Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
This task depends on groups working collaboratively, discussing and
reasoning to agree a final product.
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
What can you see? What do you notice? What questions can you ask?
I found these clocks in the Arts Centre at the University of
Warwick intriguing - do they really need four clocks and what times
would be ambiguous with only two or three of them?
You want to make each of the 5 Platonic solids and colour the faces
so that, in every case, no two faces which meet along an edge have
the same colour.
See if you can anticipate successive 'generations' of the two
animals shown here.
The second in a series of articles on visualising and modelling shapes in the history of astronomy.
The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.
Can you recreate these designs? What are the basic units? What
movement is required between each unit? Some elegant use of
procedures will help - variables not essential.
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
Can you describe this route to infinity? Where will the arrows take you next?
A toy has a regular tetrahedron, a cube and a base with triangular
and square hollows. If you fit a shape into the correct hollow a
bell rings. How many times does the bell ring in a complete game?
This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
Investigate the number of paths you can take from one vertex to
another in these 3D shapes. Is it possible to take an odd number
and an even number of paths to the same vertex?
Try this interactive strategy game for 2
Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?
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?
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
Can you arrange the shapes in a chain so that each one shares a
face (or faces) that are the same shape as the one that follows it?
A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
Can you fit the tangram pieces into the outlines of the candle and sundial?
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 article for teachers describes how modelling number properties
involving multiplication using an array of objects not only allows
children to represent their thinking with concrete materials,. . . .
Here's a simple way to make a Tangram without any measuring or
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outlines of the workmen?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.
Which of these dice are right-handed and which are left-handed?
The triangle ABC is equilateral. The arc AB has centre C, the arc
BC has centre A and the arc CA has centre B. Explain how and why
this shape can roll along between two parallel tracks.
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of the chairs?
We start with one yellow cube and build around it to make a 3x3x3
cube with red cubes. Then we build around that red cube with blue
cubes and so on. How many cubes of each colour have we used?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
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?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you fit the tangram pieces into the outline of this goat and giraffe?