The author examines a well known number trick, in other number bases, and finds that equivalent results arise. (CT)

The study of number bases, facilitated by programing a microcomputer, helps students make mathematics discoveries. Several programs are given and discussed. (MNS)

In this study, Piagetian theory is extended to explore ways in which children construct their understanding of our notational system and place value. Eighty children aged 4 to 9 were asked to group objects, draw pictures of grouped quantities, write numerals to indicate amounts, and theorize about the relationship between their written numerals…

The system of International Standard Book Numbers uses a check code based on modular arithmetic. This system, the use of a simple machine to compute check digits, and related classroom activities are described. (SD)

Activities involving set union and intersection, graphing solutions of open sentences, and negation are described. These activities afford students with opportunities for computational practice as well as instruction on equations and inequalities. (SD)

The author observes that checking the closure property is redundant for most number systems and therefore hard for students to understand. He defines several systems which are not closed, develops two concepts related to closure, and provides many related examples. (SD)

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 a new kind of addition and multiplication, operations, closure, identity, mathematical…

The varied forms and semantic factors of Japanese ordinal expressions are related to one another in a coherent system. In Japanese, the cardinal number form is a numeral compound in construction with a referent. The numeral compound consists of a number and a numeral adjunct. Numeral adjuncts are derived from bound forms, or numeral suffixes, and…

Topics covered in the first chapter of Unit 8 of this SMSG series include square roots, operations with radicals, operations with real numbers, and the structure of the real number system. The second chapter deals with measurement of area (for rectangular regions, other polygons, and circles), volume and surface area, computation involving…

This publication is part of a series of guides written by Pennsylvania's Department of Public Instruction and is designed to present some of the unifying concepts in mathematics to elementary teachers. This pamphlet discusses the commutative, associative, and closure properties for addition and multiplication of whole numbers, and the distributive…

Examples are given of several compound games of strategy that involve mathematical theory and provide new bases for understanding and axiomatizing the concept of "number." (MN)

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 mathematics teacher who avoided students' questions about zero, notes that children are able to interpret this concept and any system of numeration in a language that they have made up and can understand. (AM)