Enrolling Now for 2026-27 School Year.
Enrolling Now for 2026-27 School Year.
Mathematical Models with Applications Math Models Learning Coach Guide Contents Equations and Inequalities Unit12 Linear Functions Unit13 Quadratic Functions Unit14 Patterns Unit15 Exponential Functions Unit16 Variation Models Unit17 Financial Models Unit18 Probability Unit19 Statistical Studies and Modeling Unit20 Geometric Models Unit21 Trigonometric Models Unit22 Part A:Welcome to Mathematical Models with Applications 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 Mathematical Models with Applications 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 need help, 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 the 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 Mathematical Models with Applications, your learner will build on previous skills and concepts to master the goals below: use linear, quadratic, exponential, variation, financial, geometric, and trigonometric models model growth and decay scenarios using exponential functions describe real-world scenarios for variation models apply mathematical principles to personal finances represent probability and apply probability models to events read and create graphical displays of information analyze data to determine center and variation demonstrate understanding of basic geometric principles calculate the perimeter, area, and volume of geometric figures demonstrate understanding of basic trigonometric principles demonstrate systematic problem-solving approaches 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 needed. 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 the 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, 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 taught in the unit. The Knowledge Check is not a graded assessment. Each lesson has its own components to help guide your learner through the lesson. 1. Lesson Overview: At the beginning of every lesson, your learner will see the lesson overview. This section contains lesson objectives, lesson vocabulary, materials your learner will need for the lesson, and the suggested lesson length. 2. Engage: The first section of the lesson is Engage. In this section, learners will be introduced to the lesson by making a connection to past and present knowledge and will get ready for the lesson’s instruction. 3. Discover: New content and instruction is presented in the Discover section. Your learner will interact with the lesson content through defined vocabulary terms, videos, audio, and Pause and Think activities. Your learner will be able to practice and answer questions as they work through the lesson. 4. Show: Learners will demonstrate what they have learned in the lesson through a series of practice questions. 5. Summary: This section recaps the day’s objectives and prepares learners for a future lesson or assessment. 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 have 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 work habits. In addition to assignments and projects, this course also includes quizzes and tests. 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: GeoGebra is a digital math tool learners can use to access free online scientific, graphing, or CAS calculator and virtual math interactives. Learners may use the GeoGebra calculators or interactives to solve problems or produce graphical representations as needed. Interactive Games: Learners will engage in interactive games that promote engagement and refining skills. These benefits contribute to more effective and enjoyable learning experiences. Stop and Jots: Stop and Jots are opportunities for learners to work offline to solve problems and record answers in their Lesson Companion. Lesson Companion: The Mathematical Models with Applications Lesson Companion 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: Extra practice opportunities allow learners to refine their skills in each unit. 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. Part C:Unit Information Equations and Inequalities Unit Unit Assessments Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Unit Overview In this unit, your learner will review the foundations of algebra, including expressions, equations, and variables. They will review using rates, ratios, and proportions to describe real-world problems. The second half of this unit concentrates on simplifying expressions and solving equations algebraically. Solutions to inequalities will be found algebraically and graphically using number line representations. Kit Materials grid paper, Mathematical Models with Applications Lesson Companion, Mathematical Models with Applications Extra Practice Workbook, TI-30XIIS Calculator Household Materials paper or notebook pencil Unit Discussion Questions How are equations and inequalities different? What are some real-life situations where you might use equations or inequalities? What did you find the most interesting about this unit? Unit Notables In this unit, learners will understand the act of manipulating an equation by keeping it balanced. Learners will see special cases of equations that have no solution and infinitely many solutions. Knowing how to simplify expressions and solve equations and inequalities is foundational to future mathematics courses, so encourage your learner to ask questions when they feel unsure or stuck. Linear Functions Unit Unit Overview In this unit, your learner will explore linear functions and their characteristics. They will also learn about representations of linear functions, including tables, graphs, and equations. Your learner will also explore systems of equations and inequalities. Solutions to systems of linear equations will then be explored along with solving linear inequalities graphically and algebraically. Unit Assessments Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Household Materials paper or notebook pencil Kit Materials grid paper, Mathematical Models with Applications Lesson Companion, Mathematical Models with Applications Extra Practice Workbook, TI-30XIIS Calculator Unit Notables Your learner will explore a statistical process called linear regression in this unit. This skill is valuable across various fields, from science and economics to social studies, and is essential in careers in data science and analytics. If your learner is interested in a career in these fields, encourage them to explore the skills and training needed to join that profession. Unit Discussion Questions Why do you think understanding linear functions is so important? Can you explain what linear regression is and give an example of how it is used? What did you find most challenging in this unit? Quadratic Functions Unit Unit Overview In this unit, your learner will learn about quadratic functions and how they can model real-world situations using quadratic functions and quadratic regression models. Solutions to quadratic equations and inequalities will then be explored using different strategies, including graphing and solving algebraically. Unit Assessments Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Unit Discussion Questions What are some real-world applications of quadratic functions? How is quadratic regression related to linear regression? How would you rate your understanding of quadratic functions? Kit Materials grid paper, Mathematical Models with Applications Lesson Companion, Mathematical Models with Applications Extra Practice Workbook, TI-30XIIS Calculator Household Materials paper or notebook pencil Unit Notables Your learner will build their knowledge of modeling real-world scenarios with quadratic functions, which will help them solve practical problems, make informed decisions, and apply mathematical concepts to real-world situations more effectively. The concepts in this unit will be useful in physics and other math courses. Patterns Unit Unit Assessments Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Unit Overview In this unit, your learner will explore visual and mathematical patterns. They will also discover that numeric sequences are functions. Through many examples, they will learn to identify geometric and arithmetic sequences and their respective characteristics. Your learner will also interpret sequences arising from mathematical situations, using representations such as lists, ordered pairs, and tables. They will then progress to using function notation to define sequences recursively and explicitly. Kit Materials Mathematical Models with Applications Lesson Companion, Mathematical Models with Applications Extra Practice Workbook, TI-30XIIS Calculator Household Materials paper or notebook pencil Unit Notables Your learner will explore the Fibonacci sequence and will discover its prevalence in nature and human design, illustrating the deep connection between mathematics and the real world. You and your learner can explore its presence in nature together by examining spiral shells, like the shells of mollusks, or by examining the spiral patterns of a flower. Unit Discussion Questions How do arithmetic and geometric sequences differ in their patterns and rules? Where are patterns and sequences seen in real life? For what reason would you use the recursive versus the explicit formula? Exponential Functions Unit Unit Overview In this unit, your learner will explore different types of exponential functions. They will compare exponential and linear functions and use their models to analyze and make predictions about real-world scenarios. They will interpret exponential growth and decay representations and create graphs for both types of functions. They will also examine the financial applications of exponential functions. Unit Assessments Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Household Materials paper or notebook pencil Kit Materials grid paper, Mathematical Models with Applications Lesson Companion, Mathematical Models with Applications Extra Practice Workbook, ruler, TI-30XIIS Calculator Unit Discussion Questions How can you identify whether a function is linear, exponential, or neither? What are real-world examples that can be modeled by exponential growth? Was there anything you were surprised by in this unit? Unit Notables In this unit, your learner will model real-life scenarios with exponential growth and decay functions. A way to help visualize each of these function types is to have them graph the function on paper or using an online graphing tool. Encourage your learner to discuss the implications of interest and the exponential nature of interest. Variation Models Unit Unit Assessments Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Unit Overview In this unit, your learner will explore how to model real-world situations using variation equations. They will begin by learning about the types of variation, including direct, partial, inverse, joint, and combined variation. Your learner will be introduced to real-world applications of each type of variation and solve problems involving each. Finally, they will complete a project, in which they will model a scenario and make a prediction using this model. Household Materials paper or notebook pencil Kit Materials Mathematical Models with Applications Lesson Companion, Mathematical Models with Applications Extra Practice Workbook, TI-30XIIS Calculator Unit Notables In this unit, your learner will create an equation, table of values, and graph that models a real-world variation scenario. They will then modify that equation based on additional information and use that model to make predictions. Determining the number of independent variables will be one important step in determining the type of variation that is appropriate for the scenario. Unit Discussion Questions How does variation relate to linear functions? What are the differences between direct, partial, and inverse variation? What did you find the most interesting about this unit? Financial Models Unit Unit Overview In this unit, your learner will differentiate between various types of pay and calculate total costs with discounts and tips. This unit will also teach them how to analyze ratios and rates to evaluate deals and understand the benefits of budgeting. Finally, they will explore money management, savings accounts, interest calculations, investment risks, loan types, and mortgage options. This unit will teach how to make informed financial decisions and manage their personal finances. Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Exam _______________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Unit Discussion Questions Once you set up a personal budget, how do you stick to it? What kinds of investments have low levels of risk? What are the advantages and disadvantages of borrowing money? Kit Materials Mathematical Models with Applications Lesson Companion, Mathematical Models with Applications Extra Practice Workbook, TI-30XIIS Calculator Household Materials paper or notebook pencil Unit Notables In this unit, your learner will explore the process of money management as it pertains to creating and maintaining a personal budget. You can encourage your learner to explore this further by researching a desired profession and creating a budget based on the potential earnings from that line of work. Unit Assessments Probability Unit Unit Overview In this unit, your learner will explore probability. They will learn the basics of probability and how to estimate the likelihood of events taking place. Your learner will explore both theoretical and experimental probability and represent outcomes using sample spaces. They will also learn to use combinations and permutations to solve real-world application problems. Unit Assessments Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Kit Materials Mathematical Models with Applications Lesson Companion, Mathematical Models with Applications Extra Practice Workbook, TI-30XIIS Calculator Household Materials dot cubes paper or notebook pencil Unit Notables Your learner will see how experimental and theoretical probability and the likelihood of an event happening is used in everyday life. Encourage your learner to perform an experiment with dot cubes, a coin, or a deck of cards to observe differences in theoretical and experimental probability. Unit Discussion Questions What is something you would like to learn more about from this unit? When in your daily life might you need to determine the likelihood of something happening? What are some reasons the likelihood of an event occurring can get more complicated to determine? Statistical Studies and Modeling Unit Unit Assessments Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Unit Overview In this unit, your learner will review the fundamental concepts of statistical studies and explore statistical modeling. The learners will determine how to identify correlations and causality, which will explain the characteristics of the data surrounding events. The normal distribution of data will be explored in relation to the central tendency of data samples. Displaying data and recognizing characteristics of a data set are also examined in this unit. Kit Materials Mathematical Models with Applications Lesson Companion, Mathematical Models with Applications Extra Practice Workbook, TI-30XIIS Calculator Household Materials paper or notebook pencil Unit Discussion Questions What are some common ways to display the results of a statistical study? How can data be biased? What are some common ways that you are misled by statistical studies, especially in advertising? Unit Notables In this unit, your learner will learn to effectively display data using a variety of methods and develop an understanding of choosing one method over another. Encourage your learner to notice and interpret displays of data around them in ads they see and articles they read. Geometric Models Unit Unit Assessments Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Unit Overview In this unit, your learner will begin with the fundamentals of geometry, including points, lines, line segments, rays, and planes. They will explore how to classify angles and polygons and apply critical thinking in geometry by working with conditional statements and angles within triangles. Your learner will measure distance in the real world using similar triangles and proportions and learn about units of measurement, perimeter, area, surface area, and volume of geometric figures. Household Materials pencil Kit Materials Math Model Lesson Companion, Math Models Extra Practice Workbook, TI-84+ Graphing Calculator Unit Discussion Questions What are the geometric fundamentals of our 3D world? How do jet pilots know how fast and at what angle to descend their aircraft in order to make a safe landing on the runway? What did you find most challenging in this course? Unit Notables Your learner will utilize scaling laws to accurately depict large objects. c figures will be explored. The second half of the unit will deal with trigonometry and the study of right triangles. In this unit your learner will examine how to model real-world situations by using geometry. The fundamental of geometry, including points, lines, planes, and calculating perimeter and areas of irregular geometric figures will be explored. The second half of the unit will deal with trigonometry and the study of right triangles. Household Materials paper or notebook pencil Kit Materials Mathematical Models with Applications Lesson Companion, Mathematical Models with Applications Extra Practice Workbook, ruler, TI-30XIIS Calculator Math Model Lesson Companion, Math Models Extra Practice Workbook, TI-84+ Graphing Calculator Unit Notables Your learner will construct and analyze conditional statements and their logical equivalents (converse, inverse, contrapositive), and use these statements to justify reasoning. Your learner might begin to notice such statements being used in everyday conversations. Unit Discussion Questions What is a polygon, and how can you tell if a shape is a polygon? How do you decide which unit of measurement is best to use for a given object? What did you like learning about most in this unit? Trigonometric Models Unit Unit Assessments Quiz _________________________ Test _________________________ Assignment ________________ Project _____________________ Have your learner identify which assessment type they see in their unit. Check all that apply. Unit Overview In this unit, your learner will explore trigonometry and the study of right triangles. They will simplify radicals and use the Pythagorean theorem to find the missing side lengths of a right triangle. Your learner will use sine, cosine, tangent, and their inverses to solve right triangles. Finally, they will apply right triangle trigonometry to problems involving angles of elevation and depression. Household Materials pencil Kit Materials Math Model Lesson Companion, Math Models Extra Practice Workbook, TI-84+ Graphing Calculator Unit Discussion Questions What are the geometric fundamentals of our 3D world? How do jet pilots know how fast and at what angle to descend their aircraft in order to make a safe landing on the runway? What did you find most challenging in this course? Unit Notables Your learner will utilize scaling laws to accurately depict large objects. c figures will be explored. The second half of the unit will deal with trigonometry and the study of right triangles. In this unit your learner will examine how to model real-world situations by using geometry. The fundamental of geometry, including points, lines, planes, and calculating perimeter and areas of irregular geometric figures will be explored. The second half of the unit will deal with trigonometry and the study of right triangles. Kit Materials grid paper, Mathematical Models with Applications Lesson Companion, Mathematical Models with Applications Extra Practice Workbook, ruler, TI-30XIIS Calculator Math Model Lesson Companion, Math Models Extra Practice Workbook, TI-84+ Graphing Calculator Household Materials paper or notebook pencil Unit Notables Your learner will design a triangular sail for a small boat, calculate the necessary dimensions of the sail, and determine its area and perimeter using Pythagorean theorem. Encourage your learner to research the ways the Pythagorean theorem is used in a variety of professions and careers. Unit Discussion Questions How can you differentiate between angles of elevation and angles of depression? How are calculations using triangles useful in the real world? What did you find most challenging in this course?
Enrolling Now for 2026-27 School Year.
