authors rick wunderlich gifted consultant advisors robert...
TRANSCRIPT
AuthorsBruce McAskillB.Sc., B.Ed., M.Ed., Ph.D.Mathematics ConsultantVictoria, British Columbia
Wayne WattB.Sc., B.Ed., M.Ed.Mathematics ConsultantWinnipeg, Manitoba
Stella AblettB.Sc., B.Ed., M.Ed.Mulgrave School, West
Vancouver (Independent)British Columbia
Blaise JohnsonB.Sc., B.Ed.School District 45 (West Vancouver)British Columbia
Greg McInultyB.Sc., B.Ed.Edmonton Public SchoolsAlberta
Tricia PerryB.Ed.St. James-Assiniboia School DivisionManitoba
Michael WebbB.Sc., M.Sc., Ph.D.Mathematics ConsultantToronto, Ontario
Rick WunderlichB.Ed.School District 83 (North Okanagan/Shuswap)British Columbia
Chris ZarskiB.Ed., M.Ed.Evergreen Catholic Separate
Regional Division No. 2Alberta
Assessment/Pedagogy ConsultantsBruce McAskillB.Sc., B.Ed., M.Ed., Ph.D.Mathematics ConsultantVictoria, British Columbia
Wayne WattB.Sc., B.Ed., M.Ed.Mathematics ConsultantWinnipeg, Manitoba
Chris ZarskiB.Ed., M.Ed.Evergreen Catholic Separate
Regional Division No. 2Alberta
Aboriginal ConsultantCheryl MakokisEdmonton Public Schools Alberta
Gifted ConsultantRobert WongEdmonton Public SchoolsAlberta
Literacy and Numeracy ConsultantIan StrachanCalgary Board of EducationAlberta
Problem Solving, Mental Math, and Estimation ConsultantGreg McInultyEdmonton Public SchoolsAlberta
Special Education ConsultantJoanne AldridgeEdmonton Public SchoolsAlberta
Technology ConsultantTed KeatingThompson Rivers UniversityBritish Columbia
ESL ConsultantMaureen SimsSpecial Education and ESL TeacherToronto, Ontario
AdvisorsRalph BackéThe Winnipeg School DivisionManitoba
Eric BalzariniSchool District 35 (Langley)British Columbia
Sandra HaraznyRegina Roman Catholic Separate School Division No. 81Saskatchewan
Erv HendersonMathematics ConsultantSaskatchewan
Emily KalwarowskyEdmonton Catholic Separate School District No. 7Alberta
Wanda LloydCalgary Roman Catholic Separate School District No. 1Alberta
Tony MayWest Point Grey Academy (Independent)British Columbia
James McConvilleSchool District 43 (Coquitlam)British Columbia
Enzo TimoteoMathematics ConsultantEdmonton, Alberta
MathLinks 8
Copyright © 2008, McGraw-Hill Ryerson Limited. All rights reserved. Excerpts from this publication may be reproduced under licence from Access Copyright (visit accesscopyright.ca), or with the express written permission of Nelson Education Ltd., or as permitted by law. Requests which fall outside of Access Copyright guidelines must be submitted online to cengage.com/permissions. Further questions about permissions can be emailed to [email protected].
ALL RIGHTS ARE OTHERWISE RESERVED. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanic, photocopying, scanning, recording or otherwise, except as specifically authorized.
Every effort has been made to trace ownership of all copyrighted material and to secure permission from copyright holders. In the event of any question arising as to the use of any material, we will be pleased to make the necessary corrections in future printings.
ISBN-13: 978-0-07-097338-1ISBN-10: 0-07-097338-5
2 3 4 5 21 20 19 18
Printed and bound in Canada
Statistics Canada information is used with the permission of Statistics Canada. Users are forbidden to copy the data and redisseminate them, in an original or modified form, for commercial purposes, without permission from Statistics Canada. Information on the availability of the wide range of data from Statistics Canada can be obtained from Statistics Canada’s Regional Offices, its World Wide Web site at http://www.statcan.ca, and its toll-free access number 1-800-263-1136.
Math Publisher: Linda AllisonProject Manager: Helen Masoncontent Manager: Jean FordDeveloPMental eDitors: Susan Till, Janice Dyer, Rosemary Tanner, Rita Vanden Heuvel Manager, eDitorial services: Crystal ShorttsuPervising eDitor: Shannon MartincoPy eDitor: Linda Jenkins, Red Pen ServicesPhoto research & PerMissions: Linda TanakaeDitorial assistant: Erin HartleyeDitorial coorDinator: Jennifer Keay, Christine ArnoldManager, ProDuction services: Yolanda PigdenProDuction coorDinator: Paula Browninterior Design: Pronk & Associates cover Design: Valid Design & Layoutart Direction: Tom Dart, First Folio Resource Group, Inc.electronic Page Make-uP: Tom Dart, Luciano Sebastion De Monte, Kim
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For more information contact Nelson Education Ltd., 1120 Birchmount Road, Toronto, Ontario M1K 5G4. Or you can visit our website at nelson.com.
There are many students, teachers, and administrators who the publisher, authors, and consultants of MathLinks 8 wish to thank for their thoughtful comments and creative suggestions about what would work best in their classrooms. Their input and assistance have been invaluable in making sure that the Student Resource and its related Teacher’s Resource meet the needs of students and teachers who work within the Western and Northern Canadian Protocol Common Curriculum Framework.
We would like to thank the Grade 8 students of Wilson Middle School, Lethbridge, Alberta, Principal, Craig Brack, and teachers, Nancy Bridal, and Irene Dersch, for their help in coordinating the photography sessions.
Acknowledgements
Aboriginal ReviewerPaul PalingSchool District 52 (Prince Rupert)British Columbia
Inuit ReviewerChristine PurseMathematics ConsultantBritish Columbia
Métis ReviewerGreg KingPembina Hills Regional Division No. 7Alberta
ReviewersLisa AllenRegina School District 4Saskatchewan
Ryan Bailey Northern Lights School Division No. 69Alberta
Tammy BaydockSt. James-Assiniboia School DivisionManitoba
Linda BensonSeven Oaks School Division 10Manitoba
Scott CarlsonGolden Hills School Division No. 75Alberta
Kelly ChoyYukon EducationYukon
Dale Cooper Edmonton Public SchoolsAlberta
Nicolas CurciLouis Riel School DivisionManitoba
Brad EppSchool District 73 (Kamloops/ Thompson)British Columbia
Victor EppSchool District 5 (Southeast Kootenay)British Columbia
Shelly FletcherSt. James-Assiniboia School DivisionManitoba
Barb GajdosCalgary Roman Catholic Separate School District No. 1Alberta
Domenico GalloElk Island Catholic Separate Regional Division No. 41Alberta
Laurie GatzkeRegina School District 4Saskatchewan
Lauri GoudreaultHoly Family Catholic Regional Division No. 37Alberta
Gord GramsFoothills School Division No. 38Alberta
Doug JonassonThe Pembina Trails School DivisionManitoba
Heather JonesSt. James-Assiniboia School DivisionManitoba
Jeff KrarCalgary Science School (Independent)Alberta
Luc LerminiauxRegina School District 4Saskatchewan
Miles MacFarlaneSeven Oaks School Division 10Manitoba
Martin MazurekEvergreen Catholic Separate Regional Division No. 2Alberta
Marg McDonoughMathematics ConsultantBritish Columbia
Jim MennieMathematics ConsultantBritish Columbia
Merry NenadovCalgary Board of EducationAlberta
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David NoonanElk Island Catholic Separate Regional Division No. 41Alberta
Margo PerryEdmonton Catholic SchoolsAlberta
Donna PratoEdmonton Public SchoolsAlberta
Christine PrystenskiSt. James-Assiniboia School DivisionManitoba
Nancy ReydaSt. James-Assiniboia School DivisionManitoba
Tom SherbrookWinnipeg School Division No. 1Manitoba
Robert ShkrobotEdmonton Public SchoolsAlberta
Bill SlevinskySt. Albert School District No. 6Alberta
Ian StrachanCalgary Board of EducationAlberta
Maureen SwitzerSt. James-Assiniboia School DivisionManitoba
Kandel VickGrande Yellowhead Regional Division No. 35Alberta
Greg WoitasCalgary Roman Catholic Separate School District No. 1Alberta
Anthony YamSchool District No. 41 (Burnaby)British Columbia
Shannon Zanni Regina School District 4Saskatchewan
Field TestersAmy BadoEvergreen Catholic Separate Regional Division No. 2Alberta
Ryan Bailey Northern Lights School Division No. 69Alberta
Linda BensonSeven Oaks School Division 10Manitoba
Nicolas CurciLouis Riel School DivisionManitoba
Victor EppSchool District 5 (Southeast Kootenay)British Columbia
Shelly FletcherSt. James-Assiniboia School DivisionManitoba
Patrick GiommiSt. Margaret’s School (Independent)British Columbia
Sandra HaraznyRegina Roman Catholic Separate School Division No. 81Saskatchewan
Blaise JohnsonSchool District 45 (West Vancouver)British Columbia
Emily KalwarowskyEdmonton Catholic Separate School District No. 7Alberta
Jeff KrarCalgary Science School (Independent)Alberta
Blair LloydSchool District 73 (Kamloops/ Thompson)British Columbia
Patti LovalloEdmonton Public SchoolsAlberta
Wanda LloydCalgary Roman Catholic Separate School District No. 1Alberta
Cheryl MakokisEdmonton Public SchoolsAlberta
Martin MazurekEvergreen Catholic Separate Regional Division No. 2Alberta
David NoonanElk Island Catholic School Regional Division No. 41Alberta
Christine PrystenskiSt. James-Assiniboia School DivisionManitoba
Fariyal G. SamsonCalgary Board of EducationAlberta
Robert ShkrobotEdmonton Public SchoolsAlberta
Bill SlevinskySt. Albert School District No. 6Alberta
Edward SudermanSchool District 45 (West Vancouver)British Columbia
Rick WunderlichSchool District 83 (North Okanagan/Shuswap)British Columbia
Shannon Zanni Regina School District 4Saskatchewan
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A Tour of Your Textbook ...........................................................viii
Problem Solving.......................................................................... xiv
CHAPTER 1
Representing Data ................................................................... 2
Chapter 1 Foldable ................................................................................... 4
Math Link: Music Industry ...................................................................... 5
1.1 Advantages and Disadvantages of Different Graphs ................................................................... 6
1.2 Misrepresenting Data ..................................................... 18
1.3 Critiquing Data Presentation .................................... 28
Chapter Review ..................................................................................... 36
Practice Test.......................................................................................... 38
Math Games: The Plot Thickens ....................................................... 40
Challenge in Real Life: Keep Your Community Green ............... 41
CHAPTER 2
Ratios, Rates, and Proportional Reasoning ...............42
Chapter 2 Foldable ............................................................................... 44
Math Link: Multicultural Festival .................................................... 45
2.1 Two-Term and Three-Term Ratios ...................... 46
2.2 Rates ........................................................................................... 55
2.3 Proportional Reasoning ................................................ 63
Chapter Review ..................................................................................... 70
Practice Test.......................................................................................... 72
Math Games: Rolling Ratios ............................................................... 74
Challenge in Real Life: Life of a Bush Pilot ................................ 75
CHAPTER 3
Pythagorean Relationship ..................................................76
Chapter 3 Foldable ............................................................................... 78
Math Link: Game Design ....................................................................... 79
3.1 Squares and Square Roots ........................................... 80
3.2 Exploring the Pythagorean Relationship .......... 88
3.3 Estimating Square Roots .............................................. 95
3.4 Using the Pythagorean Relationship ..................101
3.5 Applying the Pythagorean Relationship ..........106
Chapter Review ...................................................................................112
Practice Test........................................................................................114
Math Games: It’s Prime Time ...........................................................116
Challenge in Real Life: Building a Staircase .............................117
CHAPTER 4
Understanding Percent ......................................................118
Chapter 4 Foldable ............................................................................120
Math Link: Water Conservation ......................................................121
4.1 Representing Percents ...................................................122
4.2 Fractions, Decimals, and Percents .......................130
4.3 Percent of a Number .....................................................138
4.4 Combining Percents .......................................................144
Chapter Review ...................................................................................150
Practice Test........................................................................................152
Math Games: Number Match ............................................................154
Challenge in Real Life: The Buying and Selling Game ............155
Chapters 1—4 Review .........................................................................156
Task: Test the Efficiency of a Ramp ...........................................159
TASK: TEST THE EFFICIENCY OF A RAMP
Contents • NEL v
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CHAPTER 5
Surface Area ..........................................................................160
Chapter 5 Foldable .............................................................................162
Math Link: City Planning ....................................................................163
5.1 Views of Three-Dimensional Objects ...............164
5.2 Nets of Three-Dimensional Objects ...................170
5.3 Surface Area of a Prism ...............................................176
5.4 Surface Area of a Cylinder ........................................182
Chapter Review ...................................................................................188
Practice Test........................................................................................190
Math Games: Let’s Face It! ...............................................................192
Challenge in Real Life: Design a Bedroom..................................193
CHAPTER 6
Fraction Operations .............................................................194
Chapter 6 Foldable .............................................................................196
Math Link: Canada’s Ecozones ........................................................197
6.1 Multiplying a Fraction and a Whole Number ...................................................................................198
6.2 Dividing a Fraction by a Whole Number .......204
6.3 Multiplying Proper Fractions ..................................210
6.4 Multiplying Improper Fractions and Mixed Numbers ................................................................2166.5 Dividing Fractions and Mixed Numbers ........222
6.6 Applying Fraction Operations ................................230
Chapter Review ...................................................................................236
Practice Test........................................................................................238
Math Games: Fabulous Fractions ..................................................240
Challenge in Real Life: Rock, Paper, Scissors..........................241
CHAPTER 7
Volume ......................................................................................242
Chapter 7 Foldable .............................................................................244
Math Link: Park Design ......................................................................245
7.1 Understanding Volume ................................................246
7.2 Volume of a Prism ..........................................................254
7.3 Volume of a Cylinder ...................................................262
7.4 Solving Problems Involving Prisms and Cylinders ................................................................................268
Chapter Review ...................................................................................276
Practice Test........................................................................................278
Math Games: Turn Up the Volume!.................................................280
Challenge in Real Life: Create a Storage Container ...............281
CHAPTER 8
Integers .....................................................................................282
Chapter 8 Foldable .............................................................................284
Math Link: Temperature Changes ..................................................285
8.1 Exploring Integer Multiplication..........................286
8.2 Multiplying Integers ......................................................293
8.3 Exploring Integer Division ........................................300
8.4 Dividing Integers ..............................................................306
8.5 Applying Integer Operations ...................................312
Chapter Review ...................................................................................318
Practice Test........................................................................................320
Math Games: Integer Race ...............................................................322
Challenge in Real Life: Running a Small Business ..................323
Chapters 5—8 Review ........................................................................324
Task: Fraction Cubes .........................................................................327
vi NEL • Contents
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CHAPTER 9
Linear Relations ....................................................................328
Chapter 9 Foldable .............................................................................330
Math Link: Adventure Travel ...........................................................331
9.1 Analysing Graphs of Linear Relations .............332
9.2 Patterns in a Table of Values ..................................342
9.3 Linear Relationships ......................................................352
Chapter Review ...................................................................................360
Practice Test........................................................................................362
Math Games: Friends and Relations .............................................364
Challenge in Real Life: Comparing Wages .................................365
CHAPTER 10
Solving Linear Equations...................................................366
Chapter 10 Foldable ...........................................................................368
Math Link: Modelling Equations ......................................................369
10.1 Modelling and Solving One-StepEquations: ax = b, x __ a = b ...........................................370
10.2 Modelling and Solving Two-Step Equations: ax + b = c ..................................................380
10.3 Modelling and Solving Two-StepEquations: x __ a + b = c ...................................................388
10.4 Modelling and Solving Two-Step Equations: a(x + b) = c ..............................................394
Chapter Review ...................................................................................400
Practice Test........................................................................................402
Math Games: Rascally Riddles .......................................................404
Challenge in Real Life: The Earth’s Core ....................................405
CHAPTER 11
Probability ...............................................................................406
Chapter 11 Foldable ............................................................................408
Math Link: Probability Games .........................................................409
11.1 Determining Probabilities Using Tree Diagrams and Tables ....................................................410
11.2 Outcomes of Independent Events ........................419
11.3 Determining Probabilities Using Fractions .................................................................................426
Chapter Review ...................................................................................436
Practice Test........................................................................................438
Math Games: Play Fair! ......................................................................440
Challenge in Real Life: Treasure Hunt.........................................441
CHAPTER 12
Tessellations .........................................................................442
Chapter 12 Foldable ...........................................................................444
Math Link: Mosaic Designs ................................................................445
12.1 Exploring Tessellations With Regular and Irregular Polygons .................................................446
12.2 Constructing Tessellations Using Translations and Refl ections ...................................452
12.3 Constructing Tessellations Using Rotations ...............................................................................457
12.4 Creating Escher-Style Tessellations ....................461
Chapter Review ...................................................................................466
Practice Test........................................................................................468
Math Games: Playing at Tiling ........................................................470
Challenge in Real Life: Border Design .........................................471
Chapters 9—12 Review .......................................................................472
Task: Put Out a Forest Fire ..............................................................475
Answers ...................................................................................................476
Glossary ...................................................................................517
Index ...........................................................................................522
Contents • NEL vii
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Chapter OpenerEach chapter begins with a two-page spread which introduces you to what you will learn in the chapter.
Foldables™Each chapter includes a Foldable to help you organize what you are learning and keep track of what you need to work on. Instructions on where and how to record information on the Foldable will help you use it as a study tool.
Numbered Sections The numbered sections often start with a visual to connect the topic to a real setting. The purpose of this introduction is to help you make connections between the math in the section and the real world, or to make connections to what you already know.
Math LinkEach chapter introduces a Math Link that helps you connect math and your own personal experiences. You will often revisit the Math Link at the end of a lesson. This is an opportunity for you to build concepts and understanding. The Wrap It Up! at the end of each chapter gives you an opportunity to demonstrate your understanding of the chapter concepts.
Representing DataRepresenting DataData surrounds you everywhere you turn. It is up to you to identify and compare daily information. Have you considered how athletic statistics are determined, how newspaper and magazine surveys are supported, or how industries use information to predict sales?
A graph is a visual way of displaying data. There are many decisions to make when you create a graph. What type of graph will you use? What portion of the data will you display? How will the display communicate your message?
What You Will Learn� to compare how diff erent graphs represent the same data� to identify the advantages and disadvantages of diff erent graphs� to explore how data can be misrepresented� to justify using a specifi c graph to represent data
• interval• bar graph• circle graph• line graph• pictograph
• double bar graph• double line graph• trend• distort
Key Words
A KWL chart can help you understand and learn new material more easily• The K in KWL stands for Know.• The W in KWL stands for Want.• The L in KWL stands for Learned.Copy the following KWL chart into your math journal or notebook. Brainstorm with a partner what you already know about representing data.• Record your ideas in the fi rst column.• List any questions you have about representing data in the second column.• After you complete the chapter, complete the fi nal column of the KWL chart.
Representing Data
Literacy Link
What I Know What I Want to
Know What I Learned
2 MHR • Chapter 1
Chapter 1 • MHR 3
viii NEL • A Tour of Your Textbook
Making the Foldable
• 11 × 17 sheet of paper• ruler• stapler• several sheets of notebook paper cut into quarters or
large index cards• scissors (optional)
Step 1 Fold an 11 × 17 sheet of paper into thirds lengthwise.Step 2 Label the outside of your Foldable as shown.
Step 3 Unfold the paper. Fold the bottom edge upward approximately 8 cm. Staple the outer edges and along each crease to make three pockets.
Step 4 Label each section and pocket as shown.Step 5 Label the back of the Foldable as shown. Math Link Introduction
Wrap It Up!
Ideas
Using the FoldableUse the back of the Foldable for your answers to the Math Link introduction on page 5. As you work through each section of Chapter 1,
make notes about examples and Key Ideas on quarter sheets of paper or index cards and put them in the appropriate pocket. Place your responses to the Math Link for each section in the same place. Write the Key Words above the appropriate pocket.
Keep track of what you need to work on. Check off each item as you deal with it.As you think of ideas for the Wrap It Up!, record
them on the back of the Foldable.
Chapter 1:Representing
Data
1.1 Advantages and
Disadvantages ofDifferent GraphsKey Words .............
..............................
..............................
1.2 MisrepresentingData
Key Words ............................................................................
8 cm
1.3 Critiquing Data
Presentation
Key Words ..............
..............................
.
..............................
.What I Need to Work On
..............................
..............................
..............................
What I Need to Work On..........................................................................................
What I Need to Work On
..............................
..............................
..............................
4 MHR • Chapter 1
WRAP IT UP!Suppose you are a reporter for the school’s newspaper. Search the Internet, magazines, or newspapers for data about a topic related to the music industry. For example, you might want to use data about sales, favourite artists, attendance at tours, or popularity of diff erent types of music.
a) Make a table that displays your data.
b) Decide on two diff erent ways to represent the data by drawing one graph that represents the data accurately and another graph that misrepresents the data.
c) You have been asked to write articles that relate to each of your graphs.What will the headlines of your articles be? Explain your thinking.
Practice Test • MHR 39
MATH LINKMusic IndustryMusic producers sell hundreds of millions of recordings each year. Although music is popular, predicting the sales of a new release can be challenging due to new technology. Will a new release be a hit or a fl op? Music producers collect information to help them predict sales. For example, is the artist new? Is the artist currently touring? Who does the music appeal to? How could you organize the information that music producers gather?
1. The circle graph shows the music preferences of young Canadian adults between the ages of 14 and 19.a) What was the favourite type of music? What is the least favourite type of music?b) Research the music preferences of young adults between the ages of 14 and 19 in your province or territory. Does this circle graph provide a good representation of preferences where you live? Explain.
2. The double bar graph shows Canadian sales of music in diff erent formats.a) What were the sales for DVDs in 2006? b) Compare the sales for CDs in 2006 and 2007. c) How do you see this data changing over time? Explain your reasoning.
3. The table shows the music market shares for several music producers.
Music Producer Market Share (%)Sony BMG26
Universal Music Group 32Warner Music Group 15EMI Group
9Independent Labels 18
a) Represent the data using a bar graph and a circle graph.b) Which graph do you prefer? Explain.In this chapter, you will collect, analyse, and display data about the music industry. What is your favourite type of music?
DVD
40 000
80 000
140 000
160 000
20 000
0
60 000
100 000
120 000
Music Sales in Canada
CD
Format
Sale
s ($
Tho
usan
ds)
Jan-May 2006
Jan-May 2007
Music Preferences in YoungCanadian Adults (Ages 14 to 19)
Rap
Rock and Roll
Country
Classical
50%
25%
13%
10%
2%
Alternative
Math Link • MHR 5
You use ratios to enlarge or reduce graphics and pictures. Discuss with
a partner how you could use ratios to describe these two images.
How can you compare an enlargement to its original image?Jason made the following enlargement of a prairie dog. Kate asked how he enlarged it. Jason could not remember. Use ratios to help him answer Kate’s question.
Two-Term and Three-Term RatiosFocus on…After this lesson, you will be able to...� represent two-term and three-term ratios� identify, describe, and record ratios from real-life
examples� represent a ratio as a fraction or as a percent� solve problems using ratios
• ruler
46 MHR • Chapter 2
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• An activity is designed to help you build your ownunderstanding of the new concept and lead towardanswers to the key question.
• A summary of the main newconcepts is given in the KeyIdeas box.
Check Your Understanding• Practise: These are questions to check your
knowledge and understanding of what youhave learned.
• Apply: In these questions, you need to applywhat you have learned to solve problems.
• Extend: These questions may be more challengingand may make connections to other lessons.
A Tour of Your Textbook • NEL ix
A three-part lesson follows.y
container. How can he use this information to figure out how many boxes the shipping container will hold?
How does the area of the base of a right prism relate to its volume?
1. a) Use centimetre cubes to build models of four different right rectangular prisms.
b) What is the area of the base for each model? Record your data.
c) What is the height of each model? Record your data.
• centimetre cubes
base (of a prism or cylinder)
• any face of a prism that shows the named shape of the prism
• the base of a rectangularprism is any face
• the base of a triangular prism is a triangular face.
• the base of a cylinder is a circular face
height (of a prism or cylinder)
• the perpendiculardistance between the two bases of a prism or cylinder
Example 1: Determine the Volume Using the Base and the Height
Determine the volume of each right prism or cylinder.
a)
A = 35 cm2
3 cm
b)
A = 12 cm2
10 cm
c)
5 cm
A = 27 cm2
• The volume of a right cylinder or a right prism can be determined by multiplying the area of the base by the height of the cylinder or prism.
Volume = area of base × height of cylinder V = 20 × 8 V = 160The volume of the cylinder is 160 cm3.
Volume = area of base × height of prism V = 17 × 10 V = 170The volume of the triangular prism is 170 cm3.
8 cm
A = 20 cm2
10 cm
A = 17 cm2
• Examples and Solutionsdemonstrate how to usethe concept.
• Questions in the Communicate theIdeas section let you talk or writeabout the concepts and assesswhether you understand the ideas.
1. Evan calculated the volume of a right cylinder. Charlotte calculated the volume of a right rectangular prism. Did either of them make an error in their solutions? Explain how you know.
A = 15 cm2
2 cm
Volume = area of base X height
V = 15 X 2V = 30
The volume of the cylinder is 30 cm3.
3 cm9 cm
7 cm
A = 63 cm2
Volume = area of base X height
V = 63 X 7V = 441
The volume of the rectangular prism is 441 cm3.
For help with #3 and #4, refer to Example 1 on pages 247–248.
3. Determine the volume of each right prism or cylinder.a)
4 cm
A = 15 cm2
b)
12 cm
A = 18 cm2
c) A = 96 cm2
20 cm
4. What is the volume of each right prism?a) area of base = 12 cm2, height = 8 cmb) area of base = 18 cm2, height = 4 cmc) height = 9 cm, area of base = 14 cm2
250 MHR • Chapter 7
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The Examples and their worked Solutions include several tools to help you understand the work.
• Notes in a thought bubble help you think through the steps.
• Sometimes different methods of solving the same problem areshown. One way may make more sense to you than the other.
• Problem Solving Strategies are pointed out.
• Calculator key press sequences are shown where appropriate.
• Most Examples are followed by a Show You Know. Thesequestions help you check that you understand the skillcovered in the Example.
How does MathLinks 8 help you learn?
Understanding VocabularyKey Words are listed on the Chapter Opener. Perhaps you already know the meaning of some of them. Great! If not, watch for these terms the fi rst time they are used in the chapter. The meaning is given close by in the margin.
A Literacy Link at the beginning of each chapter provides tips to help you read and interpret the chapter content.
Other Literacy Links throughout the chapter assist you in reading and interpreting items in math. These tips will help you in other subjects as well.
Understanding ConceptsThe Explore the Math activities are designed to help you construct your own understanding of new concepts. The key question tells you what the activity is about. Short steps, with illustrations, lead you to make some conclusions in the Refl ect on Your Findings question.
• two-term ratio• three-term ratio• part-to-part ratio• part-to-whole ratio
• rate• unit rate• unit price• proportion
Key Words
x •NEL A Tour of Your Textbook
two-term ratio• compares two
quantities measured in the same units
• written as a : b or a to b
blue : red is 6 : 4
Focus on…After this lesson, you will be able to...� multiply integers
using integer chips
4. Use integer chips to model each multiplication. Copy and complete each multiplication statement.a) (+3) × (+5) = � b) (+2) × (+3) = �c) (+4) × (-3) = � d) (+3) × (-4) = �
5. Can you use the same method as in #1 to #4 to complete the multiplication (-2) × (+3) or the multiplication (-3) × (-4)? Explain.
6. a) The diagrams show how to model the multiplications from #5 by using zero pairs. Describe each model.
(-2) × (+3) (-3) × (-4)
b) Copy and complete each multiplication statement. (-2) × (+3) = � (-3) × (-4) = �
7. Use integer chips to model each multiplication. Copy and complete each multiplication statement.a) (-4) × (-3) = � b) (-5) × (+2) = �c) (-2) × (+4) = � d) (-1) × (-4) = �
Refl ect on Your Findings 8. How can you use integer chips to multiply two integers? In your description, state when you use zero pairs. How do you determine the number of zero pairs to use?
Understanding MultiplicationThe product of 4 and 2 is 8, because 4 × 2 = 8.
The multiplication statement 4 × 2 = 8 means that 4 groups of 2 make 8. You can also think of 4 × 2 as the repeated addition 2 + 2 + 2 + 2.
Literacy Link
Modelling With Zero PairsA zero pair is a pair of integer chips, with one chip representing +1 and one chip representing -1.
+1 −1
A zero pair represents zero because (+1) + (-1) = 0.Any whole number of zero pairs represents zero.
Literacy LinkThe Columbia Icefield is the largest mass of ice in North America below the Arctic Circle. The icefield lies across the Alberta–British Columbia border in the Rockies. Six large glaciers flow from the icefield. One of them, the Athabasca Glacier, is a popular tourist destination in Jasper National Park.
The Athabasca Glacier has been melting for over a century. The front edge or “snout” of the glacier has been receding at an average of approximately 12 m per year. At that rate, how far would it recede in four years?
How can you use integer chips to multiply two integers? 1. Multiplication can be expressed as a repeated addition. (+3) × (+2) = (+2) + (+2) + (+2)a) Use red integer chips to model the addition (+2) + (+2) + (+2).b) Copy and complete the multiplication statement (+3) × (+2) = �.
2. a) Express (+4) × (+3) as a repeated addition.b) Use red integer chips to model the addition.c) Copy and complete the multiplication statement (+4) × (+3) = �. 3. a) Express (+3) × (-5) as a repeated addition.b) Use blue integer chips to model the addition.c) Copy and complete the multiplication statement (+3) × (-5) = �.
The Columbia Icefi eld is a major source of fresh water. Melt water from the icefi eld feeds rivers that fl ow to the Arctic Ocean, the Pacifi c Ocean, and Hudson’s Bay.
Representing IntegersInteger chips are coloured disks that represent integers. In this book, one red chip represents +1, and one blue chip represents -1.
+1 −1
Literacy Link
• red and blue integer chips
Use enough zero pairs so that there are two groups of three red chips available to remove.
Exploring Integer Multiplication
286 MHR • Chapter 8
8.1 Exploring Integer Multiplication • MHR 287
Example 2: Solve EquationsKia is making a square quilt with a 4-cm wide border around it. She wants the completed quilt to have a perimeter of 600 cm. What must the dimensions of Kia’s quilt be before she adds the border?
SolutionLet s represent the unknown side length
s + 8
4 cm
s
4 cm
of the quilt before the border is added. A border of 4 cm is added to each side. That means the side length of the quilt after the border is added is s + 8.Model with the equation 4(s + 8) = 600.Method 1: Divide FirstIsolate the variable s. 4(s + 8) = 600
4(s + 8)
________ 4
= 600 ____ 4
Divide by 4 to undo the multiplication. s + 8 = 150 s + 8 - 8 = 150 - 8 Subtract 8 to undo the addition. s = 142The quilt dimensions before adding the border should be 142 cm × 142 cm.Method 2: Use the Distributive Property FirstIsolate the variable s. 4(s + 8) = 600 4s + 32 = 600 Multiply both s and 8 by 4. 4s + 32 - 32 = 600 - 32 Subtract 32 from both sides of the equation.4s = 568
4s ___ 4
= 568 ____ 4
Divide both sides of the equation by 4. s = 142The quilt dimensions before adding the border should be 142 cm × 142 cm.Check:Left Side = 4(s + 8) Right Side = 600 = 4(142 + 8)
= 4(150)= 600
Left Side = Right SideThe solution is correct.
Solve each equation. a) -2(x - 3) = 12 b) -20 = 5(3 + p)
Draw a Diagram
Strategies
The length must be multiplied by 4 because there are four sides to
the square quilt.
To use the distributive property, multiply the
terms in the brackets by 4.4(s + 8) = 4 × (s + 8)
= (4 × s) + (4 × 8)= 4s + 32
The distributive property states that a(b + c) equals a × b + a × c.
Literacy Link
396 MHR • Chapter 10
In math, the word of often means to multiply.
Literacy Link
A KWL chart can help you understand and learn new material more easily• The K in KWL stands for Know.• The W in KWL stands for Want.• The L in KWL stands for Learned.
Copy the following KWL chart into your math journal or notebook. Brainstorm with a partner what you already know about representing data.• Record your ideas in the fi rst column.• List any questions you have about representing
data in the second column.
• After you complete the chapter, complete the fi nal column of the KWL chart.
Representing Data
Literacy Link
What I Know What I Want to
Know What I Learned
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The exercises begin with Communicate the Ideas. These questions focus your thinking on the Key Ideas you learned in the section. By discussing these questions in a group, or doing the action called for, you can see whether you understand the main points and are ready to begin the Check Your Understanding.
The fi rst few questions in the Check Your Understanding can often be done by following one of the worked Examples.
A Tour of Your Textbook • NEL xi
For help with #4 to #5, refer to Example 1 on page 96.
4. Estimate the square root of each number, to one decimal place. Check with a calculator.a) 72 b) 103 c) 55
5. Estimate each value, to one decimal place. Check your answer with a calculator.a) √
___14 b) √
___86 c) √
____136
For help with #6 to #9, refer to Example 2 on page 97.
6. What is an example of a whole number that has a square root between 9 and 10?
7. Identify a whole number with a square root between 11 and 12.
8. Identify all possible whole numbers with a square root larger than 2 and smaller than 3. 9. What are all possible whole numbers that have a square root between 4 and 5?
10. Kai uses an entire can of paint on a square backdrop for the school play. The label on the can states that one can covers 27 m2 of wall surface. Estimate the backdrop’s side length, to one decimal place.
11. The square has an area of 20 cm2.
20 cm2
a) Use perfect squares to estimate the side length to one decimal place.b) Check your answer using a ruler to measure the side of the square. Measure to the nearest tenth of a centimetre.
12. While shopping online, Ji Hun fi nds a square rug with an area of 11 m2. He needs to know if it will fi t in his 4 m × 5 m bedroom.a) Estimate the side length of the rug, to one decimal place.b) Check your estimate with a calculator. c) Will the rug fi t? Explain.
13. Stella is planning an outdoor wedding. She would like a square dance fl oor with an area of 115 m2.a) Determine the side length of the dance fl oor, to the nearest tenth of a metre.b) Stella fi nds out that the dance fl oor will be made up of fl oorboards that each measure 1 m2. What are the two side lengths the dance fl oor can have that are closest to what she wants?
c) What are the two square areas for the dance fl oor that Stella can choose from?d) Which area will Stella choose? Explain.
4 4.5 5
√16 √17 √25
• To estimate the square root of a whole number that is not a perfect square,locate the perfect squares on either side of the numbercalculate the square roots of these two perfect squaresestimate based on the position between the two perfect squaresFor example, estimate the square root of 17: √
___ 17 ≈ 4.1
• To identify a whole number that has a square root between two given numbers,determine the perfect squares of the two consecutive whole numberschoose a whole number between the two perfect squaresFor example, identify a whole number that has a square root between 5 and 6:
52 = 25 62 = 36 √
___ 30 will have a value between 5 and 6.• When using a calculator to fi nd the square root of a natural number that is not a perfect square, the value shown on the calculator is only an approximation.
C 8 √⎯ 2.828427125
1. Explain how to estimate √ ___
28 to one decimal place without using a calculator. Compare your answer with a classmate’s.
2. Find a whole number that has a square root between 3 and 4. Explain how you found it. 3. Jason is doing his math homework. He has to fi nd the square root of 10. He presses √⎯ 10 on his calculator and the screen displays 3.16227766. However, when 3.16227766 is multiplied by itself, the answer is not 10. Explain.
5 6
√25 √36√
98 MHR • Chapter 3
3.3 Estimating Square Roots • MHR 99
Problem Solving At the beginning of the student resource there is an overview of the four steps you can use to approach Problem Solving. Samples of problem solving strategies are shown. You can refer back to this section if you need help choosing a strategy to solve a problem. You are also encouraged to use your own strategies.
Mental Math and EstimationThis Mental Math and Estimation logo does one of two things:1. It signals where you can use mental math and estimation.2. It provides useful tips for using mental math and estimation.
Other Features Did You Know?These are interesting facts related to math topics you are learning.
Subject LinksThis feature links the current topic to another subject area.
Web LinksYou can fi nd extra information related to some questions on the Internet. Log on to www.mathlinks8.ca and you will be able to link to recommended Web sites.
You could also determine 1.5% of $20 000 as:
30% of 20 000 is 6000.
3% of 20 000 is 600.
1.5% of 20 000 is 300.
In Roman times, the term centurion was used to describe an offi cer in the Roman Legion who was in charge of 100 soldiers. There was one centurion per cent, meaning there was one centurion per 100 soldiers. What other English words do you know that include cent?
History Link
The Columbia Icefi eld is a major source of fresh water. Melt water from the icefi eld feeds rivers that fl ow to the Arctic Ocean, the Pacifi c Ocean, and Hudson’s Bay.
Web Link
To generate tessellations on the computer, go to www.mathlinks8.ca and follow the links.
Problem Solving • MHR xiii
People solve mathematical problems at home, at work, and at play. There are
many different ways to solve problems. In MathLinks 8, you are encouraged
to try different methods and to use your own ideas. Your method may be
different but it may also work.
A Problem Solving Model
Where do you begin with problem solving? It may help to use the following
four-step process.
Read the problem carefully.
• Think about the problem. Express it in your own words.
• What information do you have?
• What further information do you need?
• What is the problem asking you to do?
Select a strategy for solving the problem. Sometimes you need more than one
strategy.• Consider other problems you have solved successfully. Is this problem like one
of them? Can you use a similar strategy? Strategies that you might use include:
– Model It – Estimate and Check
– Draw a Diagram – Solve a Simpler Problem
– Make an Organized List or Table – Identify all Possibilities
– Work Backwards – Use a Variable
– Guess and Check – Solve an Equation
– Look for a Pattern – Make an Assumption
• Decide whether any of the following might help. Plan how to use them.
– tools such as a ruler or a calculator
– materials such as grid paper or a number line
Solve the problem by carrying out your plan.
• Use mental math to estimate a possible answer.
• Do the calculations.
• Record each of your steps.
• Explain and justify your thinking.
Examine your answer. Does it make sense?
• Is your answer close to your estimate?
• Does your answer fi t the facts given in the problem?
• Is the answer reasonable? If not, make a new plan. Try a different strategy.
• Consider solving the problem a different way. Do you get the same answer?
• Compare your methods with those of your classmates.
Understand
Plan
Do It!
Look Back
xiv MHR • Problem Solving
Problem 1 Carolin has a rectangular vegetable garden that measures 4 m by 6 m. She wants to divide the garden into three equal sections to plant three diff erent vegetables. What is the area of each section?
StrategyExample
The garden is a rectangle with a length of 6 m and a width of 4 m.A = l × wA = 6 × 4A = 24The area of the garden is 24 m2.
Use a Variable
The garden is a rectangle with a length of 6 m and a width of 4 m.A = l × wA = 6 × 4A = 24The area of the garden is 24 m2.Let S represent the area of each section. S = area of garden ÷ number of sectionsS = 24 ÷ 3S = 8The area of each section is 8 m2.
Use a Variable
Here are several strategies you can use to help solve problems. Your ideas on how to solve the problems might be different from any of these.
Model It Use 24 square tiles to model the garden. Each tile represents 1 m2.
Divide the tiles into three equal groups to represent the three sections.
There are eight tiles in each group.The area of each section is 8 m2.
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xii NEL • A Tour of Your Textbook
Chapter Review and Practice Test
There is a Chapter Review and a Practice Test at the end of each chapter. The chapter review is organized by section number so you can look back if you need help with a question. The test includes the different types of questions that you will fi nd on provincial tests: multiple choice, numerical response, short answer, and extended response.
Cumulative Review
To help you reinforce what you have learned, there is a review of the previous four chapters at the end of Chapters 4, 8, and 12. Each of these special reviews is followed by a Task.
Task
These tasks require you to use skills from more than one chapter. You will also need to use your creativity.
Math Games and Challenge in Real Life
The last two pages of each chapter provide Math Games and a Challenge in Real Life. Math Games provide an interesting way to practise the skills you learned during the chapter. Most games can be played with a partner. Some can be played with a larger group. Enjoy them with your friends and family. The Challenge in Real Life provides an interesting problem that shows how the math you learned in the chapter relates to jobs, careers, or daily life.
AnswersAnswers are provided for all Practise, Apply, Extend, and Review questions. Sample answers are given for questions that have a variety of possible answers or that involvecommunication. If you need help, read thesample and then try to give an alternative response. Answers are omitted for the Math Link questions and for Practice Tests because teachers may use these questions to assess your progress.
GlossaryRefer to the illustrated Glossary at the back of the student resource if you need to check the exact meaning of mathematical terms.
Test the Effi ciency of a Ramp
Civil engineers design and build structures such as bridges, roads, and
ramps. Before doing the actual construction, they test the design for
strength and effi ciency. Your team’s task is to design a ramp that allows
a vehicle to travel the farthest.
1. Use books, a chair, or other
material to create a platform
with a height of your choice.
Round the height to the nearest
centimetre. Height, a: �
2. a) Design a ramp so that a vehicle can roll down without falling off
the side.
b) Record the length of the ramp from the edge of the platform to
the fl oor to the nearest centimetre. Length of ramp, c: �
3. Does your ramp design use a right triangle? Using the method of
your choice, calculate the length of the base in your triangle, b.
Justify your response.
4. Test your ramp by placing your vehicle at the top of the ramp, with
its front wheels even with the edge of the platform. Let go of the
vehicle without pushing it. Measure the distance the vehicle travels
from the foot of the ramp to where it stops. You may wish to do
three trials and take the average distance.
5. Repeat steps 3 and 4 for at least two different lengths of ramp.
Complete the chart provided to you.
6. The most effi cient ramp is the one that allows the vehicles to travel
the farthest.
a) Based on your result, what is the ratio of a to b distances that
resulted in the most effi cient design? Express your answer as a
percent.
b) Compare your ratio to those found by other teams. Explain any
similarities and differences.
• toy vehicles, such as
Hot Wheels®• material for platform
(books, chair)
• material for ramps
(boards, stiff
cardboard)
• metre stick
• tape measure
• Trial Record
b
a c
ramp
platform
Task • MHR 159
Rolling Ratios
1. Play Rolling Ratios with a partner. These are the rules:
• Each player rolls one die to decide who will play fi rst.
If there is a tie, roll again.
• In one round, each partner takes a turn.
• For each turn, roll all three dice.
• Record the ratio of the least value to the sum of the
rolled values, in fraction form.
• Express the fraction as a decimal. If necessary, use
a calculator and round to the nearest hundredth.
• Add the decimals from your turns. The fi rst player
to reach 2.5 or higher wins.
• If both players reach 2.5 in the same round, the player
with the higher total wins. If the totals are tied, the
players continue playing until one of them pulls ahead.
2. Modify the rules of the game. For example, change the
number of dice or choose a different ratio. Play your
modifi ed version of the game.
74 MHR • Chapter 2
• three dice per pair
of students
• calculator per student
I rolled a 2, a 4, and a 5. The
sum of the rolled values is
2 + 4 + 5 = 11, so the ratio
of the least value to
the sum of the values
is 2 : 11 or 2 ___ 11
.
So, 2 ___ 11
= 0.18, to the
nearest hundredth.
C 2 ÷ 11 = 0.181818182
Challenge in Real Life • MHR 323
Running a Small BusinessSmall business owners need to keep track of their fi nances—both the money they take in from customers and the money they pay out to suppliers.
You be the small business owner! Assume that you own a games store. Part of your job is to keep track of your fi nancial accounts.The table below the visual shows information about some of the games you carry.• You buy them from a supplier at one price.• You sell them to customers at a higher price.
1. Choose a + or - sign to place beside each value in the table. Choose the sign by considering how each value affects your account (money in or money out). Justify your choice of signs. 2. Show how the multiplication or division of integers can be used to model each situation below. Justify your choices. a) You buy 12 copies of Game Z from the supplier. b) You spend $72 to buy these copies of Game Z from the supplier. c) You sell three copies of Game Y to customers. d) A customer returns two copies of Game X for a refund. e) You fi nd that four copies of Game Y have defects. You return them to the supplier.
3. If you buy 36 copies of Game X from the supplier, how many will you have to sell to break even on them? Show your thinking. 4. Create a scenario for a typical week of buying, selling, returns, and so on. Design a table that summarizes your transactions for the week. Your table should demonstrate your understanding of how multiplication and division of integers can be applied.
When you break even on something, you neither gain nor lose money.
Literacy Link
Buy from Supplier
Game X $14Game Y $10Game Z $6
Sell toCustomers
Game X $24Game Y $15Game Z $11
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Problem Solving • NEL xiii
People solve mathematical problems at home, at work, and at play. There are many different ways to solve problems. In MathLinks 8, you are encouraged to try different methods and to use your own ideas. Your method may be different but it may also work.
A Problem Solving ModelWhere do you begin with problem solving? It may help to use the following four-step process.
Read the problem carefully.• Think about the problem. Express it in your own words.• What information do you have?• What further information do you need?• What is the problem asking you to do?
Select a strategy for solving the problem. Sometimes you need more than one strategy.• Consider other problems you have solved successfully. Is this problem like one
of them? Can you use a similar strategy? Strategies that you might use include:– Model It – Estimate and Check– Draw a Diagram – Solve a Simpler Problem– Make an Organized List or Table – Identify all Possibilities– Work Backwards – Use a Variable– Guess and Check – Solve an Equation– Look for a Pattern – Make an Assumption
• Decide whether any of the following might help. Plan how to use them.– tools such as a ruler or a calculator– materials such as grid paper or a number line
Solve the problem by carrying out your plan.• Use mental math to estimate a possible answer.• Do the calculations.• Record each of your steps.• Explain and justify your thinking.
Examine your answer. Does it make sense?• Is your answer close to your estimate?• Does your answer fi t the facts given in the problem?• Is the answer reasonable? If not, make a new plan. Try a different strategy.• Consider solving the problem a different way. Do you get the same answer?• Compare your methods with those of your classmates.
Understand
Plan
Do It!
Look Back
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xiv NEL • Problem Solving
Problem 1 Carolin has a rectangular vegetable garden that measures 4 m by 6 m. She wants to divide the garden into three equal sections to plant three diff erent vegetables. What is the area of each section?
Strategy Example
The garden is a rectangle with a length of 6 m and a width of 4 m.A = l × wA = 6 × 4A = 24The area of the garden is 24 m2.
Use a Variable
The garden is a rectangle with a length of 6 m and a width of 4 m.A = l × wA = 6 × 4A = 24The area of the garden is 24 m2.
Let S represent the area of each section. S = area of garden ÷ number of sectionsS = 24 ÷ 3S = 8The area of each section is 8 m2.
Use a Variable
Here are several strategies you can use to help solve problems. Your ideas on how to solve the problems might be different from any of these.
Model It Use 24 square tiles to model the garden. Each tile represents 1 m2.
Divide the tiles into three equal groups to represent the three sections.
There are eight tiles in each group.The area of each section is 8 m2.
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Problem Solving • NEL xv
Problem 2 Amil is downloading some software. It has taken 56 s to complete 1 __ 4 of the download.
What is the total time that the download will likely take?
Strategy Example
Let t represent the total time required to complete the download.1 __ 4 of the total time is 56 s. The equation that models this situation
is t __ 4 = 56.
t __ 4 = 56
t __ 4 × 4 = 56 × 4 Multiply both sides of the equation by 4.
t = 224
The download will take about 224 s, or 3 min and 44 s.
Solve an Equation
Estimate that 56 s is close to 60 s, which is 1 min.1__ 4 of the download takes about 1 min.
Multiply by 4 to estimate the total download time.1 × 4 = 4The total download will likely take about 4 min.
Check:56 × 4 = 224The download will take about 224 s, or 3 min and 44 s.
The estimate and the calculated values are close.
Estimate and Check
There are 60 s in 1 min.
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xvi NEL • Problem Solving
A teacher is playing a guessing game with her class. Her clue is “After a refl ection in each axis of a Cartesian plane, a point is in quadrant II. What quadrant did the point start in?” What is the solution?
Strategy Example
The point can be refl ected in x-axis and then in the y-axis or it can be refl ected in the y-axis and then the x-axis. After the two refl ections, the point lies in quadrant II. So, the possible starting quadrants are quadrants I, III, or IV.
List all the possibilities, using quadrants I, III, and IV as the starting quadrants.
Identify all Possibilities
Use the fi nal position of quadrant II as the starting quadrant and work backwards.
Both possibilities result in quadrant IV. The point started in quadrant IV.
Work Backwards
Problem 3
420�2�4
�2
2
x
y
QuadrantIV
QuadrantIII
QuadrantII
QuadrantI
Starting in Quadrant I
20–2
–2
2
–1
1
–1 1 x
y III
III IV
Both possibilities result in quadrant III as a fi nal position.
Starting in Quadrant III
x
y III
III IV
20–2
–2
2
–1
1
–1 1
Both possibilities result in quadrant I as a fi nal position.
Starting in Quadrant IV
x
y III
III IV
20–2
–2
2
–1
1
–1 1
Both possibilities result in quadrant II as a fi nal position.
The point started in quadrant IV.
x
y III
III IV
20–2
–2
2
–1
1
–1 1
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Problem Solving • NEL xvii
Sharon’s family owns and operates a small restaurant. They have many small square tables and stacking chairs. What is the greatest number of people that can be seated when 10 tables are put together?
Strategy Example
Assume that only one person can sit along each side of a table.
When 10 tables are put together in a line, 4 + 2 × 9 people can be seated. This is 22 people.
Consider other possible arrangements.
When 3 tables are put together in an L-shape, 8 people can be seated. This is the same as when the tables are in a line.
When 4 tables are put together to form a square, 8 people can be seated. This is less than when the tables are in a line.
Other arrangements of tables cannot seat more people than when the tables are arranged in a line. So, the greatest number of people that can be seated when 10 tables are put together is 22 people.
Make an Assumption
Draw a Diagram
Make an Organized List or Table
Look for a Pattern
Identify all Possibilities
Problem 4
Diagram Number of Tables Number of People
1 4
2 6
3 8
4 10
The table shows a pattern. One table seats
four people. With each extra table, two more people
can be seated.
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