�C in January. Find the range ofthe highest and lowest temperatures inCalgary.

4. ROLLER COASTER A roller coaster beginsat 90 feet above ground level. Then itdescends 105 feet. Find the height ofthe coaster after the first descent.

5. SAVINGS Sonia has $235 in her savingsaccount. She withdraws $45. What isleft in her savings account?

6. BEACH Wai and Kuri were digging inthe sand at the beach. Wai dug a holethat was 15 inches below the surface,and Kuri dug a hole that was 9 inchesbelow the surface. Find the differencein the depths of their holes.

Less

on

3–5


Pre-Activity Complete the Mini Lab at the top of page 128 in your textbook.Write your answers below.

1. Write a related addition sentence for each subtraction sentence.

Use a number line to find each difference. Write an equivalentaddition sentence for each.

2. 1 � 5

3. �2 � 1

4. �3 � 4

5. 0 � 5

6. Compare and contrast subtraction sentences with their relatedaddition sentences.

Reading the LessonTell how you would solve each of the following on a number line.Then solve.

7. �8 � (�6)

8. 6 � 8

Helping You Remember9. Write the rule that tells how to subtract integers. Then give an example.

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn MathematicsSubtracting Integers


Distance on the Number LineTo find the distance between two points on a number line, subtract theircoordinates. Then, take the absolute value of the difference.

�4 � 3 � �7

�7 � 7

You can also find the distance by finding the absolute value of the differenceof the coordinates.

�4 � 3 � 7

Graph each pair of points. Then write an expression using absolutevalue to find the distance between the points.

1. A at �5 and B at 2

2. C at �7 and D at �1

3. E at �5 and F at 5

4. W at 0 and X at 6

5. Y at �4 and Z at 0

�8 �7 �6 �5 �4 �3 �2 �1 876543210

�8 �7 �6 �5 �4 �3 �2 �1 876543210

�8 �7 �6 �5 �4 �3 �2 �1 876543210

�8 �7 �6 �5 �4 �3 �2 �1 876543210

�8 �7 �6 �5 �4 �3 �2 �1 876543210

�8 �7 �6 �5 �4 �3 �2 �1 876543210


Less

on

3–5


Multiply 5(�2).

5(�2) � �10 The integers have different signs. The product is negative.

Multiply �3(7).

�3(7) � �21 The integers have different signs. The product is negative.

Multiply �6(�9).

�6(�9) � 54 The integers have the same sign. The product is positive.

Multiply (�7)2.

(�7)2 � (�7)(�7) There are 2 factors of �7.� 49 The product is positive.

Simplify �2(6c).

�2(6c) � (�2 · 6)c Associative Property of Multiplication.� �12c Simplify.

Simplify 2(5x).

2(5x) � (2 · 5)x Associative Propery of Multiplication.� 10x Simplify.

Multiply.

1. �5(8) 2. �3(�7) 3. 10(�8)

4. �8(3) 5. �12(�12) 6. (�8)2

ALGEBRA Simplify each expression.

7. �5(7a) 8. 3(�2x) 9. 4(6f)

10. 7(6b) 11. �6(�3y) 12. 7(�8g)

ALGEBRA Evaluate each expression if a � �3, b � �4, and c � 5.

13. �2a 14. 9b 15. ab

16. �3ac 17. �2c2 18. abc

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionMultiplying Integers

The product of two integers with different signs is negative.

The product of two integers with the same sign is positive.

6

Less

on

3–6

Practice: SkillsMultiplying Integers


Multiply.

1. �4(6) 2. �2(�8)

3. 12(�4) 4. �6(5)

5. �10(�9) 6. �(5)2

7. (�5)2 8. �30(5)

9. 20(�6) 10. �14(�6)

11. (�13)2 12. �7(15)

ALGEBRA Simplify each expression.

13. �3(4y) 14. 7(�3x)

15. 7(5g) 16. 7(7w)

17. 3(�3y) 18. �2(�10h)

ALGEBRA Evaluate each expression if g � �5, h � �3, and k � 4.

19. �3g 20. 5h

21. 7gk 22. �2gh

23. �10h 24. �2h2

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word ProblemsMultiplying Integers


Multiply.

NAME ________________________________________ DATE ______________ PERIOD _____

1. TEMPERATURE Suppose the temperatureoutside is dropping 3 degrees eachhour. How much will the temperaturedrop in 8 hours?

2. DIVING A deep-sea diver descendsbelow the surface of the water at a rateof 60 feet each minute. What is thedepth of the diver after 10 minutes?

3. STOCK A computer stock lost 2 pointseach hour for 6 hours. Find the totalpoints the stock fell.

4. DROUGHT A drought can cause thelevel of the local water supply to dropby a few inches each week. Suppose thelevel of the water supply drops 2 incheseach week. How far will it havedropped in 4 weeks?

5. MONEY Mrs. Rockwell lost money onan investment at a rate of $4 per day.How much did she lose after twoweeks?

6. TENNIS BALLS Josh purchased 8 cans oftennis balls. The cans came with 3 ballsin each can. How many balls did Joshpurchase?

Reading to Learn MathematicsMultiplying Integers



1. Write a multiplication sentence that describes the model.

Find each product using counters.

2. 3(�2) 3. 4(�3)

4. 1(�7) 5. 5(�2)

6. Write a rule for finding the sign of the product of a positive and negativeinteger.

Reading the Lesson7. Give an example that shows how multiplication is the same as repeated

addition. In your example, tell what the addend is.

8. How does the sentence 4(�2) � �2(4) illustrate the Commutative Property of Multiplication?

9. Complete each of the following sentences with the word positive ornegative.

a. The product of two integers with different signs is _______________.

b. The product of two integers with the same sign is _______________.

Helping You Remember10. You know the rule for determining the sign of the product of two integers

when the signs are alike or different. Consider the product of threeintegers. With a partner summarize the signs of the products of 3integers when three, two, one or none of the integers are positive.

NAME ________________________________________ DATE ______________ PERIOD _____

Less

on

3–6


Integer MazeFind your way through the maze by moving to the expression in an adjacent section withthe next highest value.

Start−50

−55

20 − 20

−32 + 28

−12 + 2

−3 + (−4)

4 + (−12)

−13 + 12−10 + 16

−35 + 5

6 − 8

5(−9)

9(−6)

−8(5)

−3(5)

−5(−6)

−1(3)

−4(2)

−3(−5)

3(−3)(−5)

−2(−5)(−1)

6(−10)9(−1)

3 + (−3)

30 − (−10)

−4(5)(−1)

3(5)(−5)

5(−4 + 9)

(−4)2

−52

−[12 − (−8)]

2[−5 • (−5)]

−2(−12 + 7)

−2(−1)

−5

0 − 6

15 − 50

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment

Less

on

3–7


Divide 30 � (�5).

30 � (�5) The integers have different signs.

30 � (�5) � �6 The quotient is negative.

Divide �100 � (�5).

�100 � (�5) The integers have the same sign.

�100 � (�5) � 20 The quotient is positive.

Divide.

1. �12 � 4 2. �14 � (�7)

3. �18

24. �6 � (�3)

5. �10 � 10 6. ��

8200

7. 350 � (�25) 8. �420 � (�3)

9. 54450

10. �

12656

ALGEBRA Evaluate each expression if d � �24, e � �4, and f � 8.

11. 12 � e 12. 40 � f

13. d � 6 14. d � e

15. f � e 16. e2 � f

17. �ed 18. ef � 2

19. f

e2

2

20. dfe

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionDividing Integers

The quotient of two integers with different signs is negative.

The quotient of two integers with the same sign is positive.


Divide.

1. �15 � 3 2. �24 � (�8)

3. 22 � (�2) 4. �49 � (�7)

5. �8 � (�8) 6. �36

4

7. 225 � (�15) 8. �09

9. �38 � 2 10. 644

11. �500 � (�50) 12. �189 � (�21)

ALGEBRA Evaluate each expression if m � �32, n � 2, and p � �8.

13. m � n 14. p � 4

15. p2 � m 16. m � p

17. �

np 18. p � n2

19. n

p2

2 20. 18

p� n

21. m � (np) 22. mp � n

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: SkillsDividing Integers


Divide.

Practice: Word ProblemsDividing Integers

NAME ________________________________________ DATE ______________ PERIOD _____

1. STOCK MARKET During a 5-dayworkweek, the stock market decreasedby 65 points. Find the average dailychange in the market for the week.

2. MOTION Mr. Diaz decreased the speedof his car by 30 miles per hour over aperiod of 10 seconds. Find the averagechange in speed each second.

3. WEATHER Over the past seven days,Mrs. Cho found that the temperatureoutside had dropped a total of35 degrees. Find the average drop intemperature each day.

4. BASKETBALL The basketball team losttheir last 6 games. They lost by a totalof 48 points. Find the average numberof points by which each game was lost.

5. POPULATION The enrollment at DavisMiddle School dropped by 60 studentsover a 5-year period. What is theaverage yearly drop in enrollment?

6. SUBMARINE A submarine descends at arate of 60 feet each minute. How longwill it take it to descend to a depth of660 feet below the surface?

Less

on

3–7



Find each quotient using counters.

1. �6 � 2

2. �12 � 3

Reading the LessonWrite two division sentences related to each of the followingmultiplication sentences.

3. �6(�3) � 18 4. �21(�2) � 42

5. �6(3) � �18 6. 2(�21) � �42

7. Complete each of the following sentences with the word positive ornegative.

a. The quotient of two integers with different signs is _______________.

b. The quotient of two integers with the same sign is _______________.

8. In the division sentence �72 � 8 � �9, identify the dividend, the divisor,and the quotient.

Helping You Remember9. Describe how the operations of multiplication and division are opposite of

each other. Are these operations opposite in all cases? What is the oneinteger that cannot be a divisor?

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn MathematicsDividing Integers


Division by Zero?Some interesting things happen when you try to divide by zero. For example,look at these two equations.

50 � x

00 � y

If you can write the equations above, you can also write the two equationsbelow.

0 � x � 5 0 � y � 0

However, there is no number that will make the left equation true. Thisequation has no solution. For the right equation, every number will make ittrue. The solutions for this equation are “all numbers.”

Because division by zero leads to impossible situations, it is not a “legal” stepin solving a problem. People say that division by zero is undefined, or notpossible, or simply not allowed.

Describe the solution set for each equation.

1. 4x � 0 2. x � 0 � 0

3. x � 0 � x 4. 0x � 0

5. 0x � x 6.

0x � 5

What values for x must be excluded to prevent division by 0?

7. x12 8. x �

11

9. x �1

1 10. 20x

11. 2x1� 2 12. 3x

1� 6

Explain what is wrong with this “proof.”

13. Step 1 0 � 1 � 0 and 0 � (�1) � 0

Step 2 Therefore, 00

� 1 and 00

� �1.

Step 3 Therefore, 1 � �1.


Less

on

3–7

Write the letter for the correct answer in the blank at the right of each question.1. Write an integer that represents 8�C below 0.

A. �8 B. 8 C. �8 D. 8 1.

2. Evaluate 3.F. 6 G. �3 H. 3 I. 0 2.

3. Evaluate �9.A. 0 B. 9 C. 18 D. �9 3.

4. Write the integers represented by S and T on the number line.F. S, 4; T, �2 G. S, �4; T, 2H. S, 2; T, �4 I. S, �2; T, 4 4.

5. Order 4, �5, 3, and 0 from least to greatest.A. 0, 3, 4, �5 B. �5, 0, 3, 4 C. 4, 3, 0, �5 D. 0, �5, 3, 4 5.

6. Simplify 4(9a).F. 13a G. 5a H. 36a I. 49a 6.

7. What value of z makes 14 � 3 � z a true sentence?A. 11 B. 17 C. �11 D. �17 7.

Replace each � to make a true sentence.

8. �4 � 0F. � G. � H. � I. � 8.

9. 3 � �6A. � B. � C. � D. � 9.

Use the graph to name the ordered pair for each point.

10. JF. (0, �2) G. (0, 2)H. (�2, 0) I. (2, 0) 10.

11. MA. (�3, 3) B. (3, 3)C. (�3, �3) D. (3, �3) 11.

12. RF. (2, 4) G. (4, 2) H. (�2, 4) I. (2, �4) 12.

13. TA. (1, �4) B. (�1, �4) C. (�1, 4) D. (�4, �1) 13.

y

xO

�2�3�4

�2�3�4 21 43

1234

J

TM

R

�2 �1 0 2 3�3�4�5�6 1 4 5

S T


Chapter 3 Test, Form 1

Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Add, subtract, multiply, or divide.

14. 8 � (�7)F. 1 G. �1 H. 15 I. �15 14.

15. �7(�6)A. �1 B. �42 C. 42 D. �13 15.

16. 18 � (�9)F. 9 G. 2 H. �9 I. �2 16.

17. 35 � 12A. �23 B. 23 C. 47 D. �47 17.

18. (�3)2

F. �9 G. �1 H. �6 I. 9 18.

19. 0 � 20A. 20 B. �20 C. 2 D. 0 19.


20. 10 � aF. �6 G. 6 H. 14 I. �14 20.

21. bcA. 6 B. �6 C. 5 D. �5 21.

22. �

b12

F. �18 G. �6 H. �2 I. 2 22.

23. 9 � bA. 54 B. �3 C. 3 D. 15 23.

24. b � 2F. 4 G. �4 H. 62 I. �3 24.

25. c � 5A. �4 B. 4 C. 6 D. �6 25.

Bonus Find |t � v| when t � 9 and v � 5. B:


NAME ________________________________________ DATE ______________ PERIOD _____

Chapter 3 Test, Form 1 (continued)

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Ass

essm

ent

Write the letter for the correct answer in the blank at the right of each question.

1. Write an integer that represents a 5-yard loss.A. 5 B. �5 C. �5 D. 5 1.

2. Evaluate �7.F. 7 G. � �7 H. 14 I. �7 2.

3. Evaluate 5��2.A. �7 B. �3 C. 3 D. 7 3.

4. Write the integers represented by A and B on the number line.F. A, �3; B, �5 G. A, 3; B, �5H. A, �3; B, 5 I. A, �5; B, 3 4.

5. Order 6, �2, 3, 0, and �1 from least to greatest.A. �2, �1, 0, 3, 6 B. �2, 0, �1, 3, 6C. �1, �2, 0, 3, 6 D. 0, �1, �2, 3, 6 5.

6. Simplify �8(3z).F. 24z G. �5z H. �24z I. �11z 6.

7. What value of q makes �15 � (�9) � q a true sentence?A. �24 B. �6 C. 24 D. 6 7.


8. �5 � 2F. � G. � H. � I. � 8.

9. �1 � �7A. � B. � C. � D. � 9.


10. QF. (0, 3) G. (2, �3)H. (�2, �3) I. (�2, 3) 10.

11. EA. (0, 3) B. (2, �3)C. (3, 0) D. (�3, 0) 11.

12. PF. (�2, �3) G. (�3, �2) H. (3, �2) I. (�3, 2) 12.

13. BA. (�1, �4) B. (�1, 4) C. (�4, 1) D. (1, �4) 13.

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Chapter 3 Test, Form 2A



14. 12 � (�5)F. 7 G. �7 H. 17 I. �17 14.

15. �8(�10)A. �80 B. 80 C. �18 D. 18 15.

16. ��

4284

F. 2 G. �2 H. �24 I. 0.5 16.

17. �37 � 8A. 45 B. �29 C. �45 D. 296 17.

18. 7(�3)

F. �213 G. 4 H. 21 I. �21 18.

19. 0 � 5A. 10 B. �5 C. 0 D. 5 19.

Evaluate each expression if x � �3, y � 8, and z � �4.

20. y � (�5)F. 3 G. �13 H. 13 I. �3 20.

21. xzA. �12 B. 12 C. �7 D. �1 21.

22. �8 � yF. 0 G. �16 H. �1 I. 1 22.

23. x � 11A. 8 B. 14 C. �8 D. �14 23.

24. z22

F. 4 G. �8 H. �4 I. 8 24.

25. x � y � zA. �1 B. 1 C. 15 D. �15 25.

Bonus Find q � r when q � �3 and r � 3. B:


NAME ________________________________________ DATE ______________ PERIOD _____

Chapter 3 Test, Form 2A (continued)

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Ass

essm

ent

Chapter 3 Test, Form 2B

Write the letter for the correct answer in the blank at the right of each question.1. Write an integer that represents a loss of $20.

A. �20 B. �20 C. 20 D. 20 1.

2. Evaluate �4.F. �4 G. � �4 H. 4 I. 8 2.

3. Evaluate 7��3.A. 10 B. 4 C. �4 D. �10 3.

4. Write the integers represented by Q and R on the number line.F. Q, �3; R, 1 G. Q, 3; R, �1

H. Q, �1; R, 3 I. Q, 1; R, �3 4.

5. Order 3, �4, 0, 1, and �2 from least to greatest.A. �4, �2, 0, 1, 3 B. 3, 1, 0, �2, �4C. 3, 1, 0, �4, �2 D. �2, �4, 0, 1, 3

5.

6. Simplify �5(7r).F. 35r G. �35r H. 2r I. �12r 6.

7. What value of s makes �18 � (�5) � s a true sentence?A. 13 B. �23 C. 23 D. �13 7.


8. 10 � �10F. � G. � H. � I. � 8.

9. �3 � 5A. � B. � C. � D. � 9.


10. SF. (5, �5) G. (�1, 3)H. (5, 5) I. (�5, 5) 10.

11. RA. (�6, 5) B. (5, �6)C. (5, 5) D. (6, 5) 11.

12. AF. (�3, 4) G. (�3, �4) H. (3, �4) I. (�4, �3) 12.

13. MA. (3, 1) B. (�1, 3) C. (1, 3) D. (3, �1) 13.

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Chapter 3 Test, Form 2B (continued)


14. 11 � (�7)F. 4 G. �4 H. �18 I. 18 14.

15. �5(�11)A. 16 B. �16 C. 55 D. �55 15.

16. �15 � (�3)F. �5 G. 5 H. �18 I. 18 16.

17. �39 � 7A. �46 B. 46 C. 273 D. �32 17.

18. 8(�4)F. �2 G. 32 H. 4 I. �32 18.

19. 0 � 7A. 0 B. �7 C. �14 D. 7 19.

Evaluate each expression if a � 4, b � 7, and c � �5.

20. b � (�4)F. �3 G. �11 H. 3 I. 11 20.

21. acA. 20 B. �20 C. �1 D. 9 21.

22. �b7

F. 14 G. 0 H. 1 I. �1 22.

23. a � 13A. �17 B. 9 C. 17 D. �9 23.

24. c2 � 5F. 5 G. �5 H. 2 I. 30 24.

25. a � b � cA. 16 B. �6 C. �16 D. 6 25.

Bonus Find s � t when s � �5 and t � 5. B:


NAME ________________________________________ DATE ______________ PERIOD _____


1. a deposit of $45 1.

2. 5�C below 0 2.

For Questions 3 and 4, evaluate each expression.

3. |�11| 3.

4. |4| � |�6| 4.

5. Graph the set of numbers {�3, 2, �5} on a number line. 5.

For Questions 6–8, replace each � with � or � to make a true sentence.

6. �16 � �22 6.

7. �5 � 1 7.

8. 12 � �1 8.

9. Order �2, 5, 0, 7, �1, and 3 from least to greatest. 9.

10. TEMPERATURE On the same day, a thermometer registered �4�F in Athens and �9�F in Seattle. Which Washington 10.city was warmer?

Name the ordered pair for each point graphed at the right. Thenidentify in which quadrant each point lies.

11. S 11.

12. T 12.

Graph and label each point.

13. Q(1, �2) 13–14.

14. W(0, 4)

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Chapter 3 Test, Form 2C

Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


15. �25 � (�12) 15.

16. 8(�11) 16.

17. 40 � (�8) 17.

18. 4 � (�2) 18.

19. (�3)2 19.

20. 6 � (�9) 20.

21. �9 � 8 21.

22. ��

63

22.

Evaluate each expression if x � �4, y � 6, and z � �3.

23. 15 � (�y) 23.

24. 20 � x 24.

25. 7 � z 25.

26. �2(3z) 26.

27. 1xy2

27.

28. x � y 28.

29. xy 29.

30. x � z 30.

For Questions 31 and 32, simplify each expression.

31. �5(3a) 31.

32. 3(�4c) 32.

33. What value of w makes �24 � (�13) � w a true sentence? 33.

Bonus Find a � b when a � �6 and b � 6. B:


NAME ________________________________________ DATE ______________ PERIOD _____

Chapter 3 Test, Form 2C (continued)

Write an integer for each situation.1. 300 feet above sea level 1.

2. a loss of $13 2.


3. |�13| 3.

4. |3|�|�5| 4.

5. Graph the set of numbers on a number line: {�6, 2, �3}. 5.


6. �7 � �5 6.

7. 0 � �35 7.

8. �1 � 1 8.

9. Order 3, �8, 4, 2, �5, and �1 from least to greatest. 9.

10. TEMPERATURE On the same day, a thermometer registered 10.�10�F in Duluth and �7�F in St. Paul. Which Minnesota city was warmer?


11. R 11.

12. Q 12.


13. A(�3, �2) 13–14.

14. S(0, 2)

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Chapter 3 Test, Form 2C

Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 3 Test, Form 2D


15. �2 � 4 15.

16. 7(�10) 16.

17. �60

317.

18. 6 � (�3) 18.

19. (�5)2 19.

20. �1 � (�11) 20.

21. �10 � 7 21.

22. �8 � (�4) 22.


23. 8 � (�b) 23.

24. 16 � c 24.

25. 9 � c 25.

26. �5(3c) 26.

27. ab � 10 27.

28. a � b 28.

29. ab 29.

30. a � c 30.


31. �6(5z) 31.

32. �4(�2y) 32.

33. What value of d makes �25 � (�16) � d a true sentence? 33.

Bonus Find |x�y| when x � �7 and y � 7. B:


NAME ________________________________________ DATE ______________ PERIOD _____

Chapter 3 Test, Form 2D (continued)

Chapter 3 Test, Form 3


1. 380 meters above sea level 1.

2. a loss of 11 yards 2.


3. |�16| 3.

4. |�3|�|1| 4.

5. Graph the set of numbers {5, �3, 2, �4} on a number line. 5.


6. �28 � �30 6.

7. �8 � 5 7.

8. 11 � �10 8.

9. Order �5, �7, 4, 0, �3, and 10 from least to greatest. 9.

10. TEMPERATURE On the same day, a thermometer registered 10.�8�C in Chicago, Illinois and �5�C in Detroit, Michigan.Which city was colder?


11. A 11.

12. B 12.


13. L(�2, �4) 13–14.

14. M(0, �3)

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Ass

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ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Chapter 3 Test, Form 3 (continued)


15. �40 � 12 15.

16. 6(�4) 16.

17. �03

17.

18. �5 � 3 � 2 18.

19. �(112) 19.

20. �13 � 18 � (�2) 20.

21. �18 � (�21) 21.

22. �56 � (�7) 22.

Evaluate each expression if q � �8, r � 5, and s � �3.

23. q � r 23.

24. �2qr 24.

25. �9 � s 25.

26. qs � 8 26.

27. �rs2 27.

28. �10

s2

� q 28.

29. �s � 2 29.

30. q � r � s 30.


31. �5(7e) 31.

32. (�2b)(3c) 32.

33. What value of a makes �18 � (�3) � a a true statement? 33.

Bonus PATTERNS Find the next two numbers in the following B:pattern: 96, �48, 24, �12, …Then describe the pattern.


NAME ________________________________________ DATE ______________ PERIOD _____

Ass

essm

ent

Demonstrate your knowledge by giving a clear, concise solution toeach problem. Be sure to include all relevant drawings and justifyyour answers. You may show your solutions in more than one way orinvestigate beyond the requirements of the problem. If necessary,record your answer on another piece of paper.

1. Horatio, Glen, Carlos, and Meredith played in the company golftournament. Their scores after the first round are listed below.

Horatio: two over par (�2)Glen: three under par (�3)Carlos: four over par (�4)Meredith: one under par (�1)

a. Explain how to compare integers.

b. Order the golf scores from least to greatest.

c. Explain what is meant by the absolute value of a number.

d. Find the absolute value of Glen’s score.

e. Glen’s second round score is �2. Use counters to find Glen’s total scoreafter two rounds.

f. Meredith’s second round score is �3. Find her total score after tworounds.

g. Horatio’s second round score is �3. Use counters to find the differencebetween Horatio’s first and second round scores.

2. On graph paper, draw a coordinate plane.

a. Graph and label the point A(4, 6). Describe how you locate this point.Identify the quadrant in which the point lies.

b. Multiply the x-coordinate of point A by �2 and multiply the y-coordinate of point A by �1. Name the new point B and give itscoordinates. Graph point B and identify the quadrant in which it lies.

c. Divide the x-coordinate of point B by 4 and divide the y-coordinate ofpoint B by �3. Name the new point C and give its coordinates. Graphpoint C and identify the quadrant in which it lies.


Chapter 3 Extended Response Assessment

Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


Chapter 3 Vocabulary Test/Review

Choose from the terms above to complete each sentence.

1. Vertical bars before and after a number indicate 1._______________, the distance a number is from zero on a number line.

2. A(n) _______________ is a number that can be graphed on 2.a number line.

3. When you _______________ a point, you locate its position 3.on a coordinate plane by drawing a dot at the location of its ordered pair.

4. The _______________ is the opposite of any number. When 4.added to the number, the sum equals 0.

5. The _______________ is the first number of an ordered pair. 5.It corresponds to a number on the x-axis.

6. The _______________ is the vertical number line of a 6.coordinate plane.

7. A(n) _______________ is an integer less than zero. 7.

8. The point at which the number lines of a coordinate plane 8.intersect is called the _______________.

9. Two integers that are the same distance from 0 on a 9.number line, but on opposite sides of 0, are called _______________ .

10. A(n) _______________ is one of four sections of a coordinate 10.plane.

In your own words, define each term.

11. coordinate plane

12. ordered pair

absolute value (p. 107)additive inverse (p. 121)coordinate grid (p. 112)coordinate plane (p. 112)graph (p. 106)integer (p. 106)

negative integer (p. 106)opposite (p. 121)ordered pair (p. 112)origin (p. 112)positive integer (p. 106)quadrant (p. 113)

x-axis (p. 112)x-coordinate (p. 112)y-axis (p. 112)y-coordinate (p. 112)

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Ass

essm

ent


1. MULTIPLE-CHOICE TEST ITEM Order the integers �2, 4, 7, �5, 1.and 1 from least to greatest A. �2, �5, 1, 4, 7 B. 1, �2, 4, �5, 7C. �5, �2, 1, 4, 7 D. 7, 4, 1, �2, �5

Write an integer for each situation. 2.

2. 15�F below 0 3. a deposit of $24 3.


4. |�3| 4.

5. |9| 5.

6. |13|�|�2| 6.

Replace each � with � or � to make a true sentence.

7. �34 � �134 7.

8. �27 � �8 8.

9. 12 � �12 9.

10. �111 � �888 10.

On the coordinate plane, graph and label each point.

1. S(1, 0) 1–3.

2. R(�3, �1)

3. T(3, �2)

4. Find 12 � (�7). 4.

5. Evaluate x � y if x � �8 and y � 4. 5.

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Chapter 3 Quiz(Lessons 3-3 and 3-4)


NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


1. Find the quotient of �56 and 14. 1.

Divide.

2. �63 � (�9) 2.

3. �21 � 7 3.

Evaluate each expression if r � 18, s � �4, and t � �3.

4. r � t 4.

5. st � 6 5.

Subtract or multiply.

1. �8 � 5 1.

2. �10(�3) 2.

3. �(92) 3.

4. 15 � (�20) 4.

Evaluate each expression if f � �4, g � 2, and h � 7.

5. �9g 5.

6. �h � 3 6.

7. h � f 7.

8. fgh 8.

Simplify each expression.

9. �2(9e) 9.

10. 5(�4s) 10.


Chapter 3 Quiz(Lesson 3-7)

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Write the letter for the correct answer in the blank at the right of each question.

1. Evaluate |�5|.A. �4 B. 5 C. �|5| D. �5 1.

2. Evaluate |�6|�|2|.F. 4 G. �8 H. 8 I. �4 2.

3. Order the integers 6, 4, 18, �4, 3, and �7 from least to greatest.A. 3, 4, 6, 18, �4, �7 B. 18, 6, 4, 3, �4, �7C. �4, �7, 3, 4, 6, 18 D. �7, �4, 3, 4, 6, 18 3.

4. Find �8 � 12.F. �20 G. �4 H. 20 I. 4 4.

5. Evaluate a � b if a � �3 and b � �14.A. �17 B. �11 C. 17 D. 11 5.

6. Identify the quadrant in which (�1, 4) lies.F. I G. II H. III I. IV 6.

Write an integer for each situation. 7.

7. a deposit of $50 8. 3 inches below normal 8.

Replace each � with � or � to make a true sentence. 9.

9. 14 � �2 10. �111 � �11 10.

Name the ordered pair for each letter and identify its quadrant.

11. Q 11.

12. U 12.

13. X 13.

14. Z 14.

15. Find (�12) � 8 � (�7). 15.


Chapter 3 Mid-Chapter Test(Lessons 3-1 through 3-4)

Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

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1. Evaluate the expression 2d � 5f if d � 4 and f � 2. 1.(Lesson 1-4)

TENNIS For Questions 2–4, use the stem-and-leaf plot below. It shows the number of matches won by each member of the East High School Tennis Team.

2. How many members are on 2.the tennis team? (Lesson 2-5)

3. Find the mean, median, mode, 3.and range for these data.(Lessons 2-3, 2-4)

3|1 � 31

4. Write a sentence or two to describe the distribution of the 4.number of matches won. (Lesson 2-5)

5. Evaluate |3| � |�2|. (Lesson 3-1) 5.

6. Order 61, �72, 50, �31, �12, and 12 from least to greatest. 6.(Lesson 3-2)

7. Which is greater, �9 or 8? (Lesson 3-2) 7.

Graph and label each point. (Lesson 3-3)

8. A(2, �2) 9. M(�3, �1) 8–9.


10. 4 � (�4) (Lesson 3-4) 10.

11. �18 � 12 (Lesson 3-5) 11.

12. �5(�6) (Lesson 3-6) 12.

13. 12 � (�3) (Lesson 3-7) 13.

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Chapter 3 Cumulative Review(Chapters 1–3)

Stem Leaf0 3 41 5 7 82 0 2 2 4 73 1 3 5 54 05 4

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Ass

essm

ent

1. Evaluate 7b � a if a � 5 and b � 2. (Lesson 1-4)

A. 9 B. 33 C. 12 D. 21 1.

2. If there are 28 basketball games during a season, how many gamesended in a winning score of 70–79points? (Lesson 2-1)

F. 28 G. 8H. 3 I. 5 2.

3. Find the median of the following data. 5, 9, 13, 4, 7, 5, 10 (Lesson 2-4)

A. 5 B. 7 C. 8 D. 9 3.

4. ENVIRONMENT The bar graph represents the content (inpercents) of U.S. landfills.Which is not a true statement? (Lesson 2-7)

F. The mode is paper.G. Metal makes up 8% of

landfills.H. Plastic and paper make up

most of landfills.I. The median is 24%. 4.

5. What is the range of data in the followingbox-and-whisker plot?(Lessons 2-3, 2-6)

A. 5 B. 16 C. 7 D. 15 5.

6. Evaluate |9| � |�4|. (Lesson 3-1)

F. 13 G. �13 H. �5 I. 5 6.

7. In which quadrant is the point (�5, 7) located? (Lesson 3-2)

A. I B. II C. III D. IV 7.

8. Evaluate �x � 11 if x � �10. (Lesson 3-5)

F. �21 G. 21 H. �1 I. 1 8.

9. Evaluate ac � b if a � �8, b � �6, and c � 3. (Lessons 3-6, 3-7)

A. �144 B. 4 C. 16 D. �4 9. DCBA

IHGF

DCBA

IHGF

DCBA

2 4 6 8 10 12 14 16 18 2220

IHGF

Other

Food

& Ya

rd W

aste

Rubb

er &

Leath

er

Metal

15

20

10

0

5

25

30

35

Perc

ent

Plasti

cPa

per

U.S. Landfill Content

8%

24%

6%

11%

30%

21%

DCBA

IHGF

DCBA


Standardized Test Practice (Chapters 1–4)

Part 1: Multiple Choice

Instructions: Fill in the appropriate oval for the best answer.

Score Frequency

50–59 2

60–69 5

70–79 ?

80–89 12

90–99 6

10. Solve 20 � n4 (Lesson 1-5) 10. 11.

11. Evaluate �ba if a � 16 and b � �2. (Lesson 3-7)

12. The frequency table 12.summarizes the number of DVDs owned by students in a classroom.Describe the interval and scale. (Lesson 2-1)

13. Find 6 � (�12). (Lesson 3-4) 13.

14. GEOMETRY Consider the points A(�2, 4), B(3, 4), C(3, 0), and D(�2, 0). (Lesson 3-3)

a. Graph the points in the same coordinate plane. Describe howyou locate point A.

b. Multiply the x-coordinate of point B by �1 and multiply the

y-coordinate of point B by 12. Name the new point B and give its

coordinates. Graph point B and identify the quadrant in which it lies.

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Part 3: Extended Response

Instructions: Write your answers below or to the right of the questions.

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

Part 2: Short Response\Grid In

Instructions: Enter your grid in answers by writing each digit of the answer in acolumn box and then shading in the appropriate circle that corresponds to that entry.Write answers to short answer questions in the space provided.


NAME ________________________________________ DATE ______________ PERIOD _____

Standardized Test Practice (continued)

(Chapters 1–4)

Numberof DVDs Tally

0–4 5

5–9 52

10–14 55

15–19 3

20–24 2 2

3

10

7

5

Frequency

© Glencoe/McGraw-Hill A1 Mathematics: Applications and Concepts, Course 2

Standardized Test PracticeStudent Recording Sheet (Use with pages 146–147 of the Student Edition.)

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Part 1:

Solve the problem and write your answer in the blank.

For grid in questions, also enter your answer by writing each number or symbolin a box. Then fill in the corresponding circle for that number or symbol.

11. 12. 14. 19.

12. (grid in)

13.

14. (grid in)

15.

16.

17.

18.

19. (grid in)

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

Select the best answer from the choices given and fill in the corresponding oval.

Multiple Choice

1.

2.

3.

4.

5.

6.

7.

8.

9.

10. IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

Part 2: Short Response/Grid in

Record your answer for Question 20 on the back of this paper.

Part 3: Extended Response

An

swer

s

General Scoring Guidelines• If a student gives only a correct numerical answer to a problem but does not show how he or she

arrived at the answer, the student will be awarded only 1 credit. All extended response questionsrequire the student to show work.

• A fully correct answer for a multiple-part question requires correct responses for all parts of thequestion. For example, if a question has three parts, the correct response to one or two parts of thequestion that required work to be shown is not considered a fully correct response.

• Students who use trial and error to solve a problem must show their method. Merely showing thatthe answer checks or is correct is not considered a complete response for full credit.

Exercise 20 Rubric

Standardized Test PracticeRubric (Use to score the Extended Response question on page 147 of the Student Edition.)

Score Specific Criteria4 The 3 points are correctly graphed on a coordinate plane with all labels in place. The

quadrant where no point on the graph is represented is recognized as quadrant IV.The figure formed by connecting the points is recognized as a triangle. Anunderstanding that the way to double the size of the triangle is to multiply eachordered pair by 2 is demonstrated. The table in expanded and all values arecorrectly computed.

3 All of the parts of the question are correctly answered, but the graph is not correctlylabeled. OROne of the points is not correctly graphed, but all other parts of the question arecorrect. ORThe quadrant where no point on the graph is represented is not recognized asquadrant IV, but all other parts of the question are correct. ORThe figure formed by connecting the points is not recognized as a triangle, but allother parts of the question are correct. ORThere is no understanding that the way to double the size of the triangle is tomultiply the ordered pair by 2, but all other parts of the question are correct. ORThere are computational errors in the expanded table, but all other parts of thequestion are correct.

2 Two parts of the question (the graph, the recognition of the quadrant, therecognition of the triangle, the understanding of how to double the size of the figure,or the completion of the table) are incorrect.

1 Only one or two parts of the question (the graph, the recognition of the quadrant,the recognition of the triangle, the understanding of how to double the size of thefigure, or the completion of the table) are correct.

0 Response is completely incorrect.



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Lesson 3–1

Answers (Lessons 3-1 and 3-2)


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tice:

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NA

ME

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ER

IOD

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HIS

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118,

109,

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or

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mat

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App

licat

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s, C

ours

e 2

Qu

anti

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ve C

om

par

iso

ns

An

un

usu

al t

ype

of p

robl

em i

s fo

un

d on

som

e st

anda

rdiz

ed m

ult

iple

-ch

oice

test

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his

pro

blem

typ

e is

cal

led

the

quan

tita

tive

com

pari

son

.

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ach

qu

anti

tati

ve c

ompa

riso

n q

ues

tion

,you

are

giv

en t

wo

quan

titi

es,o

ne

inC

olu

mn

A a

nd

one

in C

olu

mn

B.Y

ou a

re t

o co

mpa

re t

he

two

quan

titi

es a

nd

shad

e on

e of

fou

r ci

rcle

s on

an

an

swer

sh

eet.

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ade

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le A

if t

he

quan

tity

in

Col

um

n A

is

grea

ter;

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ade

circ

le B

if t

he

quan

tity

in

Col

um

n B

is

grea

ter;

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ade

circ

le C

if t

he

two

quan

titi

es a

re e

qual

;

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ade

circ

le D

if t

he

rela

tion

ship

can

not

be

dete

rmin

ed f

rom

th

ein

form

atio

n g

iven

.

Sh

ade

the

corr

ect

oval

to

the

left

of

each

pro

ble

m n

um

ber

.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

DC

BA

DC

BA

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Enric

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B A C B A A D C A C

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n A

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um

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e to

p o

f p

age

109

in y

ou

r te

xtb

oo

k.W

rite

yo

ur

answ

ers

bel

ow

.

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hat

is

the

win

d ch

ill

if t

her

e is

a w

ind

at 2

0 m

iles

per

hou

r an

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ete

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lder

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r w

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te

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ith

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ph

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raph

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ls f

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rcis

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on a

nu

mbe

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din

g t

he

Less

on

For

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an

d 5

,exp

ress

eac

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f th

e fo

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in w

ord

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grap

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nu

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phed

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um

ber

lin

e,w

hat

can

you

tel

lab

out

the

nu

mbe

r to

th

e le

ft?

the

nu

mbe

r to

th

e ri

ght?

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ple

an

swer

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e n

um

ber

to

th

e le

ft is

alw

ays

less

th

anth

e n

um

ber

to

th

e ri

gh

t.T

he

nu

mb

er t

o t

he

rig

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sg

reat

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han

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um

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th

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ft.

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pin

g Y

ou

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emb

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set

of

six

nu

mbe

rs,s

ome

posi

tive

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me

neg

ativ

e.E

xpla

in h

owyo

u c

an u

se a

nu

mbe

r li

ne

to o

rder

th

e n

um

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fro

m l

east

to

grea

test

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ee s

tud

ents

’wo

rk.

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hem

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s

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lenc

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mat

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licat

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and

Con

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s, C

ours

e 2

NA

ME

____

____

____

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____

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____

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____

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E _

____

____

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ER

IOD

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©G

lenc

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ill14

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athe

mat

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licat

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ours

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Nam

e th

e or

der

ed p

air

for

each

poi

nt

grap

hed

at

the

righ

t.T

hen

id

enti

fy t

he

qu

adra

nt

in w

hic

h e

ach

poi

nt

lies

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I

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axis

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II

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(�3,

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I10

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(3,�

5),I

V

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ph

an

d l

abel

eac

h p

oin

t on

th

e co

ord

inat

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lan

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1,3)

12.

V(2

,�4)

13.

C(4

,0)

14.

P(�

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M(�

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16.

K(�

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I(�

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D(0

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e th

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nt

on t

he

city

map

at

the

righ

t.

20.

Cit

y H

all

(0,0

)

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)

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Lesson 3–3

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lenc

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cGra

w-H

ill13

9M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Nam

e th

e or

der

ed p

air

for

poi

nt

P.T

hen

id

enti

fy t

he

qu

adra

nt

inw

hic

h P

lie

s.

•S

tart

at

the

orig

in.

•M

ove

4 u

nit

s le

ft a

lon

g th

e x-

axis

.•

Mov

e 3

un

its

up

on t

he

y-ax

is.

Th

e or

dere

d pa

ir f

or p

oin

t P

is (

�4,

3).

Pis

in

th

e u

pper

lef

t qu

adra

nt

or q

uad

ran

t II

.

Gra

ph

an

d l

abel

th

e p

oin

t M

(0,�

4).

•S

tart

at

the

orig

in.

•M

ove

0 u

nit

s al

ong

the

x-ax

is.

•M

ove

4 u

nit

s do

wn

on

th

e y-

axis

.•

Dra

w a

dot

an

d la

bel

it M

(0,�

4).

Nam

e th

e or

der

ed p

air

for

each

poi

nt

grap

hed

at

the

righ

t.T

hen

id

enti

fy t

he

qu

adra

nt

in w

hic

h

each

poi

nt

lies

.

1.P

(2,�

3),I

V2.

Q(�

3,�

2),I

II

3.R

(1,3

),I

4.S

(�2,

2),I

I

Gra

ph

an

d l

abel

eac

h p

oin

t on

th

e co

ord

inat

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lan

e.

5.A

(�1,

1)6.

B(0

,�3)

7.C

(3,2

)8.

D(�

3,�

1)

9.E

(1,�

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(1,3

)

y

xO �2

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21

43

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Stud

y Gu

ide

and

Inte

rven

tion

Th

e C

oo

rdin

ate

Pla

ne

The

co

ord

inat

e p

lan

eis

use

d to

loca

te p

oint

s.T

he h

oriz

onta

l num

ber

line

is t

he x

-axi

s.T

he v

ertic

alnu

mbe

r lin

e is

the

y-a

xis.

The

ir in

ters

ectio

n is

the

ori

gin

.

Poi

nts

are

loca

ted

usin

g o

rder

ed p

airs

.The

firs

t nu

mbe

r in

an

orde

red

pair

is t

he x

-co

ord

inat

e;th

ese

cond

num

ber

is t

he y

-co

ord

inat

e.

The

coo

rdin

ate

plan

e is

sep

arat

ed in

to fo

ur s

ectio

ns c

alle

d q

uad

ran

ts.



An

swer

s

©G

lenc

oe/M

cGra

w-H

ill14

2M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Pre-

Act

ivit

yR

ead

th

e in

tro

du

ctio

n a

t th

e to

p o

f p

age

112

in y

ou

r te

xtb

oo

k.W

rite

yo

ur

answ

ers

bel

ow

.

1.S

upp

ose

Ter

rell

sta

rts

at t

he

corn

er o

f R

uss

el a

nd

Mai

n a

nd

wal

ks

1 bl

ock

nor

th a

nd

2 bl

ocks

eas

t.N

ame

the

inte

rsec

tion

of

his

loc

atio

n.

Hig

hla

nd

an

d M

ob

ile

2.U

sin

g th

e w

ords

nor

th,s

outh

,wes

t,an

d ea

st,w

rite

dir

ecti

ons

to g

o fr

om

the

corn

er o

f S

choo

l an

d H

igh

lan

d to

th

e co

rner

of

Mai

n a

nd

Oak

.S

amp

le a

nsw

er:W

alk

6 b

lock

s w

est,

1 b

lock

so

uth

,an

d 1

blo

ck w

est.

Rea

din

g t

he

Less

on

3.T

he

wor

d co

ord

inat

eco

mes

fro

m t

wo

Lat

in w

ords

th

at m

ean

“to

arr

ange

toge

ther

.”H

ow a

re c

oord

inat

es u

sed

toge

ther

to

loca

te a

poi

nt

in a

coor

din

ate

plan

e?S

amp

le a

nsw

er:T

he

loca

tio

n o

f a

po

int

in a

co

ord

inat

e p

lan

e d

epen

ds

on

po

siti

on

alo

ng

an

x-a

xis

and

po

siti

on

alo

ng

a y

-axi

s.B

oth

po

siti

on

s,ca

lled

th

e x-

coo

rdin

ate

and

th

e y-

coo

rdin

ate,

are

nee

ded

in o

rder

to

loca

te a

po

int

in a

co

ord

inat

e p

lan

e.T

he

pai

r o

f co

ord

inat

es is

cal

led

an

ord

ered

pai

r.T

he

pai

r o

f co

ord

inat

esis

ord

ered

su

ch t

hat

th

e x-

coo

rdin

ate

is a

lway

s th

e fi

rst

nu

mb

er o

f th

ep

air

and

th

e y-

coo

rdin

ate

is a

lway

s th

e se

con

d n

um

ber

of

the

pai

r.

4.L

ook

at t

he

coor

din

ate

plan

e at

th

e ri

ght.

Nam

e th

e or

dere

d pa

ir f

or e

ach

poi

nt

grap

hed

.A

(�3,

3);

B(3

,2);

C(3

,�2)

5.In

th

e co

ordi

nat

e pl

ane

in E

xerc

ise

4,te

ll w

hic

hqu

adra

nt

each

of

the

poin

ts i

s in

.P

oin

t A

is in

qu

adra

nt

II,p

oin

t B

is in

qu

adra

nt

I,an

dp

oin

t C

is in

qu

adra

nt

IV.

Hel

pin

g Y

ou

Rem

emb

er6.

Wri

te a

way

to

rem

embe

r th

e n

ames

of

the

fou

r qu

adra

nts

of

the

coor

din

ate

plan

e.S

amp

le a

nsw

er:

Beg

in in

th

e q

uad

ran

t w

her

e b

oth

co

ord

inat

es a

re p

osi

tive

(th

e u

pp

er-r

igh

t q

uad

ran

t).T

his

isq

uad

ran

t I.

Nam

e th

e re

st o

f th

e q

uad

ran

ts b

y g

oin

g c

ou

nte

rclo

ckw

ise

aro

un

d t

he

qu

adra

nts

:II

(up

per

-lef

t q

uad

ran

t),I

II (l

ow

er-l

eft

qu

adra

nt)

,IV

(lo

wer

-rig

ht

qu

adra

nt)

.

y

xO �2

�3

�4

�2

�3

�4

21

43

1234A

B C

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ME

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E _

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ing

to L

earn

Mat

hem

atic

sT

he

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inat

e P

lan

e

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lenc

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cGra

w-H

ill14

1M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

SCH

OO

LF

or E

xerc

ises

1–4

,use

th

e co

ord

inat

e p

lan

e at

th

e ri

ght.

It

show

s a

map

of

the

room

s in

a

jun

ior

hig

h s

choo

l.

�2

�3

�4

�5

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y

xO12345

Com

pute

r Lab

Spec

ial S

ervi

ces

Engl

ish

Hist

ory

Coun

selo

r

Athl

etic

Dep

t.

Mus

ic

Exit

Mat

h

Nurs

e

Prac

tice:

Wor

d Pr

oble

ms

Th

e C

oo

rdin

ate

Pla

ne

NA

ME

____

____

____

____

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____

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____

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E _

____

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ER

IOD

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1.T

hal

ia i

s in

th

e ro

om l

ocat

ed a

t (�

2,1)

.W

hat

roo

m i

s sh

e in

? D

escr

ibe

in w

ords

how

to

get

from

th

e or

igin

to

this

poi

nt.

Co

mp

ute

r L

ab;

mov

e 2

un

its

toth

e le

ft a

nd

on

e u

nit

up

.

2.T

hal

ia’s

nex

t cl

ass

is 8

un

its

to t

he

righ

t an

d 5

un

its

dow

n o

n t

he

map

from

wh

ere

she

is n

ow.I

n w

hat

roo

m i

sT

hal

ia’s

nex

t cl

ass?

Fin

d th

e or

dere

dpa

ir t

hat

rep

rese

nts

th

e lo

cati

on o

f th

atro

om.

Mu

sic

roo

m;

(6,�

4)

3.T

yron

e is

in

th

e A

rt r

oom

,bu

t h

is n

ext

clas

s is

in

th

e H

isto

ry r

oom

.Giv

eT

yron

e di

rect

ion

s on

how

to

get

to t

he

His

tory

roo

m.

Sam

ple

an

swer

:W

alk

9 u

nit

s to

th

e ri

gh

t,an

dth

en 5

un

its

do

wn

.

4.O

n t

he

map

,wh

ich

cla

ssro

oms

are

loca

ted

in t

he

thir

d qu

adra

nt?

Des

crib

eth

e co

ordi

nat

es o

f al

l po

ints

in

th

e th

ird

quad

ran

t.S

cien

ce a

nd

Mat

hro

om

s;th

e x-

an

d y

-co

ord

inat

esar

e al

l neg

ativ

e.

5.N

EIG

HB

OR

HO

OD

Del

sin

mad

e a

map

of

his

nei

ghbo

rhoo

d in

su

ch a

way

th

atea

ch i

nte

rsec

tion

is

a po

int

on a

coor

din

ate

plan

e.R

igh

t n

ow,D

elsi

nst

ands

at

poin

t (�

4,�

3).G

ive

the

orde

red

pair

of

wh

ere

he

wil

l be

if

mov

es 5

un

its

to t

he

righ

t an

d 7

un

its

up

on t

he

map

.(1

,4)

6.N

EIG

HB

OR

HO

OD

Ref

er t

o E

xerc

ise

5.In

wh

ich

qu

adra

nt

is D

elsi

n w

hen

he

isdo

ne

wal

kin

g? D

escr

ibe

this

qu

adra

nt.

Qu

adra

nt

I;S

amp

le a

nsw

er:

Qu

adra

nt

I is

the

up

per

-rig

ht

qu

adra

nt.

Lesson 3–3



©G

lenc

oe/M

cGra

w-H

ill14

4M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Fin

d 4

�(�

6).

Met

hod

1U

se c

oun

ters

.M

eth

od 2

Use

a n

um

ber

lin

e.C

ombi

ne

a se

t of

4 p

osit

ive

cou

nte

rs•

Sta

rt a

t 0.

and

a se

t of

6 n

egat

ive

cou

nte

rs o

n a

mat

.•

Mov

e 4

un

its

righ

t.•

Th

en m

ove

6 u

nit

s le

ft.

Ad

d.

1.�

5 �

(�2)

�7

2.8

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93.

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3

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11)

55.

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100

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15

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luat

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xpre

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f a

�8,

b �

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and

c �

4.

10.

a �

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(�9)

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b �

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615

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Stud

y Gu

ide

and

Inte

rven

tion

Ad

din

g In

teg

ers

For

inte

gers

with

the

sam

e si

gn:

• th

e su

m o

f tw

o po

sitiv

e in

tege

rs is

pos

itive

.•

the

sum

of

two

nega

tive

inte

gers

is n

egat

ive.

For

inte

gers

with

diff

eren

t si

gns,

sub

trac

t th

eir

abso

lute

val

ues.

The

sum

is:

• po

sitiv

e if

the

posi

tive

inte

ger

has

the

grea

ter

abso

lute

val

ue.

• ne

gativ

e if

the

nega

tive

inte

ger

has

the

grea

ter

abso

lute

val

ue.

To a

dd in

tege

rs,

it is

hel

pful

to

use

coun

ters

or

a nu

mbe

r lin

e.

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lenc

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cGra

w-H

ill14

3M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Lati

tud

e an

d L

on

git

ud

eT

his

wor

ld m

ap s

how

s so

me

of t

he

lati

tude

an

d lo

ngi

tude

lin

es.L

atit

ude

is

mea

sure

d in

deg

rees

nor

th a

nd

sou

th o

f th

e eq

uat

or.L

ongi

tude

is

mea

sure

d in

degr

ees

east

an

d w

est

of t

he

prim

e m

erid

ian

,a l

ine

pass

ing

thro

ugh

Gre

enw

ich

,En

glan

d.(G

reen

wic

h i

s a

subu

rb o

f L

ondo

n.)

Th

e la

titu

de i

s u

sual

ly g

iven

fir

st.F

or e

xam

ple,

the

loca

tion

of

30�S

,60�

W i

slo

wer

Sou

th A

mer

ica.

(Sam

ple

an

swer

s ar

e g

iven

.Stu

den

ts m

ay p

rovi

de

mo

re s

pec

ific

pla

ces.

)

Nam

e a

pla

ce n

ear

each

loc

atio

n.U

se a

n a

tlas

or

oth

er r

efer

ence

sou

rce

to c

hec

k y

our

answ

ers.

1.30

�N,3

0�W

2.30

�S,3

0�E

3.60

�N,1

20�W

Atl

anti

c O

cean

So

uth

Afr

ica

Can

ada

4.15

�N,1

50�W

5.30

�S,1

40�E

6.25

�N,1

00�W

Haw

aii

Au

stra

liaM

exic

o

7.40

�N,1

20�W

8.45

�N,9

0�W

9.40

�N,5

�WC

alifo

rnia

Wis

con

sin

Sp

ain

10.

60�N

,45�

W11

.35

�N,1

40�E

12.

0�,6

0�E

Gre

enla

nd

Jap

anIn

dia

n O

cean

Equ

ator

Prime Meridian60

˚N

30˚N

30˚S

, 60 ˚

W

30˚N

0 ˚

0 ˚

0 ˚

30˚S

30˚S

60˚S

60˚S

60˚N

30˚E

30˚W

60˚E

90˚E

120̊E

150̊E

180̊

E

60˚W

90˚W

120˚W

150W̊En

richm

ent

NA

ME

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____

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E _

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Lesson 3–3



An

swer

s

©G

lenc

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cGra

w-H

ill14

6M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

NA

ME

____

____

____

____

____

____

____

____

____

____

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E _

____

____

____

_P

ER

IOD

__

___

Wri

te a

n a

dd

itio

n e

xpre

ssio

n t

o d

escr

ibe

each

sit

uat

ion

.Th

en f

ind

eac

h s

um

.

Prac

tice:

Wor

d Pr

oble

ms

Ad

din

g In

teg

ers

1.FO

OTB

ALL

A t

eam

gai

ns

20 y

ards

.Th

enth

ey l

ose

7 ya

rds.

20�

(�7)

;13

2.M

ON

EYR

oger

ow

es h

is m

om $

5.H

ebo

rrow

s an

oth

er $

6 fr

om h

er.

(�5)

�(�

6);

�11

3.G

OLF

Juan

ita’

s sc

ore

was

5 o

ver

par

onth

e fi

rst

9 h

oles

.Her

sco

rew

as 4

un

der

par

on t

he

seco

nd

9 h

oles

.5

�(�

4);

1

4.H

OT

AIR

BA

LLO

ON

A b

allo

on r

ises

340

feet

in

to t

he

air.

Th

en i

t de

scen

ds13

0fe

et.

340

�(�

130)

;21

0

5.C

YC

LIN

GA

cyc

list

tra

vels

dow

nh

ill

for

125

feet

.Th

en s

he

trav

els

up

a h

ill

50fe

et.

�12

5�

50;

�75

6.A

IRPL

AN

EA

pla

ne

desc

ends

1,2

00 f

eet.

Th

en i

t de

scen

ds a

not

her

500

fee

t.�

1,20

0�

(�50

0);�

1,70

0

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lenc

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ill14

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athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Tel

l w

het

her

eac

h s

um

is

pos

itiv

e,n

egat

ive,

or z

ero

wit

hou

t ad

din

g.

Ad

d.

1.5

�(�

8)�

32.

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�3

0

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3 �

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7 �

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8 �

102

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7 �

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a�

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tice:

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ger

s



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athe

mat

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App

licat

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and

Con

cept

s, C

ours

e 2

Dar

tbo

ard

Pu

zzle

s

Th

ree

dar

ts a

re t

hro

wn

.Eac

h d

art

mu

st l

and

on

a d

iffe

ren

t sp

ace

inor

der

to

cou

nt.

Fin

d t

he

hig

hes

t an

d t

he

low

est

pos

sib

le s

core

s.

1.2.

3.

hig

hes

t sc

ore:

18h

igh

est

scor

e:�

2h

igh

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scor

e:50

0lo

wes

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low

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scor

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23lo

wes

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In t

hes

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rob

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th

row

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ach

dar

t m

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lan

d o

n a

dif

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spac

e in

ord

er t

o co

un

t.S

olve

eac

h p

uzz

le.

4.F

ind

thre

e w

ays

to m

ake

the

scor

e �

5.5.

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d th

ree

way

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mak

e th

e sc

ore

0.

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ill v

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Enric

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©G

lenc

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w-H

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athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

NA

ME

____

____

____

____

____

____

____

____

____

____

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E _

____

____

____

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ER

IOD

__

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Pre-

Act

ivit

yR

ead

th

e in

tro

du

ctio

n a

t th

e to

p o

f p

age

120

in y

ou

r te

xtb

oo

k.W

rite

yo

ur

answ

ers

bel

ow

.

1.W

hat

is

the

char

ge a

t th

e to

p of

a c

lou

d w

her

e th

ere

are

mor

e pr

oton

sth

an e

lect

ron

s?p

osi

tive

2.W

hat

is

the

char

ge a

t th

e bo

ttom

of

a cl

oud

wh

ere

ther

e ar

e m

ore

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,tel

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hem

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lenc

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mat

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lenc

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cGra

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9M

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mat

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lenc

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cGra

w-H

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2M

athe

mat

ics:

App

licat

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s, C

ours

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Pre-

Act

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om

ple

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Min

i Lab

at

the

top

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pag

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8 in

yo

ur

text

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te y

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r an

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elo

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rite

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btr

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sam

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on

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l h

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earn

Mat

hem

atic

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ub

trac

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g In

teg

ers

©G

lenc

oe/M

cGra

w-H

ill15

1M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Su

btr

act.

Prac

tice:

Wor

d Pr

oble

ms

Su

btr

acti

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Inte

ger

s

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ME

____

____

____

____

____

____

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ER

IOD

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___

1.FO

OTB

ALL

A t

eam

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ned

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ards

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rst

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of

the

gam

e.T

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eylo

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ind

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l ch

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wri

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our

acco

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MPE

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as 9

in

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w t

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surf

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Fin

d th

e di

ffer

ence

in t

he

dept

hs

of t

hei

r h

oles

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in.

Lesson 3–5



An

swer

s

©G

lenc

oe/M

cGra

w-H

ill15

4M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Mu

ltip

ly 5

(�2)

.

5(�

2) �

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The

inte

gers

hav

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ffere

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igns

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Mu

ltip

ly �

3(7)

.

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7) �

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ltip

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me

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IOD

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Stud

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ide

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6

©G

lenc

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cGra

w-H

ill15

3M

athe

mat

ics:

App

licat

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and

Con

cept

s, C

ours

e 2

Dis

tan

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n t

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Nu

mb

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To

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d th

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____

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____

____

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ATE

___

____

____

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PE

RIO

D

____

_

Lesson 3–5



Prac

tice:

Wor

d Pr

oble

ms

Mu

ltip

lyin

g In

teg

ers

©G

lenc

oe/M

cGra

w-H

ill15

6M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Mu

ltip

ly.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

1.TE

MPE

RA

TUR

ES

upp

ose

the

tem

pera

ture

outs

ide

is d

ropp

ing

3 de

gree

s ea

chh

our.

How

mu

ch w

ill

the

tem

pera

ture

drop

in

8 h

ours

?�

24�

2.D

IVIN

GA

dee

p-se

a di

ver

desc

ends

belo

w t

he

surf

ace

of t

he

wat

er a

t a

rate

of 6

0 fe

et e

ach

min

ute

.Wh

at i

s th

ede

pth

of

the

dive

r af

ter

10 m

inu

tes?

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0 ft

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OC

KA

com

pute

r st

ock

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oin

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ch h

our

for

6 h

ours

.Fin

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tal

poin

ts t

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k fe

ll.

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po

ints

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RO

UG

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leve

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ater

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pply

dro

ps 2

in

ches

each

wee

k.H

ow f

ar w

ill

it h

ave

drop

ped

in 4

wee

ks?

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in.

5.M

ON

EYM

rs.R

ockw

ell

lost

mon

ey o

nan

in

vest

men

t at

a r

ate

of $

4 pe

r da

y.H

ow m

uch

did

sh

e lo

se a

fter

tw

ow

eeks

?�

$56

6.TE

NN

IS B

ALL

SJo

sh p

urc

has

ed 8

can

s of

ten

nis

bal

ls.T

he

can

s ca

me

wit

h 3

bal

lsin

eac

h c

an.H

ow m

any

ball

s di

d Jo

shpu

rch

ase?

24 t

enn

is b

alls

Lesson 3–6

Prac

tice:

Ski

llsM

ult

iply

ing

Inte

ger

s

©G

lenc

oe/M

cGra

w-H

ill15

5M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Mu

ltip

ly.

1.�

4(6)

�24

2.�

2(�

8)16

3.12

(�4)

�48

4.�

6(5)

�30

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10(�

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(5)2

�25

7.(�

5)2

258.

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0

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7(15

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105

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AS

imp

lify

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h e

xpre

ssio

n.

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y14

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�3x

)�

21x

15.

7(5g

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g16

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49w

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3(�

3y)

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h)

20h

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EBR

AE

valu

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each

exp

ress

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if

g �

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h �

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and

k �

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ME

____

____

____

____

____

____

____

____

____

____

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E _

____

____

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ER

IOD

__

___



An

swer

s

©G

lenc

oe/M

cGra

w-H

ill15

8M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Inte

ger

Maz

eF

ind

you

r w

ay t

hro

ugh

th

e m

aze

by m

ovin

g to

th

e ex

pres

sion

in

an

adj

acen

t se

ctio

n w

ith

the

nex

t h

igh

est

valu

e.

Sta

rt−5

0

−55

20 −

20

−32

+ 28

−12

+ 2

−3 +

(−4)

4 +

(−12

)

−13

+ 12

−10

+ 16

−35

+ 5 6 −

8

5(−9

)

9(−6

)−8(5

)

−3(5

)

−5(−

6)

−1(3

)

−4(2

)

−3(−

5)

3(−3

)(−5

)

−2(−

5)(−

1)

6(−1

0)9(

−1)

3 +

(−3)

30 −

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)(−1

)

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(−5)

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+ 9

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2

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− (

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ME

____

____

____

____

____

____

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____

____

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E _

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ER

IOD

__

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Enric

hmen

tRe

adin

g to

Lea

rn M

athe

mat

ics

Mu

ltip

lyin

g In

teg

ers

©G

lenc

oe/M

cGra

w-H

ill15

7M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Pre-

Act

ivit

yC

om

ple

te t

he

Min

i Lab

at

the

top

of

pag

e 13

4 in

yo

ur

text

bo

ok.

Wri

te y

ou

r an

swer

s b

elo

w.

1.W

rite

a m

ult

ipli

cati

on s

ente

nce

th

at d

escr

ibes

th

e m

odel

.4(

�2)

��

8

Fin

d e

ach

pro

du

ct u

sin

g co

un

ters

.

2.3(

�2)

�6

3.4(

�3)

�12

4.1(

�7)

�7

5.5(

�2)

�10

6.W

rite

a r

ule

for

fin

din

g th

e si

gn o

f th

e pr

odu

ct o

f a

posi

tive

an

d n

egat

ive

inte

ger.

A p

osi

tive

inte

ger

tim

es a

neg

ativ

e in

teg

er e

qu

als

an

egat

ive

inte

ger

.

Rea

din

g t

he

Less

on

7.G

ive

an e

xam

ple

that

sh

ows

how

mu

ltip

lica

tion

is

the

sam

e as

rep

eate

dad

diti

on.I

n y

our

exam

ple,

tell

wh

at t

he

adde

nd

is.

Sam

ple

an

swer

:3(

�9)

�(�

9) �

(�9)

�(�

9) �

�27

Th

e ad

den

d is

�9.

8.H

ow d

oes

the

sen

ten

ce 4

(�2)

��

2(4)

ill

ust

rate

th

e C

omm

uta

tive

P

rope

rty

of M

ult

ipli

cati

on?

Sam

ple

an

swer

:Th

e se

nte

nce

sh

ow

s th

at if

yo

uch

ang

e th

e o

rder

of

the

nu

mb

ers,

the

resu

lt is

sti

ll th

e sa

me.

Fro

m t

he

exam

ple

in t

he

Min

i Lab

,we

kno

w t

hat

4(�

2) �

�8.

Th

eref

ore

,by

the

Co

mm

uta

tive

Pro

per

ty o

f M

ult

iplic

atio

n,�

2(4)

��

8.9.

Com

plet

e ea

ch o

f th

e fo

llow

ing

sen

ten

ces

wit

h t

he

wor

d po

siti

veor

neg

ativ

e.

a.T

he

prod

uct

of

two

inte

gers

wit

h d

iffe

ren

t si

gns

is _

____

____

____

__.

neg

ativ

e

b.

Th

e pr

odu

ct o

f tw

o in

tege

rs w

ith

th

e sa

me

sign

is

____

____

____

___.

po

siti

ve

Hel

pin

g Y

ou

Rem

emb

er10

.Yo

u k

now

th

e ru

le f

or d

eter

min

ing

the

sign

of

the

prod

uct

of

two

inte

gers

wh

en t

he

sign

s ar

e al

ike

or d

iffe

ren

t.C

onsi

der

the

prod

uct

of

thre

ein

tege

rs.W

ith

a p

artn

er s

um

mar

ize

the

sign

s of

th

e pr

odu

cts

of 3

inte

gers

wh

en t

hre

e,tw

o,on

e or

non

e of

th

e in

tege

rs a

re p

osit

ive.

Th

ep

rod

uct

of

3 in

teg

ers

is p

osi

tive

wh

en a

ll 3

inte

ger

s ar

ep

osi

tive

or

wh

en o

nly

on

e in

teg

er is

po

siti

ve a

nd

th

e p

rod

uct

is n

egat

ive

in o

ther

cas

es.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Lesson 3–6



©G

lenc

oe/M

cGra

w-H

ill16

0M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Div

ide.

1.�

15 �

3�

52.

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8)3

3.22

�(�

2)�

114.

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7)7

5.�

8 �

(�8)

16.

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�9

7.22

5 �

(�15

)�

158.

�0 90

9.�

38 �

2�

1910

.6 44

16

11.

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0 �

(�50

)10

12.

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9 �

(�21

)9

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EBR

AE

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ress

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if

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�32

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d p

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8.

13.

m �

n�

1614

.p

�4

�2

15.

p2�

m�

216

.m

�p

4

17.

� np 4

18.

p �

n2

�2

19.

np2 216

20.18

p�n

�

2

21.

m �

(np)

222

.m p

�n

6

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice:

Ski

llsD

ivid

ing

Inte

ger

s

Lesson 3–7

©G

lenc

oe/M

cGra

w-H

ill15

9M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Div

ide

30 �

(�5)

.

30 �

(�5)

The

inte

gers

hav

e di

ffere

nt s

igns

.

30 �

(�5)

��

6T

he q

uotie

nt is

neg

ativ

e.

Div

ide

�10

0 �

(�5)

.

�10

0 �

(�5)

The

inte

gers

hav

e th

e sa

me

sign

.

�10

0 �

(�5)

�20

The

quo

tient

is p

ositi

ve.

Div

ide.

1.�

12 �

4�

32.

�14

�(�

7)2

3. �18

2�

94.

�6

�(�

3)2

5.�

10 �

10�

16.

� �8 20 0

4

7.35

0 �

(�25

)�

148.

�42

0 �

(�3)

140

9.5 44 50

1210

.�

12 656 �

16

ALG

EBR

AE

valu

ate

each

exp

ress

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if

d �

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,e�

�4,

and

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8.

11.

12 �

e�

312

.40

�f

5

13.

d�

6�

414

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6

15.

f�

e�

216

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2

17.

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ef�

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16

19.

f e22 4

20.

d fe 12

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

Inte

rven

tion

Div

idin

g In

teg

ers

The

quo

tient

of

two

inte

gers

with

diff

eren

t si

gns

is n

egat

ive.

The

quo

tient

of

two

inte

gers

with

the

sam

e si

gn is

pos

itive

.



An

swer

s

©G

lenc

oe/M

cGra

w-H

ill16

2M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Pre-

Act

ivit

yC

om

ple

te t

he

Min

i Lab

at

the

top

of

pag

e 13

8 in

yo

ur

text

bo

ok.

Wri

te y

ou

r an

swer

s b

elo

w.

Fin

d e

ach

qu

otie

nt

usi

ng

cou

nte

rs.

1.�

6�

2�

3

2.�

12 �

3�

4

Rea

din

g t

he

Less

on

Wri

te t

wo

div

isio

n s

ente

nce

s re

late

d t

o ea

ch o

f th

e fo

llow

ing

mu

ltip

lica

tion

sen

ten

ces.

3.�

6(�

3) �

184.

�21

(�2)

�42

18 �

(�3)

��

6;42

�(�

21)

��

2;18

�(�

6) �

�3

42 �

(�2)

��

21

5.�

6(3)

��

186.

2(�

21)

��

42�

18 �

3 �

�6;

�42

�(�

21)

�2;

�18

�(�

6) �

3�

42 �

2 �

�21

7.C

ompl

ete

each

of

the

foll

owin

g se

nte

nce

s w

ith

th

e w

ord

posi

tive

orn

egat

ive.

a.T

he

quot

ien

t of

tw

o in

tege

rs w

ith

dif

fere

nt

sign

s is

___

____

____

____

.n

egat

ive

b.

Th

e qu

otie

nt

of t

wo

inte

gers

wit

h t

he

sam

e si

gn i

s __

____

____

____

_.p

osi

tive

8.In

th

e di

visi

on s

ente

nce

�72

�8

��

9,id

enti

fy t

he

divi

den

d,th

e di

viso

r,an

d th

e qu

otie

nt.

div

iden

d:

�72

;d

ivis

or:

8;q

uo

tien

t:�

9

Hel

pin

g Y

ou

Rem

emb

er9.

Des

crib

e h

ow t

he

oper

atio

ns

of m

ult

ipli

cati

on a

nd

divi

sion

are

opp

osit

e of

each

oth

er.A

re t

hes

e op

erat

ion

s op

posi

te i

n a

ll c

ases

? W

hat

is

the

one

inte

ger

that

can

not

be

a di

viso

r?M

ult

iplic

atio

n is

th

e o

pp

osi

te o

fd

ivis

ion

in t

hat

th

e p

rod

uct

of

a q

uo

tien

t an

d d

ivis

or

giv

esth

e d

ivid

end

.Eve

n t

ho

ug

h y

ou

can

tak

e th

e p

rod

uct

of

zero

and

a n

um

ber

,zer

o c

ann

ot

be

a d

ivis

or.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Read

ing

to L

earn

Mat

hem

atic

sD

ivid

ing

Inte

ger

s

©G

lenc

oe/M

cGra

w-H

ill16

1M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Div

ide.

Prac

tice:

Wor

d Pr

oble

ms

Div

idin

g In

teg

ers

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

1.ST

OC

K M

AR

KET

Du

rin

g a

5-da

yw

orkw

eek,

the

stoc

k m

arke

t de

crea

sed

by 6

5 po

ints

.Fin

d th

e av

erag

e da

ily

chan

ge i

n t

he

mar

ket

for

the

wee

k.�

13 p

oin

ts

2.M

OTI

ON

Mr.

Dia

z de

crea

sed

the

spee

dof

his

car

by

30 m

iles

per

hou

r ov

er a

peri

od o

f 10

sec

onds

.Fin

d th

e av

erag

ech

ange

in

spe

ed e

ach

sec

ond.

�3

mp

h p

er s

3.W

EATH

ERO

ver

the

past

sev

en d

ays,

Mrs

.Ch

o fo

un

d th

at t

he

tem

pera

ture

outs

ide

had

dro

pped

a t

otal

of

35de

gree

s.F

ind

the

aver

age

drop

in

tem

pera

ture

eac

h d

ay.

�5

deg

rees

per

day

4.B

ASK

ETB

ALL

Th

e ba

sket

ball

tea

m l

ost

thei

r la

st 6

gam

es.T

hey

los

t by

a t

otal

of 4

8 po

ints

.Fin

d th

e av

erag

e n

um

ber

of p

oin

ts b

y w

hic

h e

ach

gam

e w

as l

ost.

�8

po

ints

per

gam

e

5.PO

PULA

TIO

NT

he

enro

llm

ent

at D

avis

Mid

dle

Sch

ool

drop

ped

by 6

0 st

ude

nts

over

a 5

-yea

r pe

riod

.Wh

at i

s th

eav

erag

e ye

arly

dro

p in

en

roll

men

t?�

12 s

tud

ents

an

nu

ally

6.SU

BM

AR

INE

A s

ubm

arin

e de

scen

ds a

t a

rate

of

60 f

eet

each

min

ute

.How

lon

gw

ill

it t

ake

it t

o de

scen

d to

a d

epth

of

660

feet

bel

ow t

he

surf

ace?

11 m

in

Lesson 3–7



©G

lenc

oe/M

cGra

w-H

ill16

3M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Div

isio

n b

y Ze

ro?

Som

e in

tere

stin

g th

ings

hap

pen

wh

en y

ou t

ry t

o di

vide

by

zero

.For

exa

mpl

e,lo

ok a

t th

ese

two

equ

atio

ns.

5 0�

x

0 0�

y

If y

ou c

an w

rite

th

e eq

uat

ion

s ab

ove,

you

can

als

o w

rite

th

e tw

o eq

uat

ion

sbe

low

.

0�

x�

5 0

�y

�0

How

ever

,th

ere

is n

o n

um

ber

that

wil

l m

ake

the

left

equ

atio

n t

rue.

Th

iseq

uat

ion

has

no

solu

tion

.For

th

e ri

ght

equ

atio

n,e

very

nu

mbe

r w

ill

mak

e it

tru

e.T

he

solu

tion

s fo

r th

is e

quat

ion

are

“al

l n

um

bers

.”

Bec

ause

div

isio

n b

y ze

ro l

eads

to

impo

ssib

le s

itu

atio

ns,

it i

s n

ot a

“le

gal”

step

in s

olvi

ng

a pr

oble

m.P

eopl

e sa

y th

at d

ivis

ion

by

zero

is

un

defi

ned

,or

not

poss

ible

,or

sim

ply

not

all

owed

.

Des

crib

e th

e so

luti

on s

et f

or e

ach

eq

uat

ion

.

1.4x

�0

2.x

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Lesson 3–7


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13. D

G

C

I

A

G

B

H

A

G

D

F

C

4

B

F

D

H

B

H

A

I

B

I

C

F

B

F

D

H

A

G

A

H

B

I

B

H

A

Chapter 3 Assessment Answer KeyForm 1 Form 2APage 165 Page 166 Page 167

(continued onthe next page)


An

swer

s

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B: 10

D

F

C

I

B

I

B

I

A

G

C

F

D

G

A

H

B

F

D

G

A

I

A

H

B

6

B

I

A

H

B

H

B

I

C

F

B

F

Chapter 3 Assessment Answer KeyForm 2A (continued) Form 2BPage 168 Page 169 Page 170


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13–14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

B: 12

�11

�12c

�15a

�1

�24

2

�2

18

4

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21

2

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9

6

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Q

(�1, �3); III

(�3, 2); II

Athens

�2, �1, 0, 3, 5, 7�

�

�

0 3�3�6

10

11

�5

45

Chapter 3 Assessment Answer KeyForm 2CPage 171 Page 172

(continued on the next page)


An

swer

s

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13–14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

B: 14

�9

8y

�30z

�6

�40

�3

�4

30

7

�8

13

2

�17

�12

25

9

�20

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2

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S

A

(1,�2); IV

(3, 1); I

St. Paul

�8, �5, �1, 2, 3, 4

�

�

�

0 3�3�6

8

13

�13

300

Chapter 3 Assessment Answer KeyForm 2DPage 173 Page 174


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13–14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

B:6, �3; Divide the

previous term by �2.

6

�6bc

�35e

�6

1

�2

�45

3

�12

80

�13

8

3

3

�121

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(2, 0); x-axis

(�3, 3); II

Chicago

�7, �5, �3, 0, 4, 10

�

�

�

�2 0 2�4 4

2

16

�11

380

Chapter 3 Assessment Answer KeyForm 3Page 175 Page 176


An

swer

s


Chapter 3 Assessment Answer Key Page 177, Extended Response Assessment

Scoring Rubric

Level Specific Criteria

4 The student demonstrates a thorough understanding of the mathematicsconcepts and/or procedures embodied in the task. The student hasresponded correctly to the task, used mathematically sound procedures,and provided clear and complete explanations and interpretations. Theresponse may contain minor flaws that do not detract from thedemonstration of a thorough understanding.

3 The student demonstrates an understanding of the mathematics conceptsand/or procedures embodied in the task. The student’s response to thetask is essentially correct with the mathematical procedures used and theexplanations and interpretations provided demonstrating an essential butless than thorough understanding. The response may contain minor errorsthat reflect inattentive execution of the mathematical procedures orindications of some misunderstanding of the underlying mathematicsconcepts and/or procedures.

2 The student has demonstrated only a partial understanding of themathematics concepts and/or procedures embodied in the task. Althoughthe student may have used the correct approach to obtaining a solution ormay have provided a correct solution, the student’s work lacks an essentialunderstanding of the underlying mathematical concepts. The responsecontains errors related to misunderstanding important aspects of the task,misuse of mathematical procedures, or faulty interpretations of results.

1 The student has demonstrated a very limited understanding of themathematics concepts and/or procedures embodied in the task. Thestudent’s response to the task is incomplete and exhibits many flaws.Although the student has addressed some of the conditions of the task, thestudent reached an inadequate conclusion and/or provided reasoning thatwas faulty or incomplete. The response exhibits many errors or may beincomplete.

0 The student has provided a completely incorrect solution oruninterpretable response, or no response at all.


Chapter 3 Assessment Answer Key Page 177, Extended Response Assessment

Scoring Rubric

1. a. You can use a number line tocompare integers. The valuesincrease as you go right and decreaseas you go left.

b. �3, �1, �2, �4

c. The absolute value of a number isthe number of units its graph is fromthe graph of 0 on the number line.

d. |�3|�3

e. �3 � (�2)

Glen’s score after two rounds is �1.

f. �1 � (�3) � �4

g. �2 � (�3)

The difference between Horatio’s firstand second round scores is 5.

2.

a. Graph A(4, 6) by starting at theorigin, moving 4 units to the rightand 6 units up.Point A lies in quadrant I.

b. 4 · (�2) � �8 and 6 · (�1) � �6, sopoint B has coordinates (�8, �6).Point B lies in quadrant III.

c. �8 � 4 � �2 and �6 � (�3) � 2, sopoint C has coordinates (�2, 2).Point C lies in quadrant II.

y

xO

�4�6�8

�4�6�8 42 86

2468

(�2, 2)

(4, 6)

C

A

(�8, �6)B

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�

�

�

�

�

�

�

�

�

�

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In addition to the scoring rubric found on page A26, the following sample answersmay be used as guidance in evaluating extended response assessment items.

An

swer

s

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11. Sample answer: aplane in which ahorizontal numberline and a verticalnumber lineintersect at theirzero points

12. Sample answer: thepair of numbers (x-coordinate,y-coordinate) usedto locate a point inthe coordinateplane

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Quiz (Lessons 3-3 and 3-4)

Page 179

1–3.

4.

5.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Quiz (Lesson 3-7)

Page 180

1.

2.

3.

4.

5. 2

�6

�3

7

�4

�20s

�18e

�56

11

�10

�18

35

�81

30

�13

�4

5

y

xO

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1234

S

RT

�

�

�

�

15

9

3

24

�15

C

quadrant

opposites

origin

negative integer

y-axis

x-coordinate

additive inverse

graph

integer

absolute value

Chapter 3 Assessment Answer KeyVocabulary Test/Review Quiz (Lessons 3-1 and 3-2) Quiz (Lessons 3-5 and 3-6)

Page 178 Page 179 Page 180


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

1.

2.

3.

4.

5.

6.

7.

8–9.

10.

11.

12.

13. �4

30

�30

0

y

xO

�2�3�4

�2�3�4 21 43

1234

MA

8

�72, �31, �12,12, 50, 61

1

Sample answer: Themean and median

number of wins areclose, indicating thedata are fairly well-

centered in themiddle of the range

of possible wins.About half of the

data values clusterfrom 17 to 35.

25; 23; 22 and 35; 51

16

18

�11

(�1, 4); II

(3, �2); IV

(�6, �1); III

(5, 4); I

�

�

�350

G

A

I

D

F

B

Chapter 3 Assessment Answer KeyMid-Chapter Test Cumulative ReviewPage 181 Page 182


An

swer

s

1.

2.

3.

4.

5.

6.

7.

8.

9.

10. 11.

12.

13.

14. a. Graph A(�2, 4) by starting atthe origin, moving 2 units tothe left and 4 units up.

b. �1 � 3 � �3 and �12

� � 4 � 2, so point B� has coordinates (�3, 2). Point B� lies inquadrant II.

�6

interval 5; scale0 to 24

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

8

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

8 0

DCBA

IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

Chapter 3 Assessment Answer KeyStandardized Test PracticePage 183 Page 184


y

xO

�2�3�4

�2�3�4 21 43

1234

B�

A B

D C

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