Visualising and representing

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

In this problem, we're investigating the number of steps we would climb up or down to get out of or into the swimming pool. How could you number the steps below the water?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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.