In a workshop last Saturday we did a cool activity that I have to share. It wasn't new to some people, so maybe I'm the only one who's never seen it. Each group of 2-3 people was given an orange (try to get them as spherical as possible), some wrapping ribbon (or string, something to measure the circumference with), a compass, a largish blank sheet of paper, and a calculator (later she made sure there were wet wipes to clean with). We were going to estimate the surface area of a sphere.
1. find the circumference of your orange with the ribbon. Be accurate.
2. using this measurement and prior knowledge, find the radius of the sphere.
3. with the compass draw 6 or so circles with that radius.
(teacher checks the circles before kids proceed by placing orange on top of circle and eyeballing)
4. peel the orange and fill as many circles completely as you can. (only the "orange" part is the surface area)
It was great, we fit exactly 4 circles, (which are of area pi*radius*radius), so voila we had an estimate of the surface area. Ooh aah.