Jennifer Piggott and Charlie Gilderdale describe a free interactive circular geoboard environment that can lead learners to pose mathematical questions.

How much do you have to turn these dials by in order to unlock the safes?

Can you describe the journey to each of the six places on these maps? How would you turn at each junction?

Use your knowledge of angles to work out how many degrees the hour and minute hands of a clock travel through in different amounts of time.

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

Make an equilateral triangle by folding paper and use it to make patterns of your own.

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

An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.

Have you ever noticed how mathematical ideas are often used in patterns that we see all around us? This article describes the life of Escher who was a passionate believer that maths and art can be. . . .

A metal puzzle which led to some mathematical questions.

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

Have a good look at these images. Can you describe what is happening? There are plenty more images like this on NRICH's Exploring Squares CD.

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

Pythagoras of Samos was a Greek philosopher who lived from about 580 BC to about 500 BC. Find out about the important developments he made in mathematics, astronomy, and the theory of music.