Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

Move just three of the circles so that the triangle faces in the opposite direction.

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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 outlines of these people?

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 Wai Ping, Wah Ming and Chi Wing?

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 the chairs?

Can you fit the tangram pieces into the outline of the child walking home from school?

How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

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 Ming?

Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?

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

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

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

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 this telephone?

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

Can you work out what is wrong with the cogs on a UK 2 pound coin?

Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?

Exchange the positions of the two sets of counters in the least possible number of moves

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 these rabbits?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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

A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

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 Little Ming and Little Fung dancing?

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

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

What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.

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

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

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

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

Which of these dice are right-handed and which are left-handed?

Can you fit the tangram pieces into the outline of this plaque design?

An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

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

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.