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

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 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?

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?

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

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?

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

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.

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

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.

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

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .

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.

Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over... You win if all your cards end up in the trays before you run out of cards in. . . .

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

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

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.

A metal puzzle which led to some mathematical questions.

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

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?

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

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?

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

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 environment that enables you to investigate tessellations of regular polygons

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

Discover a handy way to describe reorderings and solve our anagram in the process.

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.

How good are you at finding the formula for a number pattern ?

This resource contains interactive problems to support work on number sequences at Key Stage 4.

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

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

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

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. . . .

A tool for generating random integers.

A collection of our favourite pictorial problems, one for each day of Advent.

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.

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

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.

The classic vector racing game brought to a screen near you.

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

Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

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