The Geometric Interpretation of Difference Quotient Lesson Plan

Instructor: Maria Airth

Maria has a Doctorate of Education and over 15 years of experience teaching psychology and math related courses at the university level.

In this lesson plan, your students will engage in learning to find the difference quotient of a function through collaboration. Students will be out of their seats actively moving around as they cement their understanding of the lesson concepts.

Learning Objectives

After this lesson, students will be able to:

  • Define the difference quotient of a function
  • Describe the difference quotient from a geometric standpoint
  • Name the type of line identified by the difference quotient


60 minutes

Curriculum Standards


Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.1


Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.



  • Review concepts important to this lesson:
    • What is a function?
    • What does the word difference mean in math? What about quotient?
    • What is the slope of a line?
    • What is a secant line?
  • Ask for volunteers to solve a few functions on the board to remind your students how to work with functions. Choose simple functions such as:
    • f(x)= x - 2
    • f(2) = x - 2 = 2 - 2 = 0
    • f(x + 3)= x + 3 - 2 = x + 1

To unlock this lesson you must be a Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use

Become a member and start learning now.
Become a Member  Back
What teachers are saying about
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Create an account to start this course today
Try it risk-free for 30 days!
Create An Account