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

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

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 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?

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

How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

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?

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

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

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?

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 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.

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

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.

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?

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

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?

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

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?

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

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

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

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

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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

Can you picture where this letter "F" will be on the grid if you flip it in these different ways?

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

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

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 outline of these convex shapes?

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 the rocket?

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

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

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?

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

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

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.

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

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?

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?