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Mathematics in Action: Prealgebra Problem Solving, 3rd edition

Published by Pearson (December 27, 2010) © 2012

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The first book of the Mathematics in Action series, Prealgebra Problem Solving, Third Edition, illustrates how mathematics arises naturally from everyday situations through updated and revised real-life activities and accompanying practice exercises.

This unique approach helps students increase their knowledge of mathematics, sharpen their problem-solving skills, and raise their overall confidence in their ability to learn. Technology integrated throughout the text helps students interpret real-life data algebraically, numerically, symbolically, and graphically. The active style of this book develops students’ mathematical literacy and builds a solid foundation for future study in mathematics and other disciplines.

  • Activities-based learning allows students to take an active role in their learning. Each chapter contains thematic clusters, which in turn contain activities that cover specific concepts and skills. To complete an activity, students write directly in their books, answering questions, completing tables, and manipulating real information to develop mathematical understanding. The variety of activities within each cluster allows instructors to customize the text to fit the needs and interests of their students.
    • Lab Activities are in-class group exercises that provide intriguing, real-data applications that help students integrate and apply the mathematical concepts they have learned, and  solidify their comprehension of the material in class.
    • Project Activities give students the opportunity to practice the skills and concepts they have learned, either independently or in groups.
  • Review exercises offer ample opportunity for students to review and practice what they have learned.
    • Skills Check exercises occur periodically throughout the text to provide ample practice with basic skills.
    • What Have I Learned? review exercises require students to reflect on recently presented concepts. This feature also prepares students for upcoming material by helping them develop a strong foundation.
    • How Can I Practice? exercises at the end of each cluster are an important self-assessment tool. They show students how to apply recently-covered concepts and give students a chance to practice key skills.
    • Gateway Review exercises conclude each chapter. These exercises help students assess their understanding of the chapter concepts and then synthesize those concepts with material from previous chapters.
  • Students can use graphing calculators where appropriate as a problem-solving resource to help visualize concepts and reinforce skills. Keystroke instructions are provided to help students become comfortable with the technology, and a graphing calculator icon flags exercises where a calculator is useful.
  • Appendix icons are included throughout the text to let students know when they can refer to one of five appendices for extra help and practice.
  • Summary Boxes of the main concepts appear at the end of each activity to help students recognize and connect critical topics and concepts.

New to the Supplements Package

  • Worksheets for Classroom or Lab Practice provide extra practice to ensure that students have many opportunities to work problems related to the concepts learned in every activity. Concept Connections, a feature unique to these worksheets, offer students an opportunity to show in words that they understand the mathematical concepts they have just practiced.
  • MyMathLab enhancements for this edition include the following:
    • Premade homework assignments will be available for each section of the text.  In addition to the section-level premade assignments, the Consortium MyMathLab courses will also include chapter review assignments for each chapter.
    • Translating Word Problems Animations help students practice the translation step of solving word problems.
    • An Interactive English/Spanish glossary offers definitions of important mathematical terms in both English and Spanish. 
    • Worksheets for Classroom or Lab Practice will be available in the Tools for Success section.

Content Changes

  • All data-based activities and exercises have been updated to reflect the most recent information and data, or replaced with different topics.
  • Rewritten activities throughout the text are clearer and easier to understand.
  • Chapters 3 and 4 have been reorganized so integers, fractions, and decimals are covered in three separate chapters: Chapter 3, Problem Solving with Integers, Chapter 4, Problem Solving with Fractions, and Chapter 5, Problem Solving with Mixed Numbers and Decimals.
  • Chapters 5, 6, and 7 from the previous edition have been revised and renumbered as 6, 7, and 8.
  • Activity 3.6, Integers and Tiger Woods, contains two additional objectives: combining like terms involving integers and solving equations of the form ax + bx = c, where a + b ≠ 0.
  • Activity 5.3, Tiling the Bathroom, contains an additional objective: solving equations of the form ax + b = 0, where a ≠ 0, that involve mixed numbers.
  • Activity 5.8, Four out of Five Dentists Prefer the Brooklyn Dodgers?, which teachers proportional reasoning, is now the second activity in Chapter 6, Problem Solving with Ratios, Proportions, and Percents.
  • Lab Activity 7.7,How About Pythagoras?, contains an additional objective: using the distance formula to determine the distance between two points.
  • Several activities have moved to the Instructor’s Resource Manual with Tests and MyMathLab to streamline the course without loss of content. This includes Activities 7.2, 7.4, and 7.6 from the second edition, as well as Activity 6.9 on similar triangles.
  • Activity 7.1 in the second edition has been revised and renumbered as Activity 8.1.

Chapter 1. Whole Numbers

Activity 1.1 Education Pays

            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

            Objectives:

            1. Read tables.

            2. Read bar graphs.

            3. Interpret bar graphs.

            4. Construct graphs.

Activity 1.3 Bald Eagles Revisited

            Objectives:

            1. Add whole numbers by hand and mentally.

            2. Subtract whole numbers by hand and mentally.

            3. Estimate sums and differences using rounding.

            4. Recognize the associative property and the commutative property for addition.

            5. Translate a written statement into an arithmetic expression.

Activity 1.4 Summer Camp

            Objectives:

            1. Multiply whole numbers and check calculations using a calculator.

            2. Multiply whole numbers using the distributive property.

            3. Estimate the product of whole numbers by rounding.

            4. Recognize the associative and commutative properties for multiplication.

Activity 1.5 College Supplies

            Objectives:

            1. Divide whole numbers by grouping.

            2. Divide whole numbers by hand and by calculator.

            3. Estimate the quotient of whole numbers by rounding.

            4. Recognize that division is not commutative.

Activity 1.6 Reach for the Stars

            Objectives:

            1. Use exponential notation.

            2. Factor whole numbers.

            3. Determine the prime factorization of a whole number.

            4. Recognize square numbers and roots of square numbers.

            5. Recognize cubed numbers.

            6. Apply the multiplication rule for numbers in exponential form with the same base.

Activity 1.7 You and Your Calculator

            Objective:

            1. Use order of operations to evaluate arithmetic expressions.

What Have I Learned?

How Can I Practice?

Chapter 1 Summary

Chapter 1 Gateway Review

 

Chapter 2. Variables and Problem Solving

Activity 2.1 How Much Do I Need to Buy?

            Objectives:

            1. Recognize and understand the concept of a variable in context and symbolically.

            2. Translate a written statement (verbal rule) into a statement involving variables (symbolic rule).

            3. Evaluate variable expressions.

            4. Apply formulas (area, perimeter, and others) to solve contextual problems.

Activity 2.2 How High Will It Go?

            Objectives:

            1. Recognize input/output relationship between variables in a formula or equation (two variables only).

            2. Evaluate variable expressions in formulas and equations.

            3. Generate a table of input and corresponding output values from a given equation, formula, or situation.

            4. Read, interpret, and plot points in rectangular coordinates that are obtained from evaluating a formula or equation.

Activity 2.3 Are You Balanced?

            Objectives:

            1. Translate contextual situations and verbal statements into equations.

            2. Apply the fundamental principle of equality to solve equations of the forms x + a = b, a + x = b and x - a = b.

Activity 2.4 How Far Will You Go? How Long Will It Take?

            Objectives:

            1. Apply the fundamental principle of equality to solve equations of the form ax = b, a ≠ 0.

            2. Translate contextual situations and verbal statements into equations.

            3. Use the relationship rate · time = amount in various contexts.

Activity 2.5 Web Devices for Sale

            Objectives:

            1. Identify like terms.

            2. Combine like terms using the distributive property.

            3. Solve equations of the form ax + bx = c.

Activity 2.6 Make Me an Offer

            Objectives:

            1. Use the basic steps for problem solving.

            2. Translate verbal statements into algebraic equations.

            3. Use the basic principles of algebra to solve real-world problems.

What Have I Learned?

How Can I Practice?

Chapter 2 Summary

Chapter 2 Gateway Review

 

Chapter 3. Problem Solving with Integers

Activity 3.1 On the Negative Side

            Objectives:

            1. Recognize integers.

            2. Represent quantities in real-world situations using integers.

            3. Represent integers on the number line.

            4. Compare integers.

            5. Calculate absolute values of integers.

Activity 3.2 Maintaining Your Balance

            Objectives:

            1. Add and subtract integers.

            2. Identify properties of addition and subtraction of integers.

Activity 3.3 Whats the Bottom Line?

            Objectives:

            1. Write formulas from verbal statements.

            2. Evaluate expressions in formulas.

            3. Solve equations of the form x + b = c and b - x = c.

            4. Solve formulas for a given variable.

Activity 3.4 Riding in the Wind

            Objectives:

            1. Translate verbal rules into equations.

            2. Determine an equation from a table of values.

            3. Use a rectangular coordinate system to represent an equation graphically.

Activity 3.5 Are You Physically Fit?

            Objectives:

            1. Multiply and divide integers.

            2. Perform calculations involving a sequence of operations.

            3. Apply exponents to integers.

            4. Identify properties of calculations that involve multiplication and division with zero.

Activity 3.6 Integers and Tiger Woods

            Objectives:

            1. Use order of operations with expressions that involve integers.

            2. Apply the distributive property.

            3. Evaluate algebraic expressions and formulas using integers.

            4. Combine like terms.

            5. Solve equations of the form ax = b, where a ≠ 0, that involve integers.

            6. Solve equations of the form ax + bx = c, where a + b ≠ 0, that involve integers.

What Have I Learned?

How Can I Practice?

Chapter 3 Summary

Chapter 3 Gateway Review

 

Chapter 4. Problem Solving with Fractions

Activity 4.1 Are You Hungry?

            Objectives:

            1. Identify the numerator and the denominator of a fraction.

            2. Determine the greatest common factor (GCF).

            3. Determine equivalent fractions.

            4. Reduce fractions to equivalent fractions in lowest terms.

            5. Determine the least common denominator (LCD) of two or more fractions.

            6. Compare fractions.

Activity 4.2 Get Your Homestead Land

            Objectives:

            1. Multiply and divide fractions.

            2. Recognize the sign of a fraction.

            3. Determine the reciprocal of a fraction.

            4. Solve equations of the form ax = b, a ≠ 0, that involve fractions.

Activity 4.3 On the Road with Fractions

            Objectives:

            1. Add and subtract fractions and with the same denominators.

            2. Add and subtract fractions and with different denominators.

            3. Solve equations in the form x + b = c, and x - b = c that involve fractions.

Activity 4.4 Hanging With Fractions

            Objectives:

            1. Calculate powers and square roots of fractions.

            2. Evaluate equations that involve powers.

            3. Evaluate equations that involve square roots.

            4. Use order of operations to calculate numerical expressions that involve fractions.

            5. Evaluate algebraic expressions that involve fractions.

            6. Use the distributive property with fractions.

            7. Solve equations of the form ax + bx = c with fraction coefficients.

What Have I Learned?

How Can I Practice?

Chapter 4 Summary

Chapter 4 Gateway Review

 

Chapter 5. Problem Solving with Mixed Numbers and Decimals

Cluster 1 Mixed Numbers and Improper Fractions

Activity 5.1 Food for Thought

            Objectives:

            1. Determine equivalent fractions.

            2. Add and subtract fractions and mixed numbers with the same denominators.

            3. Convert mixed numbers to improper fractions and improper fractions to mixed numbers.

Activity 5.2 Mixing with Denominators

            Objectives:

            1. Determine the least common denominator (LCD) for two or more mixed numbers.

            2. Add and subtract mixed numbers with different denominators.

            3. Solve equations in the form x + b = c and x - b = c that involve mixed numbers.

Activity 5.3 Tiling the Bathroom

            Objectives:

            1. Multiply and divide mixed numbers.

            2. Evaluate expressions with mixed numbers.

            3. Calculate the square root of a mixed number.

            4. Solve equations of the form ax + b = 0, a ≠ 0, that involve mixed numbers.

Cluster 1 What Have I Learned?

Cluster 1 How Can I Practice?

Cluster 2 Decimals

Activity 5.4 What Are You Made Of?

            Objectives:

            1. Identify place values of numbers written in decimal form.

            2. Convert a decimal to a fraction or a mixed number and vice versa.

            3. Classify decimals.

            4. Compare decimals.

            5. Read and write decimals.

            6. Round decimals.

Activity 5.5 Dive into Decimals

            Objectives:

            1. Add and subtract decimals.

            2. Compare and interpret decimal numbers.

            3. Solve equations of the type x + b = c and x - b = c that involve decimals.

Activity 5.6 Quality Points and GPA: Tracking Academic Standing

            Objectives:

            1. Multiply and divide decimals.

            2. Estimate products and quotients involving decimals.

Activity 5.7 Tracking Temperature

            Objectives:

            1. Use the order of operations to evaluate expressions that include decimals.

            2. Use the distributive property in calculations that involve decimals.

            3. Evaluate formulas that include decimals.

            4. Solve equations of the form ax = c and ax + bx = c that involve decimals.

Activity 5.8 Think Metric

            Objectives:

            1. Know the metric prefixes and their decimal values.

            2. Convert measurements between metric quantities.

Cluster 2 What Have I Learned?

Cluster 2 How Can I Practice?

Chapter 5 Summary

Chapter 5 Gateway Review

 

Chapter 6. Problem Solving with Ratios, Proportions, and Percents

Activity 6.1 Everything is Relative

            Objectives:

            1. Understand the distinction between absolute and relative measure.

            2. Write a ratio in its verbal, fraction, decimal, and percent formats.

Activity 6.2 Four out of Five Dentists Prefer the Brooklyn Dodgers?

            Objectives:

            1. Recognize that equivalent fractions lead to a proportion.

            2. Use a proportion to solve a problem that involves ratios.

Activity 6.3 The Devastation of AIDS in Africa

            Objectives:

            1. Use proportional reasoning to apply a known ratio to a given piece of information.

            2. Write an equation using the relationship ratio · total = part and then solve the resulting equation.

Activity 6.4 Who Really Did Better?

            Objectives:

            1. Define actual and relative change.

            2. Distinguish between actual and relative change.

Activity 6.5 Dont Forget the Sales Tax

            Objectives:

            1. Define and determine growth factors.

            2. Use growth factors in problems that involve percent increases.

Activity 6.6 Its All on Sale!

            Objectives:

            1. Define and determine decay factors.

            2. Use decay factors in problems that involve percent decreases.

Activity 6.7 Take an Additional 20% Off

            Objective:

            1. Apply consecutive growth and/or decay factors to problems that involve two or more percent changes.

Activity 6.8 Fuel Economy

            Objectives:

            1. Apply rates directly to solve problems.

            2. Use proportions to solve problems involving rates.

            3. Use unit analysis or dimensional analysis to solve problems that involve consecutive rates.

What Have I Learned?

How Can I Practice?

Chapter 6 Summary

Chapter 6 Gateway Review

 

Chapter 7. Problem Solving with Geometry

Activity 7.1 Walking around Bases, Gardens, and Other Figures

            Objectives:

            1. Recognize perimeter as a geometric property of plane figures.

            2. Write formulas for, and calculate perimeters of, squares, rectangles, triangles, parallelograms, trapezoids, and

ygons.

            3. Use unit analysis to solve problems that involve perimeter.

Activity 7.2 Circles Are Everywhere

            Objectives:

            1. Measure the lengths of the diameter and circumference of circles.

            2. Develop and use formulas for calculating circumferences of circles.

Activity 7.3 Lance Armstrong and You

            Objectives:

            1. Calculate perimeters of many-sided plane figures using formulas and combinations of formulas.

            2. Use unit analysis to solve problems that involve perimeters.

Activity 7.4 Baseball Diamonds, Gardens, and Other Figures Revisited

            Objectives:

            1. Write formulas for areas of squares, rectangles, parallelograms, triangles, trapezoids, and polygons.

            2. Calculate areas of polygons using appropriate formulas.

Activity 7.5 How Big Is That Circle?

            Objectives:

            1. Develop formulas for the area of a circle.

            2. Use formulas to determine areas of circles.

Activity 7.6 A New Pool and Other Home Improvements

            Objectives:

            1. Solve problems in context using geometric formulas.

            2. Distinguish between problems requiring area formulas and those that require perimeter formulas.

Laboratory Activity 7.7 How About Pythagoras?

            Objectives:

            1. Verify and use the Pythagorean Theorem for right triangles.

            2. Calculate the square root of numbers other than perfect squares.

            3. Use the Pythagorean Theorem to solve problems.

            4. Determine the distance between two points using the distance formula.

Activity 7.8 Painting Your Way through Summer

            Objectives:

            1. Recognize geometric properties of three-dimensional figures.

            2. Write formulas for and calculate surface areas of boxes (rectangular prisms), cans (right circular cylinders).

Activity 7.9 Truth in Labeling

            Objectives:

            1. Write formulas for and calculate volumes of rectangular prisms (boxes) and right circular cylinders (cans).

            2. Recognize geometric properties of three-dimensional figures.

What Have I Learned?

How Can I Practice?

Chapter 7 Summary

Chapter 7 Gateway Review

 

Chapter 8. Problem Solving with Mathematical Models

Activity 8.1 A Model of Fitness

            Objectives:

            1. Describe a mathematical model as a set of verbal statements.

            2. Translate verbal rules into symbolic equations.

            3. Solve problems that involve equations of the form y = ax + b.

            4. Solve equations of the form y = ax + b for the input x.

            5. Evaluate the expression ax + b in the equations of the form y = ax + b to obtain an output y.

Activity 8.2 Comparing Energy Costs

            Objectives:

            1. Write symbolic equations from information organized in a table.

            2. Produce tables and graphs to compare outputs from two different mathematical models.

            3. Solve equations of the form ax + b = cx + d.

Activity 8.3 Mathematical Modeling

            Objectives:

            1. Develop an equation to model and solve a problem.

            2. Solve problems using formulas as models.

            3. Recognize patterns and trends between two variables using a table as a model.

            4. Recognize patterns and trends between two variables using a graph as a model.

What Have I Learned?

How Can I Practice?

Chapter 8 Summary

Chapter 8 Gateway Review

Appendix Learning Math Opens Doors: Twelve Keys to Success
The Consortium for Foundation Mathematics is a team of fourteen co-authors, primarily from the State University of New York and the City University of New York systems. Using the AMATYC Crossroads standards, the team developed an activity-based approach to mathematics in an effort to reach the large population of college students who, for whatever reason, have not yet succeeded in learning mathematics.

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