In this activity students will explore area as it compares to length of rectangles with a fixed perimeter by creating lists of the possible dimensions and the areas of these rectangles. Students will then graph a scatterplot of the data, find the quadratic regression, and explore the table of values to find the maximum area.

Review perimeter and area of rectangles. Download the worksheet and duplicate for each student. You may want to provide rulers or straightedges for them to use when drawing their rectangles on the grid provided on the worksheet.

A display device is helpful such as TI-SmartView or a TI-Navigator, but it is not necessary. All keystrokes are described on the worksheet with accompanying screen shots. Discuss with students what window settings are provided by using ZoomStat and why.

Discuss the resulting equation and its values for a, b, and c.