Cálculo de áreas através do Teorema de Pick para o 8° ano do ensino fundamental

Abstract

The main objective of this work is to present a differentiated approach to the calculation of areas for 8th grade elementary students, which will be carried out through the Theory of Pick. This theorem refers to the calculation of areas of simple polygons with vertices at the points of a grid squared in the plane, which allows to calculate the area using counting, analyzing the points of the edge and the interior of the polygon. A little of the history of area calculus and the mathematician George Pick will be discussed, as well as the presentation of the most usual formulas of calculating areas and demonstrations of the Pick Theorem. We perform activities in two classes on areas and an application of the theorem using maps, which allows us to parallel the traditional method of calculating areas with the proposal presented in this research.