Galileo, a famous inventor who lived about 400 years ago, came up with an idea similar to this for making a time measuring instrument. Can you turn your pendulum into an accurate minute timer?

In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain. . . .

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

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

Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.

Surprise your friends with this magic square trick.

Make a mobius band and investigate its properties.

Did you know mazes tell stories? Find out more about mazes and make one of your own.

Use the tangram pieces to make our pictures, or to design some of your own!

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

How can you make a curve from straight strips of paper?

Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.

It might seem impossible but it is possible. How can you cut a playing card to make a hole big enough to walk through?

You could use just coloured pencils and paper to create this design, but it will be more eye-catching if you can get hold of hammer, nails and string.

You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?

Follow these instructions to make a three-piece and/or seven-piece tangram.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.

A game to make and play based on the number line.

Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.

These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.

Exploring balance and centres of mass can be great fun. The resulting structures can seem impossible. Here are some images to encourage you to experiment with non-breakable objects of your own.

Make some celtic knot patterns using tiling techniques

Follow these instructions to make a five-pointed snowflake from a square of paper.

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?

Can you cut up a square in the way shown and make the pieces into a triangle?

What do these two triangles have in common? How are they related?

Learn about Pen Up and Pen Down in Logo

A description of how to make the five Platonic solids out of paper.

Can you each work out the number on your card? What do you notice? How could you sort the cards?

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

Here's a simple way to make a Tangram without any measuring or ruling lines.

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

This article for students gives some instructions about how to make some different braids.

This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

Can you lay out the pictures of the drinks in the way described by the clue cards?

More Logo for beginners. Now learn more about the REPEAT command.

This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.

Can you put these shapes in order of size? Start with the smallest.

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?