Applied Geometry Learning Coach Guide

Part A:
Welcome to Applied Geometry

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 Applied Geometry 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, ideas to help your learner if they get stuck or safety tips.

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 Applied Geometry, your learner will use the mathematical reasoning and skills they learned in previous courses. By the end of the year, your learner will be able to:

• find patterns and use them to make conclusions;
• use properties of similarity and congruence;
• represent mathematical concepts with models;
• connect mathematical concepts to everyday life;
• identify relationships between lines;
• identify relationships between angles;
• classify triangles, quadrilaterals, and other polygons; and
• compare quantities.

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.

Some lessons contain only a lesson component, while others will include a quiz before the lesson or a project component after the lesson.

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.

• 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.
• 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.
• 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.
• 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.

See example below.

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

• 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.
• 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.
• Discover: New content and instruction is presented in the Discover section. Your learner will interact with the lesson content through defined vocabulary terms, videos, GeoGebra activities 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.
• 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.

• 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.
• 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.
• 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.
• 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 uses several instructional techniques throughout the course. This includes and uses unique features such as:

GeoGebra: This course empowers your learner to become frequent users of GeoGebra’s digital tools. GeoGebra applications are strategically integrated in the course for interactive and engaging visual learning. These activities are often used to allow students to discover concepts by easily manipulating figures. Your learner can complete the activity inside edio, or open into another window if needed.

Self-Assessment: To promote active learners, self-assessment is embedded throughout the course using tools such as: Check Your Work collapsible boxes, and Just In Time feedback. Examples of some of these tools are pictured below. Learners are provided solutions to all formative assessment questions so they can analyze their own work, identify errors, and reflect on their process and approach to problem solving. This immediate feedback guides learners to be more responsible for their own learning. Support your learner in attempting a problem and writing down their work before they check the answer.

Lesson Companion: The Lesson Companion workbook provides an overview of each topic, including upcoming assessments and reference to helpful pages in the Extra Practice workbook, and pages for students to record definitions. At the end of each unit, the Lesson Companion contains one or two pages that summarize the key learning points from the unit.

Extra Practice Workbook: Your learner will also receive an Extra Practice Workbook, which contains skills-based problems that reinforce the work done in edio. These pages are not mentioned in edio and are intended to be used for your leaner to build confidence in their new skills. Contact the course teacher to get information on how best to use this resource.

Part C:
Unit Information

Basics of Geometry Unit

Unit Overview

In this unit, your learner will learn what geometry is and how geometry is used in many careers. Your learner will define basic terms of geometry and use these definitions to identify, explain, and relate these concepts.

Unit Assessments

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

Unit Discussion Questions

What career are you researching? How does that career use geometry?

What are some of the defined and undefined terms you have learned?

What has been most interesting to you so far?

Kit Materials

Applied GeometryLesson Companion,Applied Geometry Extra Practice Workbook, notebook, ruler, TI-30XIIS calculator

Household Materials

pencil, mirror

Unit Notables

Your learner will research one of a handful of careers, and how geometry is used in it.

In both assignments, your learner will be measuring angles and distances in and around the home. If they are having difficulty finding objects of the needed dimensions, encourage them to create something.

Quiz ___________________________

Test ___________________________

Assignment __________________

Project _______________________

Exam _________________________

Unit Overview

In this unit, your learner will learn what geometry is and how geometry is used in many careers. Your learner will define basic terms of geometry and use these definitions to identify, explain, and relate these concepts.

Unit Assessments

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

Unit Discussion Questions

What career are you researching? How does that career use geometry?

What are some of the defined and undefined terms you have learned?

What has been most interesting to you so far?

Kit Materials

Applied GeometryLesson Companion,Applied Geometry Extra Practice Workbook, notebook, ruler, TI-30XIIS calculator

Household Materials

pencil, mirror

Unit Notables

Your learner will research one of a handful of careers, and how geometry is used in it.

In both assignments, your learner will be measuring angles and distances in and around the home. If they are having difficulty finding objects of the needed dimensions, encourage them to create something.

Quiz ___________________________

Test ___________________________

Assignment __________________

Project _______________________

Exam _________________________

Segments and Angles Unit

Unit Overview

In this unit, your learner will learn about segment bisectors and segment addition. In addition, your learner will learn to classify angles according to their size, to measure them using a protractor, and identify important angle pairs.

Unit Assessments

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

Unit Discussion Questions

What angles did you find here in the house? Which were most difficult to find?

Have you noticed more angles and lines in the neighborhood since you are working on a street map?

Kit Materials

Applied GeometryLesson Companion,Applied Geometry Extra Practice Workbook, notebook, protractor, ruler, TI-30XIIS calculator

Household Materials

pencil

Unit Notables

Your learner will be using a protractor to create and measure angles. This skill requires some precision, and they might appreciate some support in practicing.

Quiz ___________________________

Test ___________________________

Assignment __________________

Project _______________________

Exam _________________________

Unit Overview

In this unit, your learner will learn about segment bisectors and segment addition. In addition, your learner will learn to classify angles according to their size, to measure them using a protractor, and identify important angle pairs.

Unit Assessments

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

Unit Discussion Questions

What angles did you find here in the house? Which were most difficult to find?

Have you noticed more angles and lines in the neighborhood since you are working on a street map?

Kit Materials

Applied GeometryLesson Companion,Applied Geometry Extra Practice Workbook, notebook, protractor, ruler, TI-30XIIS calculator

Household Materials

pencil

Unit Notables

Your learner will be using a protractor to create and measure angles. This skill requires some precision, and they might appreciate some support in practicing.

Quiz ___________________________

Test ___________________________

Assignment __________________

Project _______________________

Exam _________________________

Parallel and Perpendicular Lines Unit

Unit Overview

In this unit, your learner will learn about parallel lines. When parallel lines are cut by another line, many angles are formed, and these angles share many important relationships.

Unit Assessments

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

Unit Discussion Questions

Why do you think there is an entire unit about parallel and perpendicular lines. Why are they important?

Why do you think some roads are parallel or perpendicular, and some form different angles?

Kit Materials

Applied GeometryLesson Companion,Applied Geometry Extra Practice Workbook, graph paper, notebook, protractor, ruler, TI-30XIIS calculator

Household Materials

pencil

Unit Notables

The amount of algebra used increases in this unit. Encourage your learner to go to the Extra Practice workbook if they need more practice to refresh those skills.

A major topic is a transversal line. These lines cut across two or more lines. We often discuss transversals that cut across parallel lines, but the lines do not have to be parallel to consider a transversal.

Quiz ___________________________

Test ___________________________

Assignment __________________

Project _______________________

Exam _________________________

Unit Overview

In this unit, your learner will learn about parallel lines. When parallel lines are cut by another line, many angles are formed, and these angles share many important relationships.

Unit Assessments

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

Unit Discussion Questions

Why do you think there is an entire unit about parallel and perpendicular lines. Why are they important?

Why do you think some roads are parallel or perpendicular, and some form different angles?

Kit Materials

Applied GeometryLesson Companion,Applied Geometry Extra Practice Workbook, graph paper, notebook, protractor, ruler, TI-30XIIS calculator

Household Materials

pencil

Unit Notables

The amount of algebra used increases in this unit. Encourage your learner to go to the Extra Practice workbook if they need more practice to refresh those skills.

A major topic is a transversal line. These lines cut across two or more lines. We often discuss transversals that cut across parallel lines, but the lines do not have to be parallel to consider a transversal.

Quiz ___________________________

Test ___________________________

Assignment __________________

Project _______________________

Exam _________________________

Triangle Relationships

Triangle Relationships Unit

Unit Overview

In this unit, your learner will discover many properties of triangles, and learn how to identify if triangles are congruent.

Unit Assessments

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

Unit Discussion Questions

Do you think that people use geometry when they construct quilts?

Where are some other places you see congruent triangles around you?

Kit Materials

colored pencils, construction paper, geostix, graph paper, Applied Geometry Lesson Companion, Applied Geometry Extra Practice Workbook, notebook, protractor, ruler, scissors, TI-30XIIS calculator

Household Materials

pencil

Unit Notables

This course does not teach “proofs” in the way your learner might have learned them in a geometry course. In this unit, your learner will use logic and experimentation to discover all the triangle congruence theorems.

Your learner may use other types of paper for the origami activities in this unit if construction paper is too thick.

Quiz ___________________________

Test ___________________________

Assignment __________________

Project _______________________

Exam _________________________

Unit Overview

In this unit, your learner will discover many properties of triangles, and learn how to identify if triangles are congruent.

Unit Assessments

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

Unit Discussion Questions

Do you think that people use geometry when they construct quilts?

Where are some other places you see congruent triangles around you?

Kit Materials

colored pencils, construction paper, geostix, graph paper, Applied Geometry Lesson Companion, Applied Geometry Extra Practice Workbook, notebook, protractor, ruler, scissors, TI-30XIIS calculator

Household Materials

pencil

Unit Notables

This course does not teach “proofs” in the way your learner might have learned them in a geometry course. In this unit, your learner will use logic and experimentation to discover all the triangle congruence theorems.

Your learner may use other types of paper for the origami activities in this unit if construction paper is too thick.

Quiz ___________________________

Test ___________________________

Assignment __________________

Project _______________________

Exam _________________________

Right Triangles and Trigonometry Unit

Unit Overview

In this unit, the learner will learn about the Pythagorean Theorem, its converse and the sine, cosine, and tangent ratios. They will then apply these concepts to solve problems found in mathematics and the real world.

Unit Assessments

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

Unit Discussion Questions

How useful is your clinometer? What else do you think you could use it to measure?

How is trigonometry used outside of a math class?

Kit Materials

Applied Geometry Lesson Companion, Applied Geometry Extra Practice Workbook, notebook, protractor, ruler, scissors, straw, string, TI-30XIIS calculator, washer

Household Materials

pencil, tape

Unit Notables

During the second day of the project in this unit, your learner is asked to find a tree that they will use to plan a treehouse. If there are no suitable trees nearby, they can use another tall object.

Quiz ___________________________

Test ___________________________

Assignment __________________

Project _______________________

Exam _________________________

Unit Overview

In this unit, the learner will learn about the Pythagorean Theorem, its converse and the sine, cosine, and tangent ratios. They will then apply these concepts to solve problems found in mathematics and the real world.

Unit Assessments

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

Unit Discussion Questions

How useful is your clinometer? What else do you think you could use it to measure?

How is trigonometry used outside of a math class?

Kit Materials

Applied Geometry Lesson Companion, Applied Geometry Extra Practice Workbook, notebook, protractor, ruler, scissors, straw, string, TI-30XIIS calculator, washer

Household Materials

pencil, tape

Unit Notables

During the second day of the project in this unit, your learner is asked to find a tree that they will use to plan a treehouse. If there are no suitable trees nearby, they can use another tall object.

Quiz ___________________________

Test ___________________________

Assignment __________________

Project _______________________

Exam _________________________

Quadrilaterals and Polygons

Unit Overview

In this unit, learners discover quadrilaterals and their properties, and how to classify them. In addition, they will learn about angles of polygons and how to determine area of polygons.

Unit Assessments

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

Unit Discussion Questions

What do the various kinds of quadrilaterals have in common? What makes them different?

What did you find interesting or surprising in this unit?

What did you find most challenging in the course so far?

Kit Materials

Applied Geometry Lesson Companion, Applied Geometry Extra Practice Workbook, compass, construction paper,geostix, notebook, protractor, ruler, scissors, TI-30XIIS calculator

Household Materials

pencil

Unit Notables

Your learner can draw on separate pieces of paper if they need more space while completing their project. Be sure they upload all their images.

Your learner can use different types of paper for the origami assignment. Origami paper often has different colors on each side, to make the resulting figure more colorful.

Quiz ___________________________

Test ___________________________

Assignment __________________

Project _______________________

Exam _________________________

Unit Overview

In this unit, learners discover quadrilaterals and their properties, and how to classify them. In addition, they will learn about angles of polygons and how to determine area of polygons.

Unit Assessments

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

Unit Discussion Questions

What do the various kinds of quadrilaterals have in common? What makes them different?

What did you find interesting or surprising in this unit?

What did you find most challenging in the course so far?

Kit Materials

Applied Geometry Lesson Companion, Applied Geometry Extra Practice Workbook, compass, construction paper,geostix, notebook, protractor, ruler, scissors, TI-30XIIS calculator

Household Materials

pencil

Unit Notables

Your learner can draw on separate pieces of paper if they need more space while completing their project. Be sure they upload all their images.

Your learner can use different types of paper for the origami assignment. Origami paper often has different colors on each side, to make the resulting figure more colorful.

Quiz ___________________________

Test ___________________________

Assignment __________________

Project _______________________

Exam _________________________

Similarity and Transformation

Unit Overview

In this unit, your learner will experiment with similarity and transformations. This includes similar triangles and similar polygons and how to transform geometric figures by using dilations, rotations, reflections, and translations.

Unit Assessments

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

Unit Discussion Questions

Have you ever used a ratio in real life, without realizing that you were using math?

How are the similarity theorems like the congruence theorems? How are they different?

What was the most interesting part of this unit?

Kit Materials

Applied Geometry Lesson Companion, Applied Geometry Extra Practice Workbook, colored pencils, compass, construction paper, glue, graph paper, notebook, protractor, ruler, scissors, string, TI-30XIIS calculator

Household Materials

pencil, tape

Unit Notables

Your learner will research the cost of various ingredients for a recipe. They can go to grocery store websites, or go to a store, to check items in person.

The final assignment allows Your learner to create their own tessellations. If they are unsure what to do, encourage your learner to research the artwork of M.C. Escher, a famous artist who used tessellations.

Quiz ___________________________

Test ___________________________

Assignment __________________

Project _______________________

Exam _________________________

Unit Overview

In this unit, your learner will experiment with similarity and transformations. This includes similar triangles and similar polygons and how to transform geometric figures by using dilations, rotations, reflections, and translations.

Unit Assessments

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

Unit Discussion Questions

Have you ever used a ratio in real life, without realizing that you were using math?

How are the similarity theorems like the congruence theorems? How are they different?

What was the most interesting part of this unit?

Kit Materials

Applied Geometry Lesson Companion, Applied Geometry Extra Practice Workbook, colored pencils, compass, construction paper, glue, graph paper, notebook, protractor, ruler, scissors, string, TI-30XIIS calculator

Household Materials

pencil, tape

Unit Notables

Your learner will research the cost of various ingredients for a recipe. They can go to grocery store websites, or go to a store, to check items in person.

The final assignment allows Your learner to create their own tessellations. If they are unsure what to do, encourage your learner to research the artwork of M.C. Escher, a famous artist who used tessellations.

Quiz ___________________________

Test ___________________________

Assignment __________________

Project _______________________

Exam _________________________

Circles

Unit Overview

In this unit, your learner will learn about circles and their properties. This includes arcs and how different angles, and their arcs are related, and sectors and their areas.

Unit Assessments

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

Unit Discussion Questions

Where do you see circles, arcs, and sectors in the real world?

How have you used the skills of ratios and similarities in this unit?

Kit Materials

Applied Geometry Lesson Companion, Applied Geometry Extra Practice Workbook, compass, colored pencils, graph paper, notebook, protractor, ruler, scissors, TI-30XIIS calculator

Household Materials

pencil

Unit Notables

Your learner will use a compass to draw circles throughout this unit. The compass point is sharp, so we recommend they always have a stack of paper as they use it so it does not leave marks on the writing surface your learner is using.

Encourage your learner to practice until they can make circles easily.

Quiz ___________________________

Test ___________________________

Assignment __________________

Project _______________________

Exam _________________________

Unit Overview

In this unit, your learner will learn about circles and their properties. This includes arcs and how different angles, and their arcs are related, and sectors and their areas.

Unit Assessments

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

Unit Discussion Questions

Where do you see circles, arcs, and sectors in the real world?

How have you used the skills of ratios and similarities in this unit?

Kit Materials

Applied Geometry Lesson Companion, Applied Geometry Extra Practice Workbook, compass, colored pencils, graph paper, notebook, protractor, ruler, scissors, TI-30XIIS calculator

Household Materials

pencil

Unit Notables

Your learner will use a compass to draw circles throughout this unit. The compass point is sharp, so we recommend they always have a stack of paper as they use it so it does not leave marks on the writing surface your learner is using.

Encourage your learner to practice until they can make circles easily.

Quiz ___________________________

Test ___________________________

Assignment __________________

Project _______________________

Exam _________________________

Surface Area and Volume

Unit Overview

In this unit, your learner will discover the volume and surface area of prisms, cylinders, pyramids, cones, and spheres.

Unit Assessments

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

Unit Discussion Questions

What would you need to make the sandcastle in your project?

Which shapes would be easiest to make out of sand and which would be the most difficult to make?

Why do you think the pyramids are something we associate with ancient civilizations?

Unit Notables

This unit introduces “nets” of three-dimensional objects. If your learner has difficulty visualizing how these relate, encourage them to create nets and fold them to see the relationship between the flat representation and the actual object. The Nothing but Nets lesson includes a link to a website that can create custom nets.

Kit Materials

Applied Geometry Lesson Companion, Applied Geometry Extra Practice Workbook, compass, glue, graph paper, notebook, ruler, scissors, TI-30XIIS calculator

Household Materials

pencil, tape

Quiz ___________________________

Test ___________________________

Assignment __________________

Project _______________________

Exam _________________________

Unit Overview

In this unit, your learner will discover the volume and surface area of prisms, cylinders, pyramids, cones, and spheres.

Unit Assessments

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

Unit Discussion Questions

What would you need to make the sandcastle in your project?

Which shapes would be easiest to make out of sand and which would be the most difficult to make?

Why do you think the pyramids are something we associate with ancient civilizations?

Unit Notables

This unit introduces “nets” of three-dimensional objects. If your learner has difficulty visualizing how these relate, encourage them to create nets and fold them to see the relationship between the flat representation and the actual object. The Nothing but Nets lesson includes a link to a website that can create custom nets.

Kit Materials

Applied Geometry Lesson Companion, Applied Geometry Extra Practice Workbook, compass, glue, graph paper, notebook, ruler, scissors, TI-30XIIS calculator

Household Materials

pencil, tape

Quiz ___________________________

Test ___________________________

Assignment __________________

Project _______________________

Exam _________________________