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?

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.

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.

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

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

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.

I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?

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!

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

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?

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.

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.

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?

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

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

Turn through bigger angles and draw stars with Logo.

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

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

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?

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

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

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

I start with a red, a blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour?

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

A game in which players take it in turns to choose a number. Can you block your opponent?

This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

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

Can you fit the tangram pieces into the outline of Granma T?

Learn to write procedures and build them into Logo programs. Learn to use variables.

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