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?

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.

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

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

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

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

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

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

Make a clinometer and use it to help you estimate the heights of tall objects.

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.

On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?

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

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

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

Measure the two angles. What do you notice?

Suggestions for worthwhile mathematical activity on the subject of angle measurement for all pupils.

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.

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. . . .

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

A metal puzzle which led to some mathematical questions.