This is more of a How Can You Do This, because I bombed. Students were baffled. I’m not sure how to work the scaffolding on this one, even though I got the concept from a textbook. Any help appreciated. ADD: Suggestions to fix this lesson are in the comments.
Trailer for THEM!
Followed (after discussion) by:
Now, you may have some student give a clever answer using evolutionary biology, but at some point establish this is a Super-Science sort of situation, leading to:
Suppose you had a super-enlarger ray. How large could you make the ant so it still survives?
And here’s the textbook version (McDougal Littell, Algebra 2):
A common ant absorbs oxygen at a rate of about 6.2 milliliters per second per square centimeter of exoskeleton. It needs about 24 millilitres of oxygen per second per cubic centimeter of its body. An ant is basically cylindrical in shape, so its surface area S and volume V can be approximated by the formulas for the surface area and volume of a cylinder:
a. Approximate the surface area and volume of an ant that is 8 millimeters long and has a radius of 1.5 millimeters. Would this ant have a surface area large enough to meet its oxygen needs?
b. Consider a “giant” ant that is 8 meters long and has a radius of 1.5 meters. Would this ant have a surface area large enough to meet its oxygen needs?
So: no dice, even after simplifying the cylinder to a rectangular prism and exploring the 1x1x1 cube with the sides doubled first. (I could have led in with the Athenian Plague problem, which is roughly equivalent.)
In any case, students were paralyzed with indecision and I nearly had to do the problem for them to wrap it up. So, how could this work?