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 a clinometer and use it to help you estimate the heights of tall objects.

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

Make some celtic knot patterns using tiling techniques

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

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

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

Can you make the birds from the egg tangram?

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.

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

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?

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

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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

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

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.

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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

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?

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

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

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

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

An activity making various patterns with 2 x 1 rectangular tiles.

Turn through bigger angles and draw stars with Logo.

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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

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

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

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?

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

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

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

Can you visualise what shape this piece of paper will make when it is folded?

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

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

Learn about Pen Up and Pen Down in Logo

Write a Logo program, putting in variables, and see the effect when you change the variables.

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

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?

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

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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?