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?

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.

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?

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?

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

What can you see? What do you notice? What questions can you ask?

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

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

This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the. . . .

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

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

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

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

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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

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

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 game for 2 people. Take turns joining two dots, until your opponent is unable to move.

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?

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

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

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

How many pieces of string have been used in these patterns? Can you describe how you know?

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

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

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 the rocket?

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 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 junk?

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

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

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

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 outlines of the candle and sundial?

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.

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

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

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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.

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .

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

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