Mathematics in Action

About our authors 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 2-year and 4-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 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, 8 instructors contribute to the latest editions of the text.

Below is an Activity-level Table of Contents for this title.



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

Concept Review
Trigonometry
Getting Started with the TI-84 Plus Family of Calculators
Conics (Online in MyLab Math only)