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

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?

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

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

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

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

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

Identical discs are flipped in the air. You win if all of the faces show the same colour. Can you calculate the probability of winning with n discs?

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?

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

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

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

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.

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

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

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

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...

Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.

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

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

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

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.

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.

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

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. . . .

Match pairs of cards so that they have equivalent ratios.

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

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

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

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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?

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

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

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. . . .

Match the cards of the same value.

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 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.

Use Excel to explore multiplication of fractions.

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

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.

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

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

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

An environment that enables you to investigate tessellations of regular polygons

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.

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

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!