work in progress:
Some children are making a game for a school fete. They are going to hide 100 prizes behind the squares on a treasure map.
People pay £3 to pick a square and they are guaranteed to win a prize!
The prizes are ten-pound notes, fifty pence coins and ten pence coins.

The children want to hide exactly £100 of prize money. Work out how they can do this.

Are there any other ways it can be done?
Show that it is also possible to do if the prizes are £10, £1 and 50p
How many solutions are there this time?


If, however, the group seem to be utterly swamped, ask them to put their work to one side, and try the problem from the hints below, keeping very alert to notice any strategies that seem to be useful. Explain that simplifying the problem is a useful strategy they might use in all sorts of tricky mathematical situations. With any luck, different students will find the two different solutions. Ask for class feedback on strategy. Ask for feedback on the results/solutions.With any luck, both the solutions will turn up here. There may be surprise, check with the class that both the solutions really do work. Ask the natural question "are there any more? how can we know when we have them all?" At the board work systematically through the cases of 1, 2, 3, 4 and 5, 50 pence coins, modelling all the good ideas the students have suggested about clear recording etc. Ask students to return to the main problem and see which strategies will transfer to the difficult problem.There is a suitable follow-up question at the end ofthe problem.


Hint:
Or you might like to try investigating the situation with a 20-square treasure map and prizes of 50p, 10p and 5p.
Can you hide twenty prizes with a total value of £3? Are there any other ways it can be done?