Usando quadrados, retângulos e polinômios: uma sequência didática para o estudo de funções quadráticas e o limite da taxa de variação de uma função polinomial

Abstract

The present thesis delves into a didactic sequence designed with the goal of offering a course that guides students towards mathematical concepts departing from notable products to the application of limits in optimization problems. Through suitable modifications, this sequence has the potential to i) introduce notable products and explore second-degree equations for ninth-grade students; ii) serve as a comprehensive course on quadratic functions for first-year high school students; iii) or facilitate a concise introduction to the concept of limits for polynomial functions in pre-Calculus courses.