Table of Contents

Third Edition

Section 1.1

1.1.1 Interpreting Graphs

1.1.2 The Spring Problem

1.1.3 Modeling with Functions

1.1.4 Rates of Change

1.1.5 Setting Up Word Problems

1.1.6 Equivalent Expressions

Section 1.2

1.2.1 Composition of Functions

1.2.2 Inverse Functions

1.2.3 Piecewise-Defined Functions and Continuity

Section 1.3

1.3.1 Radians as a Unit of Measure

1.3.2 Radian Measure in the Unit Circle

1.3.3 Applications of Radian Measure

Closure

Section 2.1

2.1.1 Characteristics of Functions

2.1.2 Even and Odd Functions

2.1.3 Transformations of Functions

Section 2.2

2.2.1 Special Angles in the Unit Circle

2.2.2 Trigonometric Ratios in the Unit Circle

2.2.3 Graphs of Sine and Cosine

2.2.4 Transformations of Sine and Cosine

2.2.5 Horizontal Stretches of Sine and Cosine Graphs

Section 2.3

2.3.1 Solving Trigonometric Equations

2.3.2 Inverse Sine and Cosine

2.3.3 Graphs of Tangent and Inverse Tangent

Closure

Section 3.1

3.1.1 Operations with Rational Expressions

3.1.2 Rewriting Expressions and Equations

3.1.3 Solving Nonlinear Systems of Equations

3.1.4 Polynomial Division

3.1.5 Solving Classic Word Problems

Section 3.2

3.2.1 Using Sigma Notation

3.2.2 Area Under a Curve: Part One

3.2.3 Area Under a Curve: Part Two

3.2.4 Area Under a Curve: Part Three

Closure

Section 4.1

4.1.1 Graphs of Polynomial Functions in Factored Form

4.1.2 Writing Equations of Polynomial Functions

4.1.3 Identifying and Using Roots of Polynomials

Section 4.2

4.2.1 Graphing Transformations of y = 1x

4.2.2 Graphing Rational Functions

4.2.3 Graphing Reciprocal Functions

Section 4.3

4.3.1 Polynomial and Rational Inequalities

4.3.2 Applications of Polynomial and Rational Functions

Closure

Section 5.1

5.1.1 Applications of Exponential Functions

5.1.2 Stretching Exponential Functions

5.1.3 The Number e

Section 5.2

5.2.1 Logarithms

5.2.2 Properties of Logarithms

5.2.3 Solving Exponential and Logarithmic Equations

5.2.4 Graphing Logarithmic Functions

5.2.5 Applications of Exponentials and Logarithms

Closure

Section 6.1

6.1.1 The Law of Sines and Area

6.1.2 The Law of Cosines

6.1.3 The Ambiguous Case of the Law of Sines

Section 6.2

6.2.1 An Introduction to Vectors

6.2.2 Operations with Vectors

6.2.3 Applications of Vectors

6.2.4 The Dot Product

Closure

Section 7.1

7.1.1 An Introduction to Limits

7.1.2 Working With One-Sided Limits

7.1.3 The Definition of a Limit

7.1.4 Limits and Continuity

7.1.5 Special Limits

Section 7.2

7.2.1 Rates of Change from Data

7.2.2 Slope and Rates of Change

7.2.3 Average Velocity and Rates of Change

7.2.4 Moving from AROC to IROC

7.2.5 Rate of Change Applications

Closure

Section 8.1

8.1.1 Graphing y = asin(b(x – h)) + k

8.1.2 Modeling With Periodic Functions

8.1.3 Improving the Spring Problem

Section 8.2

8.2.1 Graphing Reciprocal Trigonometric Functions

8.2.2 Trigonometric Functions, Geometrically

Section 8.3

8.3.1 Simplifying Trigonometric Expressions

8.3.2 Proving Trigonometric Identities

8.3.3 Angle Sum and Difference Identities

8.3.4 Double-Angle and Half-Angle Identities

8.3.5 Solving Complex Trigonometric Equations

Closure

Section 9.1

9.1.1 Introduction to Matrices

9.1.2 Matrix Multiplication

9.1.3 Determinants and Inverse Matrices

9.1.4 Solving Systems Using Matrix Equations

Section 9.2

9.2.1 Linear Transformations

9.2.2 Compositions of Transformations

9.2.3 Properties of Linear Transformations Closure

Section 10.1

10.1.1 Circles and Completing the Square

10.1.2 Ellipses

10.1.3 Hyperbolas

10.1.4 Parabolas

10.1.5 Identifying and Graphing Conic Sections

Section 10.2

10.2.1 Parametrically-Defined Functions

10.2.2 Applications of Parametrically-Defined Functions

10.2.3 Conic Sections in Parametric Form

Closure

Section 11.1

11.1.1 Plotting Polar Coordinates

11.1.2 Graphs of Polar Functions

11.1.3 Families of Polar Functions

11.1.4 Converting Between Polar and Rectangular Forms

Section 11.2

11.2.1 Using the Complex Plane

11.2.2 Operations with Complex Numbers Geometrically

11.2.3 Polar Form of Complex Numbers

11.2.4 Operations with Complex Numbers in Polar Form

11.2.5 Powers and Roots of Complex Numbers

Closure

Section 12.1

12.1.1 Arithmetic Series

12.1.2 Geometric Series

12.1.3 Infinite Geometric Series 12.1.4 Applications of Geometric Series

12.1.5 The Sum of the Harmonic Series

Section 12.2

12.2.1 The Binomial Theorem

12.2.2 Binomial Probabilities

Section 12.3

12.3.1 Expected Value of a Discrete Random Variable

12.3.2 Expected Value and Decision Making

Closure

Section 13.1

13.1.1 A Race to Infinity

13.1.2 Limits to Infinity

13.1.3 Evaluating Limits at a Point Algebraically

13.1.4 Another Look at e

Section 13.2

13.2.1 Trapping Area With Trapezoids

13.2.2 Area as a Function

13.2.2A Going all to Pieces: Writing an Area Program

13.2.3 Rocket Launch

Section 13.3

13.3.1 Velocity and Position Graphs

13.3.2 Instantaneous Velocity

13.3.3 Slope Functions

13.3.4 The Definition of Derivative

13.3.5 Slope and Area Under a Curve

Closure

Third Edition

Section 1.1

1.1.1 Applying Rates and Distance

Section 1.2

1.2.1 Piecewise-Defined Functions and Continuity

1.2.2 End Behavior and Asymptotes

1.2.3 Holes, Vertical Asymptotes, and Approach Statements

1.2.4 Composite Functions and Inverse Functions

1.2.5 Attributes of Even and Odd Functions

1.2.6 Design a Flag

Section 1.3

1.3.1 Finite Differences

1.3.2 Slope Statements and Finite Differences of Non-Polynomials

1.3.3 The Slope Walk

Section 1.4

1.4.1 Distance and Velocity

1.4.2 Average Velocity on a Position Graph

1.4.3 Average Velocity on a Velocity Graph

1.4.4 Acceleration

Section 1.5

1.5.1 Area and Slope

Section 2.1

2.1.1 Area Under a Curve Using Trapezoids

2.1.2 Methods to Calculate Area Under a Curve

2.1.3 Area Under a Curve as a Riemann Sum

Section 2.2

2.2.1 Introduction to Limits as Predictions

2.2.2 Intuitive Ideas of Continuity

2.2.3 Definition of Continuity

2.2.4 Evaluating Limits

Section 2.3

2.3.1 Ramp Lab

2.3.2 Sudden Impact

2.3.3 Local Linearity

Section 2.4

2.4.1 Improving Approximation

Section 3.1

3.1.1 The Power Rule

3.1.2 Secants to Tangents, AROC to IROC

Section 3.2

3.2.1 Definition of a Derivative

3.2.2 Derivatives Using Multiple Strategies120

3.2.3 Derivatives of Sine and Cosine

Section 3.3

3.3.1 Curve Constructor: Part One

3.3.2 The Shape of a Curve

3.3.3 Curve Sketching: Derivatives

3.3.4 Ways to Describe f ′ and f ′′

Section 3.4

3.4.1 Conditions for Differentiability

3.4.2 Curve Constructor: Part Two

3.4.3 Differentiability of Specific Functions

3.4.4 Intersection of Tangents

Section 4.1

4.1.1 Definite Integrals

4.1.2 Properties of Definite Integrals

4.1.3 More Properties of Definite Integrals

Section 4.2

4.2.1 Deriving “Area Functions”

4.2.2 Indefinite and Definite Integrals

4.2.3 The Fundamental Theorem of Calculus

4.2.4 The Fundamental Theorem of Calculus

4.2.5 Integrals as Accumulators 1

Section 4.3

4.3.1 Fast Times: Parts One & Two

4.3.2 Fast Times: Parts Three & Four

4.3.3 Fast Times: Part Five

Section 4.4

4.4.1 Area Between Curves 197

4.4.2 More Area Between Curves 200

4.4.3 Multiple Methods for Calculating Area Between Curves

Section 4.5

4.5.1 Newton’s Method

Section 5.1

5.1.1 Distance, Velocity, and Acceleration Functions

5.1.2 Optimization

5.1.3 Using the Frist and Second Derivatives

5.1.4 Applying the First and Second Derivative Tests

Section 5.2

5.2.1 The Product Rule

5.2.2 The Chain Rule and Application: Part One

5.2.3 The Chain Rule and Application: Part Two

5.2.4 The Quotient Rule

5.2.5 More Trigonometric Derivatives

Section 5.3

5.3.1 Optimization Problems: Part One

5.3.2 Optimization Problems: Part Two

5.3.3 Optimization Problems: Part Three

Section 5.4

5.4.1 Chain Rule Extension of the Fundamental Theorem of Calculus

Section 5.5

5.5.1 Evaluating Limits of Indeterminate Forms

5.5.2 Using l’Hôpital’s Rule

Section 6.1

6.1.1 Exponential Functions

6.1.2 Derivatives of Exponential Functions

6.1.3 Derivatives Using Multiple Tools

6.1.4 Integrals of Exponential Functions

Section 6.2

6.2.1 Implicit Differentiation

6.2.2 Implicit Differentiation Practice

Section 6.3

6.3.1 Inverse Trigonometric Derivatives

6.3.2 Derivatives of Natural Logarithms

6.3.3 Derivatives of Inverse Functions

Section 6.4

6.4.1 Mean Value

6.4.2 Mean Value Theorem

6.4.3 Mean Value Theorem: Applications

Section 6.5

6.5.1 Improper Integrals

Section 7.1

7.1.1 Related Rates Introduction

7.1.2 Related Rates Applications: The Pythagorean Theorem

7.1.3 Related Rates Applications: Similar Triangles 323

7.1.4 Related Rates Applications: Choosing the Best Formula

7.1.5 Related Rates Applications: Trigonometry

Section 7.2

7.2.1 Undoing the Chain Rule

7.2.2 Integration with u-Substitution

7.2.3 Definite Integrals and u-Substitution

7.2.4 Varied Integration Techniques

Section 7.3

7.3.1 Solving Differential Equations

7.3.2 Newton’s Law of Cooling

7.3.3 Solving Separable Differential Equations

7.3.4 Slope Fields with Parallel Tangents

7.3.5 Plotting Slope Efficiently

7.3.6 Differential Equation and Slope Field Applications

Section 7.4

7.4.1 Euler’s Method

7.4.2 Integration By Parts

7.4.3 Integration By Parts with Substitution

7.4.4 Integration by Partial Fractions

8.1.1 Volumes by Slicing

8.1.2 The Disk Method

8.1.3 The Washer Method

8.1.4 Revolution About Horizontal and Vertical Lines

8.1.5 Changing the Axis of Rotation

8.1.6 Disk and Washer Problems

Section 8.2

8.2.1 Shell Lab

8.2.2 Comparing the Disk and Shell Methods

8.2.3 Using an Appropriate Method to Calculate Volume

Section 8.3

8.3.1 Cross-Sections Lab: General Case

8.3.2 Cross-Sections Lab: Functions Given

8.3.3 Cross-Section Problems

Section 8.4

8.4.1 Arc Length

Section 9.1

9.1.1 Infinite Geometric Series

9.1.2 More Infinite Geometric Series

9.1.3 Convergence and Divergence

Section 9.2

9.2.1 Parametric Equations

9.2.2 Converting Between Parametric and Rectilinear Form

Section 9.3

9.3.1 Introduction to Vectors

9.3.2 Vector Operations

Section 9.4

9.4.1 Graphs of Polar Equations

9.4.2 Converting Between Polar and Rectilinear Form

9.4.3 Polar Families

Section 10.1

10.1.1 Convergence of Series

10.1.2 The Divergence Test

10.1.3 The Alternating Series Test

10.1.4 The Integral Test

10.1.5 The p-Series Test

10.1.6 The Comparison Test

10.1.7 The Limit Comparison Test

10.1.8 The Ratio Test

Section 10.2

10.2.1 The Cootie Lab

10.2.2 More Logistic Differential Equations

Section 10.3

10.3.1 Power Series Convergence

10.3.2 Using Polynomials to Approximate Curves

Section 10.4

10.4.1 Absolute Convergence

10.4.2 Regrouping and Rearranging Series

Section 11.1

11.1.1 Area Bounded by a Polar Curve

11.1.2 More Polar Area

11.1.3 Area Between Polar Curves

Section 11.2

11.2.1 Applied Calculus in Component Form

11.2.2 Second Derivatives in Component Form

11.2.3 Total Distance and Arc Length

Section 11.3

11.3.1 Slopes of Polar Curves

11.3.2 More Slopes of Polar Curves

Section 11.4

11.4.1 Battling Robots

Section 12.1

12.1.1 Approximating with Polynomial Functions

12.1.2 Taylor Polynomials About x = 0

12.1.3 Taylor Polynomials About x = c

12.1.4 Taylor Series

12.1.5 Building Taylor Series Using Substitution

Section 12.2

12.2.1 Interval of Convergence Using Technology

12.2.2 Interval of Convergence Analytically

Section 12.3

12.3.1 Error Bound for Alternating Taylor Polynomials

12.3.2 Lagrange Error Bound

Section 12.4

12.4.1 Evaluating Indeterminate Forms Using Taylor Series

###### 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 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.

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.

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.

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.

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.

Correlations

Correlations