About the Book
This introductory algebra text, based on standards in the AMATYC Crossroads document, motivates college math students to develop mathematical literacy and a solid foundation for future study in mathematics and other disciplines. This first book of a two-book series presents mathematical concepts and skills through relevant activities derived from real-life situations; these activities are meaningful to students because they illustrate how mathematics arises naturally from real-world situations and problems. Mathematics in Action is based on the assumption that students learn mathematics best by deriving concepts themselves in a meaningful context. Therefore, the text takes a collaborative approach to learning. Students take an active role in their own learning by working in groups, thereby developing communication skills, a sense of independence, and a “can-do” attitude about mathematics. Technology is integrated throughout the book so that students can learn to interpret real-life data numerically, symbolically, and graphically. Regardless of their level of preparation for the course, students can use this text to increase their knowledge of mathematics, their problem-solving skills, and their overall confidence in their ability to learn.
Table of Contents:
(Each cluster includes “What Have I Learned?” and “How Can I Practice?” exercises, and each chapter concludes with a “Gateway Review”.)CHAPTER 1. NUMBER SENSE.
Cluster 1. Using Number Sense to Solve Problems.
Bookstore.
Problem Solving.
Time Management.
Problem Solving, Estimating, Tables, Bar Graphs, Using Fractions.
Course Grades and Your GPA.
Problem Solving, Using Percents, Simple Averages, Weighted Averages.
The Electric Bill.
Problem Solving, Estimating, Percents, Bar Graphs.
You and Your Calculator.
Properties of Real Numbers, Whole-Number Exponents, Scientific Notation with Large Numbers, Order of Operations, Grouping.
Target Heart Rate.
Algorithms, Percents.
Income and Expenses.
Tables, Percents, Bar Graphs.
Cluster 2. Problem Solving with Fractions.
How Much Do I Owe?
Equivalent Fractions, Addition, Subtraction, and Multiplication of Fractions.
Fractions Invade Campus Life.
Adding, Subtracting, Multiplying, and Dividing Fractions.
Delicious Recipes.
Adding, Subtracting, Multiplying, and Dividing Fractions.
Exploring Numeracy.
Cluster 3. Comparisons and Proportional Reasoning.
Which One is Better?
Ratios, Equivalent Ratios, Proportions, Fractions, Decimals, Percent.
Social Issues.
Fractions, Percent, Ratio and Proportion, Contingency Tables, Relative Frequency, Probability.
Did You Buy Enough Paint?
Rates, Proportions, Unit Analysis.
Uncle Sam's Place.
Unit Analysis, Metric System, U.S. System, Unit Conversion.
Grade Point Averages: Who Improved More?
Actual Change, Relative Change, Growth Factor, Decay Factor.
Take an Additional 10% Off.
Fractions, Decimals, Percent, Ratio, Growth Factor, Decay Factor.
Consecutive Percent Change.
Skills Check 1.
Cluster 4. Problem Solving with Signed Numbers.
Celsius Thermometers.
Adding and Subtracting Signed Numbers.
Gains and Losses in Business.
Multiplying and Dividing Signed Numbers.
Order of Operations Revisited.
Order of Operations with Signed Numbers, Negative Exponents, Scientific Notation.
Cluster 5. Problem Solving with Geometry.
Geometric Shapes.
Measurement, Perimeters, Area, Empirical Verification of Formulas.
Home Improvements.
Using Geometry Formulas in Context.
Circles are Everywhere.
Measurement, Circumference and Area Formulas.
A New Pool.
Circumference and Area Formulas in Context.
Carpenter's Square: Right Triangles.
Pythagorean Theorem, Measurement, Angles, Square Roots.
Septic Tank.
Pythagorean Theorem, Square Roots.
Basketballs, Soup Cans, Boxes, and Ice Cream Cones.
Volumes of 3-Dimensional Objects.
Exploring Numeracy.
Another New Pool.
Measurement, Scale Drawing, Volume.
Skills Check 2.
CHAPTER 2. VARIABLE SENSE.
Cluster 1. Interpreting and Constructing Tables and Graphs.
Blood-Alcohol Levels.
Interpreting Relationships Numerically, Graphically, and Verbally.
College Expenses.
Variables, Replacement Values, Writing Verbal Rules, Constructing Tables.
Earth's Temperature.
Constructing Graphs, Scaling, Plotting Points, Labeling Points.
How Many Cups Are in that Stack?
Measurement, Relationships Defined by Tables, Converting Tables to Graphs.
Body Parts.
Measurement, Relationships Defined by Tables, Converting Tables to Graphs.
Cluster 2. Solving Equations Numerically, Graphically, and Algebraically.
The Write Way to Learn Algebra.
Translating English Phrases into Symbolic (Algebraic) Expressions, Equivalent Expressions, Terminology, Verbal Rules into Symbolic Form.
The Cub Scout Fundraiser.
Relationships Defined by Tables, Graphs, and Verbal and Symbolic Forms; Introduction to Solving Equations Numerically and Graphically.
Let's Go Shopping.
Evaluating and Solving Equations of the Form y = ax and y =x +b Algebraically.
Are They the Same?
Translating English Phrases into Algebraic Expressions, Grouping Symbols, Equivalent Expressions.
Weather Fahrenheit or Celsius.
Evaluating and Solving Equations of the Form y =ax+b.
Tables of Tables.
Tables, Graphing, Symbolic Rules, Evaluating and Solving Equations of the Formy =ax +b.
Depth of Snow Deposit.
Evaluating and Solving Equations of the Formy = ax+b, Formulas.
New Formulas from Old.
Formulas, Evaluating Formulas, Solving for a Given Variable.
Cluster 3. Mathematical Modeling Involving Algebraic Expressions.
Do It Two Ways.
Distributive Property, Properties of Exponents.
Ring It Up!
Factoring Common Factors, Combining Like Terms, Using The Distributive Property To Simplify Expressions.
Math Magic.
Algebraic Expressions, Simplifying Expressions by Combining Like Terms.
More Room For Work.
Extending the Distributive Property, Multiplying Binomials.
Cluster 4. Problem Solving Involving Solution of Equations.
Building Fences.
Solving Equations Using the Distributive Property.
Refrigeration.
Solving Linear Equations Simultaneously.
The Forces That Be.
Algebraic Rules Involving Squares and Square Roots.
Summer Job Opportunities.
Critical Thinking, Algebraic Rules.
CHAPTER 3. FUNCTION SENSE.
Cluster 1. Exploring Functions.
Course Grade.
Function Representations, Function Notation.
Graphs Tell Stories.
Interpretations of Graphs; Increasing, Decreasing, and Constant Functions.
The Dangers of Asthma.
Domain, Range, Minimum and Maximum Function Values.
Cluster 2. Modeling with Functions.
How Fast Did You Lose?
Introduction to Average Rate of Change.
Nuclear Arsenals Shrinking.
Rate of Change Application.
Inflation.
Rate of Change, Exponential Function.
Apple Orchard.
Interpolation, Extrapolation, Function of the Form y = k/x.
Electricity Charges.
Linear Function, Vertical Intercept, Rate of Change.
CHAPTER 4. LINEAR FUNCTIONS.
Cluster 1. Introduction to Linear Functions.
The Snowy Tree Cricket.
Linear Functions, Constant Rate of Change, Slope.
Descending in an Airplane.
Negative, Zero, and Undefined Slope; Intercepts.
Charity Event.
Deriving a Linear Function Rule from Contextual Information, Slope-Intercept Form of a Linear Function.
Characteristics of Linear Functions.
Super Bowl Commercials.
Recognizing Linear Functions, Determining Horizontal Intercepts, Graphing Linear Equations Using Slope and Intercepts.
Interpreting Slopes and Points Contextually.
Cluster 2. Problem Solving with Linear Functions.
Predicting Population.
Deriving Linear Equations from Two Points, Functions in Slope-Intercept Form.
Housing Prices.
Deriving Linear Functions When Given Two Points.
Oxygen for Fish.
Scatterplots and Linear Regression Models.
Cluster 3. Systems of Linear Equations.
Business Checking Account.
Solving 2x2 Linear Systems Numerically, Graphically, and by Substitution; Inequalities.
Modeling a Business.
Solving 2x2 Linear Systems, Inequalities, Break-even Point.
Supply and Demand.
Solving 2x2 Linear Systems, Inequalities, Equilibrium Point.
CHAPTER 5. QUADRATIC FUNCTIONS.
Cluster 1. Quadratic Functions.
Newton's Apple.
Introducing Quadratic Functions.
Rockets in Flight.
Solving Quadratic Equations by Factoring, Zero Product Rule.
More Rockets in Flight.
Solving Quadratic Equations, Factoring Trinomials of the Form x2+bx+c.
Maximal Enclosure.
Quadratic Formula, Axis of Symmetry, Vertex.
Roots in the Garden.
Pythagorean Theorem, Solving Quadratic Equations by Using Square Roots.
Appendix A. Fractions.
Appendix B. Decimals.
Appendix C. Algebraic Extensions.
Appendix D. The TI-83 Graphing Calculator.
Glossary.
Selected Answers.
Index.
