Both this math problem, as well as the framework of Lesson Study we are using come to use from our PD with the Galileo Educational Network.
This math problem is a simple one: before class starts the teacher puts a handful of ice in a funnel dripping into a graduated cylinder. The cylinders are on tables before the students enter. A simple question is on the board:
"When did the ice start melting?"
Students can use a variety of approaches to solve the problem - eventually working back to time zero when the ice was placed into the funnel.
One of the nice elements of this problem is how it gets students directly into the problem - without relying on text for explanation.
Watch the students work through the problem and then share their ideas for critique:
Ice Melt Problem:
Adapted by Martina Metz from Wise, D.U. (1990). Using melting ice to teach radiometric dating. In Journal of Geological Education (38), 38-40, 69.