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?

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?

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?

Can you find a way to turn a rectangle into a square?

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. . . .

A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.

Use an interactive Excel spreadsheet to explore number in this exciting game!

Use an Excel spreadsheet to explore long multiplication.

The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"

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 an interactive Excel spreadsheet to investigate factors and multiples.

Use Excel to investigate the effect of translations around a number grid.

A group of interactive resources to support work on percentages Key Stage 4.

Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?

Use Excel to explore multiplication of fractions.

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

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?

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...

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

Use Excel to practise adding and subtracting fractions.

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

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?

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.

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

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?

An Excel spreadsheet with an investigation.

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 its vertical and horizontal movement at each stage.

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. . . .

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

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

Can you give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?

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.

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

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.

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. 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.

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

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 opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

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.

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 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.

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

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 moves.

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

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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