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

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

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

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

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?

Measure the two angles. What do you notice?

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

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.

A metal puzzle which led to some mathematical questions.

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

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

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

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.

Analyse these repeating patterns. Decide on the conditions for a periodic pattern to occur and when the pattern extends to infinity.

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?

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

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

Make five different quadrilaterals on a nine-point pegboard, without using the centre peg. Work out the angles in each quadrilateral you make. Now, what other relationships you can see?

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

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

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.

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. . . .

What is the sum of the angles of a triangle whose sides are circular arcs on a flat surface? What if the triangle is on the surface of a sphere?

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.

My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the. . . .

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?

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?

P is a point inside a square ABCD such that PA= 1, PB = 2 and PC = 3. How big is angle APB ?

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