Section 1.1
1.1.1 Solving Puzzles in Teams
1.1.2 Investigating the Growth of Patterns
1.1.3 Multiple Representations of Functions
Section 1.2
1.2.1 Function Machines
1.2.3 Domain and Range
Section 1.3
1.3.1 Rewriting Expressions with Exponents
1.3.2 Zero and Negative Exponents
Chapter Closure
Section 2.1
2.1.1 Seeing Growth in Linear Functions
2.1.2 Comparing △y and △x 57
2.1.3 Slope
2.1.4 y = mx + b and More on Slope
Section 2.2
2.2.1 Modeling Linear Functions
2.2.2 Rate of Change
2.2.3 Equations of Lines in a Situation
2.2.4 Dimensional Analysis
Section 2.3
2.3.1 Writing the Equation of a Line Given the Slope and a Point
2.3.2 Writing the Equation of a Line Through Two Points
2.3.3 Writing y = mx + b from Graphs and Tables
Chapter Closure
Section 3.1
3.1.1 Spatial Visualization and Reflections
3.1.2 Rotations and Translations
3.1.3 Slopes of Parallel and Perpendicular Lines
3.1.4 Defining Rigid Transformations
3.1.5 Using Transformations to Create Polygons
3.1.6 Symmetry
Section 3.2
3.2.1 Modeling Area and Perimeter with Algebra Tiles
3.2.2 Exploring an Area Model
3.2.3 Multiplying Polynomials and the Distributive Property
Section 3.3
3.3.1 Multiple Methods for Solving Equations
3.3.2 Fraction Busters
3.3.3 Solving Exponential and Complex Equations
Chapter Closure
Section 4.1
4.1.1 Line of Best Fit
4.1.2 Residuals
4.1.3 Upper and Lower Bounds
4.1.4 Least Squares Regression Line
Section 4.2
4.2.1 Residual Plots
4.2.2 Correlation
4.2.3 Association is Not Causation
4.2.4 Interpreting Correlation in Context
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 Comparing 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 Working with Multi-Variable Equations
6.1.2 Summary of Solving Equations
6.1.3 Solving Word Problems by Using Different Representations
6.1.4 Solving Word Problems by Writing Equations
Section 6.2
6.2.1 Solving Systems of Equations Using the Equal Values Method
6.2.2 Solving Systems of Equations Using Substitution
6.2.3 Making Connections: Systems and Multiple Representations
Section 6.3
6.3.1 Solving Systems Using Elimination
6.3.2 More Elimination
6.3.3 Making Connections: Systems, Solutions, and Graphs
Section 6.4
6.4.1 Choosing a Strategy for Solving a System
6.4.2 Pulling it all Together
Chapter Closure
Section 7.1
7.1.1 Defining Congruence
7.1.2 Conditions for Triangle Congruence
7.1.3 Creating a Flowchart
7.1.4 Justifying Triangle Congruence Using Flowcharts
7.1.5 More Conditions for Triangle Congruence
7.1.6 Congruence of Triangles Through Rigid Transformations
7.1.7 More Congruence Flowcharts
Section 7.2
7.2.1 Studying Quadrilaterals on a Coordinate Grid
7.2.2 Coordinate Geometry and Midpoints
7.2.3 Identifying Quadrilaterals on a Coordinate Grid
Chapter Closure
Section 8.1
8.1.1 Investigating
8.1.2 Multiple Representations of Exponential Functions
8.1.3 More Applications of Exponential Functions
8.1.4 Exponential Decay
8.1.5 Graph → Equation
8.1.6 Completing the Multiple Representations Web
Section 8.2
8.2.1 Curve Fitting
8.2.2 Curved Best-Fit Models
8.2.3 Solving a System of Exponential Functions Graphically
Chapter Closure
Section 9.1
9.1.1 Solving Linear, One-Variable Inequalities
9.1.2 More Solving Inequalities
9.1.3 Solving Absolute Value Equations and Inequalities
Section 9.2
9.2.1 Graphing Two-Variable Inequalities
9.2.2 Graphing Linear and Nonlinear Inequalities
Section 9.3
9.3.1 Systems of Inequalities
9.3.2 More Systems of Inequalities
9.3.3 Applying Inequalities to Solve Problems
Chapter Closure
Section 10.1
10.1.1 Association in Two-Way Tables
10.1.2 Investigating Data Representations
10.1.3 Comparing Data
10.1.4 Standard Deviation
Section 10.2
10.2.1 Transforming Functions
10.2.2 Arithmetic Operations with Functions
10.2.3 Proving Linear and Exponential Growth Patterns
Chapter Closure
Section 11.1
11.1.1 Introduction to Constructions
11.1.2 Constructing Bisectors
11.1.3 More Explorations with Constructions
Section 11.2
11.2.1 Solving Work and Mixing Problems
11.2.2 Solving Equations and Systems Graphically
11.2.3 Using a Best-Fit Line to Make a Prediction
11.2.4 Treasure Hunt
11.2.5 Using Coordinate Geometry and Constructions to Explore Shapes
11.2.6 Modeling with Exponential Functions and Linear Inequalities
Chapter Closure
Section A.1
A.1.1 Exploring Variables and Expressions
A.1.2 Using Zero to Simplify Algebraic Expressions
A.1.3 Using Algebra Tiles to Compare Expressions
A.1.4 Justifying and Recording Work
A.1.5 Using Algebra Tiles to Solve for x
A.1.6 More Solving Equations
A.1.7 Checking Solutions
A.1.8 Determining the Number of Solutions
A.1.9 Using Equations to Solve Problems
Appendix Closure
Checkpoint 1: Solving Linear Equations, Part 1 (Integer Coefficients)
Checkpoint 2: Evaluating Expressions and the Order of Operations
Checkpoint 3: Operations with Rational Numbers
Checkpoint 4: Laws of Exponents and Scientific Notation
Checkpoint 5: Writing the Equation of a Line
Checkpoint 6A: Solving Linear Equations, Part 2 (Fractional Coefficients)
Checkpoint 6B: Multiplying Binomials and Solving Equations with Parentheses
Checkpoint 7: Interpreting Associations
Checkpoint 8A: Rewriting Equations with More Than One Variable
Checkpoint 8B: Solving Problems by Writing Equations
Checkpoint 9: Solving Linear Systems of Equations
Checkpoint 10: Determining Congruent Triangles
Checkpoint 11: The Exponential Web
Section 1.1
1.1.1 Attributes of Polygons
1.1.2 More Attributes of Polygons
Section 1.2
1.2.1 Making Predictions and Investigating Results
1.2.2 Perimeters and Areas of Enlarging Patterns
1.2.3 Area as a Product and a Sum
1.2.4 Describing a Graph
Section 1.3
1.3.1 Angle Pair Relationships
1.3.2 Angles Formed by Transversals
1.3.3 More Angles Formed by Transversals
1.3.4 Angles and Sides of a Triangle
Chapter Closure
Section 2.1
2.1.1 Triangle Congruence Theorems
2.1.2 Flowcharts for Congruence
2.1.3 Converses
2.1.4 Proof by Contradiction
Section 2.2
2.2.1 Dilations
2.2.2 Similarity
Section 2.3
2.3.1 Conditions for Triangle Similarity
2.3.2 Determining Similar Triangles
2.3.3 Applying Similarity
2.3.4 Similar Triangle Proofs
Chapter Closure
Section 3.1
3.1.1 Using an Area Model
3.1.2 Using a Tree Diagram
3.1.3 Probability Models
3.1.4 Unions, Intersections, and Complements
3.1.5 Expected Value
Section 3.2
3.2.1 Constant Ratios in Right Triangles
3.2.2 Connecting Slope Ratios to Specific Angles
3.2.3 Expanding the Trig Table
3.2.4 The Tangent Ratio
3.2.5 Applying the Tangent Ratio
Chapter Closure
Section 4.1
4.1.1 Introduction to Factoring Expressions
4.1.2 Factoring with Area Models
4.1.3 Factoring More Quadratics
4.1.4 Factoring Completely
4.1.5 Factoring Special Cases
Section 4.2
4.2.1 Sine and Cosine Ratios
4.2.2 Selecting a Trig Tool
4.2.3 Inverse Trigonometry
4.2.4 Trigonometric Applications
Chapter Closure
Section 5.1
5.1.1 Investigating the Graphs of Quadratic Functions
5.1.2 Multiple Representations of Quadratic Functions
5.1.3 Zero Product Property
5.1.4 Writing Equations for Quadratic Functions
5.1.5 Completing the Quadratic Web
Section 5.2
5.2.1 Perfect Square Equations
5.2.2 Completing the Square
5.2.3 More Completing the Square
5.2.4 Introduction to the Quadratic Formula
5.2.5 Solving and Applying Quadratic Equations
5.2.6 Introducing Complex Numbers
Chapter Closure
Section 6.1
6.1.1 Special Right Triangles
6.1.2 Pythagorean Triples
6.1.3 Special Right Triangles and Trigonometry
6.1.4 Radicals and Fractional Exponents
Section 6.2
6.2.1 At Your Service
6.2.2 Angles on a Pool Table
6.2.3 Shortest Distance Problems 345
6.2.4 The Number System and Deriving the Quadratic Formula
6.2.5 Using Algebra to Find a Maximum
6.2.6 Analyzing a Game
Chapter Closure
Section 7.1
7.1.1 Explore-Conjecture-Prove
7.1.2 Properties of Rhombi
7.1.3 Two Column Proofs
7.1.4 More Geometric Proofs
7.1.5 Using Similar Triangles to Prove Theorems
Section 7.2
7.2.1 Conditional Probability and Independence
7.2.2 More Conditional Probability
7.2.3 Applications of Probability
Chapter Closure
Section 8.1
8.1.1 Constructing Triangle Centers
Section 8.2
8.2.1 Angles of Polygons
8.2.2 Areas of Regular Polygons
Section 8.3
8.3.1 Area Ratios of Similar Figures
8.3.2 Ratios of Similarity
Section 8.4
8.4.1 A Special Ratio 458
8.4.2 Arcs and Sectors 463
8.4.3 Circles in Context 469
Chapter Closure
Section 9.1
9.1.1 Modeling Nonlinear Data
9.1.2 Parabola Investigation
9.1.3 Graphing Form of a Quadratic Function
9.1.4 Transforming the Absolute Value Function
Section 9.2
9.2.1 Quadratic Applications with Inequalities
9.2.2 Solving Systems of Equations
Section 9.3
9.3.1 Average Rate of Change and Projectile Motion
9.3.2 Comparing the Growth of Functions
9.3.3 Piecewise-Defined Functions
9.3.4 Combining Functions
Section 9.4
9.4.1 Inverse Functions
Chapter Closure
Section 10.1
10.1.1 The Equation of a Circle
10.1.2 Completing the Square for Equations of Circles
10.1.3 The Geometric Definition of a Parabola
Section 10.2
10.2.1 Introduction to Chords
10.2.2 Angles and Arcs
10.2.3 Chords and Angles
10.2.4 Tangents
10.2.5 Tangents and Arcs
Chapter Closure
Section 11.1
11.1.1 Prisms and Cylinders
11.1.2 Volumes of Similar Solids
11.1.3 Ratios of Similarity
Section 11.2
11.2.1 Volume of a Pyramid
11.2.2 Surface Area and Volume of a Cone
11.2.3 Surface Area and Volume of a Sphere
Chapter Closure
Section 12.1
12.1.1 The Fundamental Counting Principle
12.1.2 Permutations
12.1.3 Combinations
12.1.4 Categorizing Counting Problems
Section 12.2
12.2.1 Using Geometry to Calculate Probabilities
12.2.2 Choosing a Model
12.2.3 The Golden Ratio
12.2.4 Some Challenging Probability Problems
Chapter Closure
Checkpoint 1: Solving Problems with Linear and Exponential Relationships
Checkpoint 2: Calculating Areas and Perimeters of Complex Shapes
Checkpoint 3: Angle Relationships in Geometric Figures
Checkpoint 4: Solving Proportions and Similar Figures
Checkpoint 5: Calculating Probabilities
Checkpoint 7: Factoring Quadratic Expressions
Checkpoint 8: Applying Trigonometric Ratios and the Pythagorean Theorem
Checkpoint 9: The Quadratic Web
Checkpoint 10: Solving Quadratic Equations
Checkpoint 11: Angle Measures and Areas of Regular Polygons
Checkpoint 12: Circles, Arcs, Sectors, Chords, and Tangents
Section 1.1
1.1.1 Solving a Function Puzzle in Teams
1.1.2 Using a Graphing Calculator to Explore a Function
1.1.3 Function Investigation
1.1.4 Combining Linear Functions
Section 1.2
1.2.1 Representing Points of Intersection
1.2.2 Modeling a Geometric Relationship
1.2.3 Describing Data
Chapter Closure
Section 2.1
2.1.1 Transforming Quadratic Functions
2.1.2 Modeling with Parabolas
Section 2.2
2.2.1 Transforming Other Parent Graphs
2.2.2 Describing (h, k) for Each Family of Functions
2.2.3 Transformations of Functions
2.2.4 Transforming Non-Functions
2.2.5 Developing a Mathematical Model
Section 2.3
2.3.1 Completing the Square
Chapter Closure
Section 3.1
3.1.1 Strategies for Solving Equations
3.1.2 Solving Equations Graphically
3.1.3 Multiple Solutions to Systems of Equations
3.1.4 Using Systems of Equations to Solve Problems
Section 3.2
3.2.1 Solving Inequalities with One or Two Variables
3.2.2 Using Systems to Solve a Problem
3.2.3 Applications of Systems of Inequalities
3.2.4 Using Graphs to Determine Solutions
Chapter Closure
Section 4.1
4.1.1 Survey Design
4.1.2 Samples and the Role of Randomness
4.1.3 Bias in Convenience Samples
Section 4.2
4.2.1 Testing Cause and Effect with Experiments
4.2.2 Conclusions from Studies
Section 4.3
4.3.1 Relative Frequency Histograms
4.3.2 The Normal Probability Density Function
4.3.3 Percentiles
Section 4.4
4.4.1 Cross-Sections and Solids of a Revolution
4.4.2 Modeling with Geometric Solids
4.4.3 Designing to Meet Constraints
Chapter Closure
Section 5.1
5.1.1 “Undo” Equations
5.1.2 Using a Graph to Find an Inverse
5.1.3 More Inverse Functions
Section 5.2
5.2.1 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
Chapter Closure
Section 6.1
6.1.1 Simulations of Probability
6.1.2 More Simulations of Probability
6.1.3 Simulating Sampling Variability
Section 6.2
6.2.1 Statistical Test Using Sampling Variability
6.2.2 Variability in Experimental Results
6.2.3 Quality Control
6.2.4 Statistical Process Control
Section 6.3
6.3.1 Analyzing Decisions and Strategies
Chapter Closure
Section 7.1
7.1.1 Using Logarithms to Solve Exponential Equations
7.1.2 Investigating the Properties of Logarithms
7.1.3 Writing Equations of Exponential Functions
7.1.4 An Application of Logarithms
Section 7.2
7.2.1 Determining Missing Parts of Triangles
7.2.2 Law of Sines
7.2.3 Law of Cosines
7.2.4 The Ambiguous Case
7.2.5 Choosing a Tool
Chapter Closure
Section 8.1
8.1.1 Sketching Graphs of Polynomial Functions
8.1.2 More Graphs of Polynomial Functions
8.1.3 Stretch Factors for Polynomial Functions
Section 8.2
8.2.1 Writing Equations Using Complex Roots
8.2.2 More Real and Complex Roots
Section 8.3
8.3.1 Polynomial Division
8.3.2 Factors and Rational Zeros
8.3.3 An Application of Polynomials
8.3.4 Special Cases of Factoring417
Chapter Closure
Section 9.1
9.1.1 Introductions to Periodic Models
9.1.2 Graphing the Sine Functions
9.1.3 Unit Circle ↔ Graph
9.1.4 Graphing and Interpreting the Cosine Function
9.1.5 Defining a Radian
9.1.6 Building a Unit Circle
9.1.7 The Tangent Function
Section 9.2
9.2.1 Transformations of y = sin(x)
9.2.2 One More Parameter for a Periodic Function
9.2.3 Period of a Trigonometric Function
9.2.4 Graph ↔ Equation
Chapter Closure
Section 10.1
10.1.1 Introduction to Arithmetic Series 489
10.1.2 More Arithmetic Series 497
10.1.3 General Arithmetic Series 501
10.1.4 Summation Notation and Combinations of Series 506
10.1.5 Mathematical Induction 510
Section 10.2
10.2.1 Geometric Series 518
10.2.2 Infinite Series 528
Section 10.3
10.3.1 Using a Binomial Probability Model 535
10.3.2 Pascal’s Triangle and the Binomial Theorem 541
10.3.3 The Number e 549
Chapter Closure
Section 11.1
11.1.1 Simplifying Rational Expressions
11.1.2 Multiplying and Dividing Rational Expressions
11.1.3 Adding and Subtracting Rational Expressions
11.1.4 Operations with Rational Expressions
Section 11.2
11.2.1 Creating a Three-Dimensional Model
11.2.2 Graphing Equations in Three Dimensions
11.2.3 Solving Systems of Three Equations with Three Variables
11.2.4 Using Systems of Three Equations for Curve Fitting
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
Checkpoint 2: Solving Quadratic Equations
Checkpoint 3: Function Notation and Describing a Function
Checkpoint 4: Expressions with Integer and Rational Exponents
Checkpoint 5: Transformations of Functions
Checkpoint 6: Solving Complicated Equations and Systems 663
Checkpoint 7: Solving and Graphing Inequalities 667
Checkpoint 8: Determining the Equation for the Inverse of a Function 670
Checkpoint 9A: Solving Equations with Exponents 673
Checkpoint 9B: Rewriting Expressions and Solving Equations with Logarithms 675
Checkpoint 10: Solving Triangles 678
Checkpoint 11: Roots and Graphs of Polynomial Functions 682
Checkpoint 12: Periodic Functions
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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.
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