In "MT218" the author looked at the possibility of basing a classroom activity on a simple, though not totally transparent, number-theoretic result. In this article he considers another relatively straightforward idea from number theory that could be used either as a lesson starter or as the basis of a more substantial task, requiring students to…

"The power of two" is a Royal Institution (Ri) mathematics "master-class". It is a two-and-a half-hour interactive learning session, which, with varying degree of coverage and depth, has been run with students from Year 5 to Year 11, and for teachers. The master class focuses on an historical episode--the Josephus…

A discussion of intuition, doubt, and surprise in mathematics arising from a problem involving rational points and lines. (RS)

The relationships between arithmetic, geometric, and harmonic means and the root mean square of two numbers are examined. The problem of generalizing these relationships to three variables is discussed. (SD)

A discussion of some number patterns which arose from a consideration of the number of diagonals of a general polygon. (MM)

This discussion concerns itself with difficulties encountered by students in multiplication and concludes that when children understand a problem they can usually solve it. (MP)