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

A game in which players take it in turns to choose a number. Can you block your opponent?

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?

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 this plaque design?

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

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

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

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

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

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

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 Mai Ling?

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

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

Can you make the birds from the egg tangram?

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 Ming and Little Fung dancing?

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 Little Ming playing the board game?

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

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

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming 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 child walking home from school?

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 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 outlines of the lobster, yacht and cyclist?

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

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

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

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

Can you fit the tangram pieces into the outline of these convex shapes?

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?

A challenge that requires you to apply your knowledge of the properties of numbers. Can you fill all the squares on the board?

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?

Can you fit the tangram pieces into the outline of this sports car?

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?

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

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

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

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.

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

The challenge for you is to make a string of six (or more!) graded cubes.