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 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?

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?

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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.

This resources contains a series of interactivities designed to support work on transformations at Key Stage 4.

A metal puzzle which led to some mathematical questions.

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 environment that enables you to investigate tessellations of regular polygons

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. . . .

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

Match pairs of cards so that they have equivalent ratios.

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.

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

This resource contains a range of problems and interactivities on the theme of coordinates in two and three dimensions.

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.

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

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...

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.

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.

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

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.

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

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

Use Excel to explore multiplication of fractions.

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. . . .

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

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

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 moves.

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. . . .

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 area.

On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?

Can you beat the computer in the challenging strategy game?

Use Excel to practise adding and subtracting fractions.

An Excel spreadsheet with an investigation.

Use an interactive Excel spreadsheet to investigate factors and multiples.

Use an Excel spreadsheet to explore long multiplication.

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

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

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

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

Square It game for an adult and child. Can you come up with a way of always winning this game?

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