- Research shows that showing students how simple formulas are derived can help them 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 which 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 above activity 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.
- Many civilizations created homes which had circular bases because there would be more area in them. Examples of these are the igloos of Inuit, the bush hutches of many African tribes, and the teepees of native American Indians.