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

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

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.

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

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

Make a mobius band and investigate its properties.

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?

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

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

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

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

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

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.

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

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

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

Can you each work out what shape you have part of on your card? What will the rest of it look like?

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

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

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

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

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

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?

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?

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

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

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?

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

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

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

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

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

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?

In this activity focusing on capacity, you will need a collection of different jars and bottles.

For this activity which explores capacity, you will need to collect some bottles and jars.

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

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

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

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

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.

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.