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Inverse Variation

Activity Overview

Students explore multiple representations of the inverse variation function, beginning with a geometric representation (a rectangle with fixed area), and progressing to a table of values, an algebraic expression, and finally a graph.

Key Steps

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    Students begin by visually exploring the relationship between the length and width of a rectangle when the area is kept constant. Students will change the length of the rectangle and watch how the width changes.

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    Next, students use data capture to collect the length and width values into a table. They will multiply the values together to verify that the area is staying the same for each pair of values. Students will begin making inferences about the relationship between length and width.

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    Then, students will use the formula for area of a triangle to define inverse variation. Students will graph a scatter plot of the captured values to discuss the shape of the curve.


    Finally, students will explore the graph of the inverse variation function.


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