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

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

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

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?

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

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?

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?

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

Work out how to light up the single light. What's the rule?

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

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

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

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

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

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 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.

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. . . .

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

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.

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

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.

Prove Pythagoras' Theorem using enlargements and scale factors.

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.

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 Excel to explore multiplication of fractions.

Triangle 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?

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

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

Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

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.

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?

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

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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

An Excel spreadsheet with an investigation.