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?

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?

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?

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.

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

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.

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. . . .

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

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

Match pairs of cards so that they have equivalent ratios.

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.

Use Excel to explore multiplication of fractions.

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

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?

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

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

How can we solve equations like 13x + 29y = 42 or 2x +4y = 13 with the solutions x and y being integers? Read this article to find out.

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 spreadsheet to explore long multiplication.

Use Excel to practise adding and subtracting fractions.

A metal puzzle which led to some mathematical questions.

An Excel spreadsheet with an investigation.

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

Use an interactive Excel spreadsheet to investigate factors and multiples.

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

Match the cards of the same value.

What is the quickest route across a ploughed field when your speed around the edge is greater?

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

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

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!

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.

Practise your skills of proportional reasoning with this interactive haemocytometer.

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?

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

Can you beat the computer in the challenging strategy game?

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.

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 locate these values on this interactive logarithmic scale?