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

A simple visual exploration into halving and doubling.

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

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

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

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

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

In how many ways can you halve a piece of A4 paper? How do you know they are halves?

Are these statements always true, sometimes true or never true?

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

Geometry problems at primary level that may require resilience.

Geometry problems at primary level that require careful consideration.

Geometry problems for primary learners to work on with others.

Geometry problems for inquiring primary learners.

'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?

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

Look at some of the patterns in the Olympic Opening ceremonies and see what shapes you can spot.

This resource uses loops of string as a rich way to explore 2D shape in EYFS. Alternative approaches are also offered.

Making a scale model of the solar system

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

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

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

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

How efficiently can various flat shapes be fitted together?

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

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

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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

This second article in the series refers to research about levels of development of spatial thinking and the possible influence of instruction.

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. . . .

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

Introducing a geometrical instrument with 3 basic capabilities.

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

For teachers. About the teaching of geometry with some examples from school geometry of long ago.

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?

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. . . .

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. . . .

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

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?

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. . . .

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?

The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest. . . .

What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?

A kite shaped lawn consists of an equilateral triangle ABC of side 130 feet and an isosceles triangle BCD in which BD and CD are of length 169 feet. A gardener has a motor mower which cuts strips of. . . .

M is any point on the line AB. Squares of side length AM and MB are constructed and their circumcircles intersect at P (and M). Prove that the lines AD and BE produced pass through P.