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?
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.
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
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.
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?
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.
Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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 explain the strategy for winning this game with any target?
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...
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.
Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Can you coach your rowing eight to win?
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. . . .
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?
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?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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.
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.
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.
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
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 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?
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?
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
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.
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. . . .
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 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.
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. . . .
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
An animation that helps you understand the game of Nim.
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.
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.
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
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?
Can you find triangles on a 9-point circle? Can you work out their angles?
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?
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?
Work out how to light up the single light. What's the rule?