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?

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?

A metal puzzle which led to some mathematical questions.

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

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

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.

Match pairs of cards so that they have equivalent ratios.

This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.

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

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?

A collection of resources to support work on Factors and Multiples at Secondary level.

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

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

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. . . .

An environment that enables you to investigate tessellations of regular polygons

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

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

Use Excel to explore multiplication of fractions.

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

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?

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.

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

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

This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!

Use Excel to practise adding and subtracting fractions.

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

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

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

An Excel spreadsheet with an investigation.

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?

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

Match the cards of the same value.

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

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.

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

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

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.

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

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

Practise your skills of proportional reasoning with this interactive haemocytometer.

Use an interactive Excel spreadsheet to investigate factors and multiples.

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. . . .

A tool for generating random integers.