Math Foundations Learning Coach Guide

Part A:
Welcome to Math Foundations

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 Math Foundations

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, 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

Math Foundations is designed to assess and enhance your learner’s readiness for high school mathematics. Your learner will be engaged with key arithmetic and algebraic concepts, prepared for placement into Pre-Algebra, Algebra 1A, or Algebra 1 based on their performance. The curriculum focuses on four main domains: Numbers and Operations, Algebraic Concepts, Geometry, and Probability and Statistics, with a particular emphasis on algebra readiness. Through a structured progression of units, your learner will develop foundational number skills, explore algebraic foundations, and delve into equations and basic statistics, ensuring a comprehensive preparation for later mathematical studies.

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

• understand and apply the properties of real numbers in expressions and equations;
• determine the least common multiple (LCM) and greatest common factor (GCF) of a set of values;
• simplify and evaluate algebraic expressions;
• solve linear equations and inequalities;
• model relationships using algebraic expressions and equations;
• use ratios and proportions to solve problems;
• use the slope and y-intercept to represent and interpret linear relationships with equations and graphs;
• solve algebraic equations and linear inequalities including absolute value;
• solve systems of linear equations through graphing, substitution, or elimination;
• apply probability concepts to make predictions and solve problems;
• interpret and represent data sets using pie charts, histograms, dot plots, and box plots; and
• summarize data sets using measures of center and spread.

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 strategy and study tips.

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 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: 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. 

3. Discover: New content and instruction are 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 notifies learners of a future lesson or assessment.  

This course includes quizzes and tests.

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

2. Quiz: A quiz may be given at the end of a topic or the end of a unit.

3. Unit Test Review: Before a test, learners will have the opportunity to review the content they will be assessed on in the test.

4. Unit 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:  

• Lesson Review Videos: Each lesson includes a video summary of the concepts and skills addressed.

Part C:
Unit Information

Foundational Number Skills

Unit Overview

In this unit, your learner will explore real numbers and the properties of operations that govern them. They will work to master useful mathematical tools like the Pythagorean theorem. They will also identify the least common multiple (LCM) and greatest common factor (GCF) of numbers.

Unit Assessments

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

Unit Discussion Questions

Why does the Pythagorean theorem help you find missing sides of a right triangle?

How can absolute values be used to apply operations to negative numbers?

Why do you use the properties of addition and subtraction to simplify numerical expressions?

Unit Notables

In this unit, your learner will apply the properties of numbers to simplify expressions involving rational numbers within real-world scenarios. Understanding the GCF will assist them in solving practical problems related to packaging and grouping items. Additionally, learning to find the LCM will help them solve problems involving scheduling and time-related issues.

Kit Materials

calculator

Household Materials

none

Unit Overview

In this unit, your learner will explore real numbers and the properties of operations that govern them. They will work to master useful mathematical tools like the Pythagorean theorem. They will also identify the least common multiple (LCM) and greatest common factor (GCF) of numbers.

Unit Assessments

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

Unit Discussion Questions

Why does the Pythagorean theorem help you find missing sides of a right triangle?

How can absolute values be used to apply operations to negative numbers?

Why do you use the properties of addition and subtraction to simplify numerical expressions?

Unit Notables

In this unit, your learner will apply the properties of numbers to simplify expressions involving rational numbers within real-world scenarios. Understanding the GCF will assist them in solving practical problems related to packaging and grouping items. Additionally, learning to find the LCM will help them solve problems involving scheduling and time-related issues.

Kit Materials

calculator

Household Materials

none

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Algebraic Foundations

Unit Overview

In this unit, your learner will model relationships using algebraic expressions and equations. They will graph linear equations in the coordinate plane. They will also apply the concept of slope and rate of change to solve scenarios.

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 values that should not be included or limitations in a scenario?

How can you use algebraic expressions and equations to represent real-world scenarios?

What does the slope tell you about the graph of a line?

Unit Notables

In this unit, your learner will graph linear equations, which is a foundation for solving systems of equations. This will help them model real-world situations, such as budgeting, distance-time problems, and pricing scenarios.

Kit Materials

calculator, graph paper

Household Materials

none

Unit Overview

In this unit, your learner will model relationships using algebraic expressions and equations. They will graph linear equations in the coordinate plane. They will also apply the concept of slope and rate of change to solve scenarios.

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 values that should not be included or limitations in a scenario?

How can you use algebraic expressions and equations to represent real-world scenarios?

What does the slope tell you about the graph of a line?

Unit Notables

In this unit, your learner will graph linear equations, which is a foundation for solving systems of equations. This will help them model real-world situations, such as budgeting, distance-time problems, and pricing scenarios.

Kit Materials

calculator, graph paper

Household Materials

none

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Foundations of Equations

Unit Overview

In this unit, your learner will solve equations and inequalities algebraically. They will focus on the properties of equality and the importance of their order. They will use what they have previously explored to use logic and reason to solve equations and inequalities.

Unit Assessments

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

Unit Discussion Questions

How are equations and inequalities similar?

How can you rewrite an equation in terms of a specific variable?

What are the goals you should aim to achieve in order to solve an equation?

Unit Notables

In this unit, your learner will solve equations algebraically, which is a foundation for solving problems in Algebra, Geometry and Trigonometry. They will also solve inequalities, which will help them interpret probability ranges and analyze data distributions in Statistics. Solving equations and inequalities will help them model real-world problems like budgeting and scaling recipes.

Kit Materials

calculator, graph paper

Household Materials

none

Unit Overview

In this unit, your learner will solve equations and inequalities algebraically. They will focus on the properties of equality and the importance of their order. They will use what they have previously explored to use logic and reason to solve equations and inequalities.

Unit Assessments

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

Unit Discussion Questions

How are equations and inequalities similar?

How can you rewrite an equation in terms of a specific variable?

What are the goals you should aim to achieve in order to solve an equation?

Unit Notables

In this unit, your learner will solve equations algebraically, which is a foundation for solving problems in Algebra, Geometry and Trigonometry. They will also solve inequalities, which will help them interpret probability ranges and analyze data distributions in Statistics. Solving equations and inequalities will help them model real-world problems like budgeting and scaling recipes.

Kit Materials

calculator, graph paper

Household Materials

none

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Foundations Probability and Statistics

Unit Overview

In this unit, your learner will model data using different displays such as pie charts, dot plots, histograms, and box plots. They will summarize data sets using measures of center and spread. They will also use probability concepts to make reasonable predictions.

Unit Assessments

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

Unit Discussion Questions

How can you express the likelihood of an event occurring using numbers?

What are some examples of how probability and statistics are used in everyday situations?

Why do you use measures of center, variability, and shape to analyze distributions of data?

Unit Notables

In this unit, your learner will model data using different displays which will help them build a strong foundation for future math courses like Algebra, Data Analysis, and Statistics. The concepts of probability will assist them in solving decision-making problems in real-world scenarios.

Kit Materials

calculator

Household Materials

none

Unit Overview

In this unit, your learner will model data using different displays such as pie charts, dot plots, histograms, and box plots. They will summarize data sets using measures of center and spread. They will also use probability concepts to make reasonable predictions.

Unit Assessments

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

Unit Discussion Questions

How can you express the likelihood of an event occurring using numbers?

What are some examples of how probability and statistics are used in everyday situations?

Why do you use measures of center, variability, and shape to analyze distributions of data?

Unit Notables

In this unit, your learner will model data using different displays which will help them build a strong foundation for future math courses like Algebra, Data Analysis, and Statistics. The concepts of probability will assist them in solving decision-making problems in real-world scenarios.

Kit Materials

calculator

Household Materials

none

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________

Quiz _________________________

Test _________________________

Assignment ________________

Project _____________________

Exam _______________________