The relationship of the harmonic mean of two positive real numbers to the geometric mean and to the arithmetic mean is discussed; two geometric constructions for the harmonic mean are given. (DT)

Investigates the differences between students' and instructors' perceptions of similarities among basic computation-related rational number skills. Results indicate that college students in developmental mathematics do see some relationships among rational number computation skills, although not necessarily the ones seen by instructors. (AIM)

In a course on proofs, a number of problems deal with identities for Fibonacci numbers. Some general strategies with examples are used to help discover, prove, and generalize these identities.

The sum of the divisors of a positive integer is one of the most interesting concepts in multiplicative number theory, while the number of ways of expressing a number as a sum is a primary topic in additive number theory. In this article, we describe some of the surprising connections between and similarities of these two concepts.

This article describes the use of Fermi questions as a problem-solving tool.

As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such…

This is part one of a three-part SMSG mathematics text for seventh-grade students. The text was written for those students whose mathematical talent is underdeveloped and is essentially the same subject matter presented in the SMSG text. Chapter topics include: (1) what is mathematics; (2) number symbols; (3) whole numbers; (4) non-metric…

This teacher guide is part of the materials prepared for an individualized program for ninth-grade algebra and basic mathematics students. Materials written for the program are to be used with audiovisual lessons recorded on tape cassettes. For an evaluation of the program, see ED 086 545. In this guide, the teacher is provided with objectives for…

Two ideas to use as a bulletin board display as an activity center, or as worksheets emphasizing whole number concepts are described. (JT)