In this paper, we present a "route of activities" mainly addressed to first and second year engineering students attending the basic mathematics courses. These activities are intended to be a tool both for students and teachers. On the one hand, they should help the students to acquire a deeper understanding of the mathematical ideas and increase their awareness about the learning progress; on the other hand, they should be useful to the teachers in adjusting their educational strategies by synchronizing them with the students' outcomes. The activities are based on working with coordination of multiple representations of sets in the plane; the motivation for this choice is given by the difficulties encountered by the students in the calculations of double integrals, either in the Calculus courses or in the Mechanics courses. We describe the design and the aims of the activities and analyze the tasks with regard to the mathematical competencies and the feedback given to the students. The tasks have been designed and implemented with GeoGebra and submitted to the students by using a Moodle platform.