This activity has two components that allow for the discovery of patterns which suggest the formulas for area and perimeter. Students may work individually or in groups, but groups are recommended.

Constant Area:
First, students are to find all the rectangular arrays that can be made using 24 tiles. For this exercise, no tile may be stacked on top of another. Students then chart the area and perimeter of each rectangular array made. (The area will always be twenty four, but the perimeter will change.) After recording the data on the chart, students must graph their findings. Finally, students should write 3 observations about the data on either their chart or graph sheet.

Constant Perimeter:
Second, students are to hold the perimeter of the rectangular arrays to 24 units. This may be illustrated by talking in terms of tables and the number of people who could be seated at each table. Again, no tile may be stacked on another. Students should record the area and perimeter of their arrays on the chart. ( Here the perimeter will always be 24, but the area will change.) After recording the data on the chart, students must graph their findings. Finally, students should write 3 observations about their data either on their chart or on their graph sheet.