By means of three case studies, we will present two mathematical modelling activities that are suitable for students enrolled in senior high school and the first year of mathematics at university level. The activities have been designed to enrich the learning process and promote the formation of vital modelling skills. In case studies one and two, students were given a function that modelled an elevator's movement and were asked to evaluate and improve it. In the third case study, students were given an objective--model an elevator's movement--and general guidelines on how to approach the modelling of a real life situation. Results show that when students were given an initial model, their focus was on the given model and their solutions emulated the form of the initial model. When the students were given an objective and general modelling guidelines, their emphasis was on the elevator's movement and understanding its behaviour. Both approaches are valuable, and a teacher's decision on which one to select depends largely on the course's objectives and the teacher's aims.