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?

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

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

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

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

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

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

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?

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.

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

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

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?

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

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

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 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?

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

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

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

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.

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 ...

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

Surprise your friends with this magic square trick.

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

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

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

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

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

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

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

Make a mobius band and investigate its properties.

An activity making various patterns with 2 x 1 rectangular tiles.

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

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

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?

In this article for primary teachers, Fran describes her passion for paper folding as a springboard for mathematics.

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

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.

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

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?

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

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.

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

Can you make the birds from the egg 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?