Advanced High School Courses
Table of Contents


Chapter 1: Representing Data

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Chapter 2: Two-Variable Quantitative Data

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Chapter 3: Multivariable Categorical Data

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Chapter 4:Studies and Experiments

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Chapter 5: Density Functions and Normal Distributions

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Chapter 6: Discrete Probability Distributions

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: Variability in Categorical Data Sampling

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: Drawing Conclusions From Categorical Data

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: Chi-Squared Inference Procedures

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: Drawing Conclusions From Quantitative Data

 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

Chapter 11:Comparing Means and Identifying Tests

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

Chapter 12: Inference for Regression

Section 12.1

12.1.1 Sampling Distribution of the Slope of the Regression Line 

12.1.2 Inference for the Slope of the Regression Line 

Section 12.2

12.2.1 Transforming Data to Achieve Linearity 

12.2.2 Using Logarithms to Achieve Linearity

Chapter 13: ANOVA and Beyond!

Section 13.1

13.1.1 Modeling With the Chi-Squared Distribution 

13.1.2 Introducing the F-Distribution 

Section 13.2

13.2.1 One-Way ANOVA 

Section 13.3

13.3.1 Sign Test: Introduction to Nonparametric Inference 

13.3.2 Mood’s Median Test


Chapter 1: Object Anatomy

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Chapter 2:Using Objects

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Chapter 3: Classes from Libraries

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Chapter 4: Iteration and Decisions

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Chapter 5: Arrays

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Chapter 6: Two-Dimensional Arrays

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: The ArrayList and Sorting

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: Inheritance and Polymorphism

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: Recursion

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

Chapter 10: Additional Projects and Review

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

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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.