Counting

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots, prime knots, crossing numbers and knot arithmetic.

Class 2YP from Madras College was inspired by the problem in NRICH to work out in how many ways the number 1999 could be expressed as the sum of 3 odd numbers, and this is their solution.

Sanjay Joshi, age 17, The Perse Boys School, Cambridge followed up the Madrass College class 2YP article with more thoughts on the problem of the number of ways of expressing an integer as the sum of odd numbers.

This article for teachers describes a project which explores the power of storytelling to convey concepts and ideas to children.

While musing about the difficulties children face in comprehending number structure, notation, etc., it occured to the author that there is a vast array of occasions when numbers and signs are used in anomalous ways; often these are at the earliest stages, when they must be enormously confusing. However, they also frequently happen in adult situations.

Helen Joyce interviews the neuropsychologist Brian Butterworth whose research has shown that we are all born with a "built-in" sense of cardinal number.

Nowadays the calculator is very familiar to many of us. What did people do to save time working out more difficult problems before the calculator existed?

This article for pupils explores what makes numbers special or lucky, and looks at the numbers that are all around us every day.