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?

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?

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?

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

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.

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

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?

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

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

Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.

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

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

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

An environment that enables you to investigate tessellations of regular polygons

Use Excel to explore multiplication of fractions.

A tool for generating random integers.

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

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

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

Use Excel to practise adding and subtracting fractions.

Use an interactive Excel spreadsheet to investigate factors and multiples.

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.

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.

Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over... You win if all your cards end up in the trays before you run out of cards in. . . .

Can you beat the computer in the challenging strategy game?

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.

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.

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. . . .

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

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.

Match the cards of the same value.

Practise your skills of proportional reasoning with this interactive haemocytometer.

A weekly challenge concerning prime numbers.

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

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.

Mathmo is a revision tool for post-16 mathematics. It's great installed as a smartphone app, but it works well in pads and desktops and notebooks too. Give yourself a mathematical workout!

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

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?