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?
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
A cheap and simple toy with lots of mathematics. Can you interpret
the images that are produced? Can you predict the pattern that will
be produced using different wheels?
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?
A visualisation problem in which you search for vectors which sum
to zero from a jumble of arrows. Will your eyes be quicker than
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?
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?
This task depends on groups working collaboratively, discussing and
reasoning to agree a final product.
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?
Two angles ABC and PQR are floating in a box so that AB//PQ and BC//QR. Prove that the two angles are equal.
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 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?
The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.
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. . . .
Discover a way to sum square numbers by building cuboids from small
cubes. Can you picture how the sequence will grow?
Find the point whose sum of distances from the vertices (corners)
of a given triangle is a minimum.
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 ?
Square It game for an adult and child. Can you come up with a way of always winning this game?
A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start.
How many Hamiltonian circuits can you find in these graphs?
Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?
Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Bilbo goes on an adventure, before arriving back home. Using the
information given about his journey, can you work out where Bilbo
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?
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Seven small rectangular pictures have one inch wide frames. The
frames are removed and the pictures are fitted together like a
jigsaw to make a rectangle of length 12 inches. Find the dimensions
of. . . .
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. . . .
What is the shape of wrapping paper that you would need to completely wrap this model?
To avoid losing think of another very well known game where the
patterns of play are similar.
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. . . .
Find all the ways to cut out a 'net' of six squares that can be
folded into a cube.
Imagine a stack of numbered cards with one on top. Discard the top,
put the next card to the bottom and repeat continuously. Can you
predict the last card?
A 10x10x10 cube is made from 27 2x2 cubes with corridors between
them. Find the shortest route from one corner to the opposite
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!
Lyndon Baker describes how the Mobius strip and Euler's law can
introduce pupils to the idea of topology.
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
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.
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. . . .
This article for teachers discusses examples of problems in which
there is no obvious method but in which children can be encouraged
to think deeply about the context and extend their ability to. . . .
A game for 2 players
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.
Find the ratio of the outer shaded area to the inner area for a six
pointed star and an eight pointed star.
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?
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?
ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
Show that all pentagonal numbers are one third of a triangular number.
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
A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns. . . .