Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

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

Can you deduce the familiar properties of the sine and cosine functions starting from these three different mathematical representations?

What on earth are polar coordinates, and why would you want to use them?

Make a functional window display which will both satisfy the manager and make sense to the shoppers

There were three nice solutions to this advanced problem concerning generic examples. Perhaps younger students might like to try to work through one of them, whereas older students might like to compare them.

This article looks at how images, concrete apparatus and representations can help students develop deeper understandings of abstract mathematical ideas.

This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!