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.
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.
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.
Use Excel to investigate the effect of translations around a number
Use Excel to explore multiplication of fractions.
An Excel spreadsheet with an investigation.
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?
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
Match pairs of cards so that they have equivalent ratios.
Use an interactive Excel spreadsheet to investigate factors and
Use Excel to practise adding and subtracting fractions.
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
Use an Excel spreadsheet to explore long multiplication.
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
A collection of our favourite pictorial problems, one for each day
Can you find all the 4-ball shuffles?
Use an interactive Excel spreadsheet to explore number in this
Match the cards of the same value.
Here is a chance to play a fractions version of the classic
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 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?
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
Can you discover whether this is a fair game?
An environment that enables you to investigate tessellations of
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?
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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.
Can you beat the computer in the challenging strategy game?
Square It game for an adult and child. Can you come up with a way of always winning this game?
A tool for generating random integers.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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
Start with any number of counters in any number of piles. 2 players
take it in turns to remove any number of counters from a single
pile. The winner is the player to take the last counter.
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.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
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
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
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. . . .
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?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Mo has left, but Meg is still experimenting. Use the interactivity
to help you find out how she can alter her pouch of marbles and
still keep the two pouches balanced.
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...
Try entering different sets of numbers in the number pyramids. How does the total at the top change?