Visualising and representing

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

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

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.

If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?

What's the largest volume of box you can make from a square of paper?

Can you do a little mathematical detective work to figure out which number has been wiped out?

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

Can you make sense of these three proofs of Pythagoras' Theorem?

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?