Ch 4: Model Linear Relationships: CCSS.Math.Content.8.F.B.4

About This Chapter

Share video lessons with your students to reinforce your linear relationships modeling instruction. Use the quizzes that follow each lesson to augment learning.

Standard: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models and in terms of its graph or a table of values.

About This Chapter

Students who have mastered this standard are proficient in combining two or more functions. Students understand they may substitute variables, numbers or other functions.

Lessons in this standard cover concepts such as:

  • Understanding basics of function notation
  • Tips for composing functions
  • Strategies for various ways to graph linear equations
  • Understanding rate of change and initial values of functions

Students demonstrate mastery of this standard when composing functions by beginning with the outside function. They are also proficient in evaluating the composition of functions at specific values. Mastery of this standard supports their college and career readiness because being able to model linear relationships is an important foundational skill for upper level math. In addition, working with mathematics encourages students' higher level thinking skills.

How to Use These Lessons in Your Classroom

Pretest/Posttest Composing Functions Lesson

Ask students to complete the quiz in the How to Compose Functions lesson before viewing the video, as a way to check for prior understanding. Then share and discuss the video lesson. Ask students to complete the quiz for a second time, comparing their results to the pretest.

Initial Value Lesson

Share the video lessons concerned with determining the initial value of a function. Review math vocabulary, including initial condition, constant of integration, derivative, integral and antiderivative. Work through additional problem examples, and then assign a set of practice exercises to check for student understanding.

Rate of Change Lesson

Watch the video lessons pertaining to rate of change with your class. Review the problem examples. Assign an exercise to each student, asking individuals to teach their solutions to a small group after successful completion of the problems.

6 Lessons in Chapter 4: Model Linear Relationships: CCSS.Math.Content.8.F.B.4
Test your knowledge with a 30-question chapter practice test
How to Compose Functions

1. How to Compose Functions

Function composition is the process of putting two or more functions together. This video lesson will explain how this process works and also show you how to evaluate functions that have been composed.

Composing Functions: Definition and Examples

2. Composing Functions: Definition and Examples

In this lesson, you'll learn the definition of a mathematical function and explore function notation and function tables. We will also review several examples of functions.

Model a Linear Relationship Between Two Quantities

3. Model a Linear Relationship Between Two Quantities

In this lesson, we will learn about modeling linear relationships by converting domain and range values into ordered pairs and then constructing a graph.

Determine the Rate of Change of a Function

4. Determine the Rate of Change of a Function

In this lesson, we will learn about the rate of change of a function with specific focus on linear and exponential functions while examining the graphs of both types of functions.

Determine the Initial Value of a Function

5. Determine the Initial Value of a Function

In this lesson, you will learn to determine the initial value of a function by studying functions in the form of word problems, graphs and linear equations.

Interpret Rate of Change and Initial Value

6. Interpret Rate of Change and Initial Value

In this lesson, you'll learn how to interpret the rate of change and initial value of a function. We'll also discuss applying these principles to word problems and in real-world situations.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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