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The Center for Mathematics Education Project was developed at Education Development Center,Inc. (EDC) within the Center for Mathematics Education (CME), with partial support from theNational Science Foundation.Education Development Center, Inc.Center for Mathematics EducationNewton, MassachusettsThis material is based upon work supported by the National Science Foundation underGrant No. ESI-0242476, Grant No. MDR-9252952, and Grant No. ESI-9617369. Any opinions,findings, and conclusions or recommendations expressed in this material are those of theauthor(s) and do not necessarily reflect the views of the National Science bis;Ajosch/AFP/GettyCover ImagesTaken from:Takenfrom:CME Project:1 ntTeamBy the CME Project DevelopmentTeamCopyright 2009 by Educational Development Center, Inc.Copyright 2009 by Educational Development Center, Inc.Published by Pearson Education, Inc.Publishedby Pearson Education, Inc.Upper Saddle River, New Jersey 07458Upper Saddle River, New Jersey 07458CME Common Core Additional Lessons: Algebra 1CMECommonCoreAdditional TeamLessons: Algebra 1By theCME ProjectDevelopmentBythe CMEProjectDevelopmentTeamCopyright 2012by EducationalDevelopmentCenter, Inc.Published byPearsonInc.Development Center, Inc.Copyright 2012byEducation,EducationalUpper SaddleNewEducation,Jersey 07458Publishedby River,PearsonInc.Upper Saddle River, New Jersey 07458CME Project Development TeamLead Developer: Al CuocoCME Project Development TeamLeadDeveloper: Al CuocoCore Development Team: Anna Baccaglini-Frank, Jean Benson, Nancy Antonellis D’Amato, Daniel Erman, Brian Harvey,Wayne Harvey, Bowen Kerins, Doreen Kilday, Ryota Matsuura, Stephen Maurer, Sarah Sword, Audrey Ting, and Kevinwto, Daniel Erman,WatermanBrian Harvey, Wayne Harvey, Bowen Kerins, Doreen Kilday, Ryota Matsuura, Stephen Maurer, Sarah Sword,AudreyTing,contributedand Kevin WatermanOthers whoinclude Steve Benson, Paul D’Amato, Robert Devaney, Andrew Golay, PaulGoldenberg, Jane Gorman, C. Jud Hill, Eric Karnowski, Helen Lebowitz, Joseph Leverich, Melanie Palma,Mark Saul,Nin contributedShteingold, andincludeBrett Thomas.OtherswhoSteve Benson, Paul D’Amato, Robert Devaney, Andrew Golay, PaulGoldenberg, Jane Gorman, C. Jud Hill, Eric Karnowski, Helen Lebowitz, Joseph Leverich, Melanie Palma,All rightsreserved.No part of thismaybe reproduced, in any form or by any means, without permission in writingMarkSaul,Nina Shteingold,andbookBrettThomas.from the publisher.Allrights reserved. No part of this book may be reproduced, in any form or by any means, without permissionThis special edition published in cooperation with Pearson Learning Solutions.in writing from the publisher.All trademarks, service marks, registered trademarks, and registered service marks are the property of their respectiveThisspecialeditionpublishedin cooperationwith only.Pearson Learning Solutions.ownersand areused hereinfor identificationpurposesAll trademarks, service marks, registered trademarks, and registered service marks are the property of theirPearson LearningSolutions,BoylstonSuite cation900, Boston,MA 02116respectiveownersand are501usedhereinStreet,for identifipurposesonly.A Pearson Education Companywww.pearsoned.comPearson Learning Solutions, 501 Boylston Street, Suite 900, Boston, MA 02116Printed in the United States of AmericaA Pearson Education Companywww.pearsoned.com1 2 3 4 5 6 7 8 9 10 XXXX 17 16 15 14 13 12Printed in the United States of America0002000102716610951 2 3 4 5 6 7 8 9 10 XXXX 17 16 15 14 13 12MDISBN 10: 1-256-74146-9ISBN 13: 978-1-256-74146-6000200010271661095 CH00 FM pi-xxiiii000200010271661095 CH00 FM pi-xxi.pdf26/28/12 5:14:05 PM
Contents in BriefIntroduction to the CME Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivContributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vCME Project Student Handbook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivGo Online . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiChapter 1 Arithmetic to Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Chapter 2 Expressions and Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88Chapter 3 Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186Chapter 4 Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320Chapter 5 Introduction to Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422Chapter 6 Exponents and Radicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514Chapter 7 Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606Chapter 8 Quadratics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694TI-Nspire Technology Handbook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 790TablesMath Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 800Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 801Formulas From Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 802Properties and Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 806Selected Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 846Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853iii000200010271661095 CH00 FM pi-xxiiiiii000200010271661095 CH00 FM pi-xxi.pdf36/28/12 5:14:06 PM
CME PROJECTIntroduction to theCME ProjectThe CME Project, developed by EDC’s Center forMathematics Education, is a new NSF-funded highschool program, organized around the familiarcourses of algebra 1, geometry, algebra 2, andprecalculus. The CME Project provides teachersand schools with a third alternative to the choicebetween traditional texts driven by basic skilldevelopment and more progressive texts thathave unfamiliar organizations. This programgives teachers the option of a problem-based,student-centered program, organized around themathematical themes with which teachers andparents are familiar. Furthermore, the tremendoussuccess of NSF-funded middle school programs hasleft a need for a high school program with similarrigor and pedagogy. The CME Project fills this need.The goal of the CME Project is to help studentsacquire a deep understanding of mathematics.Therefore, the mathematics here is rigorous. Wetook great care to create lesson plans that, whilechallenging, will capture and engage studentsof all abilities and improve their mathematicalachievement.The Program’s ApproachThe organization of the CME Project providesstudents the time and focus they need to developfundamental mathematical ways of thinking.Its primary goal is to develop in students robustmathematical proficiency. The program employs innovative instructionalmethods, developed over decades of classroomexperience and informed by research, that helpstudents master mathematical topics.iviv CME Project Algebra 1000200010271661095 CH00 FM pi-xxiviv000200010271661095 CH00 FM pi-xxi.pdf One of the core tenets of the CME Project is tofocus on developing students’ Habits of Mind,or ways in which students approach and solvemathematical challenges. The program builds on lessons learned fromhigh-performing countries: develop an ideathoroughly and then revisit it only to deepen it;organize ideas in a way that is faithful to howthey are organized in mathematics; and reduceclutter and extraneous topics. It also employs the best American models thatcall for grappling with ideas and problemsas preparation for instruction, moving fromconcrete problems to abstractions and generaltheories, and situating mathematics in engagingcontexts. The CME Project is a comprehensive curriculumthat meets the dual goals of mathematical rigorand accessibility for a broad range of students.About CMEEDC’s Center for Mathematics Education, ledby mathematician and teacher Al Cuoco, bringstogether an eclectic staff of mathematicians,teachers, cognitive scientists, education researchers,curriculum developers, specialists in educationaltechnology, and teacher educators, internationallyknown for leadership across the entire range of K–16mathematics education. We aim to help studentsand teachers in this country experience the thrill ofsolving problems and building theories, understandthe history of ideas behind the evolution ofmathematical disciplines, and appreciatethe standards of rigor that are central tomathematical culture.Algebra 146/28/12 5:14:08 PM
Contributors to the CME ProjectNational Advisory Board The National AdvisoryField-Test Teachers Our field-test teachersBoard met early in the project, providing criticalfeedback on the instructional design and the overallorganization. Members includegave us the benefit of their classroom experienceby teaching from our draft lessons and giving usextensive, critical feedback that shaped the draftsinto realistic, teachable lessons. They shared theirconcerns, questions, challenges, and successesand kept us focused on the real world. Some ofthem even welcomed us into their classrooms asco-teachers to give us the direct experience withstudents that we needed to hone our lessons.Working with these expert professionals hasbeen one of the most gratifying parts of thedevelopment—they are “highly qualified” in themost profound sense.Richard Askey, University of WisconsinEdward Barbeau, University of TorontoHyman Bass, University of MichiganCarol Findell, Boston UniversityArthur Heinricher, Worcester Polytechnic InstituteRoger Howe, Yale UniversityBarbara Janson, Janson AssociatesKenneth Levasseur, University of Massachusetts,LowellJames Madden, Louisiana State University,Baton RougeJacqueline Miller, Education Development CenterJames Newton, University of MarylandRobert Segall, Greater Hartford Academyof Mathematics and ScienceGlenn Stevens, Boston UniversityHerbert Wilf, University of PennsylvaniaHung-Hsi Wu, University of California, BerkeleyCore Mathematical Consultants Dick Askey,Ed Barbeau, and Roger Howe have been involved inan even more substantial way, reviewing chaptersand providing detailed and critical advice on everyaspect of the program. Dick and Roger spent manyhours reading and criticizing drafts, brainstormingwith the writing team, and offering advice oneverything from the logical organization to theactual numbers used in problems. We can’t thankthem enough.Teacher Advisory Board The Teacher AdvisoryBoard for the CME Project was essential in helpingus create an effective format for our lessons thatembodies the philosophy and goals of the program.Their debates about pedagogical issues and how todevelop mathematical topics helped to shape thedistinguishing features of the curriculum so thatour lessons work effectively in the classroom. Theadvisory board includesJayne Abbas, Richard Coffey,Charles Garabedian, Dennis Geller,Eileen Herlihy, Doreen Kilday,Gayle Masse, Hugh McLaughlin,Nancy McLaughlin, Allen Olsen,Kimberly Osborne, Brian Shoemaker,and Benjamin SinwellCalifornia Barney Martinez, Jefferson High School,Daly City; Calvin Baylon and Jaime Lao, Bell JuniorHigh School, San Diego; Colorado Rocky Cundiff,Ignacio High School, Ignacio; Illinois Jeremy Kahan,Tammy Nguyen, and Stephanie Pederson, IdaCrown Jewish Academy, Chicago; MassachusettsCarol Martignette, Chris Martino and Kent Werst,Arlington High School, Arlington, Larry Davidson,Boston University Academy, Boston; Joe Bishopand Carol Rosen, Lawrence High School, Lawrence;Maureen Mulryan, Lowell High School, Lowell;Felisa Honeyman, Newton South High School,Newton Centre; Jim Barnes and Carol Haney, RevereHigh School, Revere; New Hampshire Jayne Abbasand Terin Voisine, Cawley Middle School, Hooksett;New Mexico Mary Andrews, Las Cruces HighSchool, Las Cruces; Ohio James Stallworth, HughesCenter, Cincinnati; Texas Arnell Crayton, BellaireHigh School, Bellaire; Utah Troy Jones, WaterfordSchool, Sandy; Washington Dale Erz, Kathy Greer,Karena Hanscom, and John Henry, Port AngelesHigh School, Port Angeles; Wisconsin AnnetteRoskam, Rice Lake High School, Rice Lake.Special thanks go to our colleagues at Pearson,most notably Elizabeth Lehnertz, Joe Will,and Stewart Wood. The program benefitsfrom their expertise in every way, fromthe actual mathematics to the designof the printed page.CME Project Algebra 1 v000200010271661095 CH00 FM pi-xxvv000200010271661095 CH00 FM pi-xxi.pdf56/28/12 5:14:12 PM
1Arithmetic to AlgebraChapter Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21.0 Habits of Mind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4The Tables of Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.01 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.02 Thinking About Negative Numbers . . . . . . . . . . . . . . . . . . . . . . . . .1.03 Extending the Addition Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.04 Extending the Multiplication Table . . . . . . . . . . . . . . . . . . . . . . . . .1.05 The Basic Rules of Arithmetic—Properties of Operations. . . . . . . .Mathematical Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .891217232833The Number Line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.06 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.07 Numbers Besides the Integers—Fractions . . . . . . . . . . . . . . . . . . . .1.08 Decimals—Addresses on the Number Line . . . . . . . . . . . . . . . . . . .1.09 Number Line Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.10 Number Line Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Mathematical Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .343537414651561A1BMid-Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571CThe Algorithms of Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.11 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.12 Addition and Subtraction Algorithms . . . . . . . . . . . . . . . . . . . . . . .1.13 Adding and Subtracting Fractions . . . . . . . . . . . . . . . . . . . . . . . . . .1.14 Multiplication Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.15 Multiplying and Dividing Fractions. . . . . . . . . . . . . . . . . . . . . . . . . .Mathematical Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58596167717781Project: Using Mathematical HabitsLo . . . ong Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86vi000200010271661095 CH00 FM pi-xxvivi000200010271661095 CH00 FM pi-xxi.pdfAlgebra 166/28/12 5:14:16 PM
2Expressionsand EquationsChapter Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 882A2BExpressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 902.01 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 912.02 Modeling General Situations—Writing Expressions . . . . . . . . . . . . 932.03 Evaluating Expressions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 982.04 Simplifying Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1032.05 Rephrasing the Basic Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110Mathematical Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.06 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.07 Reversing Operations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.08 Solving Equations by Backtracking . . . . . . . . . . . . . . . . . . . . . . . . .Mathematical Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .116117120126132Mid-Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133Solving Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1342C2.09 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.10 When Backtracking Does Not Work . . . . . . . . . . . . . . . . . . . . . . . .2.11 The Basic Moves for Solving Equations . . . . . . . . . . . . . . . . . . . . .2.12 Solutions of Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.13 Focus on the Distributive Property . . . . . . . . . . . . . . . . . . . . . . . . .Mathematical Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2D2.142.152.162.17135138143148153157Word Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Building Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solving Word Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .More Than One Variable—Solving in Terms of Each Other . . . . . . . . . . . . . . . . . . . . . . . . . . . .Mathematical Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .159162167172178Project: Using Mathematical HabitsGood Questions About Perfect Squares . . . . . . . . . . . . . . . . . . . . . . . . . 179Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182Cumulative Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184Contents000200010271661095 CH00 FM pi-xxviivii000200010271661095 CH00 FM pi-xxi.pdfvii76/28/12 5:14:20 PM
3GraphsChapter Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186Introduction to Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1883A3.01 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.02 Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.03 Distance and Absolute Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.04 Graphing Related Quantities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Mathematical Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .189196202210217Statistical Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2183B3.053.063.073.08Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219Mean, Median, and Mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223Data Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230Paired Comparisons—Box-and-Whisker Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2373.09 Catogorical Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2453.10 Two-Variable Data— Scatter Plots . . . . . . . . . . . . . . . . . . . . . . . . . 253Mathematical Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262Mid-Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263Equations and Their Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2643C3.11 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.12 Equations as Point-Testers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.13 Graphing by Plotting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.14 Intersection of Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Mathematical Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .265267272279283Basic Graphs and Translations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2843D3.15 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .c3.16 Two Basic Graphs: y cx, y x —Direct and Inverse Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.17 Four More Basic Graphs:y x 2, y x 3, y "x, y u x u . . . . . . . . . . . . . . . . . . . . . . . . . . .3.18 Translating Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Mathematical Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .285289298305314Project: Using Mathematical HabitsDrawing With Graphs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318viii000200010271661095 CH00 FM pi-xxviiiviii000200010271661095 CH00 FM pi-xxi.pdfAlgebra 186/28/12 5:14:22 PM
4LinesChapter Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320All About Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3224A4.01 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.02 Pitch and Slope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.03 Rates of Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.04 Collinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Mathematical Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .323327333348347Linear Equations and Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3484B4.05 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.06 Equations of Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.07 Jiffy Graphs: Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.08 Overtaking—Slope in Distance-Time Graphs. . . . . . . . . . . . . . . . .Mathematical Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .349353358363368Mid-Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3694CIntersections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.09 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.10 Solving Systems: Substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.11 Slope and Parallel Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.12 Solving Systems: Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Mathematical Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .370371374382387393Applications of Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3944D4.13 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.14 Inequalities With One Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.15 Linear Trends in Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Mathematical Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .395398406414Project: Using Mathematical HabitsWireless Phone Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418Cumulative Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420Contents000200010271661095 CH00 FM pi-xxixix000200010271661095 CH00 FM pi-xxi.pdfix96/28/12 5:14:23 PM
5Introduction to FunctionsChapter Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4225AFunctions—The Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.01 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.02 Building Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.03 Is It a Function? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.04 Naming Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.05 Function Inputs and Outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.06 Graphing Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Mathematical Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4244254284344404454 49458Mid-Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459Functions, Graphs, and Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4605B5.07 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.08 Constant Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.09 Recursive Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Mathematical Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .461465474481Functions and Situations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4825C5.10 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.11 From Situations to Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.12 From Situations to Recursive Rules . . . . . . . . . . . . . . . . . . . . . . . . .Mathematical Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .483487496507Project: Using Mathematical HabitsManaging Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512You put in3. . . and outcomes 5 . . . . . oris it 6?x000200010271661095 CH00 FM pi-xxxx000200010271661095 CH00 FM pi-xxi.pdfAlgebra 1106/28/12 5:14:25 PM
6Exponents and RadicalsChapter Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5166A6.01 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5176.02 Squares, Cubes, and Beyond—Some Basic Rules of Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5206.03 More Basic Rules of Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5266.04 Zero and Negative Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5316.05 Scientific Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537Mathematical Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542Mid-Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543Radicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5446B6.066.076.086.09Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Defining Square Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Arithmetic With Square Roots . . .
iv Algebra 1 Introduction to the CME Project The CME Project, developed by EDC's Center for Mathematics Education, is a new NSF-funded high school program, organized around the familiar courses of algebra 1, geometry, algebra 2, and precalculus. The CME Project provides teachers and schools with a third alter native to the choice
