Table Of ContentStep Up to Success with Bracken and Miller
Your Guide to Problem Solving
Not Your Typical Application
Among the application problems appearing in this textbook are specially developed exercises and
examples that reference information taken directly from news articles, research studies, and other
fact-based sources.
83. According to an article on safety tips for blogging, two
out of three teenagers provide their age on their blog,
three out of five reveal their location, and one out of five
reveals their full name. Find the number of 3675 teenag-
ers who reveal their location on their blog. (Source: www
.microsoft.com)
Many of these applications are set up in two parts with a problem statement given irst followed by
an excerpt. Since the question appears irst and then the information needed to answer the question
follows, you experience problem solving in a more true-to-life way.
91. Find the number of albums sold at the same point last
year (2011). Round to the nearest tenth of a million.
Year to date album sales stand at 5.80 million, up 7% com-
pared to the same total at this point last year. (Source: www
.billboard.com, Jan. 11, 2012)
Though similar in length to texts or tweets, the authentic excerpts often contain more information
than is needed to solve the applications. You will need to think critically to select the relevant
information and in doing so, practice the skills needed to solve problems outside of the classroom.
Problem Solving in Five Steps
Do you need to solve an application problem? Not sure where to begin? The ive steps will help
you break the process down into an easy-to-use method you apply whenever you need to solve a
problem.
THE FIVE STEPS
Step 1 Understand the problem.
Read the problem. Identify the unknown. Assign a variable. Identify extraneous
information.
Step 2 Make a plan.
Identify the relationship between the unknown and the other information in
the problem. Decide how to find the unknown: write and solve an equation or
inequality, use a formula, draw and use a graph, evaluate a function, solve a sys-
tem of equations.
Step 3 Carry out the plan.
Step 4 Look back.
Does the answer make sense? Is it reasonable?
Check for errors in arithmetic or algebra.
Think about what you have learned from solving this problem.
Step 5 Report the solution.
Write the answer to the problem in a complete sentence.
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Enhanced WebAssign®
Your Instant Access to Practice, Problem Solving, and Mastering Concepts
Looking for more practice with problem solving? The Enhanced WebAssign online homework
course that accompanies Elementary Algebra includes key elements from the textbook to help
support you. Whether working in the textbook or online, you can access:
➤ The five steps as you practice solving a wide variety of application problems.
➤ F ind the Mistake problems to help you think critically about your work
and correct it as you analyze common errors.
In addition, Enhanced WebAssign includes other key problem types chosen from the textbook
to give you support in developing and reining problem-solving, critical thinking, and study
skills. Tutorial videos and a customizable and interactive eBook also enhance your learning
experience. Visit www.webassign.net to learn more.
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This is an electronic version of the print textbook. Due to electronic rights restrictions, some third party content may be suppressed. Editorial review has deemed that
any suppressed content does not materially affect the overall learning experience. The publisher reserves the right to remove content from this title at any time if
subsequent rights restrictions require it. For valuable information on pricing, previous editions, changes to current editions, and alternate formats,
please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest.
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ELEMENTARY
ALGEBRA
LaUra J. Bracken
LewiS-CLArK StAte CoLLege
edward S. MiLLer
LewiS-CLArK StAte CoLLege
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
Copyright 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
Elementary Algebra © 2014 Brooks/Cole, Cengage Learning
Laura J. Bracken, edward S. Miller
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to tony and the rest of
the Hogan’s family, who have
supported us in many ways as
we have written this book.
Copyright 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
about the authors
LaUra Bracken, co-author of Investigating
Prealgebra and Investigating College Mathematics,
teaches developmental mathematics at Lewis-Clark
State College. As developmental math coordinator,
Laura led the process of developing objectives,
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introductory science courses. Laura has presented at
numerous national and regional conferences and currently serves
as the regional representative for the AMAtYC Placement and
Assessment Committee. Her blog, Dev Math Diary, is at
http://devmathdiary.wordpress.com/
ed MiLLer is a professor of mathematics at Lewis-
Clark State College. He earned his PhD in general
topology at ohio University in 1989. He teaches
a wide range of courses, including elementary and
intermediate algebra. His terms as chair of the
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A regular presenter at national and regional meetings,
ed is exploring the use of multiple choice questions as a teaching
tool as well as an assessment tool.
about the cover
the cover image symbolizes the importance of self-empowerment or “stepping
up” in order to achieve your goals. Success requires independence, persistence,
responsibility, and a willingness to put your “best foot” forward—all key skills this
developmental mathematics series seeks to foster.
Copyright 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
Dear Colleagues,
Several years ago, we began writing materials to supplement our developmental mathematics textbooks and
improve student success in our classes. Although we work at a four-year state college, it essentially ofers open
admission, serving as a community college and technical school for a large region. About 60% of our students must
take developmental mathematics; many are enrolled in developmental english courses and are irst-generation
college students.
when we started to write Elementary Algebra, we identiied the range of conceptual and procedural knowledge
that students should learn to be prepared for their next mathematics course, whether that is intermediate
algebra, introductory statistics, liberal arts mathematics, or quantitative literacy. we also considered how we
could support students as they learn how to be successful in college. we used responses from faculty across
the country as well as research on this student population to inform our work.
we concluded that as students learn the mechanics of algebra, they must also build a conceptual understand-
ing of variable. they need to build connections between algebraic and graphical representations of relation -
ships. they should improve their proiciency in identifying the quantitative relationships in application
problems, and learn how to use algebra in solving these problems. while they are learning mathematics, they
can also learn about the culture of college and develop strategies that will help them persist towards their
certiicate or degree.
to support these goals, we developed features and content that include:
l A ive-step problem-solving plan based on the work of george Polya to organize student work on applications.
rather than memorize solutions to individual problems, the Five Steps help students develop strategies both
for solving problems and for relecting about the reasonability of their answers.
l Short readings called Success in College Mathematics, along with follow-up exercises, that address topics of
relevance to students who are making the transition to college-level courses and help instructors identify
issues outside of mathematics that may afect student success and retention.
l examples with detailed, step-by-step explanation. Since students often rely heavily on examples when working
on assignments and studying, each step of the detailed worked examples is accompanied by an annotation
that details the mathematical operation performed. Color-coding and bold type are also used to help enhance
the explanation of the work performed in each step of the solution.
l Multiple opportunities for review of arithmetic. Chapter r is an optional review chapter that includes a
Pretest, Posttest, and instruction in arithmetic with whole numbers, integers, fractions, decimals, and percents.
Just-in-time review or references to sections within Chapter r are included at key points within Chapters 1–9.
l end-of-chapter Study Plan and review exercises. these help guide students through test or exam preparation,
step by step. the Study Plan includes study tables for each section in the chapter along with “Can i . . .” study
questions that are linked to review exercises. references to examples and Practice Problems from within the
sections are also included for additional review, if needed.
l Algorithmic online homework capabilities through enhanced webAssign® that include unique question types
from the textbook, as well as an interactive and customizable eBook (YouBook).
l tools for instructors, such as teaching Notes in the Annotated instructor’s edition, along with Classroom
examples that mirror the examples provided in the student textbook. the PowerLecture CD-roM is also
available to instructors, and it contains examView® algorithmic computerized testing, Solution Builder (link to the
complete textbook solutions), PowerPoint slides including selected worked examples from the textbook along
with the corresponding Classroom examples, and other resources for reference and instructional support.
we welcome your feedback as you use these materials. if you have any questions or comments please
contact us at [email protected] and [email protected]. we also invite you to follow our blog at
http://devmathdiary.wordpress.com/
All the best to you and to your students.
Laura Bracken and Ed Miller
Copyright 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
What Instructors and Students Are Saying
About Bracken and Miller’s Elementary Algebra
“This book has a smart approach to problem solving, helping students to develop
good habits, and use applications throughout to bring meaning to the ideas
being taught.”
“[Students] agree that the book and the course helped them to develop their
problem-solving skills and they feel more conident in their abilities.”
—Barbara Goldner, North Seattle Community College
“Problem-solving plans help me organize data to complete problems.”
“Very helpful. Gives great examples and explains problems very well.”
“This book is easy to understand. it’s very helpful and gives clear examples.”
“i found breaking down word problems into sections was helpful.”
“[Success in college Mathematics] helped assess personal goals.”
[Find the Mistake] “if i could ind the mistakes in other problems it would be
easier to ind the mistakes in my own work.”
—Class Test Students, North Seattle Community College
“i absolutely LOVe these [Find the Mistake]. error analysis is a huge tool that is
often overlooked. it is also helpful to get them to write down their steps or “show
their work.”
—Jane West, Trident Technical College
“The fact that the applications include excerpts from current research and reports
provides the real-life context that the authors desire as well as increasing student
interest, and the number of problems with extraneous information will force
students to read carefully for important information. These problems do not
appear periodically; they are intentional and consistent.”
—Shelly Hansen, Colorado Mesa University
“The ive-step problem-solving plan is outstanding. The real-world applications
are easier solved if this ive-step strategy is used. This is one of the strongest parts
of the textbook.”
—Nicoleta Bila, Fayetteville State University
“i love these [Success in college Mathematics]. i think that many students take
developmental math (and need to repeat it so much) because they’re lacking in
study skills and/or experiencing a transition-to-college culture shock. This feature
is very useful in reminding the student that the burden of learning is on them, and
it also helps the students be more aware of their own learning.”
—Daniel Kleinfelter, College of the Desert
vi
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