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.

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

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

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

What shape would fit your pens and pencils best? How can you make it?

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

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

Make some celtic knot patterns using tiling techniques

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.

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.

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?

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

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

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

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

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

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

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

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.

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

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

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?

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.

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

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 ...

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

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

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

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

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

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?

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?

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

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?

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

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

Turn through bigger angles and draw stars with Logo.

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

Learn about Pen Up and Pen Down in Logo

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

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

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

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?

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