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?

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

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?

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

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?

Use an Excel spreadsheet to explore long multiplication.

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

Use an interactive Excel spreadsheet to investigate factors and multiples.

Use Excel to practise adding and subtracting fractions.

An Excel spreadsheet with an investigation.

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

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

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

An environment that enables you to investigate tessellations of regular polygons

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.

Use Excel to explore multiplication of fractions.

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.

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

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

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

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

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 set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?

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

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

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.

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.

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

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

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?

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.

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

Match pairs of cards so that they have equivalent ratios.

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?

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?

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. . . .

Can you beat the computer in the challenging strategy game?

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .

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.

Match the cards of the same value.

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. . . .

A metal puzzle which led to some mathematical questions.

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

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