I recently was notified that a former student’s idea is expected to be published in the Mathematics Teacher in early Fall, 2011. Ian discovered a way to use a single quadratic function with a variable y-intercept to capture a limited number of values of an increasingly long sum of absolute value functions. I’ll link a copy of the brief article once it is published.
The coolest part of the development of this idea is that Ian’s access to a CAS and the encouragement of his class to explore their ideas made this problem possible. When Ian needed to learn additional mathematics (induction) to prove his theorem, he was receptive and confident.