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?

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

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

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.

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 an Excel spreadsheet to explore long multiplication.

A tool for generating random integers.

An Excel spreadsheet with an investigation.

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

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

Use Excel to explore multiplication of fractions.

Use Excel to practise adding and subtracting fractions.

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

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.

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

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

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

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

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

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

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

An environment that enables you to investigate tessellations of regular polygons

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

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

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

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

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

Use an interactive Excel spreadsheet to investigate factors and multiples.

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

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

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

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.

Can you beat the computer in the challenging strategy game?

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.

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.

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?

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.

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.

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.

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 work through these direct proofs, using our interactive proof sorters?

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.