Informal Derivation of Pi

7.GM.5 Understand the formulas for area and circumference of a circle and use them to solve real-world and other mathematical problems; give an informal derivation of the relationship between circumference and area of a circle.

I gave the students hula hoops and some coasters, and next year I might save some container lids or something to create a few more things for them to measure and work with. Then i gave them strings and measuring tapes (there were measuring tapes in some of the manipulative kits I found at the end of last year!) and had them figure out the relationship between the circumference and diameter. They all came pretty close to pi, which was cool.

I need to review the instruction sheets I gave them to make sure the language is as clear as possible, or else create an instruction video.

I liked this activity and the students seemed to as well, but it’s frequently really challenging for my students to reverse the direction of the problem. They have the idea that circumference/diameter = pi, and some of them even got that pi is like a unit rate, or a very specific variable, but they can’t seem to remember the process that circumference = diameter * pi. I need to think of more ways to extend this activity to help with that.


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