As children spend more and more time on electronic devices and social networks, there is a growing concern about the influence that these activities may have on their development and social well-being. In this context, the present research is aimed at analysing the influence that Internet use may have on 6th grade primary school students' academic performance in Spain. In order to do so, we have employed a methodological approach that combines econometric and interval multiobjective programming techniques, which has let us identify the traits and Internet use patterns that allow students to maximise their academic performance in terms of scores in four competences. Our results show that, while daily use of the Internet to listen to music or search for information about other topics of interest can favor the maximization of educational outcomes, the use of social networks should be limited as much as possible to avoid hindering the educational process.