PurposeThis article aims at presenting the concept of the Brazilian university’s third mission and its relevance for predicting teaching behavior. To that end, this article presents a conceptual model of that third mission in Brazil and how its relationship with stakeholders was built.Design/methodology/approachThis is a conceptual article. The authors analyze the third mission and the Brazilian educational model to suggest predicting teaching behavior as a possibility to optimize the third mission in higher education institutions.FindingsThe Brazilian third mission is related to civilian participation, John Dewey’s democratic education management, Paulo Freire’s transformative education, Triple-Helix and the knowledge ecology. This association enables insight into the relevance of the third mission and into the need for professors’ participation.Practical implicationsRevealing the factors of behavior prediction to perform the third mission is the first mission of the theory of planned behavior. Based on these data, the theory suggests interventions without changing teaching behavior. This possibility might increase the adherence of the professor to activities related to the third mission.Originality/valueThis article contributes to studies on the development of the third mission and to the sharing of a conceptual model that is partially different from the European model, thus promoting broader results for stakeholders. The indications made here can lead to empirical studies to further approximate the higher education institutions and the various sectors of society. Moreover, there is room for investigations that aim at a conceptual convergence at the international level for the third mission, as it happens for teaching and researching.