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)

A series of questions can be posed and resolved in the process of teaching that the decimal expansions of rationals are terminating or repeating. (SD)

Three methods for using four-function, counting calculators for developing understanding of the meaning of square roots and operations on whole and rational numbers are described. (MP)

Understanding rational numbers is often an elusive goal in mathematics. Presented is an approach for teaching rational numbers that has been used with many preservice and elementary school teachers. With some adaptation, the approach could be used with secondary school students. (RH)

A method for finding a fraction having a value between two given fractions is illustrated and proved. (DT)

This is unit three of a fifteen-unit secondary mathematics textbook. This unit contains two chapters. The first chapter discusses integers and the second chapter discusses rational numbers. Operations with both types of numbers as well as the structure of the systems are discussed. (MK)

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 natural numbers, positive integers, sets, well ordering, lower bound, upper bound,…

Analysis of characteristics of rational numbers in magazines written for children, teenagers, and adults indicated that difficult mathematical concepts that appear in the media are much more prevalent in adults' magazines than in the others. Discusses numeracy demands of everyday life. Appendix contains coding scheme. (34 references) (Author/MKR)

Five open-ended problems are suggested which lead students to investigate basic number properties and numeration characteristics. (JP)

This text is one of the sequence of textbooks produced for low achievers in the seventh and eighth grades by the School Mathematics Study Group (SMSG). There are eight texts in the sequence, of which this is the sixth. This set of volumes differs from the regular editions of SMSG junior high school texts in that very little reading is required.…

Several methods for finding rational numbers which lie between two given rational numbers are described. (DT)

This article presents a simple procedure to generate a sequence of rational numbers converging on the square root of 2, yielding common fraction approximations that motivate and illuminate the definition of real numbers based on rationals. Examples suggest that any irrational number can be approximated as closely as desired. A bibliography is…