Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

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?

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

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

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?

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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

Can you sort these triangles into three different families and explain how you did it?

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

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?

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

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.

Complete the squares - but be warned some are trickier than they look!

We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

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

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.

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

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?

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

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.

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

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

Can you find all the different triangles on these peg boards, and find their angles?

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

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

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

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

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

How many possible necklaces can you find? And how do you know you've found them all?

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?

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.

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

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

Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?

This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?

Shapes are added to other shapes. Can you see what is happening? What is the rule?