The curriculum resources used for teaching secondary mathematics vary considerably from school to school. Some schools base their teaching largely on a single published scheme, while others design their own schemes of learning, curating their resources from a range of (often free) online sources. Both approaches seem problematic from the perspective of experiencing the mathematics curriculum as a coherent story, and neither seems likely to take best advantage of the accumulated body of knowledge in the education research literature about effective didactics for mathematics. In this position paper, as we embark on the collaborative, research-informed design of a complete, fully-resourced, free-to-access mathematics curriculum for students aged 11-14, we use the conceptual framework of "mathematics curriculum as a story" to draw out five key curriculum design principles. A mathematics curriculum should harness and develop the skills and expertise of teachers; balance the teaching of fluency, reasoning and problem solving; give explicit attention to important errors and misconceptions; compare and contrast alternative methods; and engineer coherence through strategic use of consistent representations and contexts. We use these five principles to set out our vision for the next step in research-informed mathematics curriculum design.