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

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

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

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.

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

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

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?

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!

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

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

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.

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

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

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

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

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

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

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 ...

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

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?

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?

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 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?

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?

Can you each work out what shape you have part of on your card? What will the rest of it look like?

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

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

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

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?

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

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

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

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?

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

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

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.

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?

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

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

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

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.

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

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?