Ratio and proportion

problem
Contact

Age

14 to 16

Challenge level

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?
problem
Plane to see

Age

16 to 18

Challenge level

P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex.
problem
Napoleon's hat

Age

16 to 18

Challenge level

Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?
problem
Areas and ratios

Age

16 to 18

Challenge level

Do you have enough information to work out the area of the shaded quadrilateral?
problem
At a glance

Age

14 to 16

Challenge level

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
problem
Golden thoughts

Age

14 to 16

Challenge level

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.
article
Ratio or proportion?

An article for teachers which discusses the differences between ratio and proportion, and invites readers to contribute their own thoughts.
article
Pi, a very special number

Read all about the number pi and the mathematicians who have tried to find out its value as accurately as possible.
article
Roasting old chestnuts 3

Mainly for teachers. More mathematics of yesteryear.
problem
Washing elephants

Age

11 to 14

Challenge level

How long will it take Mary and Nigel to wash an elephant if they work together?