This paper discusses a proposal for exploration and verification of numerical and algebraic behavior correspondingly to Generalized Fibonacci model. Thus, it develops a special attention to the class of Fibonacci quaternions and Fibonacci octonions and with this assumption, the work indicates an investigative and epistemological route, with assistance of software CAS Maple. The advantage of its use can be seen from the algebraic calculation of some Fibonacci's identities that showed unworkable without the technological resource. Moreover, through an appreciation of some mathematical definitions and recent theorems, we can understand the current evolutionary content of mathematical formulations discussed over this writing. On the other hand, the work does not ignore some historical elements which contributed to the discovery of quaternions by the mathematician William Rowan Hamilton (1805-1865). Finally, with the exploration of some simple software's commands allows the verification and, above all, the comparison of the numerical datas with the theorems formally addressed in some academic articles.