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
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.
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.
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
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
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.
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 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?
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?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
Match the cards of the same value.
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?
How good are you at estimating angles?
Match pairs of cards so that they have equivalent ratios.
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.
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?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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.
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?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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. . . .
Discover a handy way to describe reorderings and solve our anagram
in the process.
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
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?
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
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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
An environment that enables you to investigate tessellations of
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
Can you discover whether this is a fair game?
Use Excel to explore multiplication of fractions.
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.
This resources contains a series of interactivities designed to
support work on transformations at Key Stage 4.
Use this animation to experiment with lotteries. Choose how many
balls to match, how many are in the carousel, and how many draws to
make at once.
Use an interactive Excel spreadsheet to investigate factors and
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
A tool for generating random integers.
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
Use an Excel spreadsheet to explore long multiplication.
An environment that simulates a protractor carrying a right- angled
triangle of unit hypotenuse.
This resource contains interactive problems to support work on
number sequences at Key Stage 4.