The purpose of this study was to deconstruct the relationship between visual static models and students' written solutions to fraction problems using a large sample of students' solutions. Participants in the study included 162 third-grade and 209 fourth-grade students from 17 different classrooms. Students' written responses to open-ended tasks were examined to determine common solutions and errors when using visual static models. The results indicate that (a) common students errors relate to how students interpret the given model or their own model of the situation, and (b) students' flexibility with visual static models is related to successful written solutions. Students with errors generally demonstrated a lack of flexibility in interpreting their own and the given visual static models. Researchers hypothesize that students' exposure to varied mathematical representations influences their ability to flexibly use static visual representations. They recommend that students have a solid understanding of real-world mathematics situations in order to successfully create and interpret visual static models of mathematics.