Section 1.1
1.1.1 Solving Puzzles in Teams
1.1.2 Investigating the Growth of Patterns
1.1.3 Investigating the Graphs of Quadratic Functions
Section 1.2
1.2.1 Describing a Graph
1.2.2 Cube Root and Absolute Value Functions
1.2.3 Function Machines
1.2.4 Functions
1.2.5 Domain and Range
Chapter Closure
Section 2.1
2.1.1 Seeing Growth in Linear Representations
2.1.2 Slope
2.1.3 Comparing Δy and Δx
2.1.4 y = mx + b and More on Slope
Section 2.2
2.2.1 Slope as Motion
2.2.2 Rate of Change
2.2.3 Equations of Lines in Situations
Section 2.3
2.3.1 Finding an Equation Given a Slope and a Point
2.3.2 Finding the Equation of a Line Through Two Points
Extension Activity Finding y = mx + b from Graphs and Tables
Chapter Closure
Section 3.1
3.1.1 Simplifying Exponential Expressions
3.1.2 Zero and Negative Exponents
Section 3.2
3.2.1 Equations Algebra Tiles
3.2.2 Exploring an Area Model
3.2.3 Multiplying Binomials and the Distributive Property
3.2.4 Using Generic Rectangles to Multiply
Section 3.3
3.3.1 Solving Equations With Multiplication and Absolute Value
3.3.2 Working With Multi-Variable Equations
3.3.3 Summary of Solving Equations
Chapter Closure
Section 4.1
4.1.1 Solving Word Problems by Writing Equations
4.1.2 One Equation or Two?
Section 4.2
4.2.1 Solving Systems of Equations Using Substitution
4.2.2 Making Connections: Systems, Solutions, and Graphs
4.2.3 Solving Systems Using Elimination
4.2.4 More Elimination
4.2.5 Choosing a Strategy for Solving Systems
Section 4.3
4.3.1 Pulling it all Together
Chapter Closure
Section 5.1
5.1.1 Representing Exponential Growth
5.1.2 Rebound Ratios
5.1.3 The Bouncing Ball and Exponential Decay
Section 5.2
5.2.1 Generating and Investigating Sequences
5.2.2 Generalizing Arithmetic Sequences
5.2.3 Recursive Sequences
Section 5.3
5.3.1 Patterns of Growth in Tables and Graphs
5.3.2 Using Multipliers to Solve Problems
5.3.3 Comparing Sequences to Functions
Chapter Closure
Section 6.1
6.1.1 Line of Best Fit
6.1.2 Residuals
6.1.3 Upper and Lower Bounds
6.1.4 Least Squares Regression Line
Section 6.2
6.2.1 Residual Plots
6.2.2 Correlation
6.2.3 Association is Not Causation
6.2.4 Interpreting Correlation in Context
6.2.5 Curved Best-Fit Models
Chapter Closure
Section 7.1
7.1.1 Investigating y = bx
7.1.2 Multiple Representations of Exponential Functions
7.1.3 More Applications of Exponential Growth
7.1.4 Exponential Decay
7.1.5 Graph → Equation
7.1.6 Completing the Multiple Representations Web
Section 7.2
7.2.1 Curve Fitting and Fractional Exponents
7.2.2 More Curve Fitting
7.2.3 Solving a System of Exponential Functions Graphically
Chapter Closure
Section 8.1
8.1.1 Introduction to Factoring Quadratics
8.1.2 Factoring with Generic Rectangles
8.1.3 Factoring with Special Cases
8.1.4 Factoring Completely
8.1.5 Factoring Shortcuts
Section 8.2
8.2.1 Multiple Representations for Quadratic Functions
8.2.2 Zero Product Property
8.2.3 More Ways To Find the x-Intercepts
8.2.4 Completing the Quadratic Web
8.2.5 Completing the Square
Chapter Closure
Section 9.1
9.1.1 Solving Quadratic Equations
9.1.2 Introduction to the Quadratic Formula
9.1.3 More Solving Quadratic Equations
9.1.4 Choosing a Strategy
Section 9.2
9.2.1 Solving Linear, One-Variable Inequalities
9.2.2 More Solving Inequalities
Section 9.3
9.3.1 Graphing Two-Variable Inequalities
9.3.2 Graphing Linear and Non-Linear Inequalities
Section 9.4
9.4.1 Systems of Inequalities
9.4.2 More Systems of Inequalities
9.4.3 Applying Inequalities to Solve Problems
Chapter Closure
Section 10.1
10.1.1 Association in Two-Way Tables
Section 10.2
10.2.1 Solving by Rewriting
10.2.2 Fraction Busters
10.2.3 Multiple Methods for Solving Equations
10.2.4 Determining the Number of Solutions
10.2.5 Deriving the Quadratic Formula and the Number System
10.2.6 More Solving and an Application
Section 10.3
10.3.1 Intersection of Two Functions
10.3.2 Number of Parabola Intersections
10.3.3 Solving Quadratic and Absolute Value Inequalities
Chapter Closure
Section 11.1
11.1.1 Transforming Functions
11.1.2 Inverse Functions
Section 11.2
11.2.1 Investigating Data Representations
11.2.2 Comparing Data
11.2.3 Standard Deviation
Section 11.3
11.3.1 Using a Best-Fit Line to Make a Prediction
11.3.2 Relation Treasure Hunt
11.3.3 Investigating a Complex Function
11.3.4 Using Algebra to Find a Maximum
11.3.5 Exponential Functions and Linear Inequalities
Chapter Closure
Section A.1
A.1.1 Exploring Variables and Combining Like Terms
A.1.2 Simplifying Expressions by Combining Like Terms
A.1.3 Writing Algebraic Expressions
A.1.4 Using Zero to Simplify Algebraic Expressions
A.1.5 Using Algebra Tiles to Simplify Algebraic Expressions
A.1.6 Using Algebra Tiles to Compare Expressions
A.1.7 Simplifying and Recording Work
A.1.8 Using Algebra Tiles to Solve for x
A.1.9 More Solving Equations
Chapter Closure
Section 1.1
1.1.1 Creating Quilt Using Symmetry
1.1.2 Making Predictions and Investigating Results
1.1.3 Perimeters and Areas of Enlarging Tile Patterns
1.1.4 Logical Arguments
1.1.5 Building a Kaleidoscope
Section 1.2
1.2.1 Spatial Visualization and Reflection
1.2.2 Rigid Transformations: Rotation and Translations
1.2.3 Slope of Parallel and Perpendicular Lines
1.2.4 Defining Transformations
1.2.5 Using Transformations to Create Shapes
1.2.6 Symmetry
Section 1.3
1.3.1 Attributes and Characteristics of Shapes
1.3.2 More Characteristics of Shapes
Chapter Closure
Section 2.1
2.1.1 Complementary, Supplementary, and Vertical Angles
2.1.2 Angles Formed by Transversals 5
2.1.3 More Angles Formed by Transversals
2.1.4 Angles in a Triangle
2.1.5 Applying Angle Relationships
Section 2.2
2.2.1 Units of Measure
2.2.2 Areas of Triangles and Composite Shapes
2.2.3 Areas of Parallelograms and Trapezoids
2.2.4 Heights and Areas
Section 2.3
2.3.1 Triangle Inequality
2.3.2 The Pythagorean Theorem
Chapter Closure
Section 3.1
3.1.1 Dilations
3.1.2 Similarity
3.1.3 Using Ratios of Similarity
3.1.4 Applications and Notation
Section 3.2
3.2.1 Conditions for Triangle Similarity
3.2.2 Creating a Flowchart
3.2.3 Triangle Similarity and Congruence
3.2.4 More Conditions for Triangle Similarity
3.2.5 Determining Similarity
3.2.6 Applying Similarity
Chapter Closure
Section 4.1
4.1.1 Constant Ratios in Right Triangles
4.1.2 Connecting Slope Ratios to Specific Angles
4.1.3 Expanding the Trig Table
4.1.4 The Tangent Ratio
4.1.5 Applying the Tangent Ratio
Section 4.2
4.2.1 Using an Area Model
4.2.2 Using a Tree Diagram
4.2.3 Probability Models
4.2.4 Unions, Intersections, and Complements
4.2.5 Expected Value
Chapter Closure
Section 5.1
5.1.1 Sine and Cosine Ratios
5.1.2 Selecting a Trig Tool
5.1.3 Inverse Trigonometry
5.1.4 Applications
Section 5.2
5.2.1 Special Right Triangles
5.2.2 Pythagorean Triples
Section 5.3
5.3.1 Finding Missing Parts of Triangles
5.3.2 Law of Sines
5.3.3 Law of Cosines
5.3.4 Ambiguous Triangles (Optional)
5.3.5 Choosing a Tool
Chapter Closure
Section 6.1
6.1.1 Congruent Triangles
6.1.2 Conditions for Triangle Congruence
6.1.3 Congruence of Triangles Through Rigid Transformations
6.1.4 Flowcharts for Congruence
6.1.5 Converses
Section 6.2
6.2.1 Angles on a Pool Table
6.2.2 Investigating a Triangle
6.2.3 Creating a Mathematical Model
6.2.4 Analyzing a Game
6.2.5 Using Transformations and Symmetry to Design Snowflakes
Chapter Closure
Section 7.1
7.1.1 Properties of a Circle
7.1.2 Building a Tetrahedron
7.1.3 Shortest Distance Problems
7.1.4 Using Symmetry to Study Polygons
Section 7.2
7.2.1 Special Quadrilaterals and Proof
7.2.2 Properties of Rhombi
7.2.3 More Proofs with Congruent Triangles
7.2.4 More Properties of Quadrilaterals 7.2.5 Two-Column Proofs
7.2.6 Explore-Conjecture-Prove
Section 7.3
7.3.1 Studying Quadrilaterals on a Coordinate Grid
7.3.2 Coordinate Geometry and Midpoints
7.3.3 Identifying Quadrilaterals on a Coordinate Grid
Chapter Closure
Section 8.1
8.1.1 Pinwheels and Polygons
8.1.2 Interior Angles of Polygons
8.1.3 Angles of Regular Polygons
8.1.4 Regular Polygon Angle Connections
8.1.5 Finding Areas of Regular Polygons
Section 8.2
8.2.1 Area Ratios of Similar Figures
8.2.2 Ratios of Similarity
Section 8.3
8.3.1 A Special Ratio
8.3.2 Area and Circumference of a Circle
8.3.3 Circles in Context
Chapter Closure
Section 9.1
9.1.1 Three-Dimensional Solids
9.1.2 Volumes and Surface Areas of Prisms
9.1.3 Prisms and Cylinders
9.1.4 Volumes of Similar Solids
9.1.5 Ratios of Similarity
Section 9.2
9.2.1 Introduction to Constructions
9.2.2 Constructing Bisectors
9.2.3 More Explorations with Constructions
9.2.4 Other Constructions
Chapter Closure
Section 10.1
10.1.1 Introduction to Chords
10.1.2 Angles and Arcs
10.1.3 Chords and Angles
10.1.4 Tangents and Secants
10.1.5 Problem Solving with Circles
Section 10.2
10.2.1 Conditional Probability and Independence
10.2.2 Two-Way Tables
10.2.3 Applications of Probability
Section 10.3
10.3.1 The Fundamental Principle of Counting
10.3.2 Permutations
10.3.3 Combinations
10.3.4 Categorizing Counting Problems
10.3.5 Some Challenging Probability Problems
Chapter Closure
Section 11.1
11.1.1 Platonic Solids
11.1.2 Pyramids
11.1.3 Volume of a Pyramid
11.1.4 Surface Area and Volume of a Cone
11.1.5 Surface Area and Volume of a Sphere
Section 11.2
11.2.1 Coordinates on a Sphere
11.2.2 Tangents and Arcs
11.2.3 Secant and Tangent Relationships
Chapter Closure
Section 12.1
12.1.1 The Equation of a Circle
12.1.2 Completing the Square for Equations of Circles
12.1.3 Introduction to Conic Sections
12.1.4 Graphing a Parabola Using the Focus and Directrix
Section 12.2
12.2.1 Using Coordinate Geometry and Constructions to Explore Shapes
12.2.2 Euler’s Formula for Polyhedra
12.2.3 The Golden Ratio
12.2.4 Using Geometry to find Probabilities
Chapter Closure
Section 1.1
1.1.1 Solving Puzzles in Teams
1.1.2 Using a Graphing Calculator to Explore a Function
1.1.3 Domain and Range
1.1.4 Points of Intersection in Multiple Representations
Section 1.2
1.2.1 Modeling a Geometric Relationship
1.2.2 Function Investigation
1.2.3 The Family of Linear Functions
1.2.4 Function Investigation Challenge
Chapter Closure
Section 2.1
2.1.1 Modeling Non-Linear Data 55
2.1.2 Parabola Investigation 60
2.1.3 Graphing a Parabola Without a Table 66
2.1.4 Rewriting in Graphing Form 71
2.1.5 Mathematical Modeling with Parabolas 79
Section 2.2
2.2.1 Transforming Other Parent Graphs 83
2.2.2 Describing (h, k) for Each Family of Functions 91
2.2.3 Transformations of Functions 96
2.2.4 Transforming Non-Functions 100
2.2.5 Transforming Piecewise-Defined Functions 105
Chapter Closure
Section 3.1
3.1.1 Equivalent Expressions
3.1.2 Rewriting Expressions and Determining Equivalence
3.1.3 Solving by Rewriting
Section 3.2
3.2.1 Investigating Rational Functions
3.2.2 Simplifying Rational Expressions
3.2.3 Multiplying and Dividing Rational Expressions
3.2.4 Adding and Subtracting Rational Expressions
3.2.5 Creating New Functions
Chapter Closure
Section 4.1
4.1.1 Strategies for Solving Equations
4.1.2 Solving Equations and Systems Graphically
4.1.3 Finding Multiple Solutions to Systems of Equations
4.1.4 Using Systems of Equations to Solve Problems
Section 4.2
4.2.1 Solving Inequalities with One or Two Variables
4.2.2 Using Systems to Solve a Problem
4.2.3 Application of Systems of Linear Inequalities
4.2.4 Using Graphs to Find Solutions
Chapter Closure
Section 5.1
5.1.1 “Undo” Equations
5.1.2 Using a Graph to Find an Inverse
5.1.3 Finding Inverses and Justifying Algebraically
Section 5.2
5.2.1 Finding the Inverse of an Exponential Function
5.2.2 Defining the Inverse of an Exponential Function
5.2.3 Investigating the Family of Logarithmic Functions
5.2.4 Transformations of Logarithmic Functions
5.2.5 Investigating Compositions of Functions
Chapter Closure
Section 6.1
6.1.1 Creating a Three-Dimensional Model
6.1.2 Graphing Equations in Three Dimensions
6.1.3 Systems of Three-Variable Equations
6.1.4 Solving Systems of Three Equations with Three Unknowns
6.1.5 Using Systems of Three Equations for Curve Fitting
Section 6.2
6.2.1 Using Logarithms to Solve Exponential Equations
6.2.2 Investigating the Properties of Logarithms
6.2.3 Writing Equations of Exponential Functions
6.2.4 An Application of Logarithms
Chapter Closure
Section 7.1
7.1.1 Introduction to Cyclic Models
7.1.2 Graphing the Sine Function
7.1.3 Unit Circle ↔ Graph
7.1.4 Graphing and Interpreting the Cosine Function
7.1.5 Defining a Radian
7.1.6 Building a Unit Circle
7.1.7 The Tangent Function
Section 7.2
7.2.1 Transformations of y = sin x
7.2.2 One More Parameter for a Cyclic Function
7.2.3 Period of a Cyclic Function
7.2.4 Graph ↔ Equation
Chapter Closure
Section 8.1
8.1.1 Sketching Graphs of Polynomial Functions
8.1.2 More Graphs of Polynomials
8.1.3 Stretch Factors for Polynomial Functions
Section 8.2
8.2.1 Introducing Imaginary Numbers
8.2.2 Complex Roots
8.2.3 More Complex Numbers and Equations
Section 8.3
8.3.1 Polynomial Division
8.3.2 Factors and Integral Roots
8.3.3 An Application of Polynomials
Chapter Closure
Section 9.1
9.1.1 Survey Design
9.1.2 Samples and the Role of Randomness
9.1.3 Bias in Convenience Samples
Section 9.2
9.2.1 Testing Cause and Effect with Experiments
9.2.2 Conclusions From Studies
Section 9.3
9.3.1 Relative Frequency Histograms
9.3.2 The Normal Probability Density Function
9.3.3 Percentiles
Chapter Closure
Section 10.1
10.1.1 Introduction to Arithmetic Series
10.1.2 More Arithmetic Series
10.1.3 General Arithmetic Series
10.1.4 Summation Notation and Combinations of Series
Section 10.2
10.2.1 Geometric Series
10.2.2 Infinite Series
Section 10.3
10.3.1 Pascal’s Triangle and the Binomial Theorem
10.3.2 The Number e
Chapter Closure
Section 11.1
11.1.1 Simulations of Probability
11.1.2 More Simulations of Probability
11.1.3 Simulating Sampling Variability
Section 11.2
11.2.1 Statistical Test Using Sampling Variability
11.2.2 Variability in Experimental Results
11.2.3 Quality Control
11.2.4 Statistical Process Control
Section 11.3
11.3.1 Analyzing Decisions and Strategies
Chapter Closure
Section 12.1
12.1.1 Analyzing Trigonometric Equations
12.1.2 Solutions to Trigonometric Equations
12.1.3 Inverses of Trigonometric Functions
12.1.4 Reciprocal Trigonometric Functions
Section 12.2
12.2.1 Trigonometric Identities
12.2.2 Proving Trigonometric Identities
12.2.3 Angle Sum and Difference Identities
Chapter Closure
Section A.1
A.1.1 Representing Exponential Growth
A.1.2 Rebound Ratios
A.1.3 The Bouncing Ball and Exponential Decay
Section A.2
A.2.1 Generating and Investigating Sequences
A.2.2 Generalizing Arithmetic Sequences
A.2.3 Recursive Sequences
Section A.3
A.3.1 Patterns of Growth in Tables and Graphs
A.3.2 Using Multipliers to Solve Problems
A.3.3 Comparing Sequences to Functions
Appendix Closure
Section B.1
B.1.1 Investigation y = bx
B.1.2 Multiple Representations of Exponential Functions
B.1.3 More Applications of Exponential Growth
B.1.4 Exponential Decay
B.1.5 Graph → Equation
B.1.6 Completing the Multiple Representations Web
Section B.2
B.2.1 Curve Fitting and Fractional Exponents
B.2.2 More Curve Fitting
B.2.3 Solving a System of Exponential Functions Graphically
Appendix Closure
Section C.1
C.1.1 Investigating Data Representations
C.1.2 Comparing Data
C.1.3 Standard Deviation
Appendix Closure
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This professional learning is designed for teachers as they begin their implementation of CPM. This series contains multiple components and is grounded in multiple active experiences delivered over the first year. This learning experience will encourage teachers to adjust their instructional practices, expand their content knowledge, and challenge their beliefs about teaching and learning. Teachers and leaders will gain first-hand experience with CPM with emphasis on what they will be teaching. Throughout this series educators will experience the mathematics, consider instructional practices, and learn about the classroom environment necessary for a successful implementation of CPM curriculum resources.
Page 2 of the Professional Learning Progression (PDF) describes all of the components of this learning event and the additional support available. Teachers new to a course, but have previously attended Foundations for Implementation, can choose to engage in the course Content Modules in the Professional Learning Portal rather than attending the entire series of learning events again.
