To what extent does the use of computational tools offer teachers the possibility of constructing dynamic models to identify and explore diverse mathematical relations? What ways of reasoning or thinking about the problems emerge during the model construction process that involves the use of the tools? These research questions guided the development of a study that led us to document the process exhibited by high school teachers to model mathematical situations dynamically. In particular, there is evidence that the use of computational tools helped them identify and explore a set of mathematical relations or conjectures that appear throughout the interaction with the task. Thus, the participants had the opportunity of fostering an inquisitive approach to the process of model construction that led them to formulate conjectures or mathematical relations and to search for ways to support them. (Contains 16 figures and 1 table.)