Learning Resource Type

Classroom Resource

Average and Instantaneous Rate of Change Interactive

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

Students will test their knowledge of average and instantaneous rates of change represented graphically with the following scenario:

Here you are given two points, C and D, which are located along the function f(x) = x2. If you draw a line crossing those two points, you will create a secant line. Now suppose you take point D and move it closer and closer to point C. What happens to the average rate of change as the two points get closer to each other? 


In the interactive, students will:

  • move the red point in order to change the coordinates of C along the function and the slope of the tangent line.
  • move the purple point in order to change the coordinates of D and the slope of the secant line.
  • observe the changes between the different slopes as points C and D get closer and closer together.
    Mathematics (2019) Grade(s): 09-12 - Precalculus

    MA19.PRE.25

    Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Extend from polynomial, exponential, logarithmic, and radical to rational and all trigonometric functions.

    Unpacked Content

    UP:MA19.PRE.25

    Vocabulary

    • Average rate of change
    • Specified interval
    • Difference Quotient

    Knowledge

    Students know:
    • Techniques for graphing.
    • Techniques for finding a rate of change over an interval on a table or graph.
    • Techniques for estimating a rate of change over an interval on a graph.

    Skills

    Students are able to:
    • Calculate average rate of change on a specified interval when given an equation or table ofa polynomial, exponential, logarithmic, and radical to rational and all trigonometric functions.
    • Interpret the average rate of change of a polynomial, exponential, logarithmic, and radical to rational and all trigonometric functions in the context of a problem when given symbolic representations, tables, graphs, or contextual situations.
    • Estimate the average rate of change for a specific interval of a polynomial, exponential, logarithmic, and radical to rational and all trigonometric functions functions when given agraph.

    Understanding

    Students understand that:
    • The rate of change is the ratio of the change between the dependent and independent variable.
    Link to Resource

    CR Resource Type

    Interactive/Game

    Resource Provider

    CK-12
    Accessibility
    License

    License Type

    Custom
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