Although critical mathematics education has been promoted as supporting learners to engage with social justice issues, there has been little research on how learners anticipate using mathematics to make a case for a change in behaviour by an audience. The aim of this study was to identify how small groups of preservice teachers discussed the kinds of mathematical representations needed to convince specific audiences to change their behaviour. It was found that the preservice teachers took into consideration their chosen audience’s background experiences and mathematical knowledge. As well as considering the kinds of representations which were most likely to be convincing for these audiences, the preservice teachers discussed whether their calculations should be available for scrutiny in their presentations.