Product dissection activities have been very successful used in engineering courses to help anchor the knowledge and practice of engineering in students' minds. Unfortunately, most product dissection activities tend to stress form, functionality, and fabrication, missing opportunities to explore the broader impacts of engineering design decisions. In this paper, we present initial efforts to transform product dissection activities into product archaeology exercises wherein students "dig" to uncover not only the manufacturing (i.e., economic) issues of a product, but also the global and societal context that influenced its development as well as the environmental impact of the product during its life cycle. We introduce two new classes of exercises-competitive "digs" and collaborative "digs"-to engage students in similar, yet different, ways in product archaeology. Competitive "digs" pit teams of students in a time-based competition to unearth the global, societal, economic, and environmental impact of a product while collaborative "digs" allow students to work together to dig more deeply into these issues over an extended period of time. Results from pilot offerings of both of these types of exercises are summarized and discussed along with a preliminary educational assessment of one of the collaborative "digs". Improvements to the exercises and future work to formalize this new paradigm of product archaeology are also discussed.