In this paper, we focus our discussion on the strategy we follow to scaffold high school students to successfully build models of a real-life system. Our aim is for students to gradually achieve a higher level of autonomy and to use and further develop their mathematical knowledge. We present work students did when we asked them to build a model of the position of the school's elevator. Most students successfully built sound one-expression models. Those who did not, built an elegant piecewise model. They achieved this by working on the inverse problem, an exciting proposition for students at any level. Crucial to the group's success was the use of tracking software commonly used in physics, and dynamic mathematical software that empowers students to explore their models.