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?
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.
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?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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
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. . . .
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
What can you see? What do you notice? What questions can you ask?
Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
Can you make a 3x3 cube with these shapes made from small cubes?
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.
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?
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
What is the shape of wrapping paper that you would need to completely wrap this model?
Square It game for an adult and child. Can you come up with a way of always winning this game?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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?
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 fit the tangram pieces into the outline of these convex shapes?
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outline of the rocket?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
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.
Billy's class had a robot called Fred who could draw with chalk
held underneath him. What shapes did the pupils make Fred draw?
Can you fit the tangram pieces into the outline of this plaque design?
A game for two players. You'll need some counters.
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?
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 outline of the telescope and microscope?
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. . . .
Can you fit the tangram pieces into the outline of these rabbits?
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 fit the tangram pieces into the outline of this sports car?
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Which of these dice are right-handed and which are left-handed?
Can you fit the tangram pieces into the outlines of the workmen?
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 fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
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 candle and sundial?
Here are shadows of some 3D shapes. What shapes could have made
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are