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?

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

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 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?

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

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.

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

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?

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

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?

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 ...

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

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

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

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

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

Use the isometric grid paper to find the different polygons.

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

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

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.

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

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?

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.

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

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.

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

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

This problem explores the shapes and symmetries in some national flags.

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

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?

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

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?

Investigate the number of faces you can see when you arrange three cubes in different ways.

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?

What can you see? What do you notice? What questions can you ask?

Can you describe the journey to each of the six places on these maps? How would you turn at each junction?

Use the information on these cards to draw the shape that is being described.

How much do you have to turn these dials by in order to unlock the safes?

Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?

This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

Can you make a spiral for yourself? Explore some different ways to create your own spiral pattern and explore differences between different spirals.

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?