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?
Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?
See if you can anticipate successive 'generations' of the two
animals shown here.
Bilbo goes on an adventure, before arriving back home. Using the
information given about his journey, can you work out where Bilbo
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?
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
This task depends on groups working collaboratively, discussing and
reasoning to agree a final product.
This article is based on some of the ideas that emerged during the production of a book which takes visualising as its focus. We began to identify problems which helped us to take a structured view. . . .
What can you see? What do you notice? What questions can you ask?
ABC is an equilateral triangle and P is a point in the interior of
the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP
must be less than 10 cm.
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
Show that among the interior angles of a convex polygon there
cannot be more than three acute angles.
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.
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. . . .
Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
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.
Have a go at this 3D extension to the Pebbles problem.
A huge wheel is rolling past your window. What do you see?
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. . . .
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?
Can you recreate these designs? What are the basic units? What
movement is required between each unit? Some elegant use of
procedures will help - variables not essential.
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Square It game for an adult and child. Can you come up with a way of always winning this game?
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?
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?
A bus route has a total duration of 40 minutes. Every 10 minutes,
two buses set out, one from each end. How many buses will one bus
meet on its way from one end to the other end?
These are pictures of the sea defences at New Brighton. Can you
work out what a basic shape might be in both images of the sea wall
and work out a way they might fit together?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Can you fit the tangram pieces into the outline of this goat and giraffe?
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?
Lyndon Baker describes how the Mobius strip and Euler's law can
introduce pupils to the idea of topology.
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of this telephone?
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
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?
Can you fit the tangram pieces into the outline of this sports car?
Can you fit the tangram pieces into the outline of these convex shapes?
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outline of the telescope and microscope?
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 fit the tangram pieces into the outline of the rocket?
Can you fit the tangram pieces into the outline of this junk?
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. . . .
The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .
How many different triangles can you make on a circular pegboard that has nine pegs?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?