Understanding subject-specific texts requires interpreting representations--words, symbols, and images--in their intended senses. Many such representations are ambiguous, with meanings that shift depending on context and disciplinary conventions. This applies not only to words, for example, 'paper' in everyday versus academic usage, but also to symbols and images, like '--', that must be interpreted in different senses depending on context. This article introduces the "IRIS model" ("Interpreting Representations in their Intended Senses"), a theoretical framework designed to capture the interpretative processes readers engage in when navigating subject language. Unlike existing models that focus primarily on vocabulary, IRIS encompasses all semiotic resources and foregrounds the discernments needed to resolve ambiguity. Analytically, it supports text studies by making explicit the interpretative demands posed by subject-specific representations. Pedagogically, it offers a tool for fostering metacognitive and metalinguistic awareness, helping learners and educators reflect on the challenges involved in interpreting subject languages.