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

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

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

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?

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

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.

Make a mobius band and investigate its properties.

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

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

Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.

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

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

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?

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

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

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

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

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

Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?

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?

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

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

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

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?

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

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

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

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

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?

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

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?

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?

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?

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

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

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

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

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

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?

Can you make the birds from the egg tangram?

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

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?