ON SOME CONTENT-RELATED FEATURES OF TEACHING RATIONAL FRACTIONS

Abstract

This article examines several important content-relevant aspects of teaching rational fractions in middle school algebra. First, the complex role of the concept of a rational fraction is demonstrated depending on the grade level of middle school. In seventh grade, the concept of a rational fraction as an algebraic expression is a fundamental component of algebraic language, including the theory of polynomials with many variables. In eighth grade, the situation is simplified by introducing the concept of a rational fraction, and in ninth grade, the approach is refined for polynomials with one variable. Another important feature is the role of rational fractions in defining the concepts of equality and identity. The role of rational fractions in modeling and solving problems arising in applied settings is also discussed. Various situations related to rectilinear and circular uniform motion, filling and emptying of a pool, joint work, mixtures and alloys are considered as situations of the applied environment, and a mechanism for formulating the corresponding problems is presented.