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?

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

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

Can you make the birds from the egg tangram?

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?

Here is a version of the game 'Happy Families' for you to make and play.

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

Can you split each of the shapes below in half so that the two parts are exactly the same?

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?

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

Can you put these shapes in order of size? Start with the smallest.

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

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

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

These pictures show squares split into halves. Can you find other ways?

Can you fit the tangram pieces into the outline of Mai Ling?

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 Ming?

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

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?

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

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 fit the tangram pieces into the outline of this telephone?

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

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

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

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

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

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 outline of this shape. How would you describe it?

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 outlines of the chairs?

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

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

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

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

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

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

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 goat and giraffe?

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

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?

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

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

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?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

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