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

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

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

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?

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 ...

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 fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

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

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

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

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

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

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

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?

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 Mai Ling?

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 this shape. How would you describe it?

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 chairs?

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

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

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 workmen?

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

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

Can you visualise what shape this piece of paper will make when it is folded?

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

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 these rabbits?

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

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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

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

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

Can you cut up a square in the way shown and make the pieces into a triangle?

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

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

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

Can you make the birds from the egg tangram?

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?