- Podcast
- News
- Interested?
Menu
Shop
Login
Core Connections,
Course 1
Chapter 1: Introduction and Representation
| Opening | 1.OP | Chapter Opening |
|---|---|---|
| Section 1.1 | 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 | |
| Section 1.2 | 1.2.1 | Multiple Representations |
| 1.2.2 | Representing Comparisons | |
| 1.2.3 | Characteristics of Numbers | |
| 1.2.4 | Products, Factors, and Factor Pairs | |
| Section 1.3 | 1.3.1 | Attributes and Characteristics of Shapes |
| 1.3.2 | More Characteristics of Shapes | |
| Closure | 1.CL | Chapter Closure |
Chapter 2: Arithmetic Strategies and Area
| Opening | 2.OP | Chapter Opening |
|---|---|---|
| Section 2.1 | 2.1.1 | Dot Plots and Bar Graphs |
| 2.1.2 | Histograms and Stem-and-Leaf Plots | |
| Section 2.2 | 2.2.1 | Exploring Area |
| 2.2.2 | Square Units and Area of Rectangles | |
| 2.2.3 | Area and Perimeter | |
| Section 2.3 | 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 | |
| Closure | 2.CL | Chapter Closure |
Chapter 3: Portions and Integers
| Opening | 3.OP | Chapter Opening |
|---|---|---|
| Section 3.1 | 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 | |
| Section 3.2 | 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 | |
| Closure | 3.CL | Chapter Closure |
Chapter 4: Variables and Ratios
| Opening | 4.OP | Chapter Opening |
|---|---|---|
| Section 4.1 | 4.1.1 | Introduction to Variables |
| 4.1.2 | Writing Equivalent Expressions | |
| 4.1.3 | Using Variables to Generalize | |
| Section 4.2 | 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 | |
| Closure | 4.CL | Chapter Closure |
Chapter 5: Multiplying Fractions and Area
| Opening | 5.OP | Chapter Opening |
|---|---|---|
| Section 5.1 | 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 | |
| Section 5.2 | 5.2.1 | Making Sense of Decimal Multiplication |
| 5.2.2 | Fraction Multiplication Number Sense | |
| Section 5.3 | 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 | |
| Closure | 5.CL | Chapter Closure |
| Section 5.4 | Mid-Course Reflection Activities |
Chapter 6: Dividing and Building Expressions
| Opening | 6.OP | Chapter Opening |
|---|---|---|
| Section 6.1 | 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 | |
| Section 6.2 | 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 | |
| Closure | 6.CL | Chapter Closure |
Chapter 7: Rates and Operations
| Opening | 7.OP | Chapter Opening |
|---|---|---|
| Section 7.1 | 7.1.1 | Comparing Rates |
| 7.1.2 | Comparing Rates with Tables and Graphs | |
| 7.1.3 | Unit Rates | |
| Section 7.2 | 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 | |
| Section 7.3 | 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 | |
| Closure | 7.CL | Chapter Closure |
Chapter 8: Statistics and Multiplication Equations
| Opening | 8.OP | Chapter Opening |
|---|---|---|
| Section 8.1 | 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 | |
| Section 8.2 | 8.2.1 | Statistical Questions |
| Section 8.3 | 8.3.1 | Writing Multiplication Equations |
| 8.3.2 | Distance, Rate, and Time | |
| 8.3.3 | Unit Conversion | |
| Closure | 8.CL | Chapter Closure |
Chapter 9: Volume and Percents
| Opening | 9.OP | Chapter Opening |
|---|---|---|
| Section 9.1 | 9.1.1 | Volume of a Rectangular Prism |
| 9.1.2 | Nets and Surface Area | |
| Section 9.2 | 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 | |
| Closure | 9.CL | Chapter Closure |
| Section 9.3 | 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
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
Resources
- Terms of Use
- Privacy Policy
- End User Terms of Use
- Cookie Policy
- Intellectual Property Permission Request
Contacts
- Jobs
- Regional Contacts
- Meet the PL Team
- Business Office
Support
Select Month 2019 to 2015
Select Month
Select Month
Cancel
OK
Did you want to leave cpmstg.wpengine.com?
Yes
I want to leave cpmstg.wpengine.com.
Cancel
No, I want to stay on cpmstg.wpengine.com
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..
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 theProfessional 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.
Edit Content
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.
InBuilding 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 ownmath identityand cultural background impact my classroom? The focus of day one is equitable classroom culture. Participants will reflect on how theirmath identityand 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 the5 Practicesfor Orchestrating Meaningful Mathematical Discussions and curatestrategiesfor 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.
InBuilding 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 ofmastery over timeas 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 developstrategiesto 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.
InBuilding 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, supportingproductive struggle, andfacilitating meaningful mathematical discourse. In doing so, participants learn to support students collaboratively engaged with rich tasks with all elements of the EffectiveMathematics Teaching Practicesincorporated through intentional and reflective planning.
