Teacher2Teacher |
Q&A #6013 |
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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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