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

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

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.

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?

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?

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

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

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?

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

Make a mobius band and investigate its properties.

Surprise your friends with this magic square trick.

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

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

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

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

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?

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

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

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

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?

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?

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

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?

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. . . .

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

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

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 ...

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

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

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

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

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?

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

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

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

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

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

Can you make the birds from the egg tangram?

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

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