This talk is based on the research done with a Research Experience for Undergraduates (REU) group at Michigan State University in the summer of 2014. The goal of this talk is to first introduce three commonly studied objects in combinatorics: set partitions, restricted growth functions (RGFs) and two-colored Motzkin paths. We will introduce and explore these seemingly different objects, but we will find that they are actually closely related to each other. This is joint work with Robert Dorward, Jonathan Gerhard, Thomas Grubb, Carlin Purcell, Lindsey Reppuhn, and Bruce Sagan.