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?

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?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

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

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

A game in which players take it in turns to choose a number. Can you block your opponent?

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 plaque design?

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?

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

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

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

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 fit the tangram pieces into the outline of Mai Ling?

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

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

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

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 fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

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 Little Fung at the table?

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

Can you make the birds from the egg tangram?

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?

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?

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 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 the rocket?

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

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 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?

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

Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?

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

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