Education Technology

Old MacDonald's Pigpen

Activity Overview

Students solve a standard maximum value problem using the calculator. Students help Old MacDonald build a rectangular pigpen with 40 m fencing that provides maximum area for the pigs. They graph scatter plots, analyze quadratic functions, and find maximum value of a parabola.

Before the Activity

  • Use TI Connect™ to download
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 7 - 13 from the attached PDF file for the class
  • Set up the calculator for data collection
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Using the formula for the perimeter of a rectangle, determine the formula for length in terms of the perimeter and width
  • Enter widths and corresponding lengths as lists
  • Create separate lists for the area corresponding to each width
  • Ensure that the perimeter does not exceed the pre-defined value
  • Plot width and area data
  • Recognize the fact that width is the independent variable and area is the dependent variable
  • Understand that area is a function of width
  • Trace the graph and observe that the points are in the shape of a parabola
  • Perform a quadratic regression and find the equation of the curve
  • Use the calculator to find the maximum width needed to form a rectangle with the maximum area
  • Calculate the maximum area
  • Realize that when length is expressed in terms of width, the equation to find the area is quadratic
  • After the Activity

  • Students analyze the results and answer the case analysis questions on the student worksheet
  • Review student results
  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary