The concept of growth is at the foundation of the policy and practice around systems of educational accountability. It is also at the foundation of what teachers concern themselves with on a daily basis as they help children learn. Yet there is a disconnect between the criterion-referenced intuitions that parents and teachers have for what it means for students to demonstrate growth and the primarily norm-referenced metrics that are used to infer growth. One way to address this disconnect would be to develop vertically linked score scales that could be used to support both criterion-referenced and norm-referenced interpretations, but this hinges upon having a coherent conceptualization of what it is that is growing from grade to grade. In this paper, a learning-progression approach to the conceptualization of growth and the subsequent design of a vertical score scale is proposed and illustrated in the context of the Common Core State Standards for Mathematics.