The increasing attention devoted to the role of language in the different school subjects calls for approaches of integrated subject matter and language teaching and learning. In this article we argue for the importance of subject-specific genres for integrated mathematics and language teaching. Based on an exemplary analysis of geometric construction texts we show that subject-specific genres in the context of schooling might be influenced by different academic and institutional contexts. In a case study of a classroom discourse in 7th grade about geometric construction texts we show how these different contexts pose a challenge for teaching this genre. As a result, genres in school mathematics might appear as blended genres. Based on our findings we refine the notion of genre awareness as an important aspect of teacher knowledge in order to better prepare teachers for the challenges of integrated subject matter and language teaching.