In parallel with mathematical modeling studies that have gradually drawn interest in recent years, the aim of this study is to investigate the thought processes of fourth-grade students in the Butter Beans Problem and to identify possible challenges in this process. For this purpose, a qualitative study was conducted at a university-foundation primary school in the city center of a large province in Turkey during the 2013-2014 academic year. After applying a four-week preliminary study to a fourth-grade classroom, three students included in the focus group were selected using the criterion sampling technique. A focus group of three students was videotaped as they worked on the Butter Beans Problem. The conversations of the group were transcribed, examined along with the students’ written work, and then analyzed through the lens of Blum and Ferri’s modeling-process cycle. The results showed that primary fourth-grade students can successfully work with model-eliciting problems; however, they did encounter some difficulties during the modeling process.