This task depends on groups working collaboratively, discussing and
reasoning to agree a final product.
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
Glarsynost lives on a planet whose shape is that of a perfect
regular dodecahedron. Can you describe the shortest journey she can
make to ensure that she will see every part of the planet?
I found these clocks in the Arts Centre at the University of
Warwick intriguing - do they really need four clocks and what times
would be ambiguous with only two or three of them?
This is a simple version of an ancient game played all over the world. It is also called Mancala. What tactics will increase your chances of winning?
This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!
What can you see? What do you notice? What questions can you ask?
Two boats travel up and down a lake. Can you picture where they
will cross if you know how fast each boat is travelling?
A and C are the opposite vertices of a square ABCD, and have
coordinates (a,b) and (c,d), respectively. What are the coordinates
of the vertices B and D? What is the area of the square?
A cube is made from smaller cubes, 5 by 5 by 5, then some of those
cubes are removed. Can you make the specified shapes, and what is
the most and least number of cubes required ?
A visualisation problem in which you search for vectors which sum
to zero from a jumble of arrows. Will your eyes be quicker than
A bicycle passes along a path and leaves some tracks. Is it
possible to say which track was made by the front wheel and which
by the back wheel?
Discover a way to sum square numbers by building cuboids from small
cubes. Can you picture how the sequence will grow?
Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?
Two angles ABC and PQR are floating in a box so that AB//PQ and BC//QR. Prove that the two angles are equal.
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being
visible at any one time. Is it possible to reorganise these cubes
so that by dipping the large cube into a pot of paint three times
you. . . .
A rectangular field has two posts with a ring on top of each post.
There are two quarrelsome goats and plenty of ropes which you can
tie to their collars. How can you secure them so they can't. . . .
In this problem we are faced with an apparently easy area problem,
but it has gone horribly wrong! What happened?
Find the point whose sum of distances from the vertices (corners)
of a given triangle is a minimum.
A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.
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
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
To avoid losing think of another very well known game where the
patterns of play are similar.
A game for 2 players
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Find all the ways to cut out a 'net' of six squares that can be
folded into a cube.
Bilbo goes on an adventure, before arriving back home. Using the
information given about his journey, can you work out where Bilbo
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?
The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?
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.
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
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?
In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal. . . .
Imagine you are suspending a cube from one vertex (corner) and
allowing it to hang freely. Now imagine you are lowering it into
water until it is exactly half submerged. What shape does the
surface. . . .
What is the shape of wrapping paper that you would need to completely wrap this model?
This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the. . . .
The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design. Coins inserted into the machine slide down a chute into the machine and a drink is duly. . . .
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
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. . . .
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
Square It game for an adult and child. Can you come up with a way of always winning this game?
Two intersecting circles have a common chord AB. The point C moves
on the circumference of the circle C1. The straight lines CA and CB
meet the circle C2 at E and F respectively. As the point C. . . .
In the game of Noughts and Crosses there are 8 distinct winning
lines. How many distinct winning lines are there in a game played
on a 3 by 3 by 3 board, with 27 cells?
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?
In how many ways can you fit all three pieces together to make
shapes with line symmetry?
ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP
: PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED.
What is the area of the triangle PQR?
Every day at noon a boat leaves Le Havre for New York while another
boat leaves New York for Le Havre. The ocean crossing takes seven
days. How many boats will each boat cross during their journey?