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?

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

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

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 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 reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

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

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

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.

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.

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

These interactive dominoes can be dragged around the screen.

Here is a chance to play a version of the classic Countdown Game.

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...

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

Use the interactivities to complete these Venn diagrams.

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

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?

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?

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

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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

How many different triangles can you make which consist of the centre point and two of the points on the edge? Can you work out each of their angles?

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

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.

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

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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

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?

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.

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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.

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.

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 complete this jigsaw of the multiplication square?

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.

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?

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

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

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?

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?

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.