Table of Contents

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

###### Used throughout CPM middle and high school courses

###### Concrete, geometric representation of algebraic concepts.

###### Two-hour virtual session,

###### Learn how students build their conceptual understanding of simplifying algebraic expressions

###### Solving equations using these tools.

###### Determining perimeter,

###### Combining like terms,

###### Comparing expressions,

###### Solving equations

###### Use an area model to multiply polynomials,

###### Factor quadratics and other polynomials, and

###### Complete the square.

###### Support the transition from a concrete (manipulative) representation to an abstract model of mathematics..

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.

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The Building on Instructional Practice Series consists of three different events – Building on Discourse, Building on Assessment, Building on Equity – that are designed for teachers with a minimum of one year of experience teaching with CPM instructional materials and who have completed the Foundations for Implementation Series.

In **Building on Equity**, participants will learn how to include equitable practices in their classroom and support traditionally underserved students in becoming leaders of their own learning. Essential questions include: How do I shift dependent learners into independent learners? How does my own math identity and cultural background impact my classroom? The focus of day one is equitable classroom culture. Participants will reflect on how their math identity and mindsets impact student learning. They will begin working on a plan for Chapter 1 that creates an equitable classroom culture. The focus of day two and three is implementing equitable tasks. Participants will develop their use of the 5 Practices for Orchestrating Meaningful Mathematical Discussions and curate strategies for supporting all students in becoming leaders of their own learning. Participants will use an equity lens to reflect on and revise their Chapter 1 lesson plans.

In **Building on Assessment**, participants will apply assessment research and develop methods to provide feedback to students and inform equitable assessment decisions. On day one, participants will align assessment practices with learning progressions and the principle of mastery over time as well as write assessment items. During day two, participants will develop rubrics, explore alternate types of assessment, and plan for implementation that supports student ownership. On the third day, participants will develop strategies to monitor progress and provide evidence of proficiency with identified mathematics content and practices. Participants will develop assessment action plans that will encourage continued collaboration within their learning community.

In** Building on Discourse**, participants will improve their ability to facilitate meaningful mathematical discourse. This learning experience will encourage participants to adjust their instructional practices in the areas of sharing math authority, developing independent learners, and the creation of equitable classroom environments. Participants will plan for student learning by using teaching practices such as posing purposeful questioning, supporting productive struggle, and facilitating meaningful mathematical discourse. In doing so, participants learn to support students collaboratively engaged with rich tasks with all elements of the Effective Mathematics Teaching Practices incorporated through intentional and reflective planning.

Correlations

Correlations