Rational and irrational numbers

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
The root of the problem

Age

14 to 18

Challenge level

Find the sum of this series of surds.
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.