# Activities

• • • ##### Subject Area

• Math: Algebra I: Quadratic Functions
• Math: Precalculus: Functions and Graphs

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 2 from the EXPLORATIONS Book:
EasyData Activities: Modeling Algebraic Functions with Data Collection Activities.

## 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

• 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.

• 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