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?

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?

This resources contains a series of interactivities designed to support work on transformations 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?

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?

A metal puzzle which led to some mathematical questions.

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?

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

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

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

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

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

An environment that enables you to investigate tessellations of regular polygons

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

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

Use Excel to explore multiplication of fractions.

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

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"

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

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

Match pairs of cards so that they have equivalent ratios.

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. . . .

Use an Excel spreadsheet to explore long multiplication.

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

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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

A tool for generating random integers.

An Excel spreadsheet with an investigation.

Use Excel to practise adding and subtracting fractions.

Use an interactive Excel spreadsheet to investigate factors and multiples.

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

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

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

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. . . .

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?

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. . . .

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

Can you beat the computer in the challenging strategy game?

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

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?

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. . . .

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

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

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. . . .

Have you seen this way of doing multiplication ?

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

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?