Exploring and noticing

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.

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 parallelogram.

The number in the square is the mean of the four numbers surrounding it. Can you find the missing numbers? 

How did the the rotation robot make these patterns?

How many winning lines can you make in a three-dimensional version of noughts and crosses?