Math Lit

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

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