Question

Here is a great activity to do with your students that will intrigue them. You will need lots of string, rulers, and several pairs of scissors. Give your students 4 equal strings of length 12 inches. Ask them to form the first string into a circle and find its circumference and area. Ask them to cut the second string in half and form 2 circles from the resulting strings. Have them find the total circumference and area of these two circles. Ask them to next cut the third string into 3 equal parts and form 3 circles and again calculate the total circumference and area. Finally, ask them to cut the fourth string into 4 equal parts and form 4 circles and fine the total circumference and area. Guide them in showing that, in each case, the sum of the circumferences of the smaller circles is the same, but the sum of the areas of the small circles differs drastically from one case to the next. Ask them if they think this makes sense and explain why. What is your answer to this last question? Please include a table comparing the areas with zero cuts of the string, one cut, etc.

Answer 1