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 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 workmen?

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 candle and sundial?

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 outlines of Mai Ling and Chi Wing?

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

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

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

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

You have a set of the digits from 0 – 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?

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

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

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

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

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

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

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

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

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?

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

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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

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

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

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

Can you make the birds from the egg tangram?

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

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

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 playing the board game?

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

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 fit the tangram pieces into the outline of this telephone?

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

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

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

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

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