Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?

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

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

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

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

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

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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

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?

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

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

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

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?

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

Explore displacement/time and velocity/time graphs with this mouse motion sensor.

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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.

Use Excel to explore multiplication of fractions.

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

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. . . .

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

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

Which dilutions can you make using 10ml pipettes and 100ml measuring cylinders?

Which exact dilution ratios can you make using only 2 dilutions?

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

Can you fill in the mixed up numbers in this dilution calculation?

Can you break down this conversion process into logical steps?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Can you explain the strategy for winning this game with any target?

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.

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

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?

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.

A metal puzzle which led to some mathematical questions.

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.

Prove Pythagoras' Theorem using enlargements and scale factors.

Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

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

A game for 1 person to play on screen. Practise your number bonds whilst improving your memory

Find the frequency distribution for ordinary English, and use it to help you crack the code.

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

Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.