We explore the responses of 26 prospective elementary-school teachers to the claim "1/6.5 is not a fraction" asserted by a hypothetical classroom student. The data comprise scripted dialogues that depict how the participants envisioned a classroom discussion of this claim to evolve, as well as an accompanying commentary where they described their personal understanding of the notion of a fraction. The analysis is presented from the perspective of productive ambiguity, where different types of ambiguity highlight the prospective teachers' mathematical interpretations and pedagogical choices. In particular, we focus on the ambiguity inherent in the aforementioned unconventional representation and how the teachers reconciled it by invoking various models and interpretations of a fraction. We conclude with a description of how the perspective of productive ambiguity can enrich teacher education and classroom discourse.