This activity is designed to help you understand the relationship between the shape of a figure and the effect that shape has on perimeter and area. By keeping the area constant and changing the shape of the figure, you will be able to determine which shapes produce the greatest perimeters.

Group students in groups of four. Each student in the group gets a 5 X 5 squares. Each student then cuts a square apart using only straight cuts. Next, each student tapes these pieces together in a shape other than a square. Students should work to make the shapes as different as possible in each group, making some long and skinny and others more compact. Then, using one large sheet of newsprint per group, students take one shape at a time and trace each side in a continuous line to create a bar graph of the perimeter of each shape. Tape the shape traced under the appropriate line. As a group, students discuss and agree on three to five observations you can make about the relationship between perimeter and shape. Finally, students write these observations on their newsprint.