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

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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?

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

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 game in which players take it in turns to choose a number. Can you block your opponent?

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

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

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...

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

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.

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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?

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.

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

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?

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.

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

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

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

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

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. . . .

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.

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.

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

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?

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?

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

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?

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

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

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .

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.

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

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

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

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.

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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.