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?
For any right-angled triangle find the radii of the three escribed
circles touching the sides of the triangle externally.
A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?
Small circles nestle under touching parent circles when they sit on
the axis at neighbouring points in a Farey sequence.
Find the ratio of the outer shaded area to the inner area for a six
pointed star and an eight pointed star.
Imagine a rectangular tray lying flat on a table. Suppose that a plate lies on the tray and rolls around, in contact with the sides as it rolls. What can we say about the motion?
A 10x10x10 cube is made from 27 2x2 cubes with corridors between
them. Find the shortest route from one corner to the opposite
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?
A spider is sitting in the middle of one of the smallest walls in a
room and a fly is resting beside the window. What is the shortest
distance the spider would have to crawl to catch the fly?
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?
How efficiently can you pack together disks?
A blue coin rolls round two yellow coins which touch. The coins are
the same size. How many revolutions does the blue coin make when it
rolls all the way round the yellow coins? Investigate for a. . . .
Can you work out the dimensions of the three cubes?
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. . . .
Four rods are hinged at their ends to form a convex quadrilateral.
Investigate the different shapes that the quadrilateral can take.
Be patient this problem may be slow to load.
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
An introduction to bond angle geometry.
See if you can anticipate successive 'generations' of the two
animals shown here.
Have you got the Mach knack? Discover the mathematics behind
exceeding the sound barrier.
The net of a cube is to be cut from a sheet of card 100 cm square.
What is the maximum volume cube that can be made from a single
piece of card?
P is a point on the circumference of a circle radius r which rolls,
without slipping, inside a circle of radius 2r. What is the locus
A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?
Can you find a rule which relates triangular numbers to square numbers?
Can you find a rule which connects consecutive triangular numbers?
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.
An irregular tetrahedron has two opposite sides the same length a
and the line joining their midpoints is perpendicular to these two
edges and is of length b. What is the volume of the tetrahedron?
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 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?
Place a red counter in the top left corner of a 4x4 array, which is
covered by 14 other smaller counters, leaving a gap in the bottom
right hand corner (HOME). What is the smallest number of moves. . . .
Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .
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.
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!
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
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.
Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
Two boats travel up and down a lake. Can you picture where they
will cross if you know how fast each boat is travelling?
Discover a way to sum square numbers by building cuboids from small
cubes. Can you picture how the sequence will grow?
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?
Simple additions can lead to intriguing results...
Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Use the diagram to investigate the classical Pythagorean means.
What can you see? What do you notice? What questions can you ask?
A game for 2 players
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.
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.