Interactive Mathematics Program 2 PDF
Preview Interactive Mathematics Program 2
IInntteerraaccttiivvee MMaatthheemmaattiiccss Interactive Mathematics 22 Program PPrrooggrraamm ® ®® All About Alice Integrated High School Mathematics R Do Bees Build It Best? A Y E Y E A Dan Fendel Diane Resek R Lynne Alper Sherry Fraser 2 Is There Really a Difference? Key Curriculum Press ISBN 1-55953-263-7 90000> EY CURRICULUM PRE Innovators in Mathematics Education Solve It! Cookies IMP Year 2 is the second of a four-year series 9781559532631 of integrated high school mathematics 2 Interactive Mathematics Program R ® A E Y Integrated High School Mathematics Dan Fendel and Diane Resek with Lynne Alper and Sherry Fraser EY CURRICULUM PRE Innovators in Mathematics Education Project Editor This material is based upon work supported by the National Science Casey FitzSimons Foundation under award number Editorial Assistant ESI-9255262.Any opinions,findings, Jeff Gammon and conclusions or recommendations Production Editor expressed in this publication are those of the authors and do not necessarily Caroline Ayres reflect the views of the National Art Developer Science Foundation. Jason Luz Cover and Interior Design © 1998 by the Interactive Mathematics Program. Terry Lockman,Lumina Designworks All rights reserved. Production Manager Unauthorized copying of the Steve Rogers,Luis Shein Interactive Mathematics Program: Production Coordination Year 2 is a violation of federal law. Diana Krevsky,Susan Parini ®Interactive Mathematics Program Technical Graphics is a registered trademark of Key Curriculum Press.™IMPand Kristen Garneau,Natalie Hill,Greg Reeves the IMP logo are trademarks of Illustration Key Curriculum Press. Tom Fowler,Evangelia Philippidis,Sara Swan, Key Curriculum Press Diane Varner,Martha Weston,April Goodman Willy 1150 65th Street Publisher Emeryville,California 94608 Steven Rasmussen 11 10 9 8 7 6 03 02 Editorial Director ISBN 1-55953-634-9 Printed in the John Bergez United States of America MATHEMATICSREVIEW Rick Marks,Ph.D.,Sonoma State University, Rohnert Park,California MULTICULTURALREVIEWS Mary Barnes,M.Sc.,University of Melbourne, Cremorne,New South Wales,Australia Edward D.Castillo,Ph.D.,Sonoma State University, Rohnert Park,California Joyla Gregory,B.A.,College Preparatory School, Oakland,California Genevieve Lau,Ph.D.,Skyline College,San Bruno,California Beatrice Lumpkin,M.S.,Malcolm X College (retired), Chicago,Illinois Arthur Ramirez,Ph.D.,Sonoma State University, Rohnert Park,California TEACHERREVIEWS Daniel R.Bennett,Kualapuu,Hawaii Larry Biggers,San Antonio,Texas Dave Calhoun,Fresno,California Dwight Fuller,Clovis,California Daniel S.Johnson,Campbell,California Brent McClain,Hillsboro,Oregon Amy C.Roszak,Roseburg,Oregon Carmen C.Rubino,Lakewood,Colorado Jean Stilwell,Minneapolis,Minnesota Wendy Tokumine,Honolulu,Hawaii Year 2 Acknowledgments Many people have contributed to the development of the IMP™ curriculum,including the hundreds of teachers and many thousands of students who used preliminary versions of the materials.Of course,there is no way to thank all of them individually,but the IMP directors want to give some special acknowledgments. We want to give extraordinary thanks to these people who played unique roles in the development of the curriculum. • Bill Finzer was one of the original • Mary Jo Cittadino became a high directors of IMP and helped develop the school student once again during the concept of a problem-based unit. piloting of the curriculum,which gave her a unique perspective on the • Nitsa Movshovitz-Hadar suggested the central problem for Do Bees Build It curriculum. Best? and wrote the first draft of that • Lori Green left the classroom as a unit. regular teacher after piloting Year 1 and became a traveling resource for IMP • Rich Hemphill suggested the use of the Alice story as a metaphor for classroom teachers.She has compiled exponential growth and designed many of her classroom insights in the several of the activities in All About IMP Teaching Handbook. Alice. • Celia Stevenson developed the charming and witty graphics that graced • Matt Bremer piloted the entire curriculum,did the initial revision of the prepublication versions of the IMP every unit after its pilot testing,and did units. major work on subsequent revisions. In creating this program,we needed help in many areas other than writing curriculum and giving support to teachers. The National Science Foundation (NSF) has been the primary sponsor of the Interactive Mathematics Program®.We want to thank NSF for its ongoing support,and we especially want to extend our personal thanks to Dr.Margaret Cozzens,Director of NSF’s Division of Elementary, Secondary,and Informal Education,for her encouragement and her faith in our efforts. We also want to acknowledge here the initial support for curriculum development from the California Postsecondary Education Commission and the San Francisco Foundation, and the major support for dissemination from the Noyce Foundation and the David and Lucile Packard Foundation. Keeping all of our work going required the help of a first-rate office staff.This group of talented and hard-working individuals worked tirelessly on many tasks,such as sending out Interactive Mathematics Program iii Year 2 units,keeping the books balanced,helping us get our message out to the public,and handling communications with schools,teachers,and administrators.We greatly appreciate their dedication. • Barbara Ford—Secretary • Marianne Smith—Communications Manager • Tony Gillies—Project Manager • Linda Witnov—Outreach Coordinator IMP National Advisory Board We have been further supported in this work by our National Advisory Board—a group of very busy people who found time in their schedules to give us more than a piece of their minds every year.We thank them for their ideas and their forthrightness. David Blackwell Milton A.Gordon Diane Ravitch (1994 only) Professor of Mathematics and President and Professor of Senior Research Scholar, Statistics Mathematics Brookings Institution University of California,Berkeley California State University, Fullerton Roy Romer (1992–1994 only) Constance Clayton Governor Professor of Pediatrics Shirley Hill State of Colorado Chief,Division of Community Curator’s Professor of Education Health Care and Mathematics Karen Sheingold Medical College of Pennsylvania School of Education Research Director University of Missouri Educational Testing Service Tom Ferrio Manager,Professional Calculators Steven Leinwand Theodore R.Sizer Texas Instruments Mathematics Consultant Chairman Connecticut Department of Coalition of Essential Schools Andrew M.Gleason Education Hollis Professor of Mathematics Gary D.Watts and Natural Philosophy Art McArdle Educational Consultant Department of Mathematics Northern California Surveyors Harvard University Apprentice Committee We want to thank Dr.Norman Webb of the Wisconsin Center for Education Research for his leadership in our evaluation program,and our Evaluation Advisory Board,whose expertise was so valuable in that aspect of our work. • David Clarke,University of Melbourne • George Hein,Lesley College • Robert Davis,Rutgers University • Mark St.John,Inverness Research Associates Finally,we want to thank Steve Rasmussen,President of Key Curriculum Press, Casey FitzSimons,Key’s Project Editor for the IMP curriculum,and the many others at Key whose work turned our ideas and words into published form. iv Interactive Mathematics Program Year 2 Foreword Is There Really a Difference? asks the title of one Year 2 unit of the Interactive Mathematics Program (IMP). “You bet there is!”As Superintendent of Schools,I have found that IMP students in our District have more fun,are well prepared for our State Testing Program in the tenth grade,and are a more representative mix of the different groups in our geographical area than students in other pre-college math classes.Over the last few years,IMP has become an important example of curriculum reform in both our math and science programs. When we decided in 1992 to pilot the Interactive Mathematics Program,we were excited about its modern approach to restructuring the traditional high school math sequence of courses and topics and its applied use of significant technology.We hoped that IMP would not only revitalize the pre-college math program,but also extend it to virtually all ninth-grade students.At the same time,we had a few concerns about whether IMP students would acquire all of the traditional course skills in algebra, geometry,and trigonometry. Within the first year,the program proved successful and we were exceptionally pleased with the students’positive reaction and performance,the feedback from parents,and the enthusiasm of teachers.Our first group of IMP students, who graduated in June,1996,scored as well on PSATs,SATs, and State tests as a comparable group of students in the traditional program did,and subsequent IMP groups are doing the same.In addition,the students have become our most enthusiastic and effective IMP promoters when visiting middle school classes to describe math course options to Interactive Mathematics Program v Year 2 incoming ninth graders.One student commented,“IMP is the most fun math class I’ve ever had.”Another said,“IMP makes you work hard,but you don’t even notice it.” In our first pilot year,we found that the IMP course reached a broader range of students than the traditional Algebra 1 course did.It worked wonderfully not only for honors students,but for other students who would not have begun algebra study until tenth grade or later.The most successful students were those who became intrigued with exciting applications,enjoyed working in a group,and were willing to tackle the hard work of thinking seriously about math on a daily basis. IMP Year 2 places the graphing calculator and computer in central positions early in the math curriculum.Students thrive on the regular group collaboration and grow in self-confidence and skill as they present their ideas to a large group.Most importantly,not only do students learn the symbolic and graphing applications of elementary algebra,the statistics of Is There Really a Difference?, and the geometry of Do Bees Build It Best?, but the concepts have meaning to them. I wish you well as you continue your IMP path for a second year.I am confident that students and teachers using Year 2 will enjoy mathematics more than ever as they experiment, investigate,and discover solutions to the problems and activities presented this year. Reginald Mayo Superintendent New Haven Public Schools New Haven,Connecticut vi Interactive Mathematics Program Contents Note to Students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xvii Solve It! Days 1–5:Solving Equations and Understanding Situations . . . .3 A Year 2 Sampler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 Homework 1:Math,Me,and the Future . . . . . . . . . . . . . . . . . . . . . . .6 Memories of Yesteryear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 Homework 2:Building a Foundation . . . . . . . . . . . . . . . . . . . . . . . . .9 Homework 3:You’re the Storyteller . . . . . . . . . . . . . . . . . . . . . . . . . .10 Is It a Digit? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 POW 1:A Digital Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12 The Standard POW Write-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13 Homework 4:Running on the Overland Trail . . . . . . . . . . . . . . . . . .15 Lamppost Shadows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 Homework 5:1-2-3-4 Puzzle with Negatives . . . . . . . . . . . . . . . . . . .17 Days 6–12:Keeping Things Balanced . . . . . . . . . . . . . . . . . . . . . .19 Homework 6:The Mystery Bags Game . . . . . . . . . . . . . . . . . . . . . . . .20 Homework 7:You’re the Jester . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22 Substitution and Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23 Homework 8:Letters,Numbers,and a Story . . . . . . . . . . . . . . . . . . .25 Catching Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26 Homework 9:More Letters,Numbers,and Mystery Bags . . . . . . . . . .27 Back to the Lake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29 Homework 10:What Will It Answer? . . . . . . . . . . . . . . . . . . . . . . . . . .31 POW 2:Tying the Knots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33 Homework 11:Line It Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35 The Graph Solves the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36 Homework 12:Who’s Right? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37 Interactive Mathematics Program vii Year 2 Contents Days 13–21:What’s the Same? . . . . . . . . . . . . . . . . . . . . . . . . . . . .38 A Lot of Changing Sides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39 Homework 13:Why Are They Equivalent? . . . . . . . . . . . . . . . . . . . . .40 Homework 14:One Each Way . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42 Distributing the Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43 Homework 15:The Distributive Property and Mystery Lots . . . . . . . .45 Homework 16:Views of the Distributive Property . . . . . . . . . . . . . . .47 Prime Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50 POW 3:Divisor Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51 Homework 17:Exactly Three or Four . . . . . . . . . . . . . . . . . . . . . . . . .53 Taking Some Out,Part I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54 Homework 18:Subtracting Some Sums . . . . . . . . . . . . . . . . . . . . . . .56 Taking Some Out,Part II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58 Homework 19:Randy,Sandy,and Dandy Return . . . . . . . . . . . . . . .60 Homework 20:Equation Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61 Scrambling Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63 Homework 21:More Scrambled Equations and Mystery Bags . . . . . .65 Days 22–26:The Linear World . . . . . . . . . . . . . . . . . . . . . . . . . . . .67 Old Friends and New Friends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68 Homework 22:New Friends Visit Your Home . . . . . . . . . . . . . . . . . . .70 Homework 23:From One Variable to Two . . . . . . . . . . . . . . . . . . . . .71 Get It Straight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72 Homework 24:A Distributive Summary . . . . . . . . . . . . . . . . . . . . . .74 Homework 25:All by Itself . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75 Homework 26:More Variable Solutions . . . . . . . . . . . . . . . . . . . . . . .77 Days 27–31:Beyond Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . .79 Where’s Speedy? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .80 Homework 27:A Mixed Bag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .81 To the Rescue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .82 Homework 28:Swinging Pendulum . . . . . . . . . . . . . . . . . . . . . . . . . .83 Mystery Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .84 Homework 29:Functioning in the Math World . . . . . . . . . . . . . . . . .85 The Graphing Calculator Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . .88 Homework 30:A Solving Sampler . . . . . . . . . . . . . . . . . . . . . . . . . . .90 “Solve It!”Portfolio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91 viii Interactive Mathematics Program
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