Materials
circular object
string
scissors
tape

To Do and Notice
Carefully wrap string around the circumference of your circular object. (Ask a partner to help.) Cut the string when it is exactly the same length as the circumference. Now take your “string circumference” and stretch it across the diameter of your circular object. Cut as many “string diameters” from your “string circumference” as you can. How many diameters could you cut? Compare your data with others. What do you notice?

What’s Going On?
This is a hands-on way to divide a circle’s circumference by its diameter. No matter what circle you use, you’ll be able to cut 3 complete diameters and have a small bit of string left over. Estimate what fraction of the diameter this small piece could be (about 1/7). You have “cut pi,” about 3 and 1/7 pieces of string, by determining how many diameters can be cut from the circumference. Tape the 3 + pieces of string onto paper and explain their significance.

Materials
measuring tapes
calculators
hats with sizes indicated inside them

To Do and Notice
Most hat sizes range between 6 and 8. Brainstorm ideas for how such sizes could be generated. Then use measuring tape to measure peoples’ heads. (As you do this, think of where a hat sits on a head). Use calculators to manipulate measurements. Now compare your results with the sizes written inside the hats. Do your numbers look like they could be hat sizes? (Hint: Try using different units of measurement.)

What’s Going On?
Hat sizes must be related to the circumference of the head. The circumference of an adult’s head usually ranges between 21 and 25 inches. The head’s circumference divided by pi gives us the hat size.

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