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.

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

Can you make the birds from the egg tangram?

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

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

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

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 Ming playing the board game?

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

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

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

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?

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

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

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 outline of Little Ming?

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

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?

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

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 outline of this telephone?

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

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

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 outline of these rabbits?

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

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 the chairs?

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 telescope and microscope?

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

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

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?

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 outlines of these clocks?

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

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

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

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?

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

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.

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

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

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

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