## Pi: Tips and Tricks

• Research shows that when students see how simple formulas are derived, they understand the formulas better and retain them longer.
• Have students tie a rope or string onto a stick and then walk out from the stick some number of paces. Keeping the string taut, have them walk completely around the stick and count the number of paces it takes. It should take them about 6 times as many paces as they are from the stick, since C = 2 or C 6r.
• The circle is the plane figure that maximizes the area it contains. Using a long piece of rope with the two ends tied together, have students form a long narrow rectangle on the floor and count the number of students who can stand inside of it. Continue making rectangles so the measure of the length gets closer to the measure of the width with each new rectangle. The area inside should increase. Now have students form a circle with the rope and stand inside of it. They will see that they have made a shape with a lot of interior space.
• The activity mentioned above also shows that perimeter is not directly related to area, since the perimeter is constant for the rope, but the area inside varied by the shape made.
• Many civilizations created homes that had circular bases because such homes were greater in area. Examples of these are the igloos of the Inuit, the bush hutches of many African tribes, and the tepees of some American Indians.