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.
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?
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. . . .
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
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
Lyndon Baker describes how the Mobius strip and Euler's law can
introduce pupils to the idea of topology.
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,. . . .
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.
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.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
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?
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
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?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
Have a go at this 3D extension to the Pebbles problem.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
What can you see? What do you notice? What questions can you ask?
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?
What is the shape of wrapping paper that you would need to completely wrap this model?
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.
Can you find a way of representing these arrangements of balls?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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?
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?
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 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. . . .
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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?
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
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 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?
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. . . .
A game for two players. You'll need some counters.
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of these rabbits?
This article for teachers describes a project which explores
thepower of storytelling to convey concepts and ideas to children.