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?

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?

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...

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

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. . . .

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

Explore displacement/time and velocity/time graphs with this mouse motion sensor.

An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

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?

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.

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

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 Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

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 spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

To avoid losing think of another very well known game where the patterns of play are similar.

Use Excel to explore multiplication of fractions.

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.

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.

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.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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. . . .

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

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?

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. . . .

Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.

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 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?

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

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.

Practise your skills of proportional reasoning with this interactive haemocytometer.

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

Which exact dilution ratios can you make using only 2 dilutions?

Which dilutions can you make using 10ml pipettes and 100ml measuring cylinders?

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.

Can you fill in the mixed up numbers in this dilution calculation?

This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.

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?

Can you beat the computer in the challenging strategy game?

Here is a chance to play a version of the classic Countdown Game.