Algebra I
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Inverse Variation
Posted on May 6, 2010
Topic: Rational Functions
Students explore the inverse variation function with a geometric representation (a rectangle with fixed area), a table of values, an algebraic expression, and a graph.
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Activity Key Steps:
This activity is begins with an exploration of inverse variation, using a square with a fixed area. Students use a slider that adjusts the length of the grey rectangle, while the width of the rectangle changes with length so that the area remains constant. Students capture the length and width values from a similar page.
This data is stored in a spreadsheet using the Manual Data Capture feature. Students gather 10 sets of values. They use their spreadsheet further to compute the product of the length and width. Students learn that the relationship when x and y have a constant product is called inverse variation.
Students create a scatter plot of the data. They will discuss the shape that the plot displays.
Students tie the various representations of the inverse variation function together. They will see that the curve that appears resembles the shape of the scatter plot. ¶ At the end of this activity, students will be able to determine the rational function that relates to two variables that vary inversely.