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