"Find the area of skin on your hand. Discuss how accurate you think your answer is."
I gave this question to year 10 students some years ago. The number of different methods the students found was remarkable.
Most modelled the hand as a right prism, and traced around their hand to get the 'base'. Some then overlaid a centimetre grid and counted squares, while others divided it into rectangle and triangles and added the separate areas. Most subtract out the area of the nails.
Getting the area of the 'perpendicular sides' caused a lot of discussion. Some did it section by section (eg finger by finger), and even modelled the tips of the fingers as semi-circles to get greater accuracy. Others carefully laid a piece of string around their hand, and hence found the area as a single piece.
There were some quite different solutions, however. One girl found a rubber glove that fitted snugly. She cut it up and laid it flat and found the area of that. Another painted her hand (!) and noted how much paint she used. She then painted a rectangle that used the same amount of paint and determined its area.
The discussions that ensued as to the most accurate method were very passionate. The kids felt ownership of their solutions. and defended them strongly.
Rex Boggs | High above the hushed crowd, firstname.lastname@example.org | Rex tried to remain focused. | Still, he couldn't shake one Glenmore High School | nagging thought: He was an Rockhampton, Queensland | old dog and this was a new Australia | trick - Gary Larson