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.
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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 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?
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
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?
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 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.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
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.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Can you spot the similarities between this game and other games you
know? The aim is to choose 3 numbers that total 15.
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.
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?
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.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
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 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.
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.
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. . . .
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. . . .
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.
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?
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
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?
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
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?
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 game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
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?
A metal puzzle which led to some mathematical questions.
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
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...
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?
To avoid losing think of another very well known game where the
patterns of play are similar.
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
Work out how to light up the single light. What's the rule?
Here is a chance to play a version of the classic Countdown Game.
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
Could games evolve by natural selection? Take part in this web experiment to find out!
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
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.
Can you find all the 4-ball shuffles?