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

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

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?

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

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 goat and giraffe?

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

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

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

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

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

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 plaque design?

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

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

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 junk?

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

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 the lobster, yacht and cyclist?

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

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 these clocks?

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

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 Wai Ping, Wah Ming and Chi Wing?

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

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 Granma T?

Can you make five differently sized squares from the tangram pieces?

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

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?

In this activity focusing on capacity, you will need a collection of different jars and bottles.

Can you make the birds from the egg tangram?

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

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

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 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 have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?

Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.

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

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

For this activity which explores capacity, you will need to collect some bottles and jars.

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