McGraw-Hill Ryerson Mathematics 10
McGraw-Hill RyersonMathematics10Teacher’s Resource
AUTHORSBerkley BeingessnerB.Ed.Calgary Board of EducationAlbertaScott CarlsonB.Ed., B.Sc.Golden Hills School Division No. 75AlbertaBarb GajdosB.Ed.Calgary Roman Catholic SeparateSchool District No. 1AlbertaBlaise JohnsonB.Sc., B.Ed.School District 45 (West Vancouver)British ColumbiaASSESSMENT AUTHORSBruce McAskillB.Sc., B.Ed., M.Ed., Ph.D.Mathematics ConsultantVictoria, British ColumbiaWayne WattB.Sc., B.Ed., M.Ed.Mathematics ConsultantWinnipeg, ManitobaChris ZarskiB.Ed., M.Ed.Wetaskiwin Regional Division No. 11AlbertaSUPPORTINGLEARNING AUTHORSBLACKLINEMASTERS AUTHORSRon KennedyB.Ed.Mathematics ConsultantEdmonton, AlbertaHeather GrangerB.Ed.Prairie South School Division No. 210SaskatchewanStephanie MackayB.Ed.Edmonton Catholic Separate SchoolDistrict No. 7AlbertaShirley Oker-MykitukB.Ed.Edmonton Catholic Separate SchoolDistrict No. 7AlbertaEsther MorenoB.Sc.School District No. 39 (Vancouver)British ColumbiaChristine PurseB.Ed.Victoria, British ColumbiaGail PoshtarB.Ed.Calgary Roman Catholic SeparateSchool District No. 1AlbertaRick WunderlichB.Ed.School District 83 (NorthOkanagan/Shuswap)British ColumbiaFOLDABLES AUTHORDinah ZikeM.Ed.Educational ConsultantSan Antonio, TexasToronto Montréal Boston Burr Ridge, IL Dubuque, IA Madison, WI New York San FranciscoSt. Louis Bangkok Bogotá Caracas Kuala Lumpur Lisbon London MadridMexico City Milan New Delhi Santiago Seoul Singapore Sydney Taipei
McGraw-Hill RyersonMathematics 10 Teacher’s ResourceCOPIES OF THIS BOOKMAY BE OBTAINED BYCONTACTING:McGraw-Hill Ryerson Ltd.WEB OLL-FREE FAX:1-800-463-5885Copyright 2010, McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-HillCompanies. All rights reserved. No part of this publication may be reproduced ortransmitted in any form or by any means, or stored in a data base or retrieval system,without the prior written permission of McGraw-Hill Ryerson Limited, or, in the caseof photocopying or other reprographic copying, a licence from The Canadian CopyrightLicensing Agency (Access Copyright). For an Access Copyright licence, visitwww.accesscopyright.ca or call toll free to 1-800-893-5777.Any request for photocopying, recording, or taping of this publication shall be directed inwriting to Access Copyright.ISBN-13: 978-0-07-012758-6ISBN-10: 0-07-012758-1www.mcgrawhill.caTOLL-FREE CALL:1-800-565-5758OR BY MAILING YOURORDER TO:McGraw-Hill RyersonOrder Department300 Water StreetWhitby, ON L1N 9B6Please quote the ISBN andtitle when placing your order.1 2 3 4 5 6 7 8 9 0 MP 1 9 8 7 6 5 4 3 2 1 0Printed and bound in CanadaMicrosoft Excel is either a registered trademark or trademarks of Microsoft Corporationin the United States and/or other countries.TI-83 , TI-84 , and TI-Nspire are registered trademarks of Texas Instruments.Care has been taken to trace ownership of copyright material contained in this text. Thepublishers will gladly accept any information that will enable them to rectify any referenceor credit in subsequent printings.ASSOCIATE PUBLISHER, MATHEMATICS: Kristi ClarkPROJECT MANAGER: Helen MasonCONTENT MANAGER: Susan TillDEVELOPMENTAL EDITORS: Susan Till, Jodi Rauch, Rita Vanden Heuvel,Jackie Lacoursiere, Kelly CochraneMANAGER, EDITORIAL SERVICES: Crystal ShorttSUPERVISING EDITOR: Jeanette McCurdyCOPY EDITOR: John GreenEDITORIAL ASSISTANT: Erin HartleyEDITORIAL COORDINATION: Jennifer Keay, Janie Reeson, Alexandra Savage-FerrMANAGER, PRODUCTION SERVICES: Yolanda PigdenPRODUCTION COORDINATOR: Sheryl MacAdamCOVER DESIGN: Valid Design & LayoutINTERIOR DESIGN: ArtPlus Ltd.ELECTRONIC PAGE MAKE-UP: ArtPlus Ltd. & LaserWordsCOVER IMAGE: Courtesy of Getty Images; Mike Kemp, Photographer
ContentsTime Lines for Mathematics 10An Introduction to Mathematics 10Teacher’s ResourceCharacteristics of McGraw-Hill Ryerson’sMathematics 10 ProgramviiiixxMathematics: Making Links . xProcedural Fluency and Conceptual Understanding . xiInvestigateLink the IdeasCheck Your UnderstandingProblem Solving . xiiDifferentiating Instruction . xiiTen Needs of the LearnerAssessmentxvAssessment as Learning . xvAssessment for Learning . xvAssessment of Learning . xviPortfolio AssessmentMaster 1 Project RubicConcrete MaterialsxviiTechnologyxviiCapitalizing on Diversity and Real LifexviiiAlternative Learning Environments andHome ConnectionsxviiiCooperative LearningxviiiTypes of Groups . xxMental MathematicsxxiEstimation . xxiMental Imagery . xxiMental Computation . xxiContents MHRiii
Chapter CorrelationxxiiiUnit 1 Measurement1Unit 1 Opener . 1Unit 1 Project Opener . 2Chapter 1 Measurement Systems3Opening Matter and Charts . 3Chapter Opener . 71.1 SI Measurement . 91.2 Imperial Measurement . 161.3 Converting Between SI and Imperial Systems . 23Chapter 1 Review . 30Chapter 1 Practice Test . 32Chapter 2 Surface Area and Volume35Opening Matter and Charts . 35Chapter Opener . 392.1 Units of Area and Volume . 412.2 Surface Area . 512.3 Volume . 63Chapter 2 Review . 71Chapter 2 Practice Test . 72Chapter 3 Right Triangle Trigonometry75Opening Matter and Charts . 75Chapter Opener . 793.1 The Tangent Ratio . 813.2 The Sine and Cosine Ratios . 883.3 Solving Right Triangles . 94Chapter 3 Review . 100Chapter 3 Practice Test . 101ivUnit 1 Project103Unit 1 Review and Test105MHR Mathematics 10 Teacher’s Resource
Unit 2 Algebra and Number107Unit 2 Opener . 107Unit 2 Project Opener . 108Chapter 4 Exponents and Radicals109Opening Matter and Charts . 109Chapter Opener . 1134.1 Square Roots and Cube Roots . 1154.2 Integral Exponents . 1234.3 Rational Exponents . 1344.4 Irrational Numbers . 141Chapter 4 Review . 151Chapter 4 Practice Test . 152Chapter 5 Polynomials155Opening Matter and Charts .155Chapter Opener .1595.1 Multiplying Polynomials . 1615.2 Common Factors . 1705.3 Factoring Trinomials . 1785.4 Factoring Special Trinomials . 187Chapter 5 Review . 198Chapter 5 Practice Test . 200Unit 2 Project202Unit 2 Review and Test204Contents MHRv
Unit 3 Relations and Functions205Unit 3 Opener . 205Unit 3 Project Opener . 206Chapter 6 Linear Relations207Opening Matter and Charts . 207Chapter Opener . 2116.1 Graphs of Relations . 2136.2 Relations . 2216.3 Domain and Range . . 2286.4 Functions . 2356.5 Slope . 242Chapter 6 Review . 250Chapter 6 Practice Test . 251Chapter 7 Linear Equations and Graphs253Opening Matter and Charts . 253Chapter Opener . 2577.1 Slope-Intercept Form . 2597.2 General Form . 2687.3 Slope-Point Form . 2767.4 Parallel and Perpendicular Lines . 282Chapter 7 Review . 288Chapter 7 Practice Test . 290viUnit 3 Project292Unit 3 Review and Test296MHR Mathematics 10 Teacher’s Resource
Unit 4 Systems of Equations297Unit 4 Opener . 297Unit 4 Project Opener . 298Chapter 8 Solving Systems of LinearEquations Graphically299Opening Matter and Charts . 299Chapter Opener . 3038.1 Systems of Linear Equations and Graphs . 3068.2 Modelling and Solving Linear Systems . 3168.3 Number of Solutions for Systems of Linear Equations . 324Chapter 8 Review . 331Chapter 8 Practice Test . 333Chapter 9 Solving Systems of LinearEquations Algebraically335Opening Matter and Charts . 335Chapter Opener . 3399.1 Solving Systems of Linear Equations by Substitution . 3419.2 Solving Systems of Linear Equations by Elimination . 3479.3 Solving Problems Using Systems of Linear Equations . 354Chapter 9 Review . 360Chapter 9 Practice Test . 362Unit 4 Project363Unit 4 Review and Test365Blackline MastersThe blackline masters for Mathematics 10 are available on the Mathematics 10Teacher’s Resource CD-ROM.These include generic masters, chapter-specific masters, and a series ofTech Masters.Contents MHRvii
TIME LINES FOR MATHEMATICS 10The chart below shows estimated times, in minutes, for covering the materialin Mathematics 10. Please note that times will vary depending on yourparticular class and its individual students.Also note that there are alternative ways to cover and assess many outcomes.For example, student achievement of unit outcomes can be checked by havingstudents do the unit review and unit test, or, more holistically, by havingstudents complete the unit project, or by doing a combination of these things.Mathematics 10 Time Frames1234530–40679Unit Opener30–40Chapter –4030–4020–30Section �120100–140100–12060–75Section �12080–120100–12060–75Section ��24090–130Section 430–408Section 5Chapter ReviewPractice it Project60–9060–9080–10090–120Unit Review60–9060–9060–9060–90Unit TestviiiMHR Mathematics 10 Teacher’s Resource
AN INTRODUCTION TO MATHEMATICS 10TEACHER’S RESOURCEUnit MaterialEach unit begins with unit opener notes that list the General and SpecificOutcomes for the unit and provide suggestions for teaching the unit openermaterial, which includes an introduction to the unit project.Chapter MaterialEach Chapter tarts with a four-page foldout that provides an overview of the chapter outcomes and concepts, skills, and processes assessment suggestions for the use of the FoldableTM and the sectionWarm-Ups suggested timing for the numbered sections, chapter review, andpractice test a list of prerequisite skills for each section suggested assignments for most students a list of related blackline masters available on the CD-ROM a list of materials and technology tools needed for each lesson the location of Assessment as Learning, Assessment for Learning, andAssessment of Learning opportunities in the chapterThe Chapter Opener includes a description of the math that will be covered in the chapter suggestions for introducing students to the chapter’s topics suggestions for using the chapter’s unit project questionsThe opening page of each numbered section expands on the informationprovided in the foldout.The teaching notes include the following: Answers for the Investigate and Your Turn questions Planning Notes Assessment boxes that provide a variety of short assessment strategies andrelated supported learning Each chapter ends with a chapter review and a practice test. Unit reviews reinforce the chapters in the unit.Introduction MHRix
CHARACTERISTICS OF MCGRAW-HILLRYERSON’S MATHEMATICS 10 PROGRAMThe Mathematics 10 program was designed for students and educators usingthe outcomes and achievement indicators published in The WNCP CommonCurriculum Framework for Grades 10–12 Mathematics, January 2008.This resource package will support educators and all grade 10 studentsenrolled in Foundations of Mathematics and Pre-Calculus Grade 10 inAlberta, British Columbia, Manitoba, Northwest Territories, Nunavut,Saskatchewan, and Yukon.The Mathematics 10 design is based on current educational philosophy andpedagogy. The instructional design adheres to the principles set out in theWNCP Common Curriculum Framework that include beliefs about studentsand mathematics learning, the affective domain, mathematical processes, thenature of mathematics learning, and instructional focus. Other considerationsinclude chapter sequence, the role of technology, and layout.Because concern for teachers and students was paramount, the program wasdeveloped around two central questions:1. How would the instructional design benefit/support students?2. What would teachers require to support their implementation of thenew curriculum?Pedagogical ApproachThe program is based on the philosophy that the focus of student learning is todevelop a deeper understanding of mathematics and its connection to studentlives, careers, and interests. For that reason, the instructional design is basedon the premise that students can, and will, take responsibility for their learning,and that they are active and thoughtful learners. With these beliefs in mind, theresource supports a wide range of student interests and learning styles.Mathematics: Making LinksThroughout the Mathematics 10 student resource, students are given theopportunity to see the links between real life and mathematics. Every unit includes a unit project that models mathematics in the realworld, engages students’ interest, and gives students a meaningful purposefor learning the mathematics presented in the unit. The project is designedto engage students by making links between the mathematics in the unitand students’ personal experiences and interests, as well as betweenmathematics and the real world. Most concepts or procedures are introduced in a real-life context. The Big Ideas at the beginning of each chapter list in student-friendlylanguage the outcomes of the mathematics curriculum that are covered inthe chapter. These outcomes may be from different strands that naturally fittogether and further illustrate how the program makes important linksamong concepts within the discipline and with the real world.xMHR Mathematics 10 Teacher’s Resource
A career connection at the beginning of each chapter allows students tosee how the math they are learning applies to a career in the real world. Thevisuals in many chapter openers show people performing work related to themath skills in the chapter. These jobs and careers require varying amountsof education, thus con
This resource package will support educators and all grade 10 students enrolled in Foundations of Mathematics and Pre-Calculus Grade 10 in Alberta, British Columbia, Manitoba, Northwest Territories, Nunavut, Saskatchewan, and Yukon. The Mathematics 10 design
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The entire body of McGraw-Hill Ryerson Mathematics of Data Management, Solutions was created on a home computer in Microsoft Word 2000. Graphics for the solutions were created with the help of spreadsheets (Microsoft Excel 2000 and Corel Quattro Pro 8), Fathom 1.1, and TI-83 Plus graphing calculator screens captured to the computer.
The entire body of McGraw-Hill Ryerson Mathematics of Data Management, Solutions was created on a home computer in Microsoft Word 2000. Graphics for the solutions were created with the help of spreadsheets (Microsoft Excel 2000 and Corel Quattro Pro 8), Fathom 1.1, and TI-83 Plus graphing calculator screens captured to the computer.
Alexander Ferworn, CD, PhD Professor Department of Computer Science Faculty of Science Ryerson University 350 Victoria St. Toronto, Ontario, Canada M5B 2K3 (416) 979-5000 x 6968 aferworn@ryerson.ca . 1 Ryerson Office of the Vice President-Research and Innovation holds a Memorandum of Understanding (2007) with
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McGraw-Hili Ryerson Mathematics of D -J J:;j jJ 0ajSJajJ-J This book was distributed by Jack Truong for use at William Lyon Mackenzie Collegiate Institute. Tools for Data Management Specific Expectations Section Locate data to
