Can you make the birds from the egg tangram?

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.

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

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?

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

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 the rocket?

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

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 sports car?

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

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 candle and sundial?

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 the chairs?

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

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 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 Little Fung at the table?

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

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

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

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

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

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

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 Little Ming?

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

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

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 this goat and giraffe?

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

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

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

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

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

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

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

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?

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

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.

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

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

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?

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

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 these people?