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?

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?

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. . . .

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

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

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.

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

Make a mobius band and investigate its properties.

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

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

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.

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

Surprise your friends with this magic square trick.

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

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

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

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.

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.

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.

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

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

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

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

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

Here are some ideas to try in the classroom for using counters to investigate number patterns.

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

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.

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

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

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

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

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

Build a scaffold out of drinking-straws to support a cup of water

What happens when a procedure calls itself?

Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.

Turn through bigger angles and draw stars with Logo.

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

Exploring and predicting folding, cutting and punching holes and making spirals.

Make a cube out of straws and have a go at this practical challenge.

Learn about Pen Up and Pen Down in Logo

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.