See if you can anticipate successive 'generations' of the two
animals shown here.
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.
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?
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
How can you make an angle of 60 degrees by folding a sheet of paper
Can you cut up a square in the way shown and make the pieces into a
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
A huge wheel is rolling past your window. What do you see?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
Here's a simple way to make a Tangram without any measuring or
Blue Flibbins are so jealous of their red partners that they will
not leave them on their own with any other bue Flibbin. What is the
quickest way of getting the five pairs of Flibbins safely to. . . .
In how many ways can you fit all three pieces together to make
shapes with line symmetry?
You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.
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.
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,. . . .
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
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
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 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?
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.
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
Have a look at what happens when you pull a reef knot and a granny
knot tight. Which do you think is best for securing things
Can you fit the tangram pieces into the outlines of the workmen?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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. . . .
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?
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?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
Lyndon Baker describes how the Mobius strip and Euler's law can
introduce pupils to the idea of topology.
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Can you fit the tangram pieces into the outline of this sports car?
Billy's class had a robot called Fred who could draw with chalk
held underneath him. What shapes did the pupils make Fred draw?
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
Can you fit the tangram pieces into the outline of this goat and giraffe?
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
A bus route has a total duration of 40 minutes. Every 10 minutes,
two buses set out, one from each end. How many buses will one bus
meet on its way from one end to the other end?
A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable.
Decide which of these diagrams are traversable.
Make a cube out of straws and have a go at this practical