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Q&A #6013


How Pi fits into the K-12 curriculum

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From: Gail (for Teacher2Teacher Service)
Date: Mar 25, 2001 at 08:30:22
Subject: Re: How Pi fits into the K-12 curriculum

Dear Julie,
     Here is a timely activity (because we are in the process of completing
it right now in my fifth grade classroom) about the relationship between the
circumference and diameter...

I read to my students before lunch each day, and there is a wonderful short
story/picture book called Sir Cumference and the Dragon of Pi, so I chose
it, and read it, and didn't make a big deal out of it, as if it were just
another story.

Then we spent a day learning the names of the parts of a circle
(center, radius, diameter, circumference and chord)and learning to use the
compasses (I use the EZ-compass variety, because they truly are MUCH easier
for students to handle).

We spent the next day measuring the radii and diameters of about 10
different circles, a few at a time, and making observations as we measured...  
and after about half of them, students started mentioning that they were
noticing something about the data we were collecting...   you know what they 
saw... the radius doubled was the diameter, and the diameter halved was the 
radius.
 That is not a big deal to us, but to them, it was cause for major
excitement.
 None of the other geometric figures we have explored had the same
relationship all the time, for big, small and in-between sizes...   they
realized they were onto something.

The next day we revisited the radius/diameter discovery briefly, and then
went on to determine a way to measure the circumference.  I did not remind
them of the book we had read, and did not tell them how to measure.  We
sometimes forget that much about mathematics is NOT as obvious as it appears
to us, and such was the case here.  I was pretty amused by some of the
suggestions.  One group wanted to just double the diameter, so I suggested
they give that a try (and since another group thought this particular
speaker was "always" right...  they followed suit too.

Another group wanted to carefully bend the ruler around the circle (but of
course, a wooden ruler doesn't really bend...   they gave that a try.
We talked briefly about why the ruler wasn't a great choice for this
measurement...   when it was the very tool we used to find the other
"around" measurements (perimeters).  someone mentioned that the other
figures all had straight edges...

Another group thought they might be better off with the measuring tapes (ah-
finally, I thought...), but then they tried to lay the tape flat, and put a
series of tucks in it to make it curve around the circle -- and this group
has the young lady identified as "gifted"...  I was having a hard time
keeping the strategy that would work easily to myself...

Finally someone suggested that they turn the tape sideways...   and I could
breathe again...   another group wanted to use the string I had placed on
each desk.

So, we had a bunch of different methods, and many worked, some better than
others.  After discussion about the results, the doubling groups abandoned
that strategy, and after a while ( it seemed like more time than it was)
some noticed another relationship...   this time the one I wanted them to 
note -- that the diameter times 3 is ABOUT the circumference...

At that point someone mentioned the book, and though I played ignorant, they
were certain there was a reason I had chosen to read that particular book...

Friday we took the lids from a multitude of different jars, and predicted
how many times we could roll them along a meter stick.  We designed charts to
record predictions and actual answers, and started in.  After we had made
all the predictions and measured, it was time to put all the materials away,
so we just made a few quick observations...   but no earth = shaking
comments were made.

Tomorrow we will make predictions again...  this time for how many of each
lid could be laid side by side along the meter...   and then we will have
another example of how the diameter relates to the circumference, without
ever having said those words.  Will the students recognize what we have
done?
 With some careful questioning, yes...  Will I mention that the number they
have found is a special number, with a history?  sure...   it will be
exciting to them to realize that ancients did the same sort of things they
did (not with jar lids, of course) and noticed the same sorts of things...

I know this is not a K-12 perspective, but it is a real life experience in
an elementary classroom...   Hope it helps.  :-)

 -Gail, for the T2T service

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