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

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . .

Find all the ways to cut out a 'net' of six squares that can be folded into a cube.

The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?

A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't. . . .

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

Did you know mazes tell stories? Find out more about mazes and make one of your own.

A task which depends on members of the group working collaboratively to reach a single goal.

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?

This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the. . . .

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

This task requires learners to explain and help others, asking and answering questions.

This task requires learners to explain and help others, asking and answering questions.

'What Shape?' activity for adult and child. Can you ask good questions so you can work out which shape your partner has chosen?

Arranging counters activity for adult and child. Can you create the pattern of counters that your partner has made, just by asking questions?

This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.

This article describes investigations that offer opportunities for children to think differently, and pose their own questions, about shapes.

A description of some experiments in which you can make discoveries about triangles.

A task which depends on members of the group working collaboratively to reach a single goal.

This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.

Make an eight by eight square, the layout is the same as a chessboard. You can print out and use the square below. What is the area of the square? Divide the square in the way shown by the red dashed. . . .

A task which depends on members of the group working collaboratively to reach a single goal.

A farmer has a flat field and two sons who will each inherit half of the field. The farmer wishes to build a stone wall to divide the field in two so each son inherits the same area. Stone walls are. . . .

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

Introducing a geometrical instrument with 3 basic capabilities.

Making a scale model of the solar system

A simple visual exploration into halving and doubling.

What shape and size of drinks mat is best for flipping and catching?