How good are you at finding the formula for a number pattern ?
To avoid losing think of another very well known game where the patterns of play are similar.
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
Can you beat the computer in the challenging strategy game?
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.
Match pairs of cards so that they have equivalent ratios.
The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"
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 moves.
Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Can you discover whether this is a fair game?
Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
An environment that enables you to investigate tessellations of regular polygons
Discover a handy way to describe reorderings and solve our anagram in the process.
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.
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.
Can you find a way to turn a rectangle into a square?
Use Excel to explore multiplication of fractions.
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?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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. . . .
Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?
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 red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .
A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
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.
Can you give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?
This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.
There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?
Can you find all the 4-ball shuffles?
A simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at. . . .
A java applet that takes you through the steps needed to solve a Diophantine equation of the form Px+Qy=1 using Euclid's algorithm.
An Excel spreadsheet with an investigation.
P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?
Use Excel to practise adding and subtracting fractions.
Practise your skills of proportional reasoning with this interactive haemocytometer.
Have you seen this way of doing multiplication ?
A tool for generating random integers.
This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.
A collection of our favourite pictorial problems, one for each day of Advent.
Here is a chance to play a fractions version of the classic Countdown Game.
An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.