### Chapter 1:A Beginning Look at Calculus

Opening

Chapter 1 Opening

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

### Chapter 2: Rates, Sums, Limits, and Continuity

Opening

Chapter 2 Opening

Section 2.1

2.1.1

Area Under the Curve Using Trapezoids

2.1.2

Methods to Calculate Area Under a Curve

2.1.3

Area Under the 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

2.2.5s

Squeezing 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

### Chapter 3: Slope and Curve Analysis

Opening

Chapter 3 Opening

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 Strategies

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

Differentiablility of Specific Functions

3.4.4

Intersection of Tangents

### Chapter 4: The Fundamental Theorem of Calculus

Opening

Chapter 4 Opening

Section 4.1

4.1.1

Definite Integrals

4.1.2

Numerical Cases 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

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

4.4.2

More Area Between Curves

4.4.3

Multiple Methods for Calculating Area Between Curves

Section 4.5

4.5.1

Newton’s Method

### Chapter 5: Derivative Tools and Applications

Opening

Chapter 5 Opening

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

Chain Rule and Application: Part One

5.2.3

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

### Chapter 6: More Tools and Theorems

Opening

Chapter 6 Opening

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

### Chapter 7: Related Rates and Integration Tools

Opening

Chapter 7 Opening

Section 7.1

7.1.1

Related Rates Introduction

7.1.2

Related Rates Application: The Pythagorean Theorem

7.1.3

Related Rates Application: Similar Triangles

7.1.4

Related Rates Application: Choosing the Best Formula

7.1.5

Related Rates Application: 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

### Chapter 8: Volume

Opening

Chapter 8 Opening

Section 8.1

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

### Chapter 9: Pre-Calculus Review

Opening

Chapter 9 Opening

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

### Chapter 10: Convergence of Series

Opening

Chapter Opening

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

### Chapter 11: Polar and Parametric Functions

Opening

Chapter 11 Opening

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

### Chapter 12: Approximating Functions and Error

Opening

Chapter 12 Opening

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

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# 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.