This paper is the first part of a multiphase study examining students' mental models about the quantization of physical observables--light, energy, and angular momentum. Thirty-one second-year physics and physics education college students who were taking a modern physics course participated in the study. The qualitative analysis of data revealed six variations in students' mental models about the quantization of physical observables: scientific model, primitive scientific model, shredding model, alternating model, integrative model, and evolution model. These models were determined to be context dependent. In addition, some students are in a mixed-model state where they use multiple mental models in explaining a phenomenon and use these models inconsistently.