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!
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. . . .
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. . . .
To avoid losing think of another very well known game where the patterns of play are similar.
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.
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.
Match the cards of the same value.
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?
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?
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 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?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.
Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?
Can you beat the computer in the challenging strategy game?
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 give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?
The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"
Match pairs of cards so that they have equivalent ratios.
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?
Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.
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. 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.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
How good are you at estimating angles?
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?
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.
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 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. . . .
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.
This resource contains a range of problems and interactivities on the theme of coordinates in two and three dimensions.
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. . . .
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
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.
Discover a handy way to describe reorderings and solve our anagram in the process.
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.
An environment that enables you to investigate tessellations of regular polygons
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.
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?
Use Excel to explore multiplication of fractions.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
This resources contains a series of interactivities designed to support work on transformations at Key Stage 4.
This resource contains interactive problems to support work on number sequences at Key Stage 4.
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.
This set of resources for teachers offers interactive environments to support work on graphical interpretation at Key Stage 4.
An Excel spreadsheet with an investigation.
Use Excel to practise adding and subtracting fractions.
Can you discover whether this is a fair game?
Use an interactive Excel spreadsheet to investigate factors and multiples.