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

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

In this article for primary teachers, Fran describes her passion for paper folding as a springboard for mathematics.

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

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

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.

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

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?

Learn about Pen Up and Pen Down in Logo

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

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

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

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

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

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?

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

Make some celtic knot patterns using tiling techniques

This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.

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

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

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

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?

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

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?

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

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

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.

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?

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

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

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

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

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

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

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?

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?

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

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

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

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?

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

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

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.

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?

Can you each work out what shape you have part of on your card? What will the rest of it look like?

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?