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

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?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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

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

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

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?

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

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

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?

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

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

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

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

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

How many different triangles can you make on a circular pegboard that has nine pegs?

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?

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

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

Why do you think that the red player chose that particular dot in this game of Seeing Squares?

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

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

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

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?

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

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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

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

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

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

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

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

Can you fit the tangram pieces into the outlines of the convex shapes?

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

Make one big triangle so the numbers that touch on the small triangles add to 10.

Make a flower design using the same shape made out of different sizes of paper.

Can you logically construct these silhouettes using the tangram pieces?

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

Can you fit the tangram pieces into the silhouette of the junk?