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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

Length

60 minutes

Curriculum Standards

  • CCSS.MATH.CONTENT.8.F.A.1

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

  • CCSS.MATH.CONTENT.HSF.IF.C.7

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

Materials

Warm-up

  • 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

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