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?

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.

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!

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.

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.

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

Make a mobius band and investigate its properties.

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

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

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

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?

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

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?

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

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

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

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?

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

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

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

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

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

Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?

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

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

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

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

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

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 ...

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

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

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?

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?

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?

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

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.

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.

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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

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