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

Surprise your friends with this magic square trick.

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.

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

Make a mobius band and investigate its properties.

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

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

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

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

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 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.

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

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

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.

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

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

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. . . .

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

Can you split each of the shapes below in half so that the two parts are exactly the same?

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

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

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

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

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

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

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

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?

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

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

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

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

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

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

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 ...

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?

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

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.

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

What is the greatest number of squares you can make by overlapping three squares?

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