Take any parallelogram and draw squares on the sides of the parallelogram. What can you prove about the quadrilateral formed by joining the centres of these squares?

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?

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?

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

Try ringing hand bells for yourself with interactive versions of Diagram 2 (Plain Hunt Minimus) and Diagram 3 described in the article 'Ding Dong Bell'.

A tool for generating random integers.

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

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

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

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.

An environment that enables you to investigate tessellations of regular polygons

Give your further pure mathematics skills a workout with this interactive and reusable set of activities.

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?

Use Excel to explore multiplication of fractions.

Use an Excel spreadsheet to explore long multiplication.

Use an interactive Excel spreadsheet to investigate factors and multiples.

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

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.

Use Excel to practise adding and subtracting fractions.

An Excel spreadsheet with an investigation.

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

Use an interactive Excel spreadsheet to explore number in this exciting game!

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

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.

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.

Six circles around a central circle make a flower. Watch the flower as you change the radii in this circle packing. Prove that with the given ratios of the radii the petals touch and fit perfectly.

Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

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.

Try this interactivity to familiarise yourself with the proof that the square root of 2 is irrational. Sort the steps of the proof into the correct order.

A metal puzzle which led to some mathematical questions.

A spherical balloon lies inside a wire frame. How much do you need to deflate it to remove it from the frame if it remains a sphere?

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. . . .

Make and prove a conjecture about the cyclic quadrilateral inscribed in a circle of radius r that has the maximum perimeter and the maximum area.

Can you beat the computer in the challenging strategy game?

Match the cards of the same value.

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

A weekly challenge concerning prime numbers.

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

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 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.