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.
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
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.
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?
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 locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
Can you spot the similarities between this game and other games you
know? The aim is to choose 3 numbers that total 15.
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.
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?
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
Work out how to light up the single light. What's the rule?
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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.
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?
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.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
Can you set the logic gates so that the number of bulbs which are
on is the same as the number of switches which are on?
Here is a chance to play a version of the classic Countdown Game.
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?
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
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?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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. . . .
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
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
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?
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 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.
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
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
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.
Triangle numbers can be represented by a triangular array of
squares. What do you notice about the sum of identical triangle
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Could games evolve by natural selection? Take part in this web experiment to find out!
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
Can you find all the 4-ball shuffles?
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?
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?
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
Start with any number of counters in any number of piles. 2 players
take it in turns to remove any number of counters from a single
pile. The winner is the player to take the last counter.
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.