"Improving Mathematics in the Early Years and Key Stage 1" reviews the best available evidence to offer five recommendations for developing the maths skills of 3-7-year olds. Recommendations include integrating maths into different activities throughout the day -- for example, at registration and snack time -- to familiarise children…

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

The principle of the permanence of the rules of calculation is contrasted with the concretization permanence principle. Both apply to situations where some arithmetical operation known to children for numbers of a certain kind is to be extended to include further numbers. (MNS)

Representation of integers in various bases is explored, with a proof. (MNS)

Four worksheets appropriate for various grade levels 1-8 that can be used to provide experience in classifying numbers according to various attributes are given. (MK)

Six possible ways of defining prime numbers are given, and additional activities on the topic are suggested. (MK)

Six activities useful in developing the idea of prime factorization are described. Some of these activities are best done with a calculator. (MK)

Noitcarf numbers provide a simulation activity that allows teachers or education students to gain an understanding of the feelings of students who are taught mathematics by a "rules" method. They are actually an abstract presentation of operations with fractions. (MK)

Interpretation of rational numbers as fractions, ratios, percentages, and quotients of integers are discussed. Then coding conventions are noted, and equivalence classes are described. Finally, density and order are discussed. (MNS)

Part 2 considers the limit of a sequence and extends this to include ideas such as continuity, derivative, and integral. The discussion concludes with an example of a finite or "counted completely" set, the Fermat primes. (MK)

Very specific suggestions for teaching subtraction facts using addition are given. Several activities are suggested. (MK)

Ways of using the calculator as a vehicle for investigating one aspect of the square root concept are illustrated. (MK)

A study of a class of numbers called 'Good numbers' can provide students with many opportunities for investigation, conjecture, and proof. Definitions and proofs are presented along with suggested questions. (MNS)

How to take an existing magic square and surround it with a magic border is described, with a number of examples. (MNS)

The Euclidean algorithm for finding the greatest common divisor is presented. (MNS)