A point P is selected anywhere inside an equilateral triangle. What can you say about the sum of the perpendicular distances from P to the sides of the triangle? Can you prove your conjecture?

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.

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?

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

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

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.

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. . . .

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

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?

Use Excel to explore multiplication of fractions.

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

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. . . .

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.

An environment that enables you to investigate tessellations of regular polygons

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

Match pairs of cards so that they have equivalent ratios.

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

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 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. . . .

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

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

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?

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?

A tool for generating random integers.

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

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.

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

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 classic vector racing game brought to a screen near you.

Practise your skills of proportional reasoning with this interactive haemocytometer.

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

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.

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?

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. . . .

Can you beat the computer in the challenging strategy game?

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

A metal puzzle which led to some mathematical questions.

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

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

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.

Use an Excel spreadsheet to explore long multiplication.

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

A collection of resources to support work on Factors and Multiples at Secondary level.

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!

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.