Core-Plus Mathematics: Contemporary Mathematics in Context, Course 1

640 Pages·2007·24.05 MB·English

by  Christian R. Hirsch

i s e
nteractive tudent dition
2nd Edition
Christian R. Hirsch (cid:129) James T. Fey (cid:129) Eric W. Hart
Harold L. Schoen (cid:129) Ann E. Watkins
with
Beth E. Ritsema (cid:129) Rebecca K. Walker (cid:129) Sabrina Keller
Robin Marcus (cid:129) Arthur F. Coxford (cid:129) Gail Burrill
(tl tr bl)Getty Images, (br)Japack Company/CORBIS
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. Except as
permitted under the United States Copyright Act, no part of this publication may be
reproduced or distributed in any form or by any means, or stored in a database or
retrieval system, without prior permission of the publisher.
This material is based upon work supported, in part, by the
National Science Foundation under grant no. ESI 0137718.
Opinions expressed are those of the authors and not
necessarily those of the Foundation.
Send all inquiries to:
Glencoe/McGraw-Hill
8787 Orion Place
Columbus, OH 43240-4027
ISBN-13: 978-0-07-861521-4 (Student Edition) Core-Plus Mathematics
ISBN-10: 0-07-861521-6 (Student Edition) Contemporary Mathematics in Context
Course 1 Student Edition
Printed in the United States of America.
2 3 4 5 6 7 8 9 10 079/043 15 14 13 12 11 10 09 08 07
Core-Plus Mathematics 2
Development Team
Senior Curriculum Developers Advisory Board Collaborating Teachers
Christian R. Hirsch (Director) Diane Briars Mary Jo Messenger
Western Michigan University Pittsburgh Public Schools Howard Country Public Schools,
Maryland
James T. Fey Jeremy Kilpatrick
University of Maryland University of Georgia Jacqueline Stewart
Okemos, Michigan
Eric W. Hart Robert E. Megginson
Maharishi University of University of Michigan
Management Graduate Assistants
Kenneth Ruthven
Allison BrckaLorenz
Harold L. Schoen University of Cambridge
Christopher Hlas
University of Iowa
David A. Smith University of Iowa
Ann E. Watkins Duke University
Michael Conklin
California State University,
University of Maryland
Northridge
Mathematical Consultants
Jodi Edington
Deborah Hughes-Hallett
Contributing Curriculum University of Arizona / Harvard Karen Fonkert
Developers University Dana Grosser
Beth E. Ritsema Anna Kruizenga
Stephen B. Maurer
Western Michigan University
Swarthmore College Diane Moore
Rebecca K. Walker Western Michigan University
William McCallum
Grand Valley State University
University of Arizona
Undergraduate Assistants
Sabrina Keller
Doris Schattschneider
Michigan State University Cassie Durgin
Moravian College
University of Maryland
Robin Marcus
Richard Scheaffer
University of Maryland Rachael Kaluzny
University of Florida
Ashley Wiersma
Arthur F. Coxford (deceased)
Western Michigan University
University of Michigan
Evaluation Consultant
Gail Burrill Norman L. Webb
Michigan State University University of Wisconsin-Madison
(First edition only)
Technical Coordinator
Principal Evaluator
James Laser
Steven W. Ziebarth Western Michigan University
Western Michigan University
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Core-Plus Mathematics 2
Field-Test Sites
Core-Plus Mathematics 2 builds on the strengths of the 1st edition, which was shaped by multi-year
field tests in 36 high schools in Alaska, California, Colorado, Georgia, Idaho, Iowa, Kentucky,
Michigan, Ohio, South Carolina, and Texas. Each revised text is the product of a three-year cycle
of research and development, pilot testing and refinement, and field testing and further refinement.
Special thanks are extended to the following teachers and their students who participated in the
testing and evaluation of 2nd Edition Course 1.
Hickman High School Oakland Junior High School Sauk Prairie Middle School
Columbia, Missouri Columbia, Missouri Sauk City, Wisconsin
Peter Doll Teresa Barry Julie Dahlman
Erin Little Janine Jorgensen
Holland Christian High
Christine Sedgwick
School South Shore Middle School
Dana Sleeth
Holland, Michigan Holland, Michigan
Jeff Goorhouse Riverside University Lynn Schipper
Tim Laverell High School
Washington High School
Brian Lemmen Milwaukee, Wisconsin
Milwaukee, Wisconsin
Mike Verkaik Cheryl Brenner
Anthony Amoroso
Alice Lanphier
Jefferson Junior High School Debbie French
Ela Kiblawi
Columbia, Missouri
West Junior High School
Marla Clowe Rock Bridge High School
Columbia, Missouri
Lori Kilfoil Columbia, Missouri
Josephus Johnson
Martha McCabe Nancy Hanson
Rachel Lowery
Paul Rahmoeller
Sauk Prairie High School Mike Rowson
Evan Schilling
Prairie du Sac, Wisconsin Amanda Schoenfeld
Malcolm Price Lab School Joel Amidon Patrick Troup
Cedar Falls, Iowa Shane Been
James Maltas Kent Jensen
Josh Wilkinson Scott Schutt
Dan Tess
North Shore Middle School
Mary Walz
Holland, Michigan
Sheila Schippers
Brenda Katerberg
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Overview of Course 1
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1 P C
ATTERNS OF HANGE
Patterns of Change develops student ability to recognize and Lesson 1 Cause and Effect
describe important patterns that relate quantitative variables,
Lesson 2 Change Over Time
to use data tables, graphs, words, and symbols to represent
Lesson 3 Tools for Studying
the relationships, and to use reasoning and calculating tools
Patterns of Change
to answer questions and solve problems.
Lesson 4 Looking Back
Topics include variables and functions, algebraic expressions
and recurrence relations, coordinate graphs, data tables and
spreadsheets, and equations and inequalities.
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2 P D
ATTERNS IN ATA
Patterns in Data develops student ability to make sense of Lesson 1 Exploring
real-world data through use of graphical displays, measures Distributions
of center, and measures of variability.
Lesson 2 Variability
Topics include distributions of data and their shapes, as Lesson 3 Looking Back
displayed in dot plots, histograms, and box plots; measures
of center including mean and median, and their properties;
measures of variability including interquartile range and
standard deviation, and their properties; and percentiles and
outliers.
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3 L F
INEAR UNCTIONS
Linear Functions develops student ability to recognize and Lesson 1 Modeling Linear
represent linear relationships between variables and to use Relationships
tables, graphs, and algebraic expressions for linear functions
Lesson 2 Linear Equations
to solve problems in situations that involve constant rate of
and Inequalities
change or slope.
Lesson 3 Equivalent
Topics include linear functions, slope of a line, rate of Expressions
change, modeling linear data patterns, solving linear
Lesson 4 Looking Back
equations and inequalities, equivalent linear expressions.
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Overview of Course 1
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4 V -E G
ERTEX DGE RAPHS
Vertex-Edge Graphs develops student understanding of Lesson 1 Euler Circuits:
vertex-edge graphs and ability to use these graphs to Finding the Best
represent and solve problems involving paths, networks, and Path
relationships among a finite number of elements, including
Lesson 2 Vertex Coloring:
finding efficient routes and avoiding conflicts.
Avoiding Conflict
Topics include vertex-edge graphs, mathematical modeling, Lesson 3 Looking Back
optimization, algorithmic problem solving, Euler circuits and
paths, matrix representation of graphs, vertex coloring and
chromatic number.
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5 E F
XPONENTIAL UNCTIONS
Exponential Functions develops student ability to recognize Lesson 1 Exponential Growth
and represent exponential growth and decay patterns, to
Lesson 2 Exponential Decay
express those patterns in symbolic forms, to solve problems
Lesson 3 Looking Back
that involve exponential change, and to use properties of
exponents to write expressions in equivalent forms.
Topics include exponential growth and decay functions,
data modeling, growth and decay rates, half-life and
doubling time, compound interest, and properties of
exponents.
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6 P S
ATTERNS IN HAPE
Patterns in Shape develops student ability to visualize and Lesson 1 Two-Dimensional
describe two- and three-dimensional shapes, to represent them Shapes
with drawings, to examine shape properties through both
Lesson 2 Polygons and
experimentation and careful reasoning, and to use those
Their Properties
properties to solve problems.
Lesson 3 Three-Dimensional
Topics include Triangle Inequality, congruence conditions for Shapes
triangles, special quadrilaterals and quadrilateral linkages,
Lesson 4 Looking Back
Pythagorean Theorem, properties of polygons, tilings of the
plane, properties of polyhedra, and the Platonic solids.
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Overview of Course 1
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7 Q F
UADRATIC UNCTIONS
Quadratic Functions develops student ability to recognize Lesson 1 Quadratic Patterns
and represent quadratic relations between variables using Lesson 2 Equivalent Quadratic
data tables, graphs, and symbolic formulas, to solve problems Expressions
involving quadratic functions, and to express quadratic
Lesson 3 Solving Quadratic
polynomials in equivalent factored and expanded forms.
Equations
Topics include quadratic functions and their graphs, Lesson 4 Looking Back
applications to projectile motion and economic problems,
expanding and factoring quadratic expressions, and solving
quadratic equations by the quadratic formula and calculator
approximation.
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8 P C
ATTERNS IN HANCE
Patterns in Chance develops student ability to solve problems Lesson 1 Calculating
involving chance by constructing sample spaces of equally- Probabilities
likely outcomes and to solve more complex probability
Lesson 2 Modeling Chance
problems by using simulation or geometric models.
Situations
Topics include sample spaces, equally-likely outcomes, Lesson 3 Looking Back
probability distributions, mutually exclusive events, Addition
Rule, simulation, Law of Large Numbers, and geometric
probability.
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Contents
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1 P C
ATTERNS OF HANGE
Lesson 1 Cause and Effect . . . . . . . . . . . . . . . . . . . . . . . . 2
Investigations
1 Physics and Business at Five Star Amusement Park. . . . . . . . . . . . . . 4
2 Taking Chances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3 Trying to Get Rich Quick. . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
On Your Own. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Lesson 2 Change Over Time . . . . . . . . . . . . . . . . . . . . . . 26
Investigations
1 Predicting Population Change. . . . . . . . . . . . . . . . . . . . . . . . . 27
2 Tracking Change with Spreadsheets. . . . . . . . . . . . . . . . . . . . . . 32
On Your Own. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Lesson 3 Tools for Studying Patterns of Change . . . . . . . . . . 47
Investigations
1 Communicating with Symbols . . . . . . . . . . . . . . . . . . . . . . . . . 48
2 Quick Tables, Graphs, and Solutions. . . . . . . . . . . . . . . . . . . . . . 52
3 The Shapes of Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
On Your Own. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Lesson 4 Looking Back . . . . . . . . . . . . . . . . . . . . . . . . . 69
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2 PATTERNS IN DATA
Lesson 1 Exploring Distributions . . . . . . . . . . . . . . . . . . . . 74
Investigations
1 Shapes of Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
2 Measures of Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
On Your Own. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Lesson 2 Measuring Variability . . . . . . . . . . . . . . . . . . . .103
Investigations
1 Measuring Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
2 Measuring and Displaying Variability: The Five-Number
Summary and Box Plots. . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
3 Identifying Outliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4 Measuring Variability: The Standard Deviation . . . . . . . . . . . . . . . . 116
5 Transforming Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . 124
On Your Own. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Lesson 3 Looking Back . . . . . . . . . . . . . . . . . . . . . . . . . 144
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Contents
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INEAR UNCTIONS
Lesson 1 Modeling Linear Relationships . . . . . . . . . . . . . . .150
Investigations
1 Getting Credit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
2 Symbolize It . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
3 Fitting Lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
On Your Own . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .168
Lesson 2 Linear Equations and Inequalities . . . . . . . . . . . . .186
Investigations
1 Who Will Be the Doctor? . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
2 Using Your Head . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
3 Using Your Head … More or Less. . . . . . . . . . . . . . . . . . . . . . . 194
4 Making Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
On Your Own . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .201
Lesson 3 Equivalent Expressions. . . . . . . . . . . . . . . . . . . . 214
Investigations
1 Different, Yet the Same . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
2 The Same, Yet Different . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
On Your Own . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .224
Lesson 4 Looking Back. . . . . . . . . . . . . . . . . . . . . . . . . .232
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4 VERTEX-EDGE GRAPHS
Lesson 1 Euler Circuits: Finding the Best Path. . . . . . . . . . . .238
Investigations
1 Planning Efficient Routes . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
2 Making the Circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
3 Graphs and Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
On Your Own . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .250
Lesson 2 Vertex Coloring: Avoiding Conflict . . . . . . . . . . . .266
Investigations
1 Building a Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
2 Scheduling, Mapmaking, and Algorithms . . . . . . . . . . . . . . . . . . . 270
On Your Own . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
Lesson 3 Looking Back. . . . . . . . . . . . . . . . . . . . . . . . . .286
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