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?

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

Use an Excel spreadsheet to explore long multiplication.

An Excel spreadsheet with an investigation.

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

Can you set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?

Match the cards of the same value.

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

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

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.

Match pairs of cards so that they have equivalent ratios.

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

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

Have you seen this way of doing multiplication ?

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

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.

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .

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 beat the computer in the challenging strategy game?

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

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

An environment that enables you to investigate tessellations of regular polygons

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?

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.

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

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. . . .

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?

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

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

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. . . .

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.

This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.

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.

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?

Use Excel to explore multiplication of fractions.

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

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?

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?

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. . . .

A metal puzzle which led to some mathematical questions.

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

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