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

Use the isometric grid paper to find the different polygons.

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

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.

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?

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

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?

This interactivity allows you to sort logic blocks by dragging their images.

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

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

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

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?

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?

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

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.

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

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?

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?

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

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?

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

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

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.

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.

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

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

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?

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?

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?

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 ...

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?

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

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?

This problem is intended to get children to look really hard at something they will see many times in the next few months.

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

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.

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

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?

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

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

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

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

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

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?

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

The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?

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