An environment which simulates working with Cuisenaire rods.
Find out what a "fault-free" rectangle is and try to make some of
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
We can show that (x + 1)² = x² + 2x + 1 by considering
the area of an (x + 1) by (x + 1) square. Show in a similar way
that (x + 2)² = x² + 4x + 4
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
A train building game for 2 players.
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.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Train game for an adult and child. Who will be the first to make the train?
A tilted square is a square with no horizontal sides. Can you
devise a general instruction for the construction of a square when
you are given just one of its sides?
Work out the fractions to match the cards with the same amount of
Can you find all the different ways of lining up these Cuisenaire
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Do you know how to find the area of a triangle? You can count the
squares. What happens if we turn the triangle on end? Press the
button and see. Try counting the number of units in the triangle
now. . . .
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?
An interactive activity for one to experiment with a tricky tessellation
A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.
Exchange the positions of the two sets of counters in the least possible number of moves
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
You can move the 4 pieces of the jigsaw and fit them into both
outlines. Explain what has happened to the missing one unit of
An animation that helps you understand the game of Nim.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
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 to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
A generic circular pegboard resource.
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?
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?
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?
What is the greatest number of squares you can make by overlapping
Ahmed has some wooden planks to use for three sides of a rabbit run
against the shed. What quadrilaterals would he be able to make with
the planks of different lengths?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
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?
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. . . .
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
Can you work out what is wrong with the cogs on a UK 2 pound coin?
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?
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.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you