The Multimedia Research Laboratory, inserted in the Federal University of Ceará has the Multimedia Mathematics Education Group, in which they study the mathematics teaching with the methodological contribution of the Fedathi sequence (FS). In one of the study meetings, the members raised the issue of how a class in the light of the FS could be, which would address mathematical proof. To this end, the mathematical object used to illustrate the answer to this question was the ordering in the set of rational numbers, aiming at the didactic session in the mathematics undergraduate course. Thus, this research aimed to develop a model of mathematical proof approach based on the FS methodological proposal, attempting to solve the issue raised. To make this work possible, the FS research methodology was used, with a qualitative bias. Regarding the results, it was possible to develop the model with the purpose of performing mathematical proof using the FS as a teaching methodology, considering that this way of mediating knowledge is not a transmission of content, but rather, a way of providing learning.