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. . . .
Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.
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?
This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!
To avoid losing think of another very well known game where the patterns of play are similar.
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. . . .
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.
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.
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.
Can you beat the computer in the challenging strategy game?
Here is a chance to play a fractions version of the classic Countdown Game.
Use Excel to investigate the effect of translations around a number grid.
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.
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?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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?
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 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. . . .
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?
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
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.
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.
Use an interactive Excel spreadsheet to explore number in this exciting game!
Match pairs of cards so that they have equivalent ratios.
Match the cards of the same value.
A collection of our favourite pictorial problems, one for each day of Advent.
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?
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.
How good are you at estimating angles?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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?
This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.
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?
Use an interactive Excel spreadsheet to investigate factors and multiples.
Use an Excel spreadsheet to explore long multiplication.
An Excel spreadsheet with an investigation.
Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.
Use Excel to practise adding and subtracting fractions.
Can you find triangles on a 9-point circle? Can you work out their angles?
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
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 area.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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?
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.
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.
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?