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.

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

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

Factors and Multiples game for an adult and child. How can you make sure you win this game?

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 candle and sundial?

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 this shape. How would you describe it?

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

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 these rabbits?

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

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?

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

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 ...

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 5 boxes to make two-digit numbers as close to the targets as possible?

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

Make a flower design using the same shape made out of different sizes of paper.

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

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

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

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

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

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

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?

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?

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

Can you make the birds from the egg tangram?

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

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

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.

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

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?

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 this telephone?

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?

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?

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 Wai Ping, Wah Ming and Chi Wing?