### Chapter 1: Introduction and Representation

Opening Section 1.1 1.OP Chapter Opening 1.1.1 Visualizing Information 1.1.2 Perimeter and Area Relationships 1.1.3 Describing and Extending Patterns 1.1.4 Representing Data 1.1.5 Making Sense of a Logic Problem 1.2.1 Multiple Representations 1.2.2 Representing Comparisons 1.2.3 Characteristics of Numbers 1.2.4 Products, Factors, and Factor Pairs 1.3.1 Attributes and Characteristics of Shapes 1.3.2 More Characteristics of Shapes 1.CL Chapter Closure

### Chapter 2: Arithmetic Strategies and Area

Opening Section 2.1 2.OP Chapter Opening 2.1.1 Dot Plots and Bar Graphs 2.1.2 Histograms and Stem-and-Leaf Plots 2.2.1 Exploring Area 2.2.2 Square Units and Area of Rectangles 2.2.3 Area and Perimeter 2.3.1 Using Rectangles to Multiply 2.3.2 Using Generic Rectangles 2.3.3 Distributive Property 2.3.4 Generic Rectangles and the Greatest Common Factor 2.CL Chapter Closure

### Chapter 3: Portions and Integers

Opening Section 3.1 3.OP Chapter Opening 3.1.1 Using the Multiplicative Identity 3.1.2 Portions as Percents 3.1.3 Connecting Percents with Decimals and Fractions 3.1.4 Multiple Representations of a Portion 3.1.5 Completing the Web 3.1.6 Investigating Ratios 3.2.1 Addition, Subtraction, and Opposites 3.2.2 Locating Negative Numbers 3.2.3 Absolute Value 3.2.4 Length on a Coordinate Graph 3.CL Chapter Closure

### Chapter 4: Variables and Ratios

Opening Section 4.1 4.OP Chapter Opening 4.1.1 Introduction to Variables 4.1.2 Writing Equivalent Expressions 4.1.3 Using Variables to Generalize 4.2.1 Enlarging Two-Dimensional Shapes 4.2.2 Enlarging and Reducing Figures 4.2.3 Enlargement and Reduction Ratios 4.2.4 Ratios in Other Situations 4.CL Chapter Closure

### Chapter 5: Multiplying Fractions and Area

Opening Section 5.1 5.OP Chapter Opening 5.1.1 Representing Fraction Multiplication 5.1.2 Describing Parts of Parts 5.1.3 Calculating Parts of Parts 5.1.4 Multiplying Mixed Numbers 5.2.1 Making Sense of Decimal Multiplication 5.2.2 Fraction Multiplication Number Sense 5.3.1 Rearranging Areas 5.3.2 Area of a Parallelogram 5.3.3 Area of a Triangle 5.3.4 Area of a Trapezoid 5.CL Chapter Closure Mid-Course Reflection Activities

### Chapter 6: Dividing and Building Expressions

Opening Section 6.1 6.OP Chapter Opening 6.1.1 Dividing 6.1.2 Fractions as Division Problems 6.1.3 Problem Solving with Division 6.1.4 Solving Problems Involving Fraction Division 6.2.1 Order of Operations 6.2.2 Area of a Rectangular Shape 6.2.3 Naming Perimeters of Algebra Tiles 6.2.4 Combining Like Terms 6.2.5 Evaluating Algebraic Expressions 6.CL Chapter Closure

### Chapter 7: Rates and Operations

Opening Section 7.1 7.OP Chapter Opening 7.1.1 Comparing Rates 7.1.2 Comparing Rates with Tables and Graphs 7.1.3 Unit Rates 7.2.1 Analyzing Strategies for Dividing Fractions 7.2.2 Another Strategy for Division 7.2.3 Division with Fractions and Decimals 7.2.4 Fraction Division as Ratios 7.3.1 Inverse Operations 7.3.2 Distributive Property 7.3.3 Distributive Property and Expressions Vocabulary 7.3.4 Writing Algebraic Equations and Inequalities 7.CL Chapter Closure

### Chapter 8: Statistics and Multiplication Equations

Opening Section 8.1 8.OP Chapter Opening 8.1.1 Measures of Central Tendency 8.1.2 Choosing Mean or Median 8.1.3 Shape and Spread 8.1.4 Box Plots and Interquartile Range 8.1.5 Comparing and Choosing Representations 8.2.1 Statistical Questions 8.3.1 Writing Multiplication Equations 8.3.2 Distance, Rate, and Time 8.3.3 Unit Conversion 8.CL Chapter Closure

### Chapter 9: Volume and Percents

Opening Section 9.1 9.OP Chapter Opening 9.1.1 Volume of a Rectangular Prism 9.1.2 Nets and Surface Area 9.2.1 Multiplicative Growth and Percents 9.2.2 Composition and Decomposition of Percents 9.2.3 Percent Discounts 9.2.4 Simple Interest and Tips 9.CL Chapter Closure 9.3.1 A Culminating Portions Challenge 9.3.2 Representing and Predicting Patterns 9.3.3 Analyzing Data to Identify a Trend

### Checkpoint Materials

CP 1: Using Place Value to Round and Compare Decimals

CP 2: Addition and Subtraction of Decimals

CP 3: Addition and Subtraction of Fractions

CP 4: Addition and Subtraction of Mixed Numbers

CP 5: Multiple Representations of Portions

P 6: Locating Points on a Number Line and on a Coordinate Graph

CP 7A: Multiplication of Fractions and Decimals

CP 7B: Area and Perimeter of Quadrilaterals and Triangles

CP 8A: Rewriting and Evaluating Variable Expressions

CP 8B: Division of Fractions and Decimals

CP 9A: Displays of Data: Histograms and Box Plots

CP 9B: Solving One-Step Equations

### Chapter 1: Introduction and Probability

Section 1.1

1.1.1 Finding Shared and Unique Characteristics

1.1.2 Analyzing a Game

1.1.3 Finding Unknowns

1.1.4 Investigating a Proportional Relationship

1.1.5 Investigating Number Patterns

Section 1.2

1.2.1 Introduction to Probability

1.2.2 Investigating Probability

1.2.3 Modifying the Sample Space

1.2.4 Expressing Fractions as Percents

1.2.5 Rewriting Fractions

1.2.7 Compound Probability

1.2.8 Subtracting Probabilities

Chapter Closure

### Chapter 2: Fractions and Integer Addition

Section 2.1

2.1.1 Fraction-to-Decimal Conversions

2.1.2 Rewriting Decimals as Fractions

Section 2.2

2.2.1 Composing Integers

2.2.2 Adding Integers and Rational Numbers

2.2.3 More Addition of Integers and Rational Numbers

2.2.5 Multiplication of Portions

2.2.6 Multiplying Mixed Numbers

Section 2.3

2.3.1 Choosing a Scale and Graphing Data

2.3.2 More Graph Scaling

Chapter Closure

### Chapter 3:Arithmetic Properties

Section 3.1

3.1.1 Grouping Expressions

3.1.2 Identifying Terms in Expressions

Section 3.2

3.2.1 Subtraction of Integers

3.2.3 Multiplication as Repeated Subtraction

3.2.4 Multiplication of Decimals

3.2.5 Addition, Subtraction, Multiplication, and Division of Integers

Section 3.3

3.3.1 Division with Rational Numbers

3.3.2 Division with Decimals

3.3.3 Arithmetic Properties

Chapter Closure

### Chapter 4: Proportions and Expressions

Section 4.1

4.1.1 Similar Figures

4.1.2 Scale Drawings

Section 4.2

4.2.1 Recognizing Proportional Relationships

4.2.2 Proportional Relationships with Tables and Graphs

4.2.3 Unit Rate and Proportional Equations

4.2.4 Connecting Representations of Proportional Relationships

Section 4.3

4.3.1 Combining Like Terms

4.3.2 Distributive Property

4.3.3 Simplifying with Zero

Chapter Closure

### Chapter 5: Probability and Solving Word Problems

Section 5.1

5.1.1 Part-Whole Relationships

5.1.2 Finding and Using Percentages

Section 5.2

5.2.1 Probability Games

5.2.2 Computer Simulations of Probability

5.2.3 Compound Independent Events

5.2.4 Probability Tables

5.2.5 Probability Trees

5.2.6 Compound Events

Section 5.3

5.3.1 Describing Relationships Between Quantities

5.3.2 Solving a Word Problem

5.3.3 Strategies for Using the 5-D Process

5.3.4 Using Variables to Represent Quantities in Word Problems

5.3.5 More Word Problem Solving

Chapter Closure

Section 5.4

5.4 Mid-Course Reflection Activities

### Chapter 6: Solving Inequalities and Equations

Section 6.1

6.1.1 Comparing Expressions

6.1.2 Comparing Quantities with Variables

6.1.3 One Variable Inequalities

6.1.4 Solving One Variable Inequalities

Section 6.2

6.2.1 Solving Equations

6.2.2 Checking Solutions and the Distributive Property

6.2.3 Solving Equations and Recording Work

6.2.4 Using a Table to Write Equations from Word Problems

6.2.5 Writing and Solving Equations

6.2.6 Cases with Infinite or No Solutions

6.2.7 Choosing a Solving Strategy

Chapter Closure

### Chapter 7: Proportions and Percents

Section 7.1

7.1.1 Distance, Rate, and Time

7.1.2 Scaling Quantities

7.1.3 Solving Problems Involving Percents

7.1.4 Equations with Fraction and Decimal Coefficients

7.1.5 Creating Integer Coefficients

7.1.6 Creating Integer Coefficients Efficiently

7.1.7 Percent Increase and Decrease

7.1.8 Simple Interest

Section 7.2

7.2.1 Finding Missing Information in Proportional Relationships

7.2.2 Solving Proportions

Chapter Closure

### Chapter 8: Statistics and Angle Relationships

Section 8.1

8.1.1 Measurement Precision

8.1.2 Comparing Distributions

Section 8.2

8.2.1 Representative Samples

8.2.2 Inference from Random Samples

Section 8.3

8.3.1 Introduction to Angles

8.3.2 Classifying Angles

8.3.3 Constructing Shapes

8.3.4 Building Triangles

Chapter Closure

### Chapter 9: Circles and Volume

Section 9.1

9.1.1 Circumference, Diameter, and Pi

9.1.2 Area of Circles

9.1.3 Area of Composite Shapes

Section 9.2

9.2.1 Surface Area and Volume

9.2.2 Cross Sections

9.2.3 Volume of a Prism

9.2.4 Volume of Non-Rectangular Prisms

Chapter Closure

Section 9.3

9.3.1 Volume and Scaling

9.3.2 Using Multiple Math Ideas to Create an Interior Design

9.3.3 Applying Ratios

### Checkpoint Materials

Checkpoint 1: Area and Perimeter of Polygons

Checkpoint 2: Multiple Representations of Portions

Checkpoint 3: Multiplying Fractions and Decimals

Checkpoint 5: Order of Operations

Checkpoint 6: Writing and Evaluating Algebraic Expressions

Checkpoint 7A: Simplifying Expressions

Checkpoint 7B: Displays of Data: Histograms and Box Plots

Checkpoint 8: Solving Multi-Step Equations

Checkpoint 9: Unit Rates and Proportions

### Chapter 1: Problem Solving

Section 1.1

1.1.1 Interpreting Graphs

1.1.2 Finding and Generalizing Patterns

1.1.3 The Algebra Walk

1.1.4 Collecting, Organizing, and Analyzing Data

Section 1.2

1.2.1 Proportional Relationships with Graphs and Tables

1.2.2 Strategies for Solving Proportional Relationships

Chapter Closure

### Chapter 2: Simplifying with Variables

Section 2.1

2.1.1 Exploring Variables and Expressions

2.1.2 Simplifying Expressions by Combining Like Terms

2.1.3 Writing Algebraic Expressions

2.1.4 Using Zero to Simplify Algebraic Expressions

2.1.5 Using Algebra Tiles to Simplify Algebraic Expressions

2.1.6 Using Algebra Tiles to Compare Expressions

2.1.7 Simplifying and Recording Work

2.1.8 Using Algebra Tiles to Solve for x

2.1.9 More Solving Equations

Chapter Closure

### Chapter 3: Graphs and Equations

Section 3.1

3.1.1 Extending Patterns and Finding Rules

3.1.2 Using Tables, Graphs, and Rules to Make Predictions

3.1.3 Using a Graphing Calculator and Identifying Solutions

3.1.4 Completing Tables and Drawing Graphs

3.1.5 Graphs, Tables, and Rules

3.1.6 Complete Graphs

3.1.7 Identifying Common Graphing Errors

Section 3.2

3.2.1 Solving Equations and Checking Solutions

3.2.2 Determining the Number of Solutions

3.2.3 Solving Equations to Solve Problems

3.2.4 More Solving Equations to Solve Problems

3.2.5 Distributive Property Equations

Chapter Closure

### Chapter 4: Multiple Representations

Section 4.1

4.1.1 Finding Connections Between Representations

4.1.2 Seeing Growth in Different Representations

4.1.3 Connecting Linear Rules and Graphs

4.1.4 y = mx + b

4.1.5 Checking the Connections

4.1.6 Graphing a Line Without an x y Table

4.1.7 Completing the Web

Chapter Closure

### Chapter 5: Systems of Equations

Section 5.1

5.1.1 Working with Multi-Variable Equations

5.1.2 Solving Equations with Fractions

Section 5.2

5.2.1 Introduction to Systems of Equations

5.2.2 Writing Rules from Word Problems

5.2.3 Solving Systems Algebraically

5.2.4 Strategies for Solving Systems

Chapter Closure 2

5.3 Mid-Course Reflection Activities

### Chapter 6: Transformations and Similarity

Section 6.1

6.1.1 Rigid Transformations

6.1.2 Rigid Transformations on a Coordinate Graph

6.1.3 Describing Transformations

6.1.4 Using Rigid Transformations

Section 6.2

6.2.1 Multiplication and Dilation

6.2.2 Dilations and Similar Figures

6.2.3 Identifying Similar Shapes

6.2.4 Similar Figures and Transformations

6.2.5 Working With Corresponding Sides

6.2.6 Solving Problems Involving Similar Shapes

Chapter Closure

### Chapter 7: Slope and Association

Section 7.1

7.1.1 Circle Graphs

7.1.2 Organizing Data in a Scatterplot

7.1.3 Identifying and Describing Association

Section 7.2

7.2.1 y = mx + b Revisited

7.2.2 Slope

7.2.3 Slope in Different Representations

7.2.5 Proportional Equations

Section 7.3

7.3.1 Using Equations to Make Predictions

7.3.2 Describing Association Fully

7.3.3 Association Between Categorical Variables

Chapter Closure

### Chapter 8: Exponents and Functions

Section 8.1

8.1.1 Patterns of Growth in Tables and Graphs

8.1.2 Compound Interest

8.1.3 Linear and Exponential Growth

Section 8.2

8.2.1 Exponents and Scientific Notation

8.2.2 Exponent Rules

8.2.3 Negative Exponents

8.2.4 Operations with Scientific Notation

Section 8.3

8.3.1 Functions in Graphs and Tables

Chapter Closure

### Chapter 9: Angles and the Pythagorean Theorem

Section 9.1

9.1.1 Parallel Line Angle Pair Relationships

9.1.2 Finding Unknown Angles in Triangles

9.1.3 Exterior Angles in Triangles

9.1.4 AA Triangle Similarity

Section 9.2

9.2.1 Side Lengths and Triangles

9.2.2 Pythagorean Theorem

9.2.3 Understanding Square Root

9.2.4 Real Numbers

9.2.5 Applications of the Pythagorean Theorem

9.2.6 Pythagorean Theorem in Three Dimensions

9.2.7 Pythagorean Theorem Proofs

Chapter Closure

### Chapter 10: Surface Area and Volume

Section 10.1

10.1.1 Cube Roots

10.1.2 Surface Area and Volume of a Cylinder

10.1.3 Volumes of Cones and Pyramids

10.1.4 Volume of a Sphere

10.1.5 Applications of Volume

Chapter Closure

10.2.1 Indirect Measurement

10.2.2 Finding Unknowns

10.2.3 Analyzing Data to Identify a Trend

### Checkpoint Materials

1. Operations with Signed Fractions and Decimals

2. Evaluating Expressions and Using Order of Operations

3. Unit Rates and Proportions

4. Area and Perimeter of Circles and Composite Figures

5. Solving Equations

6. Multiple Representations of Linear Equations

7. Solving Equations with Fractions and Decimals  (Fraction Busters)

8. Transformations

9. Scatterplots and Association

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# Foundations for Implementation

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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# Building on Instructional Practice Series

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.

# Building on Equity

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.

# Building on Assessment

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.

# Building on Discourse

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.