This second article in the series refers to research about levels of development of spatial thinking and the possible influence of instruction.

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

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

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

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

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?

Can you make a 3x3 cube with these shapes made from small cubes?

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

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 this junk?

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

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

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

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.

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

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?

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 these clocks?

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?

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 the child walking home from school?

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 outlines of the lobster, yacht and cyclist?

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?

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

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 these rabbits?

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

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 this telephone?

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

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.

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

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?

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

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

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

How many loops of string have been used to make these patterns?

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 describe a piece of paper clearly enough for your partner to know which piece it is?

Square It game for an adult and child. Can you come up with a way of always winning this game?