In a digital world where algorithms and mathematical models impact students’ lives and society as a whole, it is important to learn critical thinking to understand and reflect upon what is happening. How will students perceive an inclusion of mathematical models that affect society in their mathematics lessons? Prior research shows that mathematical modelling is a valuable skill. However, critical thinking regarding models is currently not included in the curriculum. The theory in the study is based on critical mathematics and will include four different types of knowledge regarding mathematical modelling: pure mathematical knowledge, technical knowledge, reflective knowledge and extra-mathematical knowledge. In this study a field study was conducted in two Swedish upper secondary schools, together with a survey and focus group interviews. The study found that students’ experiences during the lessons show resemblance with critical mathematics while working with mathematical models and that the students are capable of evaluating the impact that the models have on society. The student’s experiences working with mathematical models that affect society alludes to a possibility to work towards including democracy in the mathematical classroom. This study focuses on the students’ perspective, further research regarding the teachers’ perspective could provide additional insight.