Against a backdrop of advocacy for 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 multiple teachers and student cohorts across the primary school years. The research uses design-based methodology and deploys a pedagogical cycle 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 analysis of three learning sequence vignettes. In these topics both mathematical learning (measure, data modelling and spatial reasoning) and science learning (concepts and practices), were reinforced and enriched through the interdisciplinary framing. Drawing on notes of teacher planning and review meetings, coupled with classroom data, we identify (a) the conceptual and curricular design features through which mathematics and science can synergistically interweave, (b) the epistemological design challenges involved in working with teachers to achieve this interdisciplinary alignment, and (c) the key pedagogical design features that emerged to support this integration. The research contributes to conceptualising how interdisciplinary processes that enable synergistic interweaving of mathematics and science content and processes can be effectively framed and enacted.