Kathleen Almy has been a professor of mathematics at Rock Valley College for over 10 years and has taught high school and college level math for 15 years. She has a bachelor's degree in mathematics education from Southern Illinois University and master's degree in pure mathematics from Northern Illinois University. Her passion is improving developmental math for all students including the development of courses and content that is appropriate, relevant, and meaningful. As her department's developmental math coordinator, she organized and led a successful comprehensive redesign of the program over the past 5 years. As a result of giving talks about the redesign, she has been consulting with colleges throughout Illinois and across the country to improve their developmental math programs. Since 2009, she has been a member of AMATYC's Quantway project which is affiliated with the Carnegie Foundation.  She was AMATYC’s Developmental Math Committee chair and serves on several state committees on developmental education.

Heather Foes is currently a professor of Mathematics at Rock Valley College in Rockford, Illinois and has also taught at Illinois State University, Northern Illinois University and the University of Illinois. Heather has a bachelor’s degree in chemistry and mathematics and a master’s degree in mathematics from Illinois State University. She has written solution manuals and other supplemental materials over the last ten years, as well as algorithmic questions for test-generator software and conceptual questions for MyStatLab for Pearson.

CYCLE ONE Where do we start?

Self-Assessment: Preview  

1.1 The BP Oil Spill: Focus Problem  

1.2 Getting Started: Reviewing Prealgebra  

• Use Venn diagrams
• Write equivalent fractions
• Add, subtract, multiply, and divide fractions
• Solve applied problems involving fractions

1.3 Hello, My Name Is: Graphing Points  

• Plot ordered pairs
• Determine the coordinates of a point

1.4 A Tale of Two Numbers: Ratios and Proportions  

• Interpret ratios
• Scale ratios to produce equivalent ratios
• Determine if quantities are proportional

Getting Ready for Section 1.5

1.5 Chances Are: Probability Basics  

• Find relative frequencies
• Find and interpret experimental probabilities

1.6 It’s All Relative: Understanding Integers  

• Interpret signed number situations
• Find the opposite and absolute value of a number

1.7 Sign and Size: Integer Operations  

• Add, subtract, multiply, and divide signed numbers
• Solve applied problems that involve signed-number addition, subtraction, multiplication, and division

1.8 An Ounce of Prevention: Means  

• Find and interpret the mean of a set of numbers
• Use means in applied problems

Mid-cycle recap  

1.9 Picture This: Making and Interpreting Graphs  

• Create and interpret pie graphs
• Create and interpret bar graphs
• Create and interpret line graphs

1.10 Two by Two: Scatterplots  79

• Create and interpret scatterplots
• Sketch a curve to best fit a scatterplot

Getting Ready for Section 1.11

1.11 Multiply vs. Divide: Converting Units  

• Convert units by multiplying or dividing

1.12 Up and Down: Percent Change  

• Apply a percent change
• Find percent change
• Interpret percent change

1.13 The X Factor: Algebraic Terminology  

• Differentiate between variables and constants
• Differentiate between expressions and equations
• Differentiate between factors and terms

1.14 General Number: Recognizing Patterns  

• Make conjectures and generalize patterns
• Identify and use arithmetic and geometric sequences

1.15 Social Network: Linear and Exponential Change  

• Model change with linear and exponential functions

1.16 Infinity and Beyond: Perimeter and Area  

• Calculate perimeter and area

Cycle 1 Study Sheet  

Self-Assessment: Review  

Cycle 1 Wrap-Up 

CYCLE TWO How does that work?

Self-Assessment: Preview  

2.1 Predicting a Child’s Height: Focus Problem  

Getting Ready for Section 2.2

2.2 Rule of Thumb: Weighted Means  

• Find and interpret weighted means
• Find the median and mode of a data set

2.3 Measure Up: Basic Exponent Rules  

• Apply basic exponent rules
• Use geometric formulas

2.4 Count Up: Adding Polynomials  

• Identify and add like terms

2.5 A Winning Formula: Applying Order of Operations  

• Use the order of operations to simplify expressions
• Evaluate formulas and expressions

2.6 Does Order Matter: Rewriting Expressions  

• Apply the commutative and associative properties

2.7 Fair Share: Distributive Property  

• Apply the distributive property to expressions
• Use the distributive property in applied contexts

2.8 Seat Yourself: Equivalent Expressions  

• Write an expression to represent a scenario
• Determine if two expressions are equivalent by using the commutative, associative, and distributive properties

2.9 Parts of Speech: Using Operations Correctly  

• Distinguish between an operator and an object
• Determine the object on which an operator is acting
• Recognize when the distributive property can be applied

Mid-cycle recap  

2.10 A Fine Balance: Verifying Solutions  

• Verify a solution to an equation

2.11 Separate but Equal: Solving Simple Equations  

• Write and solve one-step equations

2.12 A State of Equality: More Equation Solving  

• Solve two-step and multi-step linear equations

2.13 Quarter Wing Night: Writing and Solving Equations  

• Write an equation to model a situation
• Solve a problem numerically and algebraically

2.14 Outwit and Outlast: Using Proportions  

• Write and solve proportions

2.15 Three of a Kind: Pythagorean Theorem  

• Use the Pythagorean theorem to find the length of a side in a right triangle
• Solve problems using the Pythagorean theorem

Getting Ready for Section 2.16  

2.16 What Are the Odds?: Theoretical Probability  

• Calculate theoretical probabilities
• Compare theoretical and experimental probabilities

2.17 Size Up: Volume and Surface Area  

• Calculate volume and surface area

Cycle 2 Study Sheet  

Self-Assessment: Review  

Cycle 2 Wrap-Up

CYCLE THREE When Is It Worth It?

Self-Assessment: Preview  

3.1 Deciding to Run: Focus Problem  

3.2 What’s Trending: Correlation  

• Determine if data has a positive or negative linear correlation
• Graph the equation of the trendline
• Use the equation of the trendline to make predictions

3.3 Constant Change: Slope  

• Find the slope of a line from points, tables, and graphs
• Interpret the slope as a rate of change

3.4 Shortest Path: Distance Formula  

• Use the distance formula to find the distance between two points

3.58 More or Less: Linear Relationships  

• Make comparisons using equations, tables, and graphs

3.6 Get in Line: Slope-Intercept Form  

• Find and interpret the slope and y-intercept from a linear equation
• Graph a line using a table and using the slope and y-intercept

3.7 Chain, Chain, Chain: Writing Linear Equations  

• Write the equation of a line using a point and the slope
• Write the equation of a line using two points
• Create a linear model in an applied problem

Getting Ready for Section 3.8  

3.8 Going Viral: Exponential Functions  

• Write the equation of an exponential function using a starting value and rate of change
• Model with exponential functions
• Graph exponential functions

Mid-cycle recap  

CYCLE Three When Is It Worth It?

3.9 Untangling the Knot: Solving Nonlinear Equations  

• Solve nonlinear equations

Getting Ready for Section 3.10  

3.10 Hot and Cold: Rewriting Formulas  

• Solve an equation for a specified variable

3.11 A Common Goal: Greatest Common Factors  

• Factor an expression using the greatest common factor

3.12 Thinking Outside the Box: Factoring Quadratic Expressions  

• Factor quadratic expressions

3.13 A Formula for Success: The Quadratic Formula  

• Use the quadratic formula to solve equations

3.14 Systematic Thinking: Graphing and Substitution  

• Solve a 2 * 2 linear system of equations by graphing
• Solve a 2 * 2 linear system of equations by substitution

3.15 Opposites Attract: Elimination  

• Solve a 2 * 2 linear system of equations by elimination

3.16 The Turning Point: Quadratic Functions  

• Identify a quadratic pattern in data
• Find the vertex of a parabola

Cycle 3 Study Sheet  

Self-Assessment: Review  

Cycle 3 Wrap-Up  

CYCLE FOUR What Else Can We Do?

Self-Assessment: Preview  

4.1 Measuring Temperature Variability: Focus Problem  

4.2 A Matter of Change: Dimensional Analysis  

• Convert units using dimensional analysis

Getting Ready for Section 4.3  

4.3 Little Giants: Scientific and Engineering Notation  

• Convert numbers between scientific and standard notation
• Convert numbers into and out of engineering notation

4.4 A Model Approach: Negative Exponents  

• Use exponent rules to simplify expressions that have negative exponents

4.5 Variation on a Theme: Standard Deviation  

• Find the standard deviation of a data set
• Interpret the standard deviation of a data set

4.6 An Order of Magnitude: Understanding Logarithmic Scales   

• Interpret logarithmic scales

Mid-cycle recap   

4.7 Straight to the Point: Direct Variation   

• Identify direct variation from a graph, table, or equation
• Write models for direct variation problems
• Solve direct variation problems

Getting Ready for Section 4.8   

4.8 Gas Up and Go: Inverse Variation   

• Identify inverse variation from a table
• Write models for inverse variation problems
• Solve inverse variation problems

4.9 Ghost in the Machine: Function Notation   

• Use function notation
• Find a function input or output given the other

4.10 What’s Your Function? Vertical Line Test, Domain, and Range   

• Apply the vertical line test
• Find the domain and range from a graph

4.11 An Important Point: Vertex Form of a Quadratic Function   

• Identify the vertex of a quadratic function
• Graph a quadratic function in vertex form
• Write the vertex form of a quadratic function

4.12 A Survey of Trig: Trigonometric Functions  

• Write the six trigonometric ratios for an acute angle
• Use trigonometric functions to find the measures of sides and angles of a right triangle

Cycle 4 Study Sheet   

Self-Assessment: Review   

Cycle 4 Wrap-Up  

Excel Appendix (online) EA-1

Answers (online) A-1

Index I-1

Applications Index

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