The Midge Problem

In 1989, the Mathematical Contest in Modeling offered a wonderful problem about distinguishing a "good" midge from a "bad" midge. It is a fine example of a problem that can be used to excellent effect with students at many different levels. We have been giving a version of this problem to our Precalculus students for the past few years.

Typically, the problem is presented after we have spent time studying techniques of data analysis and linear curve fitting. A unique aspect to this problem, as you'll see, is rather than fit a line to a set of data, the students are asked to use what they've learned to fit a line to the absence of data! What follows is the statement of the problem and five different approaches that student groups have used in solving it.