Calculus Learning Coach Guide

Part A:
Welcome to Calculus

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 Calculus 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 Notables section, you may find optional activities, 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.
• Maintain communication with your learner’s teacher.

Part B:
Course Information

Course Goals

In Calculus, your learners will apply the concepts that they have learned in previous mathematics courses, including Precalculus. While Calculus is technically Algebra, it is a very specific way to do Algebra to find very specific values. These processes are complex and must be followed completely with detail. Your learner may continue using the procedures in this course if they choose to enroll in Advanced Placement (AP®) Calculus.

By the end of the year, your learner will be able to:

• develop a stronger understanding of functions and their graphs
• identify and interpret limits of functions numerically, algebraically, and graphically
• determine if a function is continuous or has points or intervals of discontinuities
• understand the connection between continuity and differentiability
• calculate derivatives using a variety of techniques
• analyze characteristics of functions and their graphs by differentiation
• explore connections between area and the definite integral
• evaluate antiderivatives using basic rules of integration
• apply the Fundamental Theorem of Calculus to evaluate definite integral
• synthesize techniques of differentiation and integration to construct mathematical concepts with models
• utilize differentiation and integration to solve mathematical concepts in everyday life such as area, velocity, and optimization

Course Format

Lesson Components:

Each day, your learner will spend 45–60 minutes completing a math lesson. Some days may take less time, while other days may take a little more time. The lesson does not need to be completed in one sitting. Encourage your learner to take short breaks as they need.

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. Optional: More to Explore: This optional section will contain 3 to 5 additional questions involving concepts from the day’s lesson. There will be solutions provided following the questions to help your learner determine whether they made any errors with the problems and how to correct them.

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

The course includes assignments and projects. These graded assignments allow your learner to show what they have learned and apply their new skills. All CCA assignments and projects include these components.

1. Assessment Overview: At the beginning of each assessment, your learner will see the assessment overview. This section contains the goals of the assessment, materials your learner will need, length of the assessment, and directions for completion.

2. Plan: In the Plan section, learners will be introduced to the assignment or project. Learners may be provided with a review of content from the previous lessons, strategies for completing the activity, graphic organizers, and grading rubrics.

3. Do: Learners put their plan into action and work to complete the assignment or project successfully. This section also provides the grading expectations and/or rubric the teacher will use to grade the work.

4. Reflect: In Reflect, learners will think back to the work they completed. They will reflect upon the experience and analyze how well they completed the task. These moments of reflection are important and allow learners to think about their learning and their work habits.

In addition to assignments and projects, this course also includes quizzes and tests.

Quiz Review: Before a quiz, learners will have the opportunity to review the content they will be assessed on in a quiz.

• 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.

Course Features

This course includes and uses unique features such as:

GeoGebra Interactive Activities: This is a digital math tool learners can use to access a free online scientific, graphing, or CAS calculator and virtual math interactives. Learners will use the GeoGebra calculator and interactives to solve problems and produce graphical representations as needed.

Lesson Companion: This course utilizes a framework of notes for learners to complete while exploring each lesson. Learners will be able to keep track of the concepts and vocabulary learned in the lesson and use the companion as an effective study guide for this course and future math courses.

Extra Practice Workbook: Each topic will include extra practice problems that align with the lessons. These are optional problems that come with an answer key before each unit test. Learners can utilize this resource to further understand the skills covered in each lesson that will be assessed on the quizzes and tests.

Part C:
Unit Information

Functions and Models

Unit Overview

In this unit, your learner will develop an elementary understanding of what calculus is and why it is needed. They will start by reviewing concepts from Algebra II, Trigonometry, and Precalculus. Your learner will evaluate polynomial, rational, exponential, logarithmic, and trigonometric functions both numerically and graphically.

Unit Assessments

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

Unit Discussion Questions

Were there any careers that use calculus that you might be interested in?

Did you like the “Transformations Assignment?” Why or why not?

What are you looking forward to learning about in this course?

Unit Notables

The skills in this unit are the foundation for learning more advanced math skills, which are utilized in many careers. Encourage your learner to explore these careers in this unit, to see if they find any interesting as future career options.

Kit Materials

CalculusExtra Practice Workbook, CalculusLesson Companion,TI-84+ calculator

Household Materials

pencil

Unit Overview

In this unit, your learner will develop an elementary understanding of what calculus is and why it is needed. They will start by reviewing concepts from Algebra II, Trigonometry, and Precalculus. Your learner will evaluate polynomial, rational, exponential, logarithmic, and trigonometric functions both numerically and graphically.

Unit Assessments

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

Unit Discussion Questions

Were there any careers that use calculus that you might be interested in?

Did you like the “Transformations Assignment?” Why or why not?

What are you looking forward to learning about in this course?

Unit Notables

The skills in this unit are the foundation for learning more advanced math skills, which are utilized in many careers. Encourage your learner to explore these careers in this unit, to see if they find any interesting as future career options.

Kit Materials

CalculusExtra Practice Workbook, CalculusLesson Companion,TI-84+ calculator

Household Materials

pencil

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Limits and Continuity

Unit Overview

In this unit, your learner will be introduced to the concepts of limits and continuity. They will review the concept of tangent lines and relate them to velocity and rates of change. They will estimate limits from graphs and tables. They will find and interpret one-sided and infinite limits. Your learner will determine whether a function is continuous.

Unit Assessments

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? 

How can you use the value of a limit to help understand functions and their graphs? 

Were there any concepts that you had learned in a previous course?

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 learner that limits are only interested in where the value is approaching.

Kit Materials

Household Materials

pencil

Unit Overview

In this unit, your learner will be introduced to the concepts of limits and continuity. They will review the concept of tangent lines and relate them to velocity and rates of change. They will estimate limits from graphs and tables. They will find and interpret one-sided and infinite limits. Your learner will determine whether a function is continuous.

Unit Assessments

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? 

How can you use the value of a limit to help understand functions and their graphs? 

Were there any concepts that you had learned in a previous course?

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 learner that limits are only interested in where the value is approaching.

Kit Materials

Household Materials

pencil

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

CalculusExtra Practice Workbook, CalculusLesson Companion, TI-84+ calculator

Derivative Properties and Rules

Unit Overview

In this unit, your learner will build on their understanding of limits to define derivatives. They will compare and contrast notation for derivatives. They will connect the concept of slope and instantaneous rates of change to derivatives. Your learner will also explore connections between continuous and differentiable functions.

Unit Assessments

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

Unit Discussion Questions

How can you explain instantaneous rate to someone not in Calculus?

Which derivative rule is the easiest to apply or remember?

Which derivative rule is the hardest to apply or remember?

Unit Notables

Your learner can find derivatives of functions and determine how they are related to instantaneous rate of change and slope. Your learner will learn the basic techniques of differentiation that are essential for this course.

Kit Materials

Household Materials

pencil

Unit Overview

In this unit, your learner will build on their understanding of limits to define derivatives. They will compare and contrast notation for derivatives. They will connect the concept of slope and instantaneous rates of change to derivatives. Your learner will also explore connections between continuous and differentiable functions.

Unit Assessments

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

Unit Discussion Questions

How can you explain instantaneous rate to someone not in Calculus?

Which derivative rule is the easiest to apply or remember?

Which derivative rule is the hardest to apply or remember?

Unit Notables

Your learner can find derivatives of functions and determine how they are related to instantaneous rate of change and slope. Your learner will learn the basic techniques of differentiation that are essential for this course.

Kit Materials

Household Materials

pencil

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

CalculusExtra Practice Workbook, CalculusLesson Companion,colored pencils, TI-84+ calculator

Advanced Derivatives

Unit Overview

In this unit, your learner will find derivatives of more complex functions. They will use additional techniques to find derivatives and higher-order derivatives. They will also use derivatives of functions to write equations of tangent lines.

Unit Assessments

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

Unit Discussion Questions

How do you remember the values of sine and cosine on the unit circle?

What is different about parametric equations compared to other equations?

Unit Notables

Your learner will be expanding on applying the basic derivative rules to include additional functions. Encourage your learner to try to memorize the derivatives of exponential, logarithmic, and trigonometric functions. Also, knowing the values of the unit circle will be extremely helpful.

Kit Materials

Household Materials

pencil

Unit Overview

In this unit, your learner will find derivatives of more complex functions. They will use additional techniques to find derivatives and higher-order derivatives. They will also use derivatives of functions to write equations of tangent lines.

Unit Assessments

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

Unit Discussion Questions

How do you remember the values of sine and cosine on the unit circle?

What is different about parametric equations compared to other equations?

Unit Notables

Your learner will be expanding on applying the basic derivative rules to include additional functions. Encourage your learner to try to memorize the derivatives of exponential, logarithmic, and trigonometric functions. Also, knowing the values of the unit circle will be extremely helpful.

Kit Materials

Household Materials

pencil

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

CalculusExtra Practice Workbook, CalculusLesson Companion,colored pencils, TI-84+ calculator

Applications of Derivatives

Unit Overview

In this unit, your learner will apply methods of differentiation to evaluate graphs of functions by finding extrema, points of inflection, intervals of increasing or decreasing, concavity, and asymptotes. They will investigate new theorems, rules, and methods to extend their knowledge of limits and derivatives.

Unit Assessments

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

Unit Discussion Questions

Did you like the “A Fly on the Wall Project?” Why?

What did you find interesting about position, velocity, and acceleration?

What does a related rate mean?

Unit Notables

If your learner struggles with remembering rules, remind them that L’Hopital’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.

Kit Materials

Household Materials

pencil

Unit Overview

In this unit, your learner will apply methods of differentiation to evaluate graphs of functions by finding extrema, points of inflection, intervals of increasing or decreasing, concavity, and asymptotes. They will investigate new theorems, rules, and methods to extend their knowledge of limits and derivatives.

Unit Assessments

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

Unit Discussion Questions

Did you like the “A Fly on the Wall Project?” Why?

What did you find interesting about position, velocity, and acceleration?

What does a related rate mean?

Unit Notables

If your learner struggles with remembering rules, remind them that L’Hopital’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.

Kit Materials

Household Materials

pencil

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

CalculusExtra Practice Workbook, CalculusLesson Companion,TI-84+ calculator

Integrals

Unit Overview

In this unit, your learner will integrate prior knowledge of calculating area into Riemann sums and the trapezoidal rule to estimate area under a curve. They will use the Fundamental Theorem of Calculus to explore connections between derivatives and integrals.

Unit Assessments

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

Unit Discussion Questions

How were you able to improve your understanding of antiderivatives?

Did you like finding definite integrals more than indefinite integrals? Why?

What ways did you learn to estimate area? Which seemed the easiest to use?

Unit Notables

Your learner is now working with antiderivatives. They will practice techniques such as the power rule, substitution, and integration by parts to assist with evaluating integrals. Since these are reversing previous rules, encourage your learner to think of it as undoing what they did in previous units.

Kit Materials

Household Materials

pencil

Unit Overview

In this unit, your learner will integrate prior knowledge of calculating area into Riemann sums and the trapezoidal rule to estimate area under a curve. They will use the Fundamental Theorem of Calculus to explore connections between derivatives and integrals.

Unit Assessments

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

Unit Discussion Questions

How were you able to improve your understanding of antiderivatives?

Did you like finding definite integrals more than indefinite integrals? Why?

What ways did you learn to estimate area? Which seemed the easiest to use?

Unit Notables

Your learner is now working with antiderivatives. They will practice techniques such as the power rule, substitution, and integration by parts to assist with evaluating integrals. Since these are reversing previous rules, encourage your learner to think of it as undoing what they did in previous units.

Kit Materials

Household Materials

pencil

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

CalculusExtra Practice Workbook, CalculusLesson Companion, TI-84+ calculator

Applications of Integrals

Unit Overview

In this unit, your learner will apply integration techniques to find the area under a curve and between two curves. They will calculate arc length and surface area and explore different techniques to find volumes of rotating solids.

Unit Assessments

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

Unit Discussion Questions

In what ways did you find volumes of solids?

What are you most proud of learning in this course?

What are your future plans for your mathematics courses?

Unit Notables

This is the final unit in the course. In this unit, your learner will investigate how the area under the curve is the accumulation of change. Encourage your learner to develop models to assist them in grasping the concepts within this unit. Additionally, writing out the equations for disc and washer methods will be helpful.

Kit Materials

Household Materials

pencil

Unit Overview

In this unit, your learner will apply integration techniques to find the area under a curve and between two curves. They will calculate arc length and surface area and explore different techniques to find volumes of rotating solids.

Unit Assessments

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

Unit Discussion Questions

In what ways did you find volumes of solids?

What are you most proud of learning in this course?

What are your future plans for your mathematics courses?

Unit Notables

This is the final unit in the course. In this unit, your learner will investigate how the area under the curve is the accumulation of change. Encourage your learner to develop models to assist them in grasping the concepts within this unit. Additionally, writing out the equations for disc and washer methods will be helpful.

Kit Materials

Household Materials

pencil

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

CalculusExtra Practice Workbook, CalculusLesson Companion,graph paper, TI-84+ calculator