This talk presents a practical and replicable model for engaging undergraduate students in publishable mathematical research through intentional scaffolding and mentorship. I illustrate this model using a joint publication with an undergraduate coauthor as a case study. The key is to take small, well-designed research steps rooted in undergraduate coursework and computational exploration. These steps can lead to substantive scholarly outcomes. I focus on an applied mathematical modeling project and describe how students are introduced to research through accessible entry points like numerical experimentation, parameter exploration, and visualization. They then progress toward interpretation, refinement, and contributing to a final manuscript.