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

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.

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

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?

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

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

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

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.

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?

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

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

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

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

Can you cut up a square in the way shown and make the pieces into a triangle?

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

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

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

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

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

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

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

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

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?

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

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

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

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?

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.

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?

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.

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

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

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

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?

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

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

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

Reasoning about the number of matches needed to build squares that share their sides.

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

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

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

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?