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?

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.

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 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?

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. . . .

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

This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!

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

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.

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

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?

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.

Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.

Match pairs of cards so that they have equivalent ratios.

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

Can you beat the computer in the challenging strategy game?

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

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

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

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

Practise your skills of proportional reasoning with this interactive haemocytometer.

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

An environment that enables you to investigate tessellations of regular polygons

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

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

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

A tool for generating random integers.

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.

A metal puzzle which led to some mathematical questions.

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?

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

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

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?

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

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. . . .

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

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

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

Use Excel to explore multiplication of fractions.

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?

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?

Use an interactive Excel spreadsheet to investigate factors and multiples.

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

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

Use Excel to practise adding and subtracting fractions.

An Excel spreadsheet with an investigation.

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.