Despite longstanding calls to integrate school science and mathematics, concerns remain about how to achieve high-quality learning in both subjects. In reporting on a teaching approach that aimed to achieve this outcome, the authors focus particularly on the teacher's role. The Interdisciplinary Mathematics and Science project (IMS), an Australian Research Council study, aimed to integrate learning in both subjects through investigative inquiry processes. Teachers guide students to construct, evaluate, and refine multimodal representations in a four-stage teaching model. This article describes the key design principles of this interdisciplinary approach and the focus of the inquiry process. The authors outline the teaching model's stages as a basis for illustrating how teachers have enacted these stages across different topics.