Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Can you find triangles on a 9-point circle? Can you work out their angles?
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?
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...
An animation that helps you understand the game of Nim.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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.
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.
Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?
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?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
How good are you at estimating angles?
Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?
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.
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?
A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?
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
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
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?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
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?
A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .
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.
Here is a chance to play a version of the classic Countdown Game.
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. . . .
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.
To avoid losing think of another very well known game where the patterns of play are similar.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.
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?
Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?
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?
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.
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
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...
Can you explain the strategy for winning this game with any target?
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?
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.
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?
Can you discover whether this is a fair game?
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.