What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

Exploring and predicting folding, cutting and punching holes and making spirals.

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?

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

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?

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

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

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

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

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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

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

Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.

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

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

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 the rocket?

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

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

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

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

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

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

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.

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

Reasoning about the number of matches needed to build squares that share their sides.

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.

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

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

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?

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

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

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 the candle and sundial?

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

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?