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

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?

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

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.

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?

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.

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.

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

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

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

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

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

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

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.

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. . . .

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

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

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?

Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?

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 way to turn a rectangle into a square?

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

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

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...

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

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

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

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

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.

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

Match pairs of cards so that they have equivalent ratios.

Use Excel to explore multiplication of fractions.

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

Use an Excel spreadsheet to explore long multiplication.

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. . . .

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

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.

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.

An Excel spreadsheet with an investigation.

Use Excel to practise adding and subtracting fractions.

Use an interactive Excel spreadsheet to investigate factors and multiples.

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

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