The aim of this paper is to show how engaging students in real-life mathematical situations can stimulate their mathematical creative thinking. We analyzed the mathematical modeling of two girls, aged 10 and 13 years, as they worked on an authentic task involving the selection of a track team. The girls displayed several modeling cycles that revealed their thinking processes, as well as cognitive and affective features that may serve as the foundation for a methodology that uses model-eliciting activities to promote the mathematical creative process.