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

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?

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.

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.

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.

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

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

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

Surprise your friends with this magic square trick.

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

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

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.

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

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

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

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

Can you fit the tangram pieces into the outline of this goat and giraffe?

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

Can you fit the tangram pieces into the outline of this plaque design?

Can you fit the tangram pieces into the outlines of the chairs?

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

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

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

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

Can you fit the tangram pieces into the outline of the telescope and microscope?

Can you fit the tangram pieces into the outlines of the workmen?

Can you fit the tangram pieces into the outlines of the candle and sundial?

Can you fit the tangram pieces into the outline of these rabbits?

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

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

Can you deduce the pattern that has been used to lay out these bottle tops?

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

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

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

Can you make the birds from the egg tangram?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

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?

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?

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