Identidades dos números de Fibonacci: uma proposta de sequência didática para turmas olímpicas de nível 2

Abstract

The increase of the number of participants at the Mathematical Olympiads spread all over the country, especially at the Brazilian Mathematical Olympiad of Public Schools (OBMEP), forces us to think about how to prepare the students to face these competitions. Therefore, a didactic sequence for the development of Fibonacci numbers is proposed, that aims to train some of the students' abilities: through alternative proofs for seven Fibonacci identities, they will be led to use their spatial intelligence and rely on it to create conjectures and develop strategies to sustain such affirmations. For this, a close relationship will be established between the Fibonacci numbers and basic elements of combination, which must be manipulated, as a matter of priority, by the students, making them assume the protagonism of the classes and be the center of discussions. Also, there are elements brought that can contribute to the adaptation of the didactic sequence to Olympic classes of other levels or even in regular high school classes, with the possibility of interdisciplinarity between Mathematics and Biology or Literature, for example.