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.

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?

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.