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Dear Mitch,

My teacher assigned a different thing for each kid to present to the class, and I got circumferences of circles and how you can check if the radius is the right length after you're given the size of the whole circumference.  I wanted to know if there is some really awesome thing I can do, because the teacher is laid-back and would like it if I had some way she's never seen to check if the kids' radius is the right length after they figure it out from the other stuff she gives us and the two formulas, the one that says: 

(Pi) x (length of the radius-squared) = the circle's area,

And the one that says: 

(2 x pi)  x  (length of the radius) = the circle's circumference.

Can you think of something that would be totally new and tight?

It would be great if you could, 

Melinda G.

Brooklyn, NY


Dear Melinda, 

Although it's impossible to know what your teacher has seen over the years, assuming she's not brand new at this), but there is something I've done a couple of times and I've never heard of anyone else trying it – though, of course, it's quite possible that lots of teachers come up with the same ideas without ever communicating or finding out about each other's approach.  I won't bore you with personal stories, but I can't help myself from telling you that the lesson I am about to describe is one of only three or four that have ever come to me in a dream!  Honestly, a dream! 

You have to get your hands on what I call an old-fashioned turntable or record player.  By that I mean one of those machines with the circle that spins and the arm with the diamond point that makes music from the large black vinyl records that were replaced by CD's, but which have recently become a novelty for collectors.  By the way, turntables are still being made and sold, but don't go out and buy one for just one lesson; ask around, as I think most schools and libraries still have them around in a storage closet somewhere.  Then find a record of a recording that is popular enough again to be selling in CD form.  Several of the Beatles' albums would be good examples of this.  So, for the lesson you need the turntable and one or two records (preferably of something your classmates would recognize (but otherwise, any record will do, as long as it has several separate songs on each side, as almost all albums do).

Before the lesson, print a class-supply of photocopies of the center label of each side that lists the songs recorded on that side in the order of recording.  You will also notice that the length of each song is printed next to that song – which I think was for the benefit of D.J.'s on the radio to figure out how many songs and which ones to play between announcements and advertisements.

Finally, you'll need a yard stick or a meter stick or tape measure.

For maximum drama, try to keep the turntable and records out of sight, such as in a box or behind a pile of books on the teacher's desk or whatever.

Oh, and know the 'size' of the record/circle; beforehand, measure the radius and write that down on a card and measure the circumference with a tape measure (and check to make sure your numbers fit into the formulas you mention and produce reasonably accurate answers). 

NOTE:  the radius is easy to find, as it is the measurement from the little hole in the record's center to the record's edge in any direction.  Get all those measurements down on your card and try to memorize them.  If that is tricky, then just make sure you have your card with you.

Present the formulas and give them the radius.

Let them view the list of songs on the photocopy. 

Now, I am going to leave some of this up to your imagination, or it would not be as interesting, but here's one hint:

Break the class up into groups based on which song they should try to pinpoint by radius.  Have them try the math...

And here's a second hint: 

Present your turntable and real record, measure their answer from the center of the circle, turn the machine on and lower the needle... and if the song is the one they'd hoped to land on, BINGO!  If not, have them try again... 

Let me know how it goes!

Hope this helps,