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?
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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 locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.
An animation that helps you understand the game of Nim.
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.
Can you work out which spinners were used to generate the frequency charts?
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?
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 find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?
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?
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...
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 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.
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?
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.
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?
A game for 1 person to play on screen. Practise your number bonds whilst improving your memory
7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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. . . .
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?
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?
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?
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.
To avoid losing think of another very well known game where the patterns of play are similar.
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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?
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.
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.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Can you find all the 4-ball shuffles?
Can you explain the strategy for winning this game with any target?
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .
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.
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 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. . . .
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.