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.

A game to make and play based on the number line.

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. . . .

Follow these instructions to make a three-piece and/or seven-piece tangram.

Make some celtic knot patterns using tiling techniques

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

This package contains hands-on code breaking activities based on the Enigma Schools Project. Suitable for Stages 2, 3 and 4.

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.

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

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

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.

Make a mobius band and investigate its properties.

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

How can you make a curve from straight strips of paper?

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

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

Surprise your friends with this magic square trick.

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.

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

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 your own double-sided magic square. But can you complete both sides once you've made the pieces?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

Can you each work out the number on your card? What do you notice? How could you sort the cards?

Here are some ideas to try in the classroom for using counters to investigate number patterns.

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

Follow these instructions to make a five-pointed snowflake from a square of paper.

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

If you'd like to know more about Primary Maths Masterclasses, this is the package to read! Find out about current groups in your region or how to set up your own.

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

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

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?

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?

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

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

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

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

Learn about Pen Up and Pen Down in Logo

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

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

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

Can you put these shapes in order of size? Start with the smallest.

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?