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