Mathematics in Action: Prealgebra Problem Solving, 3rd Edition

615 Pages·2011·7.89 MB·English

by  Consortium for Foundation Mathematics

Mathematics
in Action
Prealgebra Problem Solving
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Mathematics
in Action
Prealgebra Problem Solving
Third Edition
The Consortium for Foundation Mathematics
Ralph Bertelle Columbia-Greene Community College
Judith Bloch University of Rochester
Roy Cameron SUNY Cobleskill
Carolyn Curley Erie Community College—South Campus
Ernie Danforth Corning Community College
Brian Gray Howard Community College
Arlene Kleinstein SUNY Farmingdale
Kathleen Milligan Monroe Community College
Patricia Pacitti SUNY Oswego
Rick Patrick Adirondack Community College
Renan Sezer LaGuardia Community College
Patricia Shuart Polk State College—Winter Haven,Florida
Sylvia Svitak Queensborough Community College
Assad J.Thompson LaGuardia Community College
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Mathematics in action : prealgebra problem solving / the Consortium for Foundation intended pedagogical
Mathematics.—3rd ed. purposes and the
p. cm. needs of other
instructors who rely
ISBN-13: 978-0-321-69859-9 (student ed.)
on these materials.
ISBN-10: 0-321-69859-2 (student ed.)
ISBN-13: 978-0-321-69282-5 (instructor ed.)
ISBN-10: 0-321-69282-9 (instructor ed.)
1. Mathematics. I. Consortium for Foundation Mathematics.
QA39.3.M384 2012
510—dc22 2009052324
Copyright ©2012, 2008, 2004, Pearson Education, Inc.
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1 2 3 4 5 6 7 8 9 10—EB—14 13 12 11 10
Contents
Preface xiv
TotheStudent xx
CHAPTER 1 Whole Numbers 1
Activity 1.1 Education Pays 1
Objectives: 1.Read and write whole numbers.
2.Compare whole numbers using inequality symbols.
3.Round whole numbers to specified place values.
4.Use rounding for estimation.
5.Classify whole numbers as even or odd,prime,or composite.
6.Solve problems involving whole numbers.
Activity 1.2 Bald Eagle Population Increasing Again 9
Objectives: 1.Readtables.
2.Read bar graphs.
3.Interpretbar graphs.
4.Constructgraphs.
Activity 1.3 Bald Eagles Revisited 17
Objectives: 1.Add whole numbers by hand and mentally.
2.Subtractwhole numbers by hand and mentally.
3.Estimate sums and differences using rounding.
4.Recognizethe associative property and the commutative property
for addition.
5.Translate a written statementinto an arithmetic expression.
Activity 1.4 Summer Camp 28
Objectives: 1.Multiply whole numbers and check calculations using a calculator.
2.Multiply whole numbers using the distributive property.
3.Estimatethe productof whole numbers by rounding.
4.Recognizethe associative and commutative properties
for multiplication.
v
vi Contents
Activity 1.5 College Supplies 36
Objectives: 1.Divide whole numbers by grouping.
2.Divide whole numbers by hand and by calculator.
3.Estimatethe quotientof whole numbers by rounding.
4.Recognizethatdivision is notcommutative.
Activity 1.6 Reach forthe Stars 45
Objectives: 1.Use exponential notation.
2.Factor whole numbers.
3.Determinethe prime factorization of a whole number.
4.Recognize square numbers and roots of square numbers.
5.Recognize cubed numbers.
6.Applythe multiplication rule for numbers in exponential
form with the same base.
Activity 1.7 You and Your Calculator 55
Objective: 1.Use order of operationsto evaluate arithmetic expressions.
WhatHave I Learned? 62
How Can I Practice? 65
Chapter 1 Summary 70
Chapter 1 Gateway Review 75
CHAPTER 2 Variables and Problem Solving 83
Activity 2.1 How Much Do I Need to Buy? 83
Objectives: 1.Recognize and understand the conceptof a variable
in contextand symbolically.
2.Translate a written statement(verbal rule) into a statementinvolving
variables (symbolic rule).
3.Evaluate variable expressions.
4.Applyformulas(area,perimeter,andothers)tosolvecontextualproblems.
Activity 2.2 How High Will ItGo? 95
Objectives: 1.Recognizethe input/outputrelationship between variables
in a formula or equation (two variables only).
2.Evaluate variable expressions in formulas and equations.
3.Generate a table of inputand corresponding outputvalues from a given
equation,formula,or situation.
4.Read,interpret,and plotpoints in rectangular coordinatesthatare
obtained from evaluating a formula or equation.
Activity 2.3 AreYouBalanced? 103
Objectives: 1.Translate contextual situations and verbal statements into equations.
2.Applythe fundamental principle of equality to solve equations of the
formsx + a = b,a + x = bandx - a = b.
Contents vii
Activity 2.4 How FarWillYou Go? How LongWill ItTake? 110
Objectives: 1.Applythe fundamental principle of equality to solve equations in the
formax = b,a Z 0.
2.Translate contextual situations and verbal statements into equations.
#
3.Usethe relationship rate time = amountin various contexts.
Activity 2.5 Web Devices for Sale 117
Objectives: 1.Identify liketerms.
2.Combine liketerms using the distributive property.
3.Solve equations of the formax + bx = c.
Activity 2.6 Make Me an Offer 123
Objectives: 1.Usethe basic steps for problem solving.
2.Translate verbal statements into algebraic equations.
3.Usethe basic principles of algebrato solve real-world problems.
WhatHave I Learned? 131
How Can I Practice? 132
Chapter 2 Summary 136
Chapter 2 Gateway Review 139
CHAPTER 3 Problem Solving with Integers 143
Activity 3.1 Onthe Negative Side 143
Objectives: 1.Recognize integers.
2.Representquantities in real-world situations using integers.
3.Representintegers on the number line.
4.Compare integers.
5.Calculate absolute values of integers.
Activity 3.2 MaintainingYourBalance 151
Objectives: 1.Add and subtractintegers.
2.Identify properties of addition and subtraction of integers.
Activity 3.3 What’sthe Bottom Line? 160
Objectives: 1.Write formulas from verbal statements.
2.Evaluate expressions in formulas.
3.Solve equations of the formx + b = candb - x = c.
4.Solve formulas for a given variable.
Activity 3.4 Riding in theWind 167
Objectives: 1.Translate verbal rules into equations.
2.Determine an equation from a table of values.
3.Use a rectangular coordinate system to representan equation
graphically.
viii Contents
Activity 3.5 AreYou Physically Fit? 175
Objectives: 1.Multiply and divide integers.
2.Perform calculationsthatinvolve a sequence of operations.
3.Apply exponentsto integers.
4.Identify properties of calculationsthatinvolve multiplication
and division with zero.
Activity 3.6 Integers and TigerWoods 186
Objectives: 1.Use order of operations with expressionsthatinvolve integers.
2.Applythe distributive property.
3.Evaluate algebraic expressions and formulas using integers.
4.Combine liketerms.
5.Solve equations of the formax = b,wherea Z 0,thatinvolve
integers.
6.Solve equations of the formax + bx = c,wherea + b Z 0,
thatinvolve integers.
WhatHave I Learned? 195
How Can I Practice? 198
Chapter 3 Summary 206
Chapter 3 Gateway Review 209
CHAPTER 4 Problem Solving with Fractions 213
Activity 4.1 AreYouHungry? 213
Objectives: 1.Identifythe numerator and the denominator of a fraction.
2.Determinethe greatestcommon factor (GCF).
3.Determine equivalentfractions.
4.Reduce fractionsto equivalentfractions in lowestterms.
5.Determinethe leastcommon denominator (LCD) of two or more
fractions.
6.Compare fractions.
Activity 4.2 GetYour Homestead Land 222
Objectives: 1.Multiply and divide fractions.
2.Recognizethe sign of a fraction.
3.Determinethe reciprocal of a fraction.
4.Solve equations of the formax = b,a Z 0,thatinvolve fractions.
Activity 4.3 Onthe Road with Fractions 233
Objectives: 1.Add and subtractfractions with the same denominator.
2.Add and subtractfractions with differentdenominators.
3.Solve equations in the formx + b = candx - b = c thatinvolve
fractions.
Contents ix
Activity 4.4 Hanging with Fractions 242
Objectives: 1.Calculate powers and square roots of fractions.
2.Evaluate equationsthatinvolve powers.
3.Evaluate equationsthatinvolve square roots.
4.Use order of operationsto calculate numerical expressions
thatinvolve fractions.
5.Evaluate algebraic expressionsthatinvolve fractions.
6.Usethe distributive property with fractions.
7.Solve equations of the formax + bx = c with fraction coefficients.
WhatHave I Learned? 252
How Can I Practice? 254
Chapter 4 Summary 261
Chapter 4 Gateway Review 264
Problem Solving with Mixed Numbers
CHAPTER 5
and Decimals 269
Cluster 1 Mixed Numbers and Improper Fractions 269
Activity 5.1 Food forThought 269
Objectives: 1.Determine equivalentfractions.
2.Add and subtractfractions and mixed numbers with the same
denominator.
3.Convertmixed numbers to improper fractions and improper fractions
to mixed numbers.
Activity 5.2 Mixing with Denominators 279
Objectives: 1.Determinethe leastcommon denominator (LCD) fortwo or more mixed
numbers.
2.Add and subtractmixed numbers with differentdenominators.
3.Solve equations in the formx + b = c andx - b = c thatinvolve
mixed numbers.
Activity 5.3 TilingtheBathroom 289
Objectives: 1.Multiply and divide mixed numbers.
2.Evaluate expressions with mixed numbers.
3.Calculatethe square rootof a mixed number.
4.Solve equations of the formax + b = 0,a Z 0,thatinvolve mixed
numbers.
Cluster1 WhatHave I Learned? 298
How Can I Practice? 300