Transforming an observable phenomenon into a tractable model is a challenging process, from determining the appropriate modeling scale to making realistic simplifying assumptions. However, many modeling texts are anchored around problems that have already been synthesized into a digestible format, which inhibits an opportunity to engage students in the decision-making process that leads to a model's design. In this paper, I discuss course elements that provide opportunities for students to participate in the early stages of a model's construction. These include open-ended projects and deconstructed textbook problems, which I explore within the context of an applied mathematical modeling seminar that emphasizes models from the life sciences.