Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

As part of Liverpool08 European Capital of Culture there were a huge number of events and displays. One of the art installations was called "Turning the Place Over". Can you find our how it works?

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

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.

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?

Here is a chance to create some Celtic knots and explore the mathematics behind them.

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?

Which of the following cubes can be made from these nets?

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?

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?

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.

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

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Make some celtic knot patterns using tiling techniques

Turn through bigger angles and draw stars with Logo.

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?

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

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

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

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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.

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

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

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

The challenge for you is to make a string of six (or more!) graded cubes.

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?

A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?

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

Delight your friends with this cunning trick! Can you explain how it works?

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

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

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

Factors and Multiples game for an adult and child. How can you make sure you win this game?

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

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

Can Jo make a gym bag for her trainers from the piece of fabric she has?

Make a flower design using the same shape made out of different sizes of paper.

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

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

What shape is made when you fold using this crease pattern? Can you make a ring design?

Can you deduce the pattern that has been used to lay out these bottle tops?

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

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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