On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
A package contains a set of resources designed to develop pupils'
mathematical thinking. This package places a particular emphasis on
“visualising” and is designed to meet the needs. . . .
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. . . .
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
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?
A game for 2 players. Can be played online. One player has 1 red
counter, the other has 4 blue. The red counter needs to reach the
other side, and the blue needs to trap the red.
This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.
This article for teachers discusses examples of problems in which
there is no obvious method but in which children can be encouraged
to think deeply about the context and extend their ability to. . . .
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
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.
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
A cheap and simple toy with lots of mathematics. Can you interpret
the images that are produced? Can you predict the pattern that will
be produced using different wheels?
Move just three of the circles so that the triangle faces in the
Can you make a 3x3 cube with these shapes made from small cubes?
These are pictures of the sea defences at New Brighton. Can you
work out what a basic shape might be in both images of the sea wall
and work out a way they might fit together?
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,. . . .
Lyndon Baker describes how the Mobius strip and Euler's law can
introduce pupils to the idea of topology.
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?
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?
Have a go at this 3D extension to the Pebbles problem.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
What is the shape of wrapping paper that you would need to completely wrap this model?
This second article in the series refers to research about levels
of development of spatial thinking and the possible influence of
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?
Can you find a way of representing these arrangements of balls?
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
What can you see? What do you notice? What questions can you ask?
The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?
This article is based on some of the ideas that emerged during the production of a book which takes visualising as its focus. We began to identify problems which helped us to take a structured view. . . .
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.
Can you fit the tangram pieces into the outline of this plaque design?
A game for two players. You'll need some counters.
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outline of the rocket?
Can you fit the tangram pieces into the outline of this junk?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
Can you fit the tangram pieces into the outline of these convex shapes?
Can you fit the tangram pieces into the outline of the telescope and microscope?
One face of a regular tetrahedron is painted blue and each of the
remaining faces are painted using one of the colours red, green or
yellow. How many different possibilities are there?
Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?
Imagine a pyramid which is built in square layers of small cubes.
If we number the cubes from the top, starting with 1, can you
picture which cubes are directly below this first cube?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?