Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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?
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?
Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?
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?
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. . . .
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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?
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.
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
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.
An animation that helps you understand the game of Nim.
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?
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 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.
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
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.
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?
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. . . .
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
An Excel spreadsheet with an investigation.
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.
Imagine picking up a bow and some arrows and attempting to hit the
target a few times. Can you work out the settings for the sight
that give you the best chance of gaining a high score?
Can you explain the strategy for winning this game with any target?
Identical discs are flipped in the air. You win if all of the faces
show the same colour. Can you calculate the probability of winning
with n discs?
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?
Here is a chance to play a version of the classic Countdown Game.
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.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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.
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Use Excel to explore multiplication of fractions.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
Can you find all the 4-ball shuffles?
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...
How many different triangles can you make which consist of the
centre point and two of the points on the edge? Can you work out
each of their angles?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Match the cards of the same value.
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
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.
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.