When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

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. . . .

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.

Cellular is an animation that helps you make geometric sequences composed of square cells.

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

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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

A metal puzzle which led to some mathematical questions.

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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?

An environment that enables you to investigate tessellations of regular polygons

Match the cards of the same value.

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

Match pairs of cards so that they have equivalent ratios.

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

Can you beat the computer in the challenging strategy game?

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

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

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

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.

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

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?

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

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

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 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.

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

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?

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

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. . . .

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.

Prove Pythagoras' Theorem using enlargements and scale factors.

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. . . .

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

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?

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

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.

Find the frequency distribution for ordinary English, and use it to help you crack the code.

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Use an interactive Excel spreadsheet to investigate factors and multiples.

Use Excel to practise adding and subtracting fractions.

An Excel spreadsheet with an investigation.

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