AbstractIn this article, I analyze episodes from two third-grade classrooms drawn from a larger classroom teaching experiment to explore how these students began to incorporate nonnumerical symbols in their mathematical expressions when asked to represent indeterminate quantities. The article addresses two research questions: What understandings did these third-grade students construct when they used nonnumerical symbols to represent indeterminate quantities, and how did these understandings vary during the course of working on a single task? What were some of the challenges these third-grade students faced when they first used nonnumerical symbols to represent indeterminate quantities, and how did these challenges vary while working on the Candy Boxes task? Using the constructs of semantic space and form/function relationships, I argue that teaching and learning environments that encourage children’s use of nonnumerical symbols, such as variable notation, to represent indeterminate quantities can support...