Médias, Desigualdade das Médias e a Resolução de Problemas

Abstract

One of the significant challenges for teaching mathematics today is how to make it more accessible to students so that they can perceive their presence in everyday situations. In this context, the critical concept of mean is not well explored in schools, and the relations with practical situations are restricted to the arithmetic mean. This work examines the arithmetic, geometric, harmonic and quadratic means through an in-depth study of its properties and the resolution of contextualized problems. It is also sought to interpret geometrically the segments means. Interesting day-to-day problems, but little explored in elementary and secondary school, are those involving optimization. Generally, these questions are restricted to the use of differential calculus derivatives, allowing their discussions only at the higher level. This work proposes the use of the means inequalities for the resolution of several optimization problems, separated according to their characteristics, making them accessible to secondary school students.