If you move the tiles around, can you make squares with different coloured edges?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
Can you work out what step size to take to ensure you visit all the dots on the circle?
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?
Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its speed at each stage.
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What sizes of rectangle contain exactly 100 squares? Can you find them all?
Take a look at the video and try to find a sequence of moves that will untangle the ropes.
