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

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 outline of Little Ming?

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

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

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?

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 shape. How would you describe it?

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 Mai Ling and Chi Wing?

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

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 clocks?

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

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

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 outline of Mai Ling?

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

What shape is made when you fold using this crease pattern? Can you make a ring design?

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

Can you deduce the pattern that has been used to lay out these bottle tops?

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

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

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

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

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

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

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

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

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 ...

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 Little Ming and Little Fung dancing?

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?

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?

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

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

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

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 outline of Granma T?

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

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

Can you make the birds from the egg tangram?

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

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?

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?

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