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?

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

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

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

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?

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

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

Can you make the birds from the egg tangram?

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?

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

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

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

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

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

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 see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?

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

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

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

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

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

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

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 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 outline of Little Fung at the table?

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

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 the chairs?

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 Little Ming playing the board game?

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

Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

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

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

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

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?

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

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

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?

The class were playing a maths game using interlocking cubes. Can you help them record what happened?

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.