Exploring and noticing

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

A cinema has 100 seats. Is it possible to fill every seat and take exactly £100?

There are lots of different methods to find out what the shapes are worth - how many can you find?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Can you find the values at the vertices when you know the values on the edges?

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Sequences of multiples keep cropping up...

Here is a chance to play a fractions version of the classic Countdown Game.