Interactive Mathematics Program 2 1st Ed

466 Pages·2016·21 MB·English

by  Dan Fendel

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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