We have celebrated Pi Day in sixth grade for several years now, and each year, we add a little something more.
I didn't say anything to the students when the day started. Even though I was wearing this shirt, only one student asked ("Does that have something to do with St. Patrick's Day?"). I can conclude two things: They don't know much about Greek symbols and they don't care what we wear (Thereby proving that Farley should be able to wear jeans and flip flops every day!)
|I got my shirt at Cafe Press. Click the picture to link to the site.|
Before we began the project, I gave them a quick review lesson on centimeters and showed them how it was easy to measure the parts of a whole using this system... and that they would indicate tenths with decimals.
They had a worksheet that invited them to do the following:
Measure the distance around each can (in centimeters)
Measure the distance across the can (in centimeters)
Divide "around" by "across" and write the answer (in centimeters)
Even though they had to work cooperatively, there was very little grumbling (apparently my St. Patrick's Day shirt had put them in a good mood). They measured and laughed and measured again. As I took pictures, I was surprised to discover who wore nail polish and who didn't and who was currently wearing a temporary (?) tattoo! (I decided it was best not to post the incriminating evidence.) The things you learn when you have a camera!
Most students had time to measure at least four of the six cans. At this point, I asked them to tell me the measure of the "around" divided by "across" for two of the cans (both of which were included in all of the boxes and identified as those needed to be measured--with the remaining cans completed in the remaining time).
Their answers were interesting: 2.9, 3.18. 3.25, 2.77, 3.08, 3.35, 3.09. 3.45, 3.28, 27, 2.89, 3,21, 3.22, 3.16 and 3.45. We talked about the measure of 27 being an "outlier" (also part of the math unit) until one member of the partnership shouted,"Oh, you want the amount after we DIVIDE? Oh! 3.1"
After a discussion of variables in experiments, we also decided that the measurement was hampered by stretching the string and how "it's really hard to divide..."
Then I asked "Why did you get answers that were so similar?" This sparked a lively discussion and a variety of interesting responses! I gave them a chance to see if this was coincidental or was there something behind the similar measurements.
Finally, they completed the last part of the experiment: This required them to measure the distance around the can and CUT the string. Then, they measured the distance across and cut that amount repeatedly until they couldn't cut any more and taped the cut pieces and the remainder onto a piece of paper. The goal was to count how many whole measures and then to estimate how much of a whole piece (across) the little remainder piece was. Here I had some pretty accurate insight into what my students do NOT know... "It's about 23 tenths" and "It's a little more than half" were sadly amusing. Most students felt that "less than one fourth" was accurate and one brave soul ventured "One or two tenths..."
Note to self: Have plenty of tape on hand! Some students used more tape than string to display their results...
I told them we had a quick math quiz to check their division skills. I gave them 30 seconds to divide 22 by 7 as far as they could (As this is not an exact expression of pi, you will get a repeating decimal if you give them too long to work, so a limited amount of time is important.)
I had prepared a flip chart about measuring circles. We reviewed the correct vocabulary--and I had been pleased to hear some students saying "circumference" and "diameter" while they were measuring the cans. Once we got to the page where the distance around the our classroom trash can be divided by the distance across the can to produce a measurement of 3.14832 cm, someone said, "Hey! That's close to what I got when I measured one of the cans!" And so it went.
The next few flip chart pages explained a bit about pi and I told them we could simplify the whole process and help Velcro it into our memories by singing a little song. I explained that pi can't be resolved as a quantity and it can never be written down as an exact or complete number. Pi is non-terminating and non-repeating! (Oooo. Some of them LOVED those words!)
It was a fun day! I think they students learned a lot. And I learned a lot that will help guide my teaching over the next few weeks. However, I still seem to find myself thinking about cherry pie...