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?

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

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.

Measure the two angles. What do you notice?

A metal puzzle which led to some mathematical questions.

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?

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

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

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. . . .

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. . . .

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

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

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

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

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