Senior secondary mathematics students could justifiably question the relevance of subject matter they are being required to understand. One response to this is to place the learning experience within a context that clearly demonstrates a non-trivial application of the material, and which thereby provides a definite purpose for the mathematical tools under consideration. The endeavor of placing increasing emphasis on the ability of students to apply mathematical thinking to the task of modelling real situations requires that a process for developing a mathematical model be taught explicitly, and that sufficient opportunities are provided to students to engage them in that process so that when they are confronted by an apparently complex situation they have the thinking and operational skills, as well as the disposition, to enable them to proceed. This article develops a model of a physical situation that can be explained through application of senior secondary mathematical concepts, and which has elements of all phases of the modelling process. The authors focus on calculating the pattern of a transit of Venus and determining when transits will occur by formulating a mathematical model for high school students. Some assumptions made in course of developing the model are described and the implications for teaching are discussed. (Contains 7 figures.)