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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