Developmental Mathematics and Its Applications
(DevMap) Project
PROJECT SUMMARY
Students who attend twoyear colleges often arrive on campus lacking
the basic skills necessary to succeed in collegelevel work. This
is a particularly serious problem for students in Science, Mathematics,
Engineering, and Technology (SMET) programs, who may have significant
deficits in their mathematics backgrounds but high aspirations for
their future success. Students in this situation need to build both
their mathematical skills and confidence in their ability to solve
challenging problems in order to succeed in the mathematicsintensive
programs they have selected.
At the 1997 National Center for Research in Vocational Education
(NCRVE) workshop, "Beyond Eighth Grade," industry representatives
emphasized the need for "systems thinking" that enables employees
to recognize complexities inherent in situations subject to multiple
inputs and diverse constraints. In addition, sciencebased fields
such as agricultural biotechnology require technicians who are able
to formulate a problem in terms of relevant factors and design an
experiment to determine the influence of those various factors.
Yet, most developmental programs in mathematics, at both two and
fouryear colleges, offer students what amounts to a replication
of the high school mathematics curriculum they either studied and
forgot or never studied.
We now have a chance for real and positive change. Both the National
Council of Teachers of Mathematics (NCTM) Standards, published
in 1989, and Crossroads
in Mathematics: Standards for Introductory College Mathematics Before
Calculus, published by the American Mathematical Association
of TwoYear Colleges (AMATYC) in 1995, advocate an integrated approach
to mathematics content. Given students' needs in developmental mathematics,
the vision of the AMATYC Standards, and COMAP's experience, we are
creating a oneyear sequence, Developing Mathematics through
Applications. We believe there are several benefits to our approach.
 The program will not be divided into topics called algebra,
geometry, intermediate algebra and trigonometry, although all
the major concepts in those courses will be covered.
 The applicationsbased curriculum will appeal to mature students
who are choosing to pursue postsecondary education; the applications
can be drawn from areas in which students may find themselves
working or from situations that they recognize from their daily
lives.
 Solving the problems posed in DevMap will call for
integrating technology in a natural way as compared to the "drillandpractice"
use of technology currently found in many developmental mathematics
programs.
An advisory board informed the project. Members of this board
were drawn from mathematics faculty at two and fouryear colleges,
leaders of AMATYC, and business and industry organizations.
PROJECT LEADERSHIP
Dr. Solomon Garfunkel  Executive Director of COMAP
Dr. Garfunkel has served as project director for Undergraduate Mathematics
and its Applications (UMAP) and High School Mathematics and its
Applications (HiMAP). He was the project director and host for the
series For All
Practical Purposes: Introduction to Contemporary Mathematics.
Most recently he was CoPrincipal Investigator on the ARISE project
that developed the secondary standards based series, Mathematics:
Modeling Our World and is currently Principal Investigator
on the Developmental Mathematics and its Applications (DevMap) project. Dr. Garfunkel taught at the University of Connecticut and
Cornell University before founding COMAP in 1980.
Dr. Susan L. Forman  Professor of Mathematics, Bronx Community
College,
The City University of New York
Dr. Forman served as Senior Program Officer for Education at the
Charles A. Dana Foundation and as Director of College and University
Programs for the Mathematical Sciences Education Board of the National
Academy of Sciences. Her other experiences include positions as
Coordinator of Academic Computing at the City University of New
York and at the Fund for the Improvement of PostSecondary Education.
She is currently the CoPrincipal Investigator on the Developmental
Mathematics and its Applications (DevMap) project at COMAP and teaching
at the Bronx Community College.
PRODUCT
The DevMap Project is committed to developing a twosemester program
that offers an alternative approach to the elementary and intermediate
algebra courses currently taught at most two and fouryear colleges.
The project is producing materials that present the mathematical
content from an integrated point of view through the use of authentic
applications, many of which are drawn from the technological workplace.
Students completing this program will be prepared to enter a course
in precalculus.
The project's principal investigators and writers have worked
hard to create a curriculum that aligns with the new vision of both
pedagogy and content for effective mathematics education set forth
in Crossroads
in Mathematics.
PRINCIPAL AUTHORS
Nancy Crisler  COMAP, faculty member Washington, University,
St. Louis, MO
Ms. Crisler was a high school mathematics teacher, and for ten years
served as the K–12 Mathematics supervisor for the Pattonville
School District in St. Louis County, MO. She was a member of the
ARISE writing team and provided staff development to teachers for
that project. She is coauthor of Discrete
Mathematics Through Applications. Currently she is a
primary author for the Developmental Mathematics and its Applications
(DevMap) project at COMAP and teaches at Washington University
in St. Louis, MO.
Gary Simundza  faculty member, Applied Mathematics & Sciences
Department,
Wentworth Institute of Technology, Boston, MA
Professor Simundza has been teaching physics and mathematics for
the past 25 years. He was director and principal investigator for
the National Science Foundationfunded Mathematics for TechnologyLaboratory
Investigations project. He is member of the writing team for the
Developmental Mathematics and its Applications (DevMap) project
at COMAP and teaches at Wentworth Institute of Technology in Boston,
MA.
Developing Mathematics through Applications
© 2003
Developed and published by COMAP
PHILOSOPHY AND GOALS — FROM THE AUTHORS
This book is a different kind of developmental mathematics text.
We believe that any mathematics worth learning is best learned in
the context of its use by real people in real jobs. Without neglecting
necessary practice with fundamental skills, we emphasize connections
between mathematics and the workplace, both in the body of the text
and in the exercises. Interesting applications motivate students
to learn, and guided discovery helps them succeed in their learning
by developing habits of persistence and achievement. The AMATYC
Standards have been thoroughly embraced by this book: Active investigation
of mathematics is emphasized throughout, and it is expected that
students will conduct much of this investigation in small, collaborative
groups. The content integrates data analysis, measurement, and geometry
with traditional topics in algebra. A modeling theme runs throughout
the text, as students learn to construct a variety of models, including
equations, graphs, tables, arrow diagrams, narrative descriptions,
and geometric and statistical models. Access to computing technology
is assumed, although the text can be used successfully without it.
Many of the contextual situations in the text require students to
read for mathematical content. Indeed, an essential part of acquiring
the ability to model the world with mathematics is learning to see
how mathematics is embedded in those situations. We hope students
will be encouraged to increase their reading level as they see that
careful reading helps them achieve mathematics competence. Vocabulary
is kept accessible and unfamiliar concepts are clearly explained
in terms that students will be able to understand.
FEATURES
 Focuses on mathematical modeling
Uses a discovery approach with active involvement of the students
Provides connections to realworld applications through investigations,
activities, and projects
Uses technology throughout the curriculum
Emphasizes functions
Uses multiple representations in concept development
Provides opportunities to collect and analyze real data
Promotes problem solving by providing a wide variety of openended
problems
 Suggests a variety of teaching methods through the use of Teacher
Notes
CHAPTER ORGANIZATION
 Preparation Reading  Each chapter begins with a brief
introduction that sets the stage for the mathematical development
to come, and may include contextual connections or discussions
of modeling aspects. It also includes a list of the goals of the
chapter.
 Chapter Sections
 What You Need to Know  A list of necessary prerequisite
knowledge.
 What You Will Learn  A list of the mathematical
objectives of the section.
 Activities  The first section of each chapter
contains an activity that requires students to work in groups
and perform an experiment or otherwise collect data. They
are then guided in a stepbystep manner to explore a core
mathematical concept that will recur throughout the chapter.
 Discoveries  Later sections frequently contain
explorations that are similar to activities in that they are
intended to be done in groups. A discovery is usually a more
focused examination of a single mathematical topic and does
not necessarily involve active experimentation. If data are
needed, they are often provided rather than collected.
 Examples  Numerous examples with detailed solutions
are provided in the body of each section.
 Exercises
 Investigations  These should be considered
as adjuncts to the body of each section and may present
new material. They contain indepth examinations of particular
subtopics or applications and some contain guided explorations
that are similar to discoveries. Investigations provide
an opportunity for each instructor to customize the text
for his or her own purposes and students' needs.
 Projects and Group Activities  These are
similar to the activities that begin each chapter. They
require students to work cooperatively and often involve
research or experimentation of some sort.
 Additional Practice  These provide necessary
skill practice with some problems being contextual. They
are not necessarily in order from easy to difficult, partly
so that students will not just quit after trying a few
easy problems.
 Chapter Review  This section summarizes the key
concepts of the chapter and contains a sampling of exercises
from each section similar to the additional practice exercises.
 Glossary  A summary of the new terms introduced
in the chapter.
TABLE OF CONTENTS
COURSE
1 (Book 1) 

Chapter
1 

Measurement 
Section
1.1 

Measuring
Length 
Section
1.2 

Linear
Measurement and the Pythagorean Theorem 
Section
1.3 

Describing
the Results of Measurement 
Section
1.4 

Measuring
a Surface: Area 
Section
1.5 

Volume,
Surface Area, and Geometric Models 
Section
1.6 

Other
Kinds of Measurement 

Chapter
2 

Linear
Models 
Section
2.1 

Measuring
Indirectly 
Section
2.2 

Exploring
Algebraic Expressions 
Section
2.3 

Solving
Linear Equations 
Section
2.4 

Functions
and Their Representations 
Section
2.5 

Linear
Functions 
Section
2.6 

Creating
Linear Models 

Chapter
3 

Modeling
Behavior from Data 
Section
3.1 

Collecting
Data and Determining a Model 
Section
3.2 

Scatter
plots and DataDriven Models 
Section
3.3 

Lines
of Best Fit 
Section
3.4 

Using
Models to Make Predictions 

Chapter
4 

Polynomials

Section
4.1 

Introduction
to Polynomials 
Section
4.2 

Exponents 
Section
4.3 

Operations
with Polynomials 
Section
4.4 

Factoring
Polynomials 
Section
4.5 

Modeling
with Polynomial Functions 

COURSE
2 (Book 2) 

Chapter
5 

Quadratic
Functions and Radicals 
Section
5.1 

Parabolas 
Section
5.2 

Quadratic
Functions and Their Graphs 
Section
5.3 

Modeling
Data with Quadratic Functions 
Section
5.4 

Roots
and Radicals 
Section
5.5 

Fractional
Exponents and Radical Equations 
Section
5.6 

Distance
in the Plane; Circles 

Chapter
6 

Rational
Expressions and Systems of Equations 
Section
6.1 

Introduction
to Rational Functions 
Section
6.2 

Modeling
with Rational Functions 
Section
6.3 

Multiplying
and Dividing Rational Expressions 
Section
6.4 

Solving Rational
Equations 
Section
6.5 

Systems
of Equations 

Chapter
7 

Probability 
Section
7.1 

The
Meaning of Probability 
Section
7.2 

Probabilities
for Compound Events 
Section
7.3 

Finding
Probabilities from Data 
Section
7.4 

Combining
Probabilities 
Section
7.5 

Probability
Distributions 
Section
7.6 

Drawing
Conclusions from Data 
Section
7.7 

Modeling Through Simulations 



Chapter
8 

Trigonometry 
Section
8.1 

Similar
Triangles 
Section
8.2 

Properties
of Triangles 
Section
8.2 

Trigonometric
Ratios 
Section
8.3 

Modeling
with Right Triangles 
Section
8.4 

Trigonometric
Ratios for NonAcute Angles 
