The problem provides a visual context in which to consider how graphs can represent horizontal and vertical movement over time.

A possible start to using the interactivity in a classroom could involve asking students to sketch the graphs in advance, before seeing the polygon(s) roll. Their suggestions could be displayed for all to see and discuss.

The pause button could be used to focus discussion on the different stages of the "journeys" and to make conjectures about what will follow.

Possible follow up questions:

• Some graphs start at the origin and others don't. Can you explain why?

• Some graphs have sections that are horizontal and others don't. Can you explain why?

• Why is the horizontal speed not constant during each stage of the "journey"?

This problem is the third of three related problems.

The first two problems are How far does it move? and Speeding up, slowing down .