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?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?
Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?
How good are you at estimating angles?
You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.
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.
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
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. . . .
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
A game for 1 person to play on screen. Practise your number bonds whilst improving your memory
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.
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?
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.
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.
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?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
An animation that helps you understand the game of Nim.
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?
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 locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?
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?
Here is a chance to play a version of the classic Countdown Game.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
To avoid losing think of another very well known game where the patterns of play are similar.
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?
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
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.
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.
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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. . . .
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
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?
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?
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!