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.

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

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

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.

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

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.

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 some celtic knot patterns using tiling techniques

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?

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

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

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

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

This package contains hands-on code breaking activities based on the Enigma Schools Project. Suitable for Stages 2, 3 and 4.

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

Make a mobius band and investigate its properties.

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

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

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

What shape and size of drinks mat is best for flipping and catching?

Design and construct a prototype intercooler which will satisfy agreed quality control constraints.

These practical challenges are all about making a 'tray' and covering it with paper.

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

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.

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

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

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.

Turn through bigger angles and draw stars with Logo.

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?

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.

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

A jigsaw where pieces only go together if the fractions are equivalent.

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

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

How can you make an angle of 60 degrees by folding a sheet of paper twice?

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.

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

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

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?