These high-quality middle school math programs prepare 6th, 7th, and 8th grade students with powerful mathematical thinking and problem-solving skills.
Includes two unique middle school programs and a support class:
• Meaningful Mathematics
• Multimodal program utilizing both digital & print materials
• Dynamic teacher-guided pacing technology
• Intentional mix of digital, print, and manipulatives
• Consumable student book called the Mathematician’s Notebook
• CPM’s time-tested program
• Based on research & CPM’s Three Pillars
• Option of digital and/or print materials
• English and Spanish
What does a full blend of print and digital look like? In this multimodal series, digital and print materials work in tandem to maximize student engagement. The choice of medium for each aspect of a lesson is based on how and where students learn best.
Students have a personal notebook to record the messy work of learning. Here, they highlight key concepts, questions, rough draft thinking, mistakes, corrections, and their inspirations. The Mathematician’s Notebook provides diagrams and graphs for students to work with, and plenty of space so that students have room for error and experimentation.
Concise goals for each lesson are presented to the teacher and to students in the chapter introductions, referenced in the Reflection & Practice problems, and revisited in Chapter Closures. The Mathematician’s Notebook contains a printed copy of the Learning Targets where students can keep track of their progress throughout the course.
Problems are designed to facilitate student learning per the learning intent. To maximize student sensemaking and engagement, lessons have been intentionally constructed using a variety of venues for student work.
Inspiring Connections guides teachers through lessons.
The authors describe how they envision the lesson progressing. These notes are summarized into brief descriptions, which can serve as a reminder after reading the full Authors’ Vision.
The Lesson at a Glance provides a quick orientation to the lesson. It lists things to consider as you prepare to teach the lesson: the overview, learning intent, materials needed, aligning standards, and additional resources.
Lessons are designed for students to work in teams during a 45-minute period.
Students collaborate in teams for the large majority of class time. As a means to help all students have a voice and be an integral part of their team, four roles are presented in the Prelude and referred to throughout the curriculum. The roles are Representative, Coordinator, Organizer, and Investigator.
A variety of Study Team and Teaching Strategies (STTS) are suggested in the Authors’ Vision throughout Inspiring Connections. These strategies may be used to help structure team interactions and facilitate engagement. As you gain experience with the curriculum and get to know your students, you will likely develop your own favorite strategies to use regularly.
Prelude
Chapter 1
1.1 Numbers and Data≈
1.2 Shapes and Area
1.3 Expressions
Chapter 2
2.1 Ratio Language
2.2 Equivalent Ratios
2.3 Measurement
Chapter 3
3.1 Measures of Center
3.2 Integers
3.3 Absolute Value
3.4 Coordinate Plane
Chapter 4
4.1 Fractions, Decimals, and Percents
4.2 Percents
4.3 Unit Rates in Tables and Graphs
Chapter 5
5.1 Variation in Data
5.2 Area
Chapter 6
6.1 Rules of Operations
6.2 Multiples and Factors
Chapter 7
7.1 Whole Number and Decimal Division
7.2 Fraction Division
Chapter 8
8.1. Algebra Tiles
8.2 Expressions
8.3 Equations and Inequalities
Chapter 9
9.1 Equations and Inequalities Continued
9.2 Rate Problems
Chapter 10
10.1 Two Dimensions
10.2 Three Dimensions
Chapter 11
11.1 Ratios and Proportions
11.2 The Number System
11.3 Expressions and Equations
Prelude
Chapter 1
1.1 Numbers and Data≈
1.2 Shapes and Area
1.3 Expressions
Chapter 2
2.1 Ratio Language
2.2 Equivalent Ratios
2.3 Measurement
Chapter 3
3.1 Measures of Center
3.2 Integers
3.3 Absolute Value
3.4 Coordinate Plane
Chapter 4
4.1 Fractions, Decimals, and Percents
4.2 Percents
4.3 Unit Rates in Tables and Graphs
Chapter 5
5.1 Variation in Data
5.2 Area
Chapter 6
6.1 Rules of Operations
6.2 Multiples and Factors
Chapter 7
7.1 Whole Number and Decimal Division
7.2 Fraction Division
Chapter 8
8.1. Algebra Tiles
8.2 Expressions
8.3 Equations and Inequalities
Chapter 9
9.1 Equations and Inequalities Continued
9.2 Rate Problems
Chapter 10
10.1 Two Dimensions
10.2 Three Dimensions
Chapter 11
11.1 Ratios and Proportions
11.2 The Number System
11.3 Expressions and Equations
Prelude
Chapter 1
1.1 Proportions and Proportional Relationships
1.2 Integer Operations
1.3 Proportions and Graphs
Chapter 2
2.1 Fraction and Decimal Conversions
2.2 Probability
2.3 Scale Drawings
2.4 Cross Sections
Chapter 3
3.1 Proportional Relationships
3.2 Data and Statistics: Using Samples to Make Predictions
Chapter 4
4.1 Multiple Representations of Proportional Relationships
4.2 Circumference and Area of a Circle
Chapter 5
5.1 Probability
5.2 Integer Operations Continuted
Chapter 6
6.1 Data Distributions
6.2 Numerical and Algebraic Expressions
6.3 Equivalent Expressions
Chapter 7
7.1 Operations With Rational Numbers
7.2 Percent Change
7.3 Percents in the Real World
Chapter 8
8.1 Multiplication and Division of Rational Numbers
8.2 Working With Expressions
8.3 Writing and Solving Equations and Inequalities
Chapter 9
9.1 Angle Relationships
9.2 Triangle Creation
9.3 Volume and Surface Area
Chapter 10
10.1: Explorations and Investigations
10.2: Restaurant Math
Prelude
Chapter 1
1.1 Data and Graphs
1.2 Introduction to Transformations
1.3 Linear Relationships
Chapter 2
2.1 Rigid Transformations
2.2 Similarity
2.3 Graphing Systems of Equations
Chapter 3
3.1 Trend Lines
3.2 Solving Equations with Algebra Tiles
3.3 Graphing Linear Equations
Chapter 4
4.1 Exponents, Part 1
4.2 Solving Equations
4.3 Exponents, Part 2
Chapter 5
5.1 Representations of a Line
5.2 Graphs & Equations of Systems
Chapter 6
6.1 Solving Systems Algebraically
6.2 Slope & Rate of Change
6.3 Associations
Chapter 7
7.1 Angles
7.2 Right Triangle Theorem
Chapter 8
8.1 Introduction to Functions
‘8.2 Characteristics of Functions
8.3 Linear and Nonlinear Functions
Chapter 9
9.1 Volume
9.2 Scientific Notation
9.3 Applications of Volume
Chapter 10
10.1 Explorations and Investigations
The team also provides a safe space for students to take risks.
CPM provides materials specifically designed to help families support students outside the classroom.
The Parent Guide iIncludes:
Teachers will have access to a series of Mathcasts to aid them in preparing lessons. Each Mathcast will outline the problems for that lesson and offer suggestions for facilitating teams.
Chapter 1: Introduction and Representation
Chapter 2: ArithmeticStrategies and Area
Chapter 3 Portions and Integers
Section 3.1
Section 3.2
Chapter 4 Variables and Ratios
Chapter 5 Multiplying Fractions and Area
Chapter 6 Dividing and Building Expressions
Chapter 7 Rates and Operations
Chapter 8 Statistics and Multiplication Equations
Chapter 9 Volume and Percents
Chapter 1: Introduction and Representation
Section 1.1 – Math in the World
Section 1.2 – Number Representation
Chapter 2: ArithmeticStrategies and Area
Section 2.1- Data Summaries
Section 2.2 – Area and Perimeter
Section 2.3 – Number Representations
Chapter 3 Portions and Integers
Section 3.1 – Percents and Decimals
Section 3.2 – Numbers and Graphing
Chapter 4 Variables and Ratios
Section 4.1 – Variable Expressions
Section 4.2 – Ratios
Chapter 5 Multiplying Fractions and Area
Section 5.1 – Fraction Operations
Section 5.2 – Rational Number Operations
Section 5.3 – Area
Chapter 6 Dividing and Building Expressions
Section 6.1 – Rational Number Division
Section 6.2 – Building Expressions
Chapter 7 Rates and Operations
Section 7.1 – Comparing Rates
Section 7.2 – Rational Number Division
Section 7.3 – Equations and Inequalities
Chapter 8 Statistics and Multiplication Equations
Section 8.1 – One Variable Statistics
Section 8.2 – Equations with Unit Conversions
Chapter 9 Volume and Percents
Section 9.1 – Exponents
Section 9.2 – Volume and Surface Area
Section 9.3 – Percents
Chapter 1: Introduction and Probability
Section 1.1 – Exploring Number Patterns
Section 1.2 – Probability
Chapter 2: Fractions and Integer Addition
Section 2.1 – Rational Number Conversions
Section 2.2 – Rational Number Multiplication
Section 2.3 – Scale
Chapter 3: Arithmetic Properties
Section 3.1 – Expressions
Section 3.2 – Arithmetic Operations
Section 3.3 – Rational Number Division
Chapter 4: Proportions and Expressions
Section 4.1 – Scaling
Section 4.2 – Proportional Relationships
Section 4.3 – Expression Properties
Chapter 5: Probability and Solving Word Problems
Section 5.1 – Proportions
Section 5.2 – Probability Modeling
Section 5.3 – Solving Word Problems
Section 5.4 – Mid-Course Reflection
Chapter 6: Solving Inequalities and Equations
Section 6.1 – Inequalities
Section 6.2 – Solving Equations
Section 6.3 – Solving Strategies
Chapter 7: Proportions and Percents
Section 7.1 – Applying Proportions
Section 7.2 – Solving Proportions
Chapter 8: Statistics and Angle Relationships
Section 8.1 – Statistical Distributions
Section 8.2 – Sampling
Section 8.3 – Angle Relationships
Chapter 9: Circles and Volume
Section 9.1 – Circles
Section 9.2 – Volume
Section 9.3 – Course Reflection
Chapter 1: Problem Solving
Section 1.1 – Problem Solving
Section 1.2 – Proportional Relationships
Chapter 2: Simplifying with Variables
Section 2.1- Variables and Expressions
Chapter 3: Graphs and Equations
Section 3.1 – Graphs
Section 3.2 – Equations
Chapter 4: Multiple Representations
Section 4.1 – Growth Representation
Chapter 5: Systems of Equations
Section 5.1 – Multi-Variable Equations
Section 5.2 – Systems of Equations
Section 5.3 – Mid-Course Reflection
Chapter 6: Transformations and Similarity
Section 6.1 – Transformations
Section 6.2 – Similarity
Chapter 7: Slope and Association
Section 7.1 – Scatter Plot
Section 7.2 – Slope
Section 7.3 – Making Predictions
Chapter 8: Exponents and Functions
Section 8.1 – Growth
Section 8.2 – Exponential Expressions
Section 8.3 – Functions
Chapter 9: Angles and the Pythagorean Theorem
Section 9.1 – Angle Relationships
Section 9.2 – Right Triangles
Chapter 10: Surface Area and Volume
Section 10.1 – Three-Dimensional Measurements
Section 10.2 – Course Reflection
Inspirations & Ideas is a compilation of lessons, arranged appropriately in units, that convey multiple objectives. Although each unit may not fully address a single objective, as a compilation, the objectives are met. The course does not attempt to address every content standard in the 8th grade curriculum. Rather, the math content in the course is used as a vehicle to change students’ beliefs and attitudes about math. Inspirations & Ideas focuses on the following themes:
© 1989-2025 CPM EDUCATIONAL PROGRAM All rights reserved. CPM Educational Program is a 501(c)(3) educational nonprofit corporation.
LEARNING LOG
Write a Learning Log entry to summarize what you learned today about the Giant One and its uses. Include examples of how the Giant One is used. Title this entry “The Giant One and Equivalent Fractions” and label it with today’s date.
LEARNING LOG
Make a rectangle from any number of tiles. Your rectangle must contain at least one of each of the following tiles: x^2, y^2 , x, y and xy. Sketch your rectangle in your Learning Log and write its area as a product and as a sum. Explain how you know that the product and sum are equivalent. Title this entry “Area as a Product and as a Sum” and label it with today’s date.
PI-10. WAY TO GO!
The map at right shows the streets in Old Town. Assume Jacqueline is standing at the corner of A and 1st Streets. Assume Jacqueline will only walk South or East. The shaded rectangles represent large buildings. Assume Jacqueline will not pass through any buildings.
The number “3” at the intersection of C and 2nd Streets means that there are three different ways she can get there from her starting position. What are those three ways? Describe them in words.
How many different ways can she walk to the corner of F and 4th Streets?
How many different ways can she walk to the corner of D and 5th Streets?
Explain how you can use your answers to parts (b) and (c) to find the number of ways she can walk to the corner of F and 5th Streets. Why does this make sense?
Find the number of different ways she can walk to the corner of I and 8th Streets.
How could you change the map so that Jacqueline has only 7 ways to get to the corner of D and 3rd streets? You can remove blocks or add them.
2.3.4
Defining Concavity
4.4.1
Characteristics of Polynomial Functions
5.2.6
Semi-Log Plots
5 Closure
Closure How Can I Apply It? Activity 3
9.3.1
Transition States
9.3.2
Future and Past States
10.3.1
The Parametrization of Functions, Conics, and Their Inverses
10.3.2
Vector-Valued Functions
11.1.5
Rate of Change of Polar Functions
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.
