In this paper, we draw on a models and modeling perspective to describe the design of a sequence of tasks, known as a model development sequence, that has been used to research the teaching and learning of mathematics. A central research goal of a models and modeling perspective is the development of principles for the design of sequences of modeling tasks and for the teaching of such sequences. We extend our earlier research by elaborating how a model development sequence can be used to support students in developing models that are not only descriptive but also have explanatory power when connected to existing mathematical models. In so doing, we elaborate language issues about representations and context as well as the implementation strategies used by the teacher.