Core Connections, Course 1, 2 and 3
Table of Contents

Core Connections,
Course 1

Chapter 1: Introduction and Representation

Opening1.OPChapter Opening
Section Information
1.1.2Perimeter and Area Relationships
1.1.3Describing and Extending Patterns
1.1.4Representing Data
1.1.5Making Sense of a Logic Problem
Section Representations
1.2.2Representing Comparisons
1.2.3Characteristics of Numbers
1.2.4Products, Factors, and Factor Pairs
Section and Characteristics of Shapes
1.3.2More Characteristics of Shapes
Closure1.CLChapter Closure

Chapter 2: Arithmetic Strategies and Area

Opening2.OPChapter Opening
Section Plots and Bar Graphs
2.1.2Histograms and Stem-and-Leaf Plots
Section Area
2.2.2Square Units and Area of Rectangles
2.2.3Area and Perimeter
Section Rectangles to Multiply
2.3.2Using Generic Rectangles
2.3.3Distributive Property
2.3.4Generic Rectangles and the Greatest Common Factor
Closure2.CLChapter Closure

Chapter 3: Portions and Integers

Opening3.OPChapter Opening
Section the Multiplicative Identity
3.1.2Portions as Percents
3.1.3Connecting Percents with Decimals and Fractions
3.1.4Multiple Representations of a Portion
3.1.5Completing the Web
3.1.6Investigating Ratios
Section, Subtraction, and Opposites
3.2.2Locating Negative Numbers
3.2.3Absolute Value
3.2.4Length on a Coordinate Graph
Closure3.CLChapter Closure

Chapter 4: Variables and Ratios

Opening4.OPChapter Opening
Section to Variables
4.1.2Writing Equivalent Expressions
4.1.3Using Variables to Generalize
Section Two-Dimensional Shapes
4.2.2Enlarging and Reducing Figures
4.2.3Enlargement and Reduction Ratios
4.2.4Ratios in Other Situations
Closure4.CLChapter Closure

Chapter 5: Multiplying Fractions and Area

Opening5.OPChapter Opening
Section Fraction Multiplication
5.1.2Describing Parts of Parts
5.1.3Calculating Parts of Parts
5.1.4Multiplying Mixed Numbers
Section Sense of Decimal Multiplication
5.2.2Fraction Multiplication Number Sense
Section Areas
5.3.2Area of a Parallelogram
5.3.3Area of a Triangle
5.3.4Area of a Trapezoid
Closure5.CLChapter Closure
Section 5.4 Mid-Course Reflection Activities

Chapter 6: Dividing and Building Expressions

Opening6.OPChapter Opening
6.1.2Fractions as Division Problems
6.1.3Problem Solving with Division
6.1.4Solving Problems Involving Fraction Division
Section of Operations
6.2.2Area of a Rectangular Shape
6.2.3Naming Perimeters of Algebra Tiles
6.2.4Combining Like Terms
6.2.5Evaluating Algebraic Expressions
Closure6.CLChapter Closure

Chapter 7: Rates and Operations

Opening7.OPChapter Opening
Section Rates
7.1.2Comparing Rates with Tables and Graphs
7.1.3Unit Rates
Section Strategies for Dividing Fractions
7.2.2Another Strategy for Division
7.2.3Division with Fractions and Decimals
7.2.4Fraction Division as Ratios
Section Operations
7.3.2Distributive Property
7.3.3Distributive Property and Expressions Vocabulary
7.3.4Writing Algebraic Equations and Inequalities
Closure7.CLChapter Closure

Chapter 8: Statistics and Multiplication Equations

Opening8.OPChapter Opening
Section of Central Tendency
8.1.2Choosing Mean or Median
8.1.3Shape and Spread
8.1.4Box Plots and Interquartile Range
8.1.5Comparing and Choosing Representations
Section Questions
Section Multiplication Equations
8.3.2Distance, Rate, and Time
8.3.3Unit Conversion
Closure8.CLChapter Closure

Chapter 9: Volume and Percents

Opening9.OPChapter Opening
Section of a Rectangular Prism
9.1.2Nets and Surface Area
Section Growth and Percents
9.2.2Composition and Decomposition of Percents
9.2.3Percent Discounts
9.2.4Simple Interest and Tips
Closure9.CLChapter Closure
Section Culminating Portions Challenge
9.3.2Representing and Predicting Patterns
9.3.3Analyzing 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


Core Connections,
Course 2

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 

1.2.6 Fraction Addition 

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 

2.2.4 Multiplication as Repeated Addition 

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 

3.2.2 Connecting Addition and Subtraction 

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

Core Connections,
Course 3

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 

7.2.4 More About Slope 

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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Algebra Tiles Blue Icon

Algebra Tiles Session

  • 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..

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.