Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

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?

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

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

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

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

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?

Can you fit the tangram pieces into the outline of these convex shapes?

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.

What happens when you try and fit the triomino pieces into these two grids?

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

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

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?

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.

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

Try to picture these buildings of cubes in your head. Can you make them to check whether you had imagined them correctly?

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

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

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 these rabbits?

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

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

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

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 Little Ming playing the board game?

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?

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

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

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?

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

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 Wai Ping, Wah Ming and Chi Wing?

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

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

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

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?

Can you picture where this letter "F" will be on the grid if you flip it in these different ways?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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

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

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

Here are shadows of some 3D shapes. What shapes could have made them?

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