We explore the critical justification for mathematical modelling in school as one that aims at enabling students to reflect – internally and externally – on the role of mathematical models in describing and shaping risk phenomena, determining people’s courses of action, and informing actual policy decision-making. We argue for the exemplarity of epidemiology from three perspectives; subjective, instrumental and critical. Respectively, these refer to the case being exemplary for students’ experienced lives, mathematical ideas and competencies, and the formatting power of mathematics in society. By analysing epidemic modelling workshops with high school students in Denmark, we claim that it is possible to live up to this justification, though some challenges remain. Possibilities arise by invoking real scenarios as a departure point and scaffolding the modelling process in a dialogical setting. The main challenge is to balance the scaffolding and prompting with dialogical features in a limited timeframe.