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.
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?
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 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.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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
Meg and Mo still need to hang their marbles so that they balance,
but this time the constraints are different. Use the interactivity
to experiment and find out what they need to do.
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.
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 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?
Match pairs of cards so that they have equivalent ratios.
To avoid losing think of another very well known game where the
patterns of play are similar.
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
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 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 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. . . .
Meg and Mo need to hang their marbles so that they balance. Use the
interactivity to experiment and find out what they need to do.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Can you find all the 4-ball shuffles?
Mo has left, but Meg is still experimenting. Use the interactivity
to help you find out how she can alter her pouch of marbles and
still keep the two pouches balanced.
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
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
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
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?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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?
Use Excel to explore multiplication of fractions.
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. . . .
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
Can you beat the computer in the challenging strategy game?
Here is a chance to play a version of the classic Countdown Game.
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.
Two engines, at opposite ends of a single track railway line, set
off towards one another just as a fly, sitting on the front of one
of the engines, sets off flying along the railway line...
Match the cards of the same value.
Can you coach your rowing eight to win?
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
An animation that helps you understand the game of Nim.
Investigate how logic gates work in circuits.
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Show how this pentagonal tile can be used to tile the plane and
describe the transformations which map this pentagon to its images
in the tiling.