Visually explore relationships in area and circumference
Before the Activity
Group students in pairs, give them calculators.
During the Activity
1. Draw a circle.
2. Add a radius to the circle.
3. Use the measurement tool to calculate the length of the radius, the area of the circle, the circumference of the circle.
4. Look at the area, is it greater or less than the circumference? Is this always true?
5. Grab the radius and pull it out, then in. Notice that the area and circumference change as the raduis changes.
6. What is the radius when the area and circumference are equal? Is this true in your neighboor's circle also?
7. What is the radius when the circumference is greater than the area?
8. What is the radius when the circumference is less than the area?
9. Use algebraic reasoning to determine why these relationships are true.
After the Activity
Students can use the formulas for area and circumference to determine when the 2 are equal, when one is greater than the other. When does a circle present as an economical choice containing an animal or product, when is a circle a poor choice?