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?

Can you make the birds from the egg tangram?

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

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

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

Can you make five differently sized squares from the tangram pieces?

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

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

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

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

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

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

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

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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?

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

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

Can you fit the tangram pieces into the outline of the rocket?

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

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

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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

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 plaque design?

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

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

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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

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?

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

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 this shape. How would you describe it?

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

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?

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

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

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

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

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

Can you fit the tangram pieces into the outline of Granma T?

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

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

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

Explore the triangles that can be made with seven sticks of the same length.

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

These practical challenges are all about making a 'tray' and covering it with paper.

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?