Algebra 2 Learning Coach Guide

Learning Coach Guide

Contents

Algebra Review and Linear Functions Unit13

Sequences and Series Unit14

Transformation of Functions Unit15

Quadratic Functions and Equations Unit16

Polynomial Functions Unit17

Conic Sections Unit18

Rational and Radical Functions Unit19

Exponential and Logarithmic Functions Unit20

Multiple Functions Unit21

Trigonometric Functions Unit22

Statistics and Probability Unit23

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 Algebra 2 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, 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

The Algebra 2 course integrates the problem-solving and modeling skills that learners need in order to better understand the real world. The learn-by-doing philosophy, embedded in the course, provides an environment where learners gain understanding by solving problems in mathematical and real-world contexts, and constructing arguments using precise language. Learners are encouraged to express their ideas and reasoning, and to listen to the reasoning of others as they build understanding of new content, all while learning to communicate mathematically. This asynchronous course, separated into 11 units, bridges the skills and knowledge of today to what learners require for their future. By the end of the year, your learner will be able to:

apply transformations to a variety of function families;

analyze graphs from various function families to determine transformations;

use functions from different function families to determine graphical characteristics;

create equations for functions from graphs;

apply function families to real-world scenarios;

use transformations to determine equations of conic sections;

develop skills used to manipulate combinations of functions;

use data to construct regression equations and make predictions;

calculate and interpret probabilities; and

develop and strengthen problem-solving skills.

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.

See example below.

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, 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. Warm Up: At the beginning of every lesson, your learner will see the Warm Up. This section contains lesson objectives, lesson vocabulary, materials your learner will need for the lesson, and the suggested lesson length. Your learner will then complete a short activity to preview a topic in the lesson and will hear from peers about approaches, observations, or questions about the activity.

2. Explore: The second section of the lesson is Explore. This section is divided into three parts.

Engage: In this part, learners will be introduced to concepts in the lesson by making a connection to careers, applications, other disciplines, or past and present knowledge to get them interested in the lesson’s instruction.

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.

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

3. Practice and Skill Builder: The third section of the lesson is Practice and Skill Builder. Every lesson will contain a Practice section, but only some of the lessons in the unit will contain a Skill Builder.

Practice: This part will contain 3 to 5 questions on the day’s content and 1 to 2 spiraling questions from past lessons or units.

Skill Builder: If a Skill Builder is included in the day’s activities, your learner will choose from 3 activities to participate in. These activities are gamified versions of mathematical topics designed to encourage critical thinking.

Summary: This section recaps the day’s objectives and notifies learners of a future lesson or assessment.

The course also includes assignments and projects. These are graded assignments allowing 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 in the middle 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:

Math Routines: included in the Warm Up activities, your learner will participate in such routines as Notice and Wonder, Math Talk, Aspects of Mathematical Modeling, and others.

Character Discourse: included in the Warm Up, 8 characters will be used to offer strategies, thoughts, and questions. You learner will hear from Sam, Devin, Riley, Farah, Drew, Jin, Nikki, and Hasain.

Video Examples: included in Discover, videos of concept explanations or teacher instruction may be used in some lessons.

GeoGebra: 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.

Math Lesson Companion: Learners will receive a Lesson Companion in which they can answer questions, take notes, and complete activities during the online lessons.

Extra Practice Notebook: The Extra Practice Notebook is a resource for learners to work extra practice problems related to each lesson.

Part C:Unit Information

Algebra Review and Linear Functions Unit

Unit Overview

This unit revisits functions from Algebra 1, skills that they will use throughout the Algebra 2 course.

In each lesson, your learner will review a math concept and vocabulary, as well as work through problems practicing the related skill. Your learner will see hints and solutions.

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

When would you use an inequality when creating a budget?

Do you understand how a linear relationship can help you estimate how much a paycheck will be?

How well do you understand operations with fractions and exponents?

Unit Notables

Linear functions are the foundation for the study of functions that occurs in Algebra 2.

It is important that your learner can use fractions and exponents comfortably.

Kit Materials

Algebra 2 Lesson Companion, Algebra 2 Extra Practice Workbook, colored pencils, grid paper, TI-84+ graphing calculator

Household Materials

none

Sequences and Series Unit

Unit Overview

In this unit, your learner will discover sequences and series by distinguishing between geometric and arithmetic sequences and series and their characteristics. In the last part of the unit, your learner will discover summation notation, partial sums, and convergent and divergent series.

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 are sequences and series used in real life?

How well do you understand finding missing terms and sums?

Unit Notables

Sequences and series are components in higher-level mathematics courses. This unit is meant to be an introduction to these concepts for your learner.

Kit Materials

Algebra 2 Lesson Companion, Algebra 2 Extra Practice Workbook, grid paper, scissors, TI-84+ graphing calculator

Household Materials

none

Transformation of Functions Unit

Unit Overview

This unit introduces most of the function families your learner will explore throughout this course. While discovering the characteristics of these function families, your learner will use shifts, reflections, and stretches or shrinks.

Your learner will also discover piecewise-defined 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 understand all of the different transformations you are learning in functions?

When would a business need to make transformations to their cost function?

What did you find interesting or unexpected about this unit?

Unit Notables

Your learner’s discovery of nonlinear functions will continue throughout this course. It is important for your learner to be able to identify and perform the transformations in this unit as transformations are used in the next six units.

Kit Materials

Algebra 2 Lesson Companion, Algebra 2 Extra Practice Workbook, colored pencils, grid paper, TI-84+ graphing calculator

Household Materials

none

Quadratic Functions and Equations Unit

Unit Overview

In this unit, your learner will solve quadratic equations and discover a new number whose square is -1, allowing them to find all solutions to quadratic equations.

Factoring and the quadratic formula are reviewed, and the method of completing the square is introduced, which will be used in the Conic Sections unit.

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 can you represent as a quadratic function and what would the maximum or minimum represent?

How well do you understand factoring, completing the square, and the quadratic formula?

What the most challenging part of this unit?

Unit Notables

Quadratic functions are very useful in physics and real-world scenarios.

It is important that your learner can find the maximum or minimum value and the zeros comfortably.

Kit Materials

Algebra 2 Lesson Companion, Algebra 2 Extra Practice Workbook, grid paper, TI-84+ graphing calculator

Household Materials

none

Polynomial Functions Unit

Unit Overview

In this unit, your learner will study higher-degree polynomials and will explore real-world situations that are modeled with polynomials. Your learner will make connections between factors and zeros, divide polynomials, and sketch graphs.

At the end of this unit, your learner will complete the first part of a four-part project.

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

There are four possible end behaviors of polynomial functions. Can you describe all of them?

How well do you understand the graphing nonlinear functions assignment?

Unit Notables

Polynomial functions may have both relative maximum and minimum values. Finding them on the graph can be difficult since the standard graphing window used on the TI-84+ may not show the turn-around points. Encourage your learner to adjust the window in the y-directions.

Kit Materials

Algebra 2 Lesson Companion, Algebra 2 Extra Practice Workbook, colored pencils, grid paper, TI-84+ graphing calculator

Household Materials

none

Conic Sections Unit

Unit Overview

In this unit, your learner will explore the four conic sections: parabola, circle, ellipse, and hyperbola. Your learner will write and graph each type of conic section when given its key characteristics. Your learner also discovers how to find intersections within conic sections.

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 well do you understand graphing the different conic sections?

Are you enjoying the project in this unit?

What does your design look like?

Unit Notables

When a plane cuts through a cone it could create one of four conic sections depending on how it cuts through the cone. For example, if the plane horizontally cuts through a cone, the result would be a circle. In this unit your learner will be working with the graphs of these conic sections.

Kit Materials

Algebra 2 Lesson Companion, Algebra 2 Extra Practice Workbook, colored pencils, grid paper,TI-84+ graphing calculator

Household Materials

none

Rational and Radical Functions Unit

Unit Overview

In this unit, your learner will explore graphing rational functions and asymptotes, discover various strategies for solving rational equations, and explore the methods for solving and graphing radical equations. They will discover that sometimes the solutions computed do not always make the original equation true.

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 was your favorite part of this unit and why?

What is a real-life example of a function that would have an asymptote?

Unit Notables

Graphing rational functions is time consuming, but it is important to perform all of the analyses.

It is important for your learner to understand that squaring both sides of an equation can create extra solutions that may not actually be solutions.

Kit Materials

Algebra 2 Lesson Companion, Algebra 2 Extra Practice Workbook, colored pencils, grid paper, TI-84+ graphing calculator

Household Materials

none

Exponential and Logarithmic Functions Unit

Unit Overview

In this unit, your learner will investigate exponential functions and logarithms, using logarithms to solve exponential equations.

Your learner will also discover the constant known as e and use it to model situations with continuous growth rates, leading to working with the natural logarithm.

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

Can you explain how interest is calculated for a bank account?

What makes an annuity differ from a savings account?

How well do you understand the relationship between exponents and logs?

Unit Notables

Your learner may not fully understand the transcendental number e, but knowing how to use it in exponential and natural logarithmic functions is sufficient for now.

The concept of a logarithm is probably new for your learner. To support your learner, you can reinforce that its purpose is to find an exponent.

Kit Materials

Algebra 2 Lesson Companion, Algebra 2 Extra Practice Workbook, colored pencils, grid paper, TI-84+ graphing calculator

Household Materials

none

Multiple Functions Unit

Unit Overview

In this unit, your learner will examine function operations, combinations, compositions, and inverses. Two functions can be composed by using one function as the independent variable for another function. Functions may also have inverses that transpose the x- and y-variables.

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 you learning about functions used in a business setting?

How well do you understand operations with multiple functions?

How well do you understand composing functions?

Unit Notables

This unit introduces your learner to the concepts of composing functions and finding function inverses. An inverse function does the opposite of the function. For example, if a function converts dollars to pesos, the inverse of this function would convert pesos back into dollars.

Kit Materials

Algebra 2 Lesson Companion, Algebra 2 Extra Practice Workbook, colored pencils, grid paper, TI-84+ graphing calculator

Household Materials

none

Trigonometric Functions Unit

Unit Overview

In this unit, your learner will discover trigonometric functions. The unit opens with a study of circular motion and reviews right triangle trigonometry. Your learner will discover the unit circle, graph sine, cosine, and tangent functions, and use these functions to model periodic situations.

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 understand how to graph a periodic function?

How well do you understand the coordinates on the unit circle?

Unit Notables

The unit circle is the foundation for the mathematical branch of Trigonometry. It is important that your learner understands how the unit circle is formed and does not simply memorize its coordinates. Trigonometric functions are used in calculus courses and above.

Kit Materials

Algebra 2 Lesson Companion, Algebra 2 Extra Practice Workbook, grid paper, TI-84+ graphing calculator

Household Materials

none

Statistics and Probability Unit

Unit Overview

In this unit, your learner will use statistical concepts and probability theory to solve mathematical and real-world problems involving uncertainty.

The unit begins with the study of linear regression and correlation, and concludes with an introduction to probability.

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 understand why data points look so scattered?

What did you find interesting or surprising about how these skills are used in different careers?

How well do you understand why conditional events change probabilities?

Unit Notables

This unit is a very brief introduction to probability and statistics.

Understanding statistical concepts helps your learner understand references to medical studies and has implications for businesses as well. All medical fields and business programs require a statistical background.

Kit Materials

Algebra 2 Lesson Companion, Algebra 2 Extra Practice Workbook, colored pencils, grid paper, TI-84+ graphing calculator

Household Materials

none