"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 student noticed an interesting fact about the base two numerals for perfect numbers. Mathematical explanations for some questions are given. (MNS)

This article reports on the use of a unique number system to facilitate teachers' understanding of the concepts of place value. Teachers' mastery of base-ten may hinder their recognition of the difficulties students have with place value, so the authors created a number system that used five symbols to represent values. Using this system, teachers…

Observation of patterns constructed on geoboards can lead to discussions of properties of primes, number sequences, and complex numbers. (SD)

Patterns and relationships found in the multiplication table of the numbers zero through nine are discussed as a means to helping students understand certain concepts. (MP)

Use of graphs in studying greatest common divisors, least common multiples, and other concepts can illustrate patterns related to the definitions of these concepts. (SD)

A model for multiplication is described and used to discuss the properties of division. (SD)

Presented are the mathematical explanation of the algorithm for representing rational numbers in base two, paper-and-pencil methods for producing the representation, some patterns in these representations, and pseudocode for computer programs to explore these patterns. (MNS)

Patterns emerging when two-digit numbers in various bases are operated on by squaring and summing the digits. (SD)

Students examined patterns emerging when numbers placed at vertices in a braided pattern were summed. (SD)

Using the methods described, pattern representation of operations in modular systems can be developed. (SD)