When teaching fractions, teachers make instructional decisions about if, when, and how to use the many different types of fraction models and manipulatives. In this study, we sought insights into their pedagogical reasoning with fraction representations via their preferences, both for solving tasks themselves and for teaching (in general and for specific fraction concepts and operations). Nearly 200 practising Australian primary teachers participated in an online survey and we drew on a Fraction Schemes theorisation to analyse quantitative and qualitative data. A majority of teachers indicated a personal preference for the set model for four out of five schemes; for one scheme most teachers preferred the circle model. Their reasons suggested that the nature of each task in a scheme and the specific fractions involved, played a role in influencing their preferences. With respect to teaching fractions, the teachers also indicated a high level of preference for teaching with the set model in general, and secondly for the rectangle model. Their preferences, except for number lines, were not found to be associated with the teachers' nominated year level. We found that a high personal preference for a set model was associated with a preference for teaching with the same model in general, but not for teaching with the matching manipulative (counters or chips). The teachers indicated a high level of preference for teaching with the fraction bars manipulative for several fraction concepts, but this was not associated with a personal preference for linear models. Implications for further research are discussed.