Free resources for teaching and assessment of key mathematical processes for 11-16 year olds

Hide the spies2

How can spies sit in a park wihout seeing each other? Is there more than one way for them to do this? 

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Description: Pupils investigate where four spies should sit in a square park so that they cannot see each other, and how many such arrangements are possible.

Suitability: Pupils working at all levels;individuals or pairs.

Time: Up to 1 hour

Equipment: Counters, cubes, cups, etc. to simulate spies and bushes

Key mathematical language: Lines of sight, arrangement/configuration, symmetry, reflection, rotation

Which benches should spies use to avoid being seen by others? How many formations are possible?