Math Lit, by Kathleen Almy and Heather Foes, provides a one-semester alternative to the traditional two-semester developmental algebra sequence for non-STEM (Science, Technology, Engineering, and Math) students. This new approach offers an accelerated pathway to college readiness through developmental math, allowing non-STEM students to move directly into liberal arts math or introductory statistics, while also preparing STEM students for intermediate algebra. Through its emphasis on contextual problem-solving, the Almy/Foes worktext and its accompanying MyMathLab^® course help students understand and practice the major themes of numeracy, proportional reasoning, algebraic reasoning, and functions.

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 1

Part 1: Gear Up

1.1 Focus Problem, Step 1: Understand the Problem

Exposure to an open-ended problem on a medical error

Previews the use of rates and units and Polya’s problem solving process

1.2 Getting Started: Syllabus

Group activity to learn course policies

Develops critical reading skills

1.3 Getting Started: Skills

Venn diagrams are used to explore prerequisite knowledge

Reviews prerequisite skills
Develops Venn diagrams

1.4 Getting Started: Groups

Personality test to improve group dynamics

Develops knowledge of the Cartesian coordinate system
Develops the ability to plot and read ordered pairs
Exposes students to the term variable

1.5 A Tale of Two Numbers (FP)

Exploration of ratios and rates used in daily life

Previews scaling fractions
Develops ratio and rates concepts including notation

1.6 Part and Whole

Conceptual review of fraction operations

Reviews fraction concepts and operations
Develops the skill of drawing a picture

1.7 The Elusive A in Math

Assess traits necessary to success in mathematics

Develops pie and bar graphs
Connects equivalent fractions and scaling
Previews working with axes and increments on them

1.8 Two by Two

Visualizing situations with scatterplots

Develops scatterplots
Applies pie graphs and plotting points

1.9 Multiply or Divide? (FP)

Daily situations that involve unit conversions by multiplying or dividing

Develops unit conversions
Applies student success knowledge from 1.7

Part 1 Recap

Part 2: Shift Gears

1.10 Focus Problem, Step 2: Devise a Plan

Revisit focus problem and develop a plan to solve it

Applies knowledge gained to date

1.11 Higher or Lower? (FP)

Compare two pay structures with graphs, tables, and Excel

Previews integers, equations, like terms, and the commutative property
Develops percent calcuations, the concept of a function, and generalizing a calculation
Applies scaling

1.12 The X Factor

Important algebraic vocabulary

Develops the terms equation, expression, constant, variable, term
Applies Venn diagrams
Reviews pi

1.13 Take Two and Call Me…

Interpreting a graph that accompanies a medicine

Connects scaling with units and rates
Develops understanding of rates and units
Applies independent/dependent variables, function concepts, and reading ordered pairs

1.14 Good Eats (FP)

Understanding nutrition labels and nutrition guidelines

Develops the concept of proportionality
Applies fraction and percent skills

1.15 General Number

Generalizing patterns with variables

Exposes students to Fibonacci sequence
Develops generalizing a pattern, inductive and deductive reasoning
Previews simplifying expressions

1.16 Up and Down (FP)

Percent situations from daily life

Previews integers
Develops the concept of percent change
Applies the skills of finding the percent of a number and increasing or decreasing a number by a percent

1.17 The Social Network

Exploration of viral growth on the internet

Previews order of operations and slope concepts
Develops the concepts of linear and exponential growth
Applies the idea of generalizing a pattern
Exposes students to building a mathematical model
Connects exponential growth and percent of increase

Part 2 Recap

Part 3: Wind Down

1.18 Focus Problem, Step 3: Carry Out the Plan

Revisit focus problem and solve it

Applies knowledge gained to date

1.19 Cookie Monster

Recipe conversion to decrease its size

Connects conversions with scaling
Applies fraction skills
Applies unit conversion skills

1.20 Picture This

Matching scenarios with graphs

Exposes students to fitting data with a curve
Connects scatterplots and types of change

1.21 Infinity and Beyond

Exploration of Sierpinski triangles and their patterns

Connects area and perimeter to generalizing a pattern
Applies concepts of area and perimeter
Exposes students to Sierpinski triangles
Connects proportionality to similar triangles

1.22 Error and Estimation: Liquid Medicine

Impact of being inaccurate with liquid medicine

Exposes students to volume concepts
Applies the concepts of constant and variable
Applies the concepts of independent and dependent variables
Applies unit conversions
Previews order of operations

1.23 Focus Problem, Step 4: Look Back

Reflect on focus problem and cycle as a whole

Debriefs the focus problem solution

Cycle Wrap-up

Active test preparation exercises

Reviews topics, skills, and concepts from the cycle
Connects cycle skills and concepts to apply them to new problems

CYCLE 2

Part 1: Gear Up

2.1 Focus Problem, Step 1: Understand the Problem

Exposure to an open-ended problem on baseball’s magic number

Previews the use of expressions, formulas, and integers

2.2 It’s All Relative (FP)

Work with atoms and ions to develop integer concepts

Develops integer concepts
Previews integer operations

2.3 Sign and Size, Part 1 (FP)

Real-life situations to develop signed number addition/subtraction rules

Develops integer operations of addition and subtraction
Applies integer concepts and operations to realistic scenarios

2.4 Sign and Size, Part 2

Use of patterns to develop signed number multiplication/division rules

Develops integer operations multiplication and division
Defines real numbers
Exposes students to imaginary numbers
Reviews the concept of square roots

2.5 An Ounce of Prevention

Grades situations to understand means

Develops means conceptually and numerically
Previews order of operations

2.6 Measure Up

Geometric formulas with units to develop exponent rules

Develops whole number exponent properties
Applies geometric formulas
Applies the use of units in calculations

2.7 Count Up (FP)

Common situations with like terms

Develops like terms
Applies knowledge of formulas
Exposes students to polynomial terminology and addition/subtraction

Part 1 Recap

Part 2: Shift Gears

2.8 Focus Problem, Step 2: Devise a Plan

Revisit focus problem and develop a plan to solve it

Applies knowledge gained to date

2.9 Order Up

Order of operations and their use in formulas

Develops the order of operations
Applies order of operations to evaluating formulas
Previews inverse operations necessary for equation solving

2.10 Does Order Matter?

Uses of the commutative and associative properties in algebra and mental math

Develops the commutative and associative properties
Develops mental math skills
Applies percent skills and adding like terms

2.11 Fair Share

Development and application of the distributive property

Develops the distributive property and mental math skills
Applies the commutative property
Applies the distributive property to multiplying polynomials
Reviews like terms and whole number exponent properties

2.12 Seat Yourself (FP)

Pattern recognition using a tables and chairs situation

Applies the distributive property and connects it to like terms
Develops the ability to write expressions

2.13 Punt, Pass, Kick

Pythagorean Theorem off a grid

Develops the Pythagorean Theorem
Develops conceptual and numeric approaches to equation solving
Previews concepts related to solving equations
Connects Pythagorean triples to similar triangles

2.14 Ramp Up

Slope on and off a grid

Develops slope concepts and calculations
Connects slope to linearity
Applies Pythagorean Theorem and unit conversions

2.15 Shortest Distance (Optional)

Pythagorean Theorem on a grid to measure distances

Applies Pythagorean Theorem, slope, and the order of operations
Develops the distance formula and measurement skills
Connects slope and the distance formula

Part 2 Recap

Part 3: Wind Down

2.16 Focus Problem, Step 3: Carry Out the Plan

Revisit focus problem and solve it

Applies knowledge gained to date

2.17 Parts of Speech

Operations vs. operators

Applies the distributive property
Develops understanding of operations

2.18 In the Swing of Things (Optional)

Investigation of a pendulum formula

Applies the order of operations
Connects functions to the order of operations
Applies function concepts

2.19 Error and Estimation: Rounding (Optional)

Impact of being inaccurate with a financial formulas

Applies the order of operations
Develops understanding of the role of accuracy and precision

2.20 Focus Problem, Step 4: Look Back

Reflect on focus problem and cycle as a whole

Debriefs the focus problem solution

Cycle Wrap-up

Active test preparation exercises

Reviews topics, skills, and concepts from the cycle
Connects cycle skills and concepts to apply them to new problems

CYCLE 3

Part 1: Gear Up

3.1 Focus Problem, Step 1: Understand the Problem

Exposure to an open-ended problem about comparing e-readers

Previews the use of linear equations

3.2 Rule of Thumb

Explore weighted means with grade situations

Applies means and rates in a new context
Develops weighted means

3.3 Working Hard for the Money (FP)

Correlation between profession and income, unemployment rate

Applies means and weighted means
Applies making scatterplots
Develops correlation, median, and mode
Previews finding the trend line
Previews slope-intercept form
Applies scaling concepts
Connects measures of center to geometry

3.4 A Fine Balance (Optional)

Using chemical equations to understand solutions to equations

Connects algebraic ideas with chemistry notation
Develops the concept of solutions to equations
Previews algebraic identities

3.5 Just a Pinch

Measuring natural variation using standard deviation

Develops standard deviation concepts and calculations
Applies means, order of operations, and signed numbers
Previews equation solving concepts

3.6 Separate but Equal (FP)

Real-life scenarios that can be solved numerically and with one-step equations

Develops one-step equations and understanding of equation solving
Connects algebraic and numeric methods of equation solving

3.7 On the Rise

Analyze an article about food packaging using algebra, geometry, and statistics

Applies mean, median, standard deviation, and bar graphs
Develops Pareto charts
Applies writing and solving one-step equations

Part 1 Recap

Part 2: Shift Gears

3.8 Focus Problem, Step 2: Devise a Plan

Revisit focus problem and develop a plan to solve it

Applies knowledge gained to date

3.9 Game On (FP)

Use pictures and algebra to solve two-step and multi-step equations

Develops solving of linear equations
Develops identities and contradictions

3.10 Quarter Wing Night (FP)

Determine the number of buffalo wings in varying scenarios

Applies equation solving techniques
Applies percent concepts

3.11 Eastbound and Down (FP)

Analyzing gas price scenarios with and without a car wash

Applies equation solving techniques
Connects linear equation solving and graphing
Reviews linearity, slope, and rate of change
Previews systems of equations

3.12 Get in Line (FP)

Explore linear situations algebraically and on a graph

Develops slope-intercept form and its uses in graphing
Connects linearity between tables, graphs, and equations
Exposes students to the concept of domain

3.13 Gas Up and Go (Optional)

Study Distance = Rate x Time to explore variation

Develops direct and inverse variation
Exposes students to combined variation
Applies equation solving

Part 2 Recap

Part 3: Wind Down

3.14 Focus Problem, Step 3: Carry Out the Plan

Revisit focus problem and solve it

Applies knowledge gained to date

3.15 Value of a Dollar (Optional)

Determine the amount of time worked to pay for a tank of gas

Develops rational functions
Applies direct and inverse variation

3.16 When is the Algebra Worth It? (Optional)

Assess when algebra is useful

Applies and extends equation solving techniques
Exposes students to non-linear equation solving

3.17 Error and Estimation: Volume

Revisit and quantify liquid medicine overfilling error

Applies slope-intercept form and graphing
Applies percent of change and unit conversions

3.18 Focus Problem, Step 4: Look Back

Reflect on focus problem and cycle as a whole

Debriefs the focus problem solution

Cycle Wrap-up

Active test preparation exercises

Reviews topics, skills, and concepts from the cycle
Connects cycle skills and concepts to apply them to new problems

CYCLE 4

Part 1: Gear Up

4.1 Focus Problem, Step 1: Understand the Problem

Exposure to an open-ended problem about making sense of a large number

Previews dimensional analysis

4.2 A Matter of Change (FP)

Work with more involved conversion problems

Develops dimensional analysis
Previews scientific notation

4.3 Little Giants (FP)

Explores very large and very small numbers

Develops scientific notation
Connects dimensional analysis to scientific notation
Applies Pareto charts and medians
Previews negative exponents and compound inequalities

4.4 Outwit and Outlast (FP)

Situations with proportionality, explored numerically and algebraically

Develops solving proportions algebraically
Connects scaling with algebraic methods of solving
Applies rates
Exposes students to concepts of apportionment

4.5 Chances Are (Optional)

Simple probability situations from daily life

Develops theoretical and experimental probabilities
Connects area to probability
Applies scientific notation
Previews compound inequalities

4.6 A Model Approach (FP)

Working with numbers in scientific notations from science scenarios

Develops negative exponents
Connects scientific notation to exponent rules
Applies exponent rules, unit conversions, and solving proportions algebraically

Part 1 Recap

Part 2: Shift Gears

4.7 Focus Problem, Step 2: Devise a Plan

Revisit focus problem and develop a plan to solve it

Applies knowledge gained to date

4.8 Chain, Chain, Chain

Linear relationships in alkanes

Exposes students to domain
Develops writing linear models using y = mx + b
Connects equation solving to linear models

4.9 Hot and Cold

Analyzing and developing temperature formulas

Develops factoring the greatest common factor
Develops solving equations for a variable
Applies slope-intercept form and equation solving

4.10 Going Viral

Statistics and models of viral marketing in social media

Exposes students to solving an exponential equation
Develops exponential models
Connects functions to exponential growth
Connects slope, growth, and statistics
Develops understanding of the concept of size
Applies factoring the GCF

4.11 The Cost of College (Optional)

Comparing tuition and fee structures

Develops solving systems with graphing and substitution
Connects graphing and algebraic methods of solving systems
Applies solving literal equations, solving equations, graphing lines
Applies writing equations of lines

4.12 Tuition Increases (Optional)

Exploring the effects of a tuition increase on revenue

Develops quadratic function modeling
Connects linear, exponential, and quadratic functions
Applies systems of equations
Applies multiplying binomials

Part 2 Recap

Part 3: Wind Down

4.13 Focus Problem, Step 3: Carry Out the Plan

Revisit focus problem and solve it

Applies knowledge gained to date

4.14 Outliers (Optional)

Modeling height using belly button height

Exposes students to residuals, the Golden ratio, and compound inequalities
Develops z-scores
Connects issues of size and scale to statistics
Applies standard deviation and mean

4.15 A Little Less (FP)

Large scale effects of plastic saving measures

Applies dimensional analysis
Develops concepts of size and scale

4.16 Error and Estimation: Order of Magnitude Optional

A new scale to make sense of size

Develops order of magnitude
Applies scientific notation and exponent rules

4.17 Focus Problem, Step 4: Look Back

Reflect on focus problem and cycle as a whole

Debriefs the focus problem solution

Cycle Wrap-up

Active test preparation exercises

Reviews topics, skills, and concepts from the cycle
Connects cycle skills and concepts to apply them to new problems

*(FP): Indicates a lesson essential to solving the focus problem

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