Mathematics in Action Algebraic, Graphical, and Trigonometric Problem Solving

For courses in Intermediate Algebra.

Active learning for active minds

The authors of the Mathematics in Action series believe that students learn mathematics best by actually doing the math within a realistic context. If a student is taking this course, why teach them the same content in the same way that they’ve already seen—yet did not retain? Following this principle, the authors provide a series of guided-discovery activities that help students to construct, reflect upon, and apply mathematical concepts, deepening their conceptual understanding as they do so. The active style of learning develops critical-thinking skills and mathematical literacy, while keeping the concepts in the context of real applications. 

The 6th Edition includes updated examples and activities for maximum interest and relevance, along with new and enhanced digital resources in MyLab™ Math to support conceptual understanding for students, wherever and whenever they need it. 

Also available with MyLab Math

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Package consists of:

• 0135115612 / 9780135115619 Mathematics in Action: Algebraic, Graphical, and Trigonometric Problem Solving 
• 0135162483 / 9780135162484 MyLab Math with Pearson eText - Standalone Access Card - for Mathematics in Action: Algebraic, Graphical, and Trigonometric Problem Solving

The Consortium for Foundation Mathematics is a group of mathematics educators, all originally from New York State, who first came together at SUNY Oswego in the summer of 1995 as part of a National Science Foundation (NSF) grant. The members of the group represented two-year and four-year colleges; commuter and residential colleges; large urban institutions and small rural institutions; and multi-campus as well as single campus institutions. 

Unified by a desire to change the status quo in order to further student success, the group’s initial objectives aimed at a new approach to developmental math that included contextual problem-solving, active collaborative learning, and authentic assessment tied more closely to real-world skills. The efforts of this initial grant resulted in new instructional materials that formed the basis of Consortium’s texts, which include range from Prealgebra to Intermediate Algebra, as well as high school titles. As one Consortium author noted, contributing to this series with its different approach “changed my views about math, and about teaching math.” Of the 16 instructors originally involved in the grant, eight instructors contribute to the latest editions of the text.

Chapter 1. Function Sense

Cluster 1: Modeling with Functions 

Activity 1.1 Parking Problems: Functions; Function Notation and Terminology

Activity 1.2 Fill ‘er Up: Defining Functions by a Symbolic Rule (Equation)

Activity 1.3 Graphically Speaking: Defining Functions: A Summary

Activity 1.4 Stopping Short: Functions as Mathematical Models

Activity 1.5 Graphs Tell Stories: Graphs of Functions as Mathematical Models

What Have I Learned?

How Can I Practice?

Cluster 2: Linear Functions

Activity 1.6 Walking for Fitness: Average Rate of Change

Activity 1.7 Depreciation: Slope-Intercept Form of an Equation of a Line

Activity 1.8 A New Camera: Point-Slope Form of an Equation of a Line

Activity 1.9 Skateboard Heaven: General Form of an Equation of a Line

Activity 1.10 College Tuition: Modeling Data with Linear Regression Equations

What Have I Learned?

How Can I Practice?

Cluster 3: Systems of Linear Equations, Inequalities, and Absolute Value Functions

Activity 1.11 Moving Out: Systems of Linear Equations in Two Variables

Activity 1.12 Fireworks: Solving Systems of Linear Equations using Algebraic Methods

Activity 1.13 Manufacturing Pewter Oil Lamps: Solving Systems of Linear Equations in Three Variables

Activity 1.14 Earth Week: Using Matrices to Solve Systems of Linear Equations

Activity 1.15 How Long Can You Live? Linear Inequalities; Compound Inequalities

Activity 1.16 Working Overtime: Piecewise Linear Functions

What Have I Learned?

How Can I Practice?

Chapter 1 Summary

Chapter 1 Gateway Review

Chapter 2. The Algebra of Functions

Cluster 1: Addition, Subtraction, and Multiplication of Polynomial Functions

Activity 2.1 Spending and Earning Money: Polynomial Functions

Activity 2.2 The Dormitory Parking Lot: Multiplication of Polynomials; Multiplicative Properties of

Exponents

Activity 2.3 Stargazing: Scientific Notation; Additional Properties and Definitions of Exponents

Activity 2.4 The Cube of a Square: Rational Exponents and nth Roots

What Have I Learned?

How Can I Practice?

Cluster 2: Composition and Inverses of Functions

Activity 2.5 Inflated Balloons: Composite Functions

Activity 2.6 Finding a Bargain: Problem Solving and Using Composite Functions 

Activity 2.7 Study Time: Inverse Functions

Activity 2.8 Temperature Conversions: Equations and Graphs of Inverse Functions

What Have I Learned?

How Can I Practice?

Chapter 2 Summary

Chapter 2 Gateway Review

Chapter 3. Exponential and Logarithmic Functions

Cluster 1: Exponential Functions

Activity 3.1 Prince George and Dracula: Increasing Exponential Functions

Activity 3.2 Half-Life of Drugs or Medication: Decreasing Exponential Functions

Activity 3.3 Spotify: More Growth and Decay Factors

Activity 3.4 Population Growth: Growth and Decay Rates; More Graphing

Activity 3.5 Time is Money: Compound Interest and Continuous Compounding

Activity 3.6 Continuous Growth and Decay: Problem Solving with Continuous Growth and Decay Models

Activity 3.7 Ebola: Modeling Data with Exponential Regression Equations

What Have I Learned?

How Can I Practice?

Cluster 2: Logarithmic Functions

Activity 3.8 The Diameter of Spheres: Logarithmic and Exponential Forms

Activity 3.9 Walking Speed of Pedestrians: Logarithmic Functions

Activity 3.10 Walking Speed of Pedestrians, continued: Modeling Data with Logarithmic Regression

Equations

Activity 3.11 The Elastic Ball: Properties of Logarithms

Activity 3.12 Changing Demographics: Solving Exponential Equations

What Have I Learned?

How Can I Practice?

Chapter 3 Summary

Chapter 3 Gateway Review

Chapter 4. Quadratic and Higher-Order Polynomial Functions

Cluster 1: Introduction to Quadratic Functions

Activity 4.1 Baseball and the Willis Tower: Equations Defining Quadratic Functions

Activity 4.2 The Shot Put: Properties of Graphs of Quadratic Functions

Activity 4.3 Spotify: Solving Quadratic Equations Numerically and Graphically

Activity 4.4 Sir Isaac Newton: Solving Quadratic Equations by Factoring

Activity 4.5 Drones: Solving Quadratic Equations Using the Quadratic Formula

Activity 4.6 Heat Index: Modeling Data with Quadratic Regression Equations

Activity 4.7 Complex Numbers

What Have I Learned?

How Can I Practice?

Cluster 2: Curve Fitting and Higher-Order Polynomial Functions

Activity 4.8 The Power of Power Functions: Direct Variation Functions and Their Graphs

Activity 4.9 Volume of a Storage Tank: Polynomial Functions and Their Graphs

Activity 4.10 Federal Prison Population: Modeling Data with Polynomial Regression Equations

What Have I Learned?

How Can I Practice?

Chapter 4 Summary

Chapter 4 Gateway Review

Chapter 5. Rational and Radical Functions

Cluster 1: Rational Functions

Activity 5.1 Speed Limits: Properties and Graphs of Functions Defined by y = k/x, k≠0

Activity 5.2 Loudness of a Sound: Inverse Variation Functions

Activity 5.3 Percent Markup: Rational Functions and Their Graphs

Activity 5.4 Blood-Alcohol Levels: Solving Rational Equations

Activity 5.5 Traffic Flow: Solving Rational Equations Using Algebraic Methods

Activity 5.6 Electrical Circuits: Operations of Rational Expressions

What Have I Learned?

How Can I Practice?

Cluster 2: Radical Functions

Activity 5.7 Skydiving: Radical Functions and Their Graphs

Activity 5.8 Falling Objects: Solving Equations Involving a Radical Expression

Activity 5.9 Propane Tank: More Radical Functions and Their Graphs

What Have I Learned?

How Can I Practice?

Chapter 5 Summary

Chapter 5 Gateway Review

Chapter 6. Introduction to Trigonometric Functions

Cluster 1: Introducing the Sine, Cosine, and Tangent Functions

Activity 6.1 The Leaning Tower of Pisa: Sine, Cosine, and Tangent of an Angle in a Right Triangle

Activity 6.2 A Gasoline Problem: Cofunctions of Complementary Angles

Activity 6.3 The Sidewalks of New York: Inverse Sine, Cosine, and Tangent Functions

Activity 6.4 Solving a Murder: Trigonometric Problem-Solving Strategy

Project Activity 6.5 How Stable is that Tower: Problem Solving Using Right Triangle Trigonometry

What Have I Learned?

How Can I Practice?

Cluster 2: Why Are the Trigonometric Functions Called Circular Functions?  

Activity 6.6 Learn Trig or Crash! Graphs of Sine and Cosine Functions

Activity 6.7 It Won’t Hertz: Radians, Frequency, and Periodic Behavior

Activity 6.8 Get in Shape: Amplitude and Period of the Sine and Cosine Functions

Activity 6.9 The Carousel: Horizontal Shifts of the Graphs of the Sine and Cosine Functions

Activity 6.10 Texas Temperatures: Modeling Data with a Sine Regression Equation

What Have I Learned?

How Can I Practice?

Chapter 6 Summary

Chapter 6 Gateway Review

Appendices

A. Concept Review

B. Trigonometry

C. Getting Started with the TI-84 Plus Family of Calculators

D. Conics (Online in MyLab Math only)

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