Tests for divisibility in bases 2 through 10 are presented. Two strategies used by a group of fourth-year students are described. (MNS)

Modular arithmetic is used to find the frequency of Friday 13th's in any year. (MM)

After briefly presenting possible origins for the use of the decimal system for counting and the duodecimal (base twelve) system for many measures, a notational scheme using six positive'' digits and six negative'' digits is presented. Examples and algorithms using this set of digits for operations with whole numbers, fractions, and in…

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

Born in 1707, Leonhard Euler was the son of a Protestant minister from the vicinity of Basel, Switzerland. With the aim of pursuing a career in theology, Euler entered the University of Basel at the age of thirteen, where he was tutored in mathematics by Johann Bernoulli (of the famous Bernoulli family of mathematicians). He developed an interest…

Mathematical concepts and experiences are recalled and organized in a flow chart format. The power of unifying ideas in mathematics often causes this sequence to be forgotten or assigned less importance than it should be. (SD)

This booklet has been written for elementary school teachers as an introductory survey of the real number system. The topics which are developed include the number line, infinite decimals, density, rational numbers, repeating decimals, irrational numbers, approximation, and operations on the real numbers. (RS)

The third student text in this SMSG series of 14 covers the following topics from number theory: the division algorithm, divisibility, prime numbers, prime factorization, common divisors and common multiples, and properties of the whole number system. A second chapter discusses properties and operations with integers. For a special edition of this…

An instructional sequence in which number lines and beads are used to illustrate addition and subtraction of directed numbers is described. (SD)

In a thesis written for the Doctor of Arts in Mathematics, the connection between Euclid's algorithm and continued fractions is developed and extended to n dimensions. Applications to computer sciences are noted. (SD)

Describes various aids and activities to help in planning lessons that will encourage the development of sound place value knowledge. Also discusses various instructional strategies to help students avoid problems which may lead to an incomplete or faulty understanding of place value. (JN)