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. . . .

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.

Can you work out which spinners were used to generate the frequency charts?

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

Prove Pythagoras' Theorem using enlargements and scale factors.

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

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. . . .

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

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. . . .

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.

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.

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

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

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

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 explain the strategy for winning this game with any target?

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?

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

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

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?

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

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?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

Use Excel to explore multiplication of fractions.

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

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

Use an interactive Excel spreadsheet to investigate factors and multiples.

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?

Use Excel to practise adding and subtracting fractions.

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

Can you find triangles on a 9-point circle? Can you work out their angles?

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

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 spreadsheet to explore long multiplication.

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

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

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?

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.