What is Pi? A "Cool" Lesson

From: Dr. Mavis Kelley
mkelley@BADLANDS.NODAK.EDU
To: The Middle-L listserv

I sent this lesson over another listserve. Thought I'd share here, too,
just in case it's helpful to anyone. If it doesn't make sense, send me a
note.

What is Pi?

This is a cool lesson. Basically, you just need a collection of jar
lids, of varying sizes, some string, scissors, rulers, and calculators. I
also use chart paper to post and analyze the data.

I have the students work in pairs. They each gather a few jar lids (you
could even limit it to one). The more lids you have them measure, the
larger the sampling size (another cool concept), and the more accurate the
results.

Then, I ask them to respond in their logs to the follow questions:
What is pi? Tell me everything you know. Then we share their thoughts at
this point. Then, I give them these directions for each jar lid. I
caution them to be as accurate as possible.

1. cut a piece of string equal to the circumference of your lid
2. cut a piece of string equal to the diameter of your string
3. Measure each.
4. Figure out how many diameter strings it would take to equal your
circumference string in length. (C divided by d, but I don't tell them
that). GIve your answer in decimal form
5. Post your answer on the chart when you are done.

Those who finish early can always measure another lid to add to the data base.

Then, when everyone is done, ask them what they notice about the data.

Analysis

They'll mention that most are in the ballpark. You can talk about why some
aren't; what might have happened. Then, you can allow students to check
their data and re--post.

Then, average the numbers. You should come up with a figure very close to
pi, 3.14.

Students may decide during analysis to throw out the highest and lowest
numbers. That's one way to deal with the data. I prefer to have them
check their measurements and change them if THEY feel its appropriate.

When we are done, we talk again about why everyone didn't come up with
exactly the same comparison, since pi IS 3.14. (Accuracy of cutting the
string, stretching the string, reading the measurement, etc.)

Finally, I ask them to write what they know about pi now and how it might
be useful. From now on, when we use pi in a formula, they know what it
stands for.

Enjoy!

Mavis