Anywhoo... we've been developing the formulas for the figures. We developed lateral area, surface area, and volume of prisms and cylinders yesterday. Today, however, I got inspired to move to spheres. How is the surface area and volume of a sphere calculated? Why?
I've never tried this before, but I thought I'd give it a shot. I brought in tangerines and clementines for everyone. Their first thought was, 'awesome free food.' We proceeded as follows: As the students peeled their fruit I said, 'Wait! Don't throw it away! Its really important!" Using string they approximated the circumference and calculated the radius. After a short lesson on how to properly use compasses, they drew circles of the same radius. 'How many circles do you think you can fill with your peel?' Estimates ensued, some big, some small. Just for fun, I asked them if they had a grapefruit instead, how many circles do they think they could fill. Surprisingly, I got a variety of answers. Some said they could fill the same amount, some thought more because it got bigger, some said less because it got bigger. Let's find out!
They proceeded to take the peel and fill in as many circles that they could.
Now, I've never tried this before. In years past, I was Johnny Boring and just handed them the equation. After some reflection as to how terrible those lessons were and how much better they could be, I collaborated with some colleagues and put this little activity together. And Boy Howdy did it go well! Seriously, it was awesome. Most students filled in four circles and put the connection of 4*pi*rsquared. It was great! And, bonus, my room smelled terrific! The students made connections, saw some cool stuff, all in all it was a great day and something I will continue to do in the future.
As an added extra, a former student of mine brought me in a baseball and I took it apart at the seams and used it to further illustrate surface area.
Now, to calculate volume of a sphere, I had them eat the fruit. That's it. We didn't derive the formula due to the fact that the derivation is awesome. And by awesome I mean gross.
To permanently (kind of) keep this lesson in my students' minds, I taped my example to a sheet of paper and hung it on my wall. I give it a week before the wonderful orange tangerine peel turns to slimy brown smelly mush. But when my students see that mush, you know what they will think about? Probably not surface area at first, but eventually they will.