Can you make the birds from the egg tangram?

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

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?

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?

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

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

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

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

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

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

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

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 Fung at the table?

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

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 this telephone?

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

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 the child walking home from school?

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

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

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

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

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

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 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?

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 outlines of the lobster, yacht and cyclist?

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

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 outlines of the chairs?

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

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

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

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?

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

Explore the triangles that can be made with seven sticks of the same length.

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 outline of Granma T?

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

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

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

Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?

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 make five differently sized squares from the tangram pieces?

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