This article presents data from a group of secondary pre-service teachers who used vee diagrams to illustrate their conceptual and methodological analyses of a problem, as part of a required mathematics methods course assignment. The individually constructed vee diagrams were analysed in terms of the extent to which they displayed principles and main concepts, adequately justified the mathematics applied in their multiple methods, and the appropriateness of the methods for early secondary level. Constructing vee diagrams prompted the pre-service teachers to re-package their own understanding of the mathematics embedded in the problem context, by organising the material in ways that were pedagogically meaningful, developmentally sound, and flexibly arranged to meet a range of ability levels. The vee diagrams' overall ratings indicate the degree to which pre-service teachers differentially achieved their intentions, conceptually and methodologically. Three exemplars provide further insights into the nature of responses that collectively differentiate between vee diagram types. Findings suggest vee diagrams provide a useful tool to illustrate the pre-service teachers' pedagogical intentions, understanding and interpretations of the mathematics contextualised in a problem. (Contains 6 figures and 1 table.)