In this paper, we present an overview of a series of 1-credit applied problem solving courses. The goal of these courses was to help students develop their oral and written communication skills, ability to work as a team, and general problem solving skills through preparation and participation in the Mathematical Contest in Modeling (MCM) and Interdisciplinary Contest in Modeling (ICM). In the first part of the course series, teams of students worked on past contest problems to simulate the contest experience over a 15-week semester. We provided feedback and guidance at each step of the modeling process, but students were ultimately responsible for all modeling choices. Students were required to write a 20-page report detailing their solutions (as in the contest) and to present their work orally. In the follow-on course, students participated in the MCM/ICM and shared their work in an oral presentation at a local conference or on campus. Here, we provide course details and share student feedback, positive outcomes (including a winning team!), and plans for future iterations of the course. We suggest that this type of experience provides an opportunity for students to engage with open-ended problems similar to those they may face in their careers.