Modeling Prompt

In this task, students will experiment with cups in order to see what shape they seem to trace out when they are rolled on a flat surface, and then refine their thinking in order to prove what the shape is. If possible, provide cups with a variety of sizes and shapes. Note that cylindrical cups will not curve as they are rolled, and so will not make the same kind of shape as cups with slanted sides.

Ask students to roll some cups around. Then ask them to guess what shape the cup traces out on the table or floor. Sketch the suggested shapes for all to see. Tell students their task is to try to prove what the shape is.