The examination by students of the associative property of a binary operation is used to illustrate how students can be involved in mathematical discovery. (MP)

The author describes an introduction to, and development of, the complex number field. (SD)

The operation of rounding is shown to lead into an investigation of an abstract mathematical system. Properties of the system are discussed and graphs of the rounding function are drawn. Some questions for discussion are given. (MP)

The topics discussed are, "Helping Students Understand the Distributive Property,""Converting from Base 10: Nonintegral Bases?,""Rapid Mental Squaring of Mixed Numbers," and "Some Nonstandard Binary Operations and their Properties." (JT)

Presents techniques and materials for instruction at secondary school and upper elementary grades in mathematical concepts of number systems structure. Grouping is used as a simple algebraic system to illustrate structure. Closure, inverse, identity, commutative and associative properties are examines relative to manipulation of geometric figureS.…

This is part two of a three-part manual for teachers using SMSG high school text materials. Each chapter contains a commentary on the text, answers to exercises, and suggested test questions. Chapter topics include quadratic equations, the complex number system, equations of the second degree, and systems of first degree equations. (MP)

This article extends number bases to negative integers, then to positive rationals and finally to negative rationals. Methods and rules for operations in positive and negative rational bases greater than one or less than negative one are summarized in tables. Sample problems are explained and illustrated. (KM)

This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series is designed to make material for the study of topics of special interest to students readily accessible in classroom quantity. Topics covered include operations, standard form, equations, graphs, and conjugates. (MP)

This is one in a series of manuals for teachers using SMSG high school supplementary materials. The pamphlet includes commentaries on the sections of the student's booklet, answers to the exercises, and sample test questions. Topics covered include complex numbers, operations, standard form, equations, graphs and conjugates. (MP)

This is part two of a two-part SMSG intermediate mathematics text for high school students. The aim of the text is to focus attention on mathematical ideas which are appropriate for study by college-capable students in the eleventh grade. Chapter topics include number systems, an introduction to coordinate geometry in the plane, the function…

Unit 9 in the SMSG's secondary school mathematics series is a student text covering the following topics in Algebra I: sets and the number line, numerals and variables, sentences and properties of operations, open sentences and English sentences, the real numbers, properties of addition, properties of multiplication, properties of order, and…