This study expands contemporary theorising about students' conceptions of equality. A nationally representative sample of New Zealand students' were asked to provide a spoken numerical response and an explanation as they solved an arithmetic additive missing number problem. Students' responses were conceptualised as acts of communication and analysed according to their mathematical structure. Specifically, students' spoken explanations were parsed and mapped using the properties of equality. These maps were classified according to their correspondence to the mathematical structure of the given problem. Students gave four different numerical responses and their explanations were interpreted as seven different conceptions of equality. These findings indicate that students' conceptions of equality are more diverse and complex than previous accounts suggest.