Using Action-Process-Object-Schema (APOS) Theory students' strategies while solving a linear transformations modelling problem in a Linear Algebra course are studied. Modelling cycles were complemented by conceptual activities designed with a previously developed genetic decomposition for this concept. The work of students during the modelling process in the classroom is described in terms of questions and knowledge emerging from their own strategies, and in terms of the difficulties they faced. Results show some affordances of the modelling situation and the use of activities, and the difficulties faced by students.