Math lovers note that March 14 (or 3/14) can be linked to the approximation for pi, which is 3.1415926535897… Pi is the ratio between the circumference of a circle and its diameter. This is true for any circle, any size, anywhere! It is a consistent ratio.
Helping students come to an understanding of this ratio can be done by collecting a number of items that are cylinders (cans of different sizes work great), and then measuring 1] across the top at the widest part (going through what would be the centre of the circle lid) and 2] around the circumference of the cylinder. A flexible measuring tape works best for the latter, but if you do not have one on hand, use a piece of string to mark the distance around the circle and then measure the length of string.
The various measurements can be recorded on a chart, and once the measuring is done, the dividing can begin. Each time the circumference measurement for a particular can is divided by its respective diameter measurement, the answer should be 3 and a bit (if not, recheck your measurements).
Using this information, the circumference of a circle can be found by multiplying the diameter times pi. If the radius of the circle is known, we double this to get the diameter, then multiply by pi. So another way to state the circumference of a circle is “pi times 2 times radius”. The length of a semicircle can be found by multiplying pi times the radius.
So, C = d x pi and C = 2r x pi.
Pi turns up regularly when we are measuring circles, and area is no exception. Students are often given the formula A=(pi)(r)(r) or “pi times radius squared” but we seldom stop to help them visualize what that might look like.
I am attaching a clip I found on the web that illustrates an activity that can be done with students to help them visualize the formula for the area of a circle. I have done this activity numerous times in the classroom, all to good effect! So get a paper circle, some scissors, a pencil, and have some fun with it!
Mathematically yours,
Carollee
