Prove Pythagoras' Theorem using enlargements and scale factors.
Can you discover whether this is a fair game?
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.
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. . . .
Match pairs of cards so that they have equivalent ratios.
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.
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 right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?
An environment that enables you to investigate tessellations of regular polygons
Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?
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.
To avoid losing think of another very well known game where the patterns of play are similar.
A metal puzzle which led to some mathematical questions.
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .
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 collection of our favourite pictorial problems, one for each day of Advent.
Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Here is a chance to play a fractions version of the classic Countdown Game.
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.
Can you give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?
A tool for generating random integers.
The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
Discover a handy way to describe reorderings and solve our anagram in the process.
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
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 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. . . .
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?
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?
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?
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. . . .
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
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.
A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .
Match the cards of the same value.
Can you beat the computer in the challenging strategy game?
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 set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?
Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?
Cellular is an animation that helps you make geometric sequences composed of square cells.
Practise your skills of proportional reasoning with this interactive haemocytometer.
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.
How good are you at finding the formula for a number pattern ?
This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.
This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.
Use Excel to explore multiplication of fractions.
Use an interactive Excel spreadsheet to explore number in this exciting game!
A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.