The teaching and learning of mathematical modelling involve engagement in real-world situations and the mathematization of such situations. In this study, the communication between teachers and students in 13 lessons (0.75-1.5 hours each) in two Norwegian upper secondary classrooms is observed and recorded to explore how modelling is communicated and to evaluate the students' agency in different episodes. Episodes in which a student takes initiative are analysed through the lens of positioning theory. An analytic tool is developed to explore the implementation of mathematical modelling in day-to-day activities by identifying the positioning and storylines of the speech/act in classroom episodes. It is found that the teacher facilitates students' agency using everyday experiences when critiquing mathematical models. There are no possibilities found for students' agency in the process of formulating a mathematical model. In these episodes, the storyline of mathematical modelling is one of finding the correct answer using given procedures, rather than engaging in real-world situations and making choices in the mathematization of such situations.