Track Design

Why do this problem?

This problem offers an authentic context within which to calculate arc lengths and requires students to present their findings in a convincing manner.

Possible approach

This printable worksheet may be useful: Track Design

Arrange the class in groups of three or four, and hand out this worksheet to each group.

Give the students plenty of time to discuss  and work on the problem in their groups. For groups not used to working collaboratively, these roles may be useful to guide students in organising themselves to work together.
 
To finish off, results could be presented as a list of the dimensions/angles that a groundskeeper would need in order to paint the lines for the running track, together with explanations of how students worked them out.

Additionally, students could be asked to produce a scale drawing of the track design to an agreed scale (1cm to 2.5m would fit on a large flipchart sheet) and then each group's drawing could be overlaid on another group's to check to see if they coincide.

Key questions

Possible extension