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

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

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

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.

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?

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?

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

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?

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?

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

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

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.

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?

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

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

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?

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?

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?

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

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

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.

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.

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?

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?

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?

An activity centred around observations of dots and how we visualise number arrangement patterns.

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

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

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

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

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

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!

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

Square It 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.

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

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 sports car?

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

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

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

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 Mai Ling and Chi Wing?