Manufacturers need to minimise the amount of material used to make
their product. What is the best cross-section for a gutter?
This problem offers a challenging extension to Nutrition and Cycling. Whereas the former problem requires students to make sense of information and engage in proportional reasoning, this is an optimisation task which students could tackle using spreadsheets.
Students will need to have worked on Nutrition and Cycling first, and will need the same set of cards.
"What if Andy could cycle for longer than seven hours a day? Imagine you are his coach, and you need to come up with a plan that makes sure his energy needs are met, but helps him to complete the race in the fastest possible time. At the end of the task, you will each get a chance to present your race plan to the rest of the group. Who can come up with the winning plan?"
Arrange the class in small groups. Students will need access to calculators or spreadsheets. While you circulate, ensure that students are recording their calculations clearly so that they will be ready to present them.
There is no 'correct' answer to this task - students will have to make decisions about whether a calorie deficit can be permitted, and whether additional off-road snacks could be allowed.
Plenty of time should be allowed at the end of the task for groups to present their plans, the decisions they made, and their reasons, with clear justifications for their results.
What are Andy's calorie needs?
What are Andy's calorie allowances?
How do these change as he cycles for a longer time?
Students may wish to represent the situation algebraically, and apply different constraints before solving the resulting equations.
Encourage students to use trial and improvement - choose a time greater than 7 hours for Andy to cycle, calculate his calorie intake and calorie needs, and then adjust up or down as necessary.