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?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
An animation that helps you understand the game of Nim.
Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
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.
Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?
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.
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?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.
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.
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
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?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
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.
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?
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?
Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
A game for 1 person to play on screen. Practise your number bonds whilst improving your memory
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
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.
Can you find triangles on a 9-point circle? Can you work out their angles?
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 make a right-angled triangle on this peg-board by joining up three points round the edge?
Can you give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?
An environment that enables you to investigate tessellations of regular polygons
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?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .
This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.
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. . . .
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
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...
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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 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. . . .
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.
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. . . .
Can you coach your rowing eight to win?