How can you make a curve from straight strips 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.

Make a mobius band and investigate its properties.

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.

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.

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

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

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

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

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

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

Here's a simple way to make a Tangram without any measuring or ruling lines.

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

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?

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

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 new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

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

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

Can you see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you make the birds from the egg tangram?

Can you fit the tangram pieces into the outlines of these people?

Can you fit the tangram pieces into the outlines of these clocks?

Can you fit the tangram pieces into the outline of the child walking home from school?

If you'd like to know more about Primary Maths Masterclasses, this is the package to read! Find out about current groups in your region or how to set up your own.

Can you fit the tangram pieces into the outline of this telephone?

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

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?

Can you fit the tangram pieces into the outline of this junk?

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

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

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

Can you fit the tangram pieces into the outline of Little Fung at the table?

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

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

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?

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

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

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?

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

Can you lay out the pictures of the drinks in the way described by the clue cards?