In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.

Follow the journey taken by this bird and let us know for how long and in what direction it must fly to return to its starting point.

Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?

Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

Can you find a way of representing these arrangements of balls?

A simple visual exploration into halving and doubling.

Looking at the 2012 Olympic Medal table, can you see how the data is organised? Could the results be presented differently to give another nation the top place?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

Can you find ways of joining cubes together so that 28 faces are visible?

Can you find a way of representing these arrangements of balls?

This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.