AP Calculus AB Learning Coach Guide

Welcome Letter

Dear Learning Coach,

Thank you for partnering with CCA and investing in your learner’s education. This Learning Coach Guide is intended to help you support your learner in their AP® Calculus AB course.

Within this guide, you will find the goals, components, and features of the online course. Please take time to read and review this information so you understand how to help your learner interact with all the course’s elements.

The Learning Coach Guide also includes information about each of the units in this course. On each page of unit information, you will discover the following.

• The Unit Overview will tell you what the focus, content, and skills of the unit will be.
• The Unit Assessment section is a place for you and your learner to preview the graded work in the course. At the start of each unit, work with your learner to look at the unit in edio and find out which types of graded work are in this unit. Write them in the box and use it as a checklist. You can check off each one as your learner completes it.
• The Unit Materials section tells you the materials your learner will need to complete the activities in this unit. You will also find the materials list repeated within each lesson so that your learner has exactly what they need at the right time.
• The Unit Discussion Questions are optional questions that you may want to ask your learner during the unit to increase home and school connections about what your learner is studying.
• In the Unit Notablessection, you may find optional activities, literature connections, career connections, technology tips, or ideas to help your learner if they get stuck.

CCA wishes you and your learner a terrific school year!

Supporting Your Learner

Your role as a Learning Coach is very important. Here are a few ways you can help your learner do their very best in the course.

• Help your learner know what time guided or live class instruction is scheduled for, and prompt them to attend sessions or watch recordings.
• Remember, it is okay for your learner to get stuck. Learning new material takes time. Encourage them to take breaks, keep trying, and even ask the teacher for help.
• Help your learner navigate technology. That may mean helping them type information or upload work into edio.
• Always encourage your learner to do their very best.
• Review the course syllabus for your learner’s course.
• Advanced Placement® (AP) courses require more from the learners than other courses. You may find that your learner needs more practice, more review, and more support to be successful when compared to non-AP® courses. 
• Excellent AP® learners should strive for mastery. Think of athletes and musicians. They practice until they are excellent. AP® learners should follow that kind of work ethic.
• Maintain communication with your learner’s teacher.

Part B
Course Information

Course Goals

InAP® Calculus AB, your learner will:

• have an understanding of calculus concepts and experience with its methods and application;
• demonstrate the accurate use of definitions and theorems to build arguments and justify conclusions;
• apply concepts, results, and problems expressed graphically, numerically, analytically, and verbally;
• explore connections among representations and build an understanding of how calculus applies limits to develop essential ideas, definitions, formulas, and theorems; and
• communicate their methods, reasoning, justifications, and conclusions mathematically.

Course Format

Lesson Components:

Each day, your learner will spend approximately 50–60 minutes completing an AP® Calculus AB lesson. Some days may take less time, while other days may take a little more time. It is common for learners taking AP® courses to spend time outside of the scheduled class time completing course reading or studying.

This section will help you to understand how your learner’s course is structured in edio.

Lesson Bundling:

Within the lesson bundles, there are different components your learner will interact with. These components will not be used every day.

1. Getting Started Lesson: There is one Getting Started lesson in this course. It can be found on Day 1 of Unit 1. This lesson includes important information about the course and contact information for your teacher.

2. Unit Overview: Each unit will include a unit overview. This describes what your learner will learn in the unit and how many assessments the unit will have.

3. Prep for Success: At the beginning of each unit, your learner will find a Prep for Success. This component offers learners tips to be successful in the course, such as study tips, important software information, safety reminders, and more.

4. Knowledge Check: There will be one Knowledge Check in each unit. The Knowledge Check is designed to check prior learning and understanding about key skills and concepts that will be taught in the unit. The Knowledge Check is not a graded assessment.

Each lesson has its own components to help guide your learner through the lesson.

1. Lesson Overview: At the beginning of every lesson, your learner will see the lesson overview. This section contains lesson objectives, lesson vocabulary, materials your learner will need for the lesson, and the suggested lesson length.

2. Engage: The first section of the lesson is Engage. In this section, learners will be introduced to the lesson by making a connection to past and present knowledge and will get ready for the lesson’s instruction.

3. Discover: New content and instruction is presented in the Discover section. Your learner will interact with the lesson content through defined vocabulary terms, videos, audio, and Pause and Think activities. Your learner will be able to practice and answer questions as they work through the lesson.

4. Show: Learners will demonstrate what they have learned in the lesson through a series of practice questions.

5. Summary: This section recaps the day’s objectives and prepares learners for a future lesson or assessment.

This course also includes quizzes, tests, and exams.

• Quiz: A quiz may be given at the end of a topic or the end of a unit.
• Test Review: Before a test, learners will have the opportunity to review the content they will be assessed on in the test.
• Test: A test will assess learning across topics or at the end of a unit.
• Exam Review: Before an exam, learners will have the opportunity to review the content they will be assessed on in the exam.
• Exam: An exam assesses learning over multiple units. Exams are usually seen as midterm and final exams in Advanced Placement courses.

Course Features

Free-Response Question (FRQ): An FRQ is a free-response question: an open-ended question found on the AP exam that typically includes a real-world context or scenario.

Part C
Unit Information

Limits and Continuity Unit

Unit Overview

In this unit, your learner will explore how limits will allow them to solve problems involving change, and your learner will better understand math models and how they are used in the real world.

Unit Assessments

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Have your learner identify which assessment type they see in their unit. Check all that apply.

Unit Discussion Questions

How do you identify the exact point where change occurs?

What did you find most challenging in this unit?

Unit Notables

Limits can help your learner approximate values based on models or equations. Sometimes, the equation is not defined at a point. Some learners struggle with this. Remind your learners that limits are only interested in where the value is approaching. This unit also includes a video on the history of calculus which encourages learners to think about how mathematical limits were discovered.

Kit Materials

graph paper, highlighter, notebook,

TI-84+ calculator

Household Materials

none

Unit Overview

In this unit, your learner will explore how limits will allow them to solve problems involving change, and your learner will better understand math models and how they are used in the real world.

Unit Assessments

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Have your learner identify which assessment type they see in their unit. Check all that apply.

Unit Discussion Questions

How do you identify the exact point where change occurs?

What did you find most challenging in this unit?

Unit Notables

Limits can help your learner approximate values based on models or equations. Sometimes, the equation is not defined at a point. Some learners struggle with this. Remind your learners that limits are only interested in where the value is approaching. This unit also includes a video on the history of calculus which encourages learners to think about how mathematical limits were discovered.

Kit Materials

graph paper, highlighter, notebook,

TI-84+ calculator

Household Materials

none

Definition and Fundamental Properties of DifferentiationUnit

Unit Overview

Your learners will determine rates of change through a variety of calculus techniques.

Your learner will find derivatives using the power rule, product rule, and quotient rule.

Unit Assessments

Quiz _________________________

Test ________________________

Assignment _______________

Project ____________________

Exam ______________________

Have your learner identify which assessment type they see in their unit. Check all that apply.

Unit Discussion Questions

What type of predictions would you like to calculate?

What did you find interesting about this unit?

Unit Notables

In the real world, your learner can make predictions about behavior based on rates of change. For example, determining the best time to buy or sell stocks, or predicting changes in population in certain areas.

Kit Materials

graph paper, highlighter, notebook,

TI-84+ calculator

Household Materials

none

Unit Overview

Your learners will determine rates of change through a variety of calculus techniques.

Your learner will find derivatives using the power rule, product rule, and quotient rule.

Unit Assessments

Quiz _________________________

Test ________________________

Assignment _______________

Project ____________________

Exam ______________________

Have your learner identify which assessment type they see in their unit. Check all that apply.

Unit Discussion Questions

What type of predictions would you like to calculate?

What did you find interesting about this unit?

Unit Notables

In the real world, your learner can make predictions about behavior based on rates of change. For example, determining the best time to buy or sell stocks, or predicting changes in population in certain areas.

Kit Materials

graph paper, highlighter, notebook,

TI-84+ calculator

Household Materials

none

Composite, Implicit, and Inverse

Differentiation Unit

Unit Overview

Your learner will apply the chain rule to find derivatives (rates of change) to continue to make predictions.

Unit Assessments

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Have your learner identify which assessment type they see in their unit. Check all that apply.

Unit Discussion Questions

Did you find the chain rule easy to use? Why?

What did you find most interesting about this unit?

Unit Notables

Your learner can find derivatives (rates of change) on functions within functions by using the chain rule. If your learner finds this challenging, remind them to start on the innermost function, and tack on the derivative of the inside to the outside. A reminder tip is for your learner to think of the outside function as wrapping paper on a present and the inside function as the actual present.

Kit Materials

graph paper, highlighter, notebook,

TI-84+ calculator

Household Materials

none

Unit Overview

Your learner will apply the chain rule to find derivatives (rates of change) to continue to make predictions.

Unit Assessments

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Have your learner identify which assessment type they see in their unit. Check all that apply.

Unit Discussion Questions

Did you find the chain rule easy to use? Why?

What did you find most interesting about this unit?

Unit Notables

Your learner can find derivatives (rates of change) on functions within functions by using the chain rule. If your learner finds this challenging, remind them to start on the innermost function, and tack on the derivative of the inside to the outside. A reminder tip is for your learner to think of the outside function as wrapping paper on a present and the inside function as the actual present.

Kit Materials

graph paper, highlighter, notebook,

TI-84+ calculator

Household Materials

none

Contextual Applications of Differentiation Unit

Unit Overview

Your learner will apply L’Hospital’s Rule to find limits in difficult cases.

Unit Assessments

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Have your learner identify which assessment type they see in their unit. Check all that apply.

Unit Discussion Questions

From the units so far, which concept has been the most challenging?

What did you find the most surprising or interesting about this unit?

What do you need to work on in order to prepare for the midterm exam?

Unit Notables

If your learner struggles with remembering rules, remind them that L’Hospital’s Rule says that the limit when dividing one function by another is the same after taking the derivative of each function. Encourage your learner to create or post images of the rule to help reinforce the concept. Your learner will take a midterm exam at the end of this unit.

Kit Materials

graph paper, highlighter, notebook,

TI-84+ calculator

Household Materials

none

Unit Overview

Your learner will apply L’Hospital’s Rule to find limits in difficult cases.

Unit Assessments

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Have your learner identify which assessment type they see in their unit. Check all that apply.

Unit Discussion Questions

From the units so far, which concept has been the most challenging?

What did you find the most surprising or interesting about this unit?

What do you need to work on in order to prepare for the midterm exam?

Unit Notables

If your learner struggles with remembering rules, remind them that L’Hospital’s Rule says that the limit when dividing one function by another is the same after taking the derivative of each function. Encourage your learner to create or post images of the rule to help reinforce the concept. Your learner will take a midterm exam at the end of this unit.

Kit Materials

graph paper, highlighter, notebook,

TI-84+ calculator

Household Materials

none

Analytical Applications of DifferentiationUnit

Unit Overview

Your learner will apply the Mean Value Theorem and the Extreme Value Theorem to find the hills and valleys of a graph. These “hills and valleys” are used to determine maximum or minimum values. First and Second Derivative helps us to find these points of interest.

Unit Assessments

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Have your learner identify which assessment type they see in their unit. Check all that apply.

Unit Discussion Questions

What are some ways the information from this unit is used in the real world?

What did you find interesting about this unit?

Unit Notables

In this unit, your learner will explore the ways a graph of real data helps to predict behavior. For example, a graph of stock prices can help determine (when to sell) maximum or (when to buy) minimum values.

Kit Materials

graph paper, highlighter, notebook,

TI-84+ calculator

Household Materials

none

Unit Overview

Your learner will apply the Mean Value Theorem and the Extreme Value Theorem to find the hills and valleys of a graph. These “hills and valleys” are used to determine maximum or minimum values. First and Second Derivative helps us to find these points of interest.

Unit Assessments

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Have your learner identify which assessment type they see in their unit. Check all that apply.

Unit Discussion Questions

What are some ways the information from this unit is used in the real world?

What did you find interesting about this unit?

Unit Notables

In this unit, your learner will explore the ways a graph of real data helps to predict behavior. For example, a graph of stock prices can help determine (when to sell) maximum or (when to buy) minimum values.

Kit Materials

graph paper, highlighter, notebook,

TI-84+ calculator

Household Materials

none

Integration and Accumulation of Change Unit

Unit Overview

Your learner will find the integral or the area under the curve to determine the accumulation of change. This accumulation has practical uses, but it also helps to better stand the behavior of the graph or data.

Unit Assessments

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Have your learner identify which assessment type they see in their unit. Check all that apply.

Unit Discussion Questions

If you had difficulty understanding derivatives, how did you improve your understanding?

What was the most interesting part of this unit?

Unit Notables

This unit includes step-by-step charts to help learners remember how to solve these problems and find the accumulation of change. It also includes images with hotspots so learners can read the text and listen to the audio explanation of how to solve these problems.

Kit Materials

graph paper, highlighter, notebook,

TI-84+ calculator

Household Materials

none

Unit Overview

Your learner will find the integral or the area under the curve to determine the accumulation of change. This accumulation has practical uses, but it also helps to better stand the behavior of the graph or data.

Unit Assessments

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Have your learner identify which assessment type they see in their unit. Check all that apply.

Unit Discussion Questions

If you had difficulty understanding derivatives, how did you improve your understanding?

What was the most interesting part of this unit?

Unit Notables

This unit includes step-by-step charts to help learners remember how to solve these problems and find the accumulation of change. It also includes images with hotspots so learners can read the text and listen to the audio explanation of how to solve these problems.

Kit Materials

graph paper, highlighter, notebook,

TI-84+ calculator

Household Materials

none

Differential EquationsUnit

Unit Overview

In this unit, your learner will learn how to solve certain differential equations and apply that knowledge to deepen understanding of exponential growth and decay.

Unit Assessments

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Have your learner identify which assessment type they see in their unit. Check all that apply.

Unit Discussion Questions

How can you develop a model for the number of computers infected by a virus given the model for the rate of how fast the computers are being infected at a particular time?

What are some ways you might use the knowledge and skills in this unit in your everyday life?

What interested you the most in this unit?

Unit Notables

In this unit, your learner will explore how slope fields help your learner find specific behaviors of change, and visualize the solution to the differential equations. As your learner thinks about exponential growth and decay it is helpful to visualize a burning candle. The height of the candle decreases and time increases.

Kit Materials

graph paper, highlighter, notebook,

TI-84+ calculator

Household Materials

none

Unit Overview

In this unit, your learner will learn how to solve certain differential equations and apply that knowledge to deepen understanding of exponential growth and decay.

Unit Assessments

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Have your learner identify which assessment type they see in their unit. Check all that apply.

Unit Discussion Questions

How can you develop a model for the number of computers infected by a virus given the model for the rate of how fast the computers are being infected at a particular time?

What are some ways you might use the knowledge and skills in this unit in your everyday life?

What interested you the most in this unit?

Unit Notables

In this unit, your learner will explore how slope fields help your learner find specific behaviors of change, and visualize the solution to the differential equations. As your learner thinks about exponential growth and decay it is helpful to visualize a burning candle. The height of the candle decreases and time increases.

Kit Materials

graph paper, highlighter, notebook,

TI-84+ calculator

Household Materials

none

Applications of Integration Unit

Unit Overview

In this unit, your learner will make mathematical connections that will allow the ability to solve a wide range of problems involving net change over an interval of time and to find areas of regions or volumes of solids defined using functions.

Unit Assessments

Quiz _________________________

Test _________________________

Assignment _____________

Project __________________

Exam ____________________

Have your learner identify which assessment type they see in their unit. Check all that apply.

Unit Discussion Questions

Do you feel that you are better able to solve net change problems? Why or why not?

What was the most interesting or surprising part of this unit?

What do you need to work on in order to prepare for the final exam? What is your plan?

Unit Notables

This is the final unit in the course. Your learner is preparing for the AP® exam and the final exam. In this unit, your learner will investigate how the area under the curve is the accumulation of change.

Kit Materials

graph paper, highlighter, notebook,

TI-84+ calculator

Household Materials

none

Unit Overview

In this unit, your learner will make mathematical connections that will allow the ability to solve a wide range of problems involving net change over an interval of time and to find areas of regions or volumes of solids defined using functions.

Unit Assessments

Quiz _________________________

Test _________________________

Assignment _____________

Project __________________

Exam ____________________

Have your learner identify which assessment type they see in their unit. Check all that apply.

Unit Discussion Questions

Do you feel that you are better able to solve net change problems? Why or why not?

What was the most interesting or surprising part of this unit?

What do you need to work on in order to prepare for the final exam? What is your plan?

Unit Notables

This is the final unit in the course. Your learner is preparing for the AP® exam and the final exam. In this unit, your learner will investigate how the area under the curve is the accumulation of change.

Kit Materials

graph paper, highlighter, notebook,

TI-84+ calculator

Household Materials

none