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Building a Better Pet Run

Activity Overview

This activity is designed to make students realize that area of a rectangle changes for different widths.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print page 52 from the attached PDF file for your class

    • During the Activity

    Distribute the page to the class.

    Follow the Activity procedures:

  • Construct segment AB and place a point C on it
  • Transfer the length of AC to another portion of the screen, and using this measure, construct a circle with radius FG (=AC)
  • Draw perpendicular lines through both F and G
  • Transfer the length of CB to F
  • Construct a perpendicular line at the point of intersection of the second compass circle and the perpendicular through F
  • Use the calculator to overlay quadrilateral FGHK, which is a rectangle
  • Move point C along segment AB and note that the perimeter of the rectangle remains same, but its area changes
  • Collect data for the width, area and perimeter of the rectangle for various positions of point C
  • Set up a scatter plot of area versus width and observe that the plot has a parabolic pattern
  • Perform a quadratic regression and determine the best-fit equation
  • Solve the problem using the graph for the equation

    • After the Activity

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary

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