Speeding Up, Slowing Down overview

This problem allows learners to explore and explain the path taken by a point on a rolling polygon. Find out what the problem involves, the benefits of using it in the classroom and the range of processes it can help learners to develop.

What the problem involves

The Speeding Up, Slowing Down problem involves experimenting with an activity that shows regular polygons ‘rolling’ along a horizontal surface and plots graphs related to the motion of a red dot. The aim is to explore and explain how the speed varies when a dot is placed in different positions on the regular polygon:

  • at the centre
  • on the edge
  • on a vertex.

A card-sorting activity is also available and the idea of using cards and working away from the computer could be extended further.

Benefits of using this problem

This problem provides a visual context in which to consider how speed–time graphs represent movement over time. It is designed to provide opportunities to discuss and refine ideas by allowing time for learners to justify predictions and then modify their views in light of what others say, and what they see. This can offer opportunities to address misconceptions and improve understanding.

The problem

Go to Speeding Up, Slowing Down on the NRICH website to find the problem and related teachers' notes.

Developing learners' process skills

The Speeding Up, Slowing Down problem can help learners develop a range of process skills, including:

  • visualising and working with dynamic images
  • exploring the effects of varying values, taking account of feedback and learning from mistakes
  • making connections between particular situations and outcomes within the context
  • making and justifying conjectures, using convincing arguments
  • engaging with someone else's mathematical reasoning.

Related Framework strands and substrands

You can view the relevant learning objectives from the Framework for secondary mathematics: