In this paper, we report on a research study that aims to understand the ways students transit between the simulation of real phenomenon and the mathematical representation, as the modelling activities are introduced by dynamic digital artefacts. The study took place in a high school in Turin, in which 9th grade students were introduced to the quadratic function through a task to be accomplished with the use of a dynamic digital simulation of a rolling ball on an inclined plane-the Galileo experiment. The semiotic mediation approach guided this study to carefully analyze the modelling activity, enhanced by the use of the digital artefact, in terms of meanings that evolve. Our results identify the signs which refer to the simulation of the real phenomenon and those which refer to the mathematical representation and bring to the fore the evolution from the artefact signs to the mathematical signs.