This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Can you work out what is wrong with the cogs on a UK 2 pound coin?
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
How many times in twelve hours do the hands of a clock form a right
angle? Use the interactivity to check your answers.
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
What are the coordinates of the coloured dots that mark out the
tangram? Try changing the position of the origin. What happens to
the coordinates now?
Use the interactivity or play this dice game yourself. How could
you make it fair?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Find out what a "fault-free" rectangle is and try to make some of
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
An animation that helps you understand the game of Nim.
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
A train building game for 2 players.
Experiment with the interactivity of "rolling" regular polygons,
and explore how the different positions of the red dot affects its
speed at each stage.
Two engines, at opposite ends of a single track railway line, set
off towards one another just as a fly, sitting on the front of one
of the engines, sets off flying along the railway line...
If you have only four weights, where could you place them in order
to balance this equaliser?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you find all the different triangles on these peg boards, and
find their angles?
Can you find all the different ways of lining up these Cuisenaire
What is the relationship between the angle at the centre and the
angles at the circumference, for angles which stand on the same
arc? Can you prove it?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
A generic circular pegboard resource.
Exchange the positions of the two sets of counters in the least possible number of moves
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
An interactive game to be played on your own or with friends.
Imagine you are having a party. Each person takes it in turns to
stand behind the chair where they will get the most chocolate.
Show how this pentagonal tile can be used to tile the plane and
describe the transformations which map this pentagon to its images
in the tiling.
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?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?