problem Making Rectangles, Making Squares Age 11 to 14 Challenge level How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?
problem Rationals Between... Age 14 to 16 Challenge level What fractions can you find between the square roots of 65 and 67?
problem Rational Roots Age 16 to 18 Challenge level Given that a, b and c are natural numbers show that if sqrt a+sqrt b is rational then it is a natural number. Extend this to 3 variables.
problem Good Approximations Age 16 to 18 Challenge level Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.
problem Be reasonable Age 16 to 18 Challenge level Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.
article What Are Numbers? Ranging from kindergarten mathematics to the fringe of research this informal article paints the big picture of number in a non technical way suitable for primary teachers and older students.
article An introduction to proof by contradiction An introduction to proof by contradiction, a powerful method of mathematical proof.
article The Dangerous Ratio This article for pupils and teachers looks at a number that even the great mathematician, Pythagoras, found terrifying.
article All is Number Read all about Pythagoras' mathematical discoveries in this article written for students.