## Table of Contents

**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