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

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

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?

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

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

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 this goat and giraffe?

How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 cube that is green all over AND a 2 x 2 cube that is yellow all over?

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

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 the rocket?

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

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

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

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 outline of this shape. How would you describe it?

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 watering can and man in a boat?

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 the child walking home from school?

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

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

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

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 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 outline of Wai Ping, Wah Ming and Chi Wing?

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

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?

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?

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

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?

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

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?

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 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.

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

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

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

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.

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.

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