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.

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?

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?

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.

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!

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.

Match the cards of the same value.

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

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

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

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.

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

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

An environment that enables you to investigate tessellations of regular polygons

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

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?

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

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

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

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.

Match pairs of cards so that they have equivalent ratios.

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

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

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

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.

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

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. . . .

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.

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

A tool for generating random integers.

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. . . .

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

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

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

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

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

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

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

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. . . .

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.

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

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Use an interactive Excel spreadsheet to investigate factors and multiples.

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