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This research paper describes a case study of the ways that engineering students demonstrate emerging engineering judgment as they make assumptions needed to model and solve an openended, ill-structured engineering science homework problem. Engineering judgment is the set of practices that engineers employ to develop mathematical models to solve the ill-structured problems encountered by professional engineers. Engineering science homework presents an underutilized opportunity for students to develop and rehearse mathematical modeling and engineering judgment by engaging with ill-structured problems. This study unpacks students' emerging engineering judgment as they identify, make, and revise assumptions to develop mathematical models to solve an ill-structured engineering science homework problem. This study asks: How do these students select, evaluate, and revise assumptions while they develop mathematical models? What do these students take into consideration as they make assumptions to develop mathematical models? We took a case study approach to look closely at the ways students made assumptions that served as the bases for mathematical models. This case took place in the context of a Statics course required of second-year engineering students at a large public university. Over fifteen weeks, the focal team of four students worked to model a swimming pool lift capable of assisting a swimmer to enter and exit the water. We identified moments in which students made assumptions that served as the bases for mathematical models. In this paper, we describe and present examples of the ways that these students selected, evaluated, and revised assumptions while solving this problem. Our analysis suggests that to make assumptions, these students considered ways to simplify the problem, the instructor's grading practices, materials availability, and system function. We conjecture that the open-ended nature of the focal problem scaffolded students to make assumptions, and that their assumption-making processes were shaped by their perceptions of the problem as both a "real-world" problem and a "school assignment." This study contributes to understanding the development of engineering judgment and points to the potential for illstructured engineering science problems to support students to develop and rehearse engineering judgment. [ABSTRACT FROM AUTHOR]