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

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.

Join pentagons together edge to edge. Will they form a ring?

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?

At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again?

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.

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

Can you use LOGO to create a systematic reproduction of a basic design? An introduction to variables in a familiar setting.

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?

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

Geometry problems for inquiring primary learners.

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

Geometry problems at primary level that may require resilience.

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

Geometry problems at primary level that require careful consideration.

Can you find triangles on a 9-point circle? Can you work out their angles?

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

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

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

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

Geometry problems for primary learners to work on with others.

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

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Can you draw perpendicular lines without using a protractor? Investigate how this is possible.

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

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

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. . . .

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.

Can you use LOGO to create this star pattern made from squares. Only basic LOGO knowledge needed.

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

You can use a clinometer to measure the height of tall things that you can't possibly reach to the top of, Make a clinometer and use it to help you estimate the heights of tall objects.

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

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?

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

Shogi tiles can form interesting shapes and patterns... I wonder whether they fit together to make a ring?

Draw some angles inside a rectangle. What do you notice? Can you prove it?