Against a backdrop of advocacy for but concerns about interdisciplinary STEM curricula, this paper explores the design principles underpinning a three-year longitudinal research project that develops and evaluates interdisciplinary mathematics and science learning sequences, involving more than 30 teachers and 300+ students in cohorts across the primary school years. The research uses design-based methodology and deploys a pedagogical cycle (orienting, posing representational challenges, evaluating and building consensus, applying and extending representations) based on representation construction and model-based reasoning, reflecting core disciplinary processes, and aimed at foundational concepts. The interdisciplinary structure of sequences in different topics, teacher pedagogy, and student reasoning and learning are illustrated through three learning sequence vignettes, drawing on micro-ethnographic video analysis of classroom activity, student interviews and pre-and post-tests. In these topics both mathematical learning (measure, data modeling and spatial reasoning) and science learning (astronomy, ecology and flight concepts, and practices), were reinforced and enriched through the interdisciplinary framing. Drawing on field notes and recordings of teacher planning and review meetings for these sequences, coupled with the classroom data, we identify a) the design features through which mathematics and science can productively interact, b) the challenges in working with teachers to achieve interdisciplinary alignment, and c) the key pedagogical features that emerged to support this integration. We identify design challenges associated with curriculum alignment, teacher expectations and epistemological orientations to learning in mathematics. The research contributes to conceptualising how interdisciplinary processes in mathematics and science teaching and learning can be effectively framed and enacted at scale.