### Why do this problem?

This problem will require students to explore and optimise a small number of connected variables with some random variation operating. They will also need to keep track of their results and summarise them effectively using statistical techniques.

### Possible approach

Show the time trial working, with the animation on, for a very unrealistic training regime. Run the time trial again with the same setting to show how the result has an unpredictable element to it, simulating real life.

Invite a few students to suggest better training regimes, subtly select one that seems better than your earlier settings, but still quite far from the optimal settings. Demonstrate how the time trial can be used to judge effects of the new regime. Do a couple more time trials with the animation turned off (for quick results). Buoyed up with confidence, suggest that the crew are now ready for a race. Switch the animation back on, and race a couple of times.

"This team obviously needs a new coach, and you have all been shortlisted for interview. You're going to need to design the best possible training regime. At the interview you will need to present the training regime that you would recommend for this crew. You will need to justify your recommendation with a summary of time trial results and the results from half a dozen races. This evidence will need to be clearly presented in a handout to be given to the interviewers."

Monitor how the students are getting on, and remind them that they need to collect data, which they need to do some statistical work on. Set a time (approx 15 mins before the end of the lesson) as the deadline when all 'candidate's' handouts will be judged even if unfinished. Keep reminding students of the deadline while they work.

Shuffle the handouts and hand them out. After a couple of minutes, everybody passes their sheets on to their neighbour. Repeat till they've seen about 4 different sheets. Ask for comments about particularly convincing presentations. Establish which training regime claims to be the best, and run a couple of races (with animation) to check the claims.

### Key questions

How can we judge whether one regime is better than another?

Could there be an even better combination? If you're sure there isn't one, what makes you so sure?

How can you present your findings in the most positive, and convincing way?

### Possible extension

Can you analyse the random aspect of this simulation? Is there the same 'amount of randomness' for every training regime? 'How much' randomness? How could you quantify the random influence?

### Possible support

Cut down some of the variables - ask students to agree one specific value for one of the types of training, and suggest all students keep it fixed until they have found the optimal settings with this constraint.