Equações diofantinas lineares: uma proposta para as séries finais do ensino fundamental

Abstract

The aim of this dissertation is to present a proposal of a didactic sequence for Linear Diophantine Equations to be applied at the nal years of middle school. It is also expected that after some classes about the subject the students will be able to identify real word problems that can be modeled and solved through Linear Diophantine Equations. In order to achieve this objective essential topics for the understanding of the contents involved in the elaboration of the didactic sequence, such as: integers, divisibility, Euclidean division, greatest common divisor, Euclid's algorithm and modular arithmetic will be reviewed. Thus, this work is justi ed since in some selective processes of military competitions, Naval College, Military College and EPCAr, and also in the tests of the Brazilian Mathematics Olympiad of Public Schools - OBMEP, have some questions that can be solved with this tool, and due the fact it is a possible topic for assimilation by the students at the nal years of middle schools since they only need basic knowledge of mathematics. In addition, it is intended to lead the student to realize that mathematics is important so that he understands and knows how to solve problem situations experienced in his daily life.