Can you make the birds from the egg tangram?

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

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 Wai Ping, Wah Ming and Chi Wing?

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

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

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

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?

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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

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

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

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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

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 playing the board game?

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 plaque design?

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

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 goat and giraffe?

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 outline of these rabbits?

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

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 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 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 outlines of the workmen?

Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

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

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

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

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

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

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 each work out the number on your card? What do you notice? How could you sort the cards?

These practical challenges are all about making a 'tray' and covering it with paper.

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?

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?

Can you fit the tangram pieces into the outline of Granma T?

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

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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