Mathematics teachers have recently begun to stress the need for teaching models and modeling approaches that encompass cognitive and meta-cognitive thought processes for every level of schooling, starting from primary school through to higher education. The objective of this study is to examine modeling processes with the help of modeling activities for 4th-year middle-school students and to determine the difficulties encountered in the processes. The study was conducted with 4th-year students from a lower socioeconomic status who were enrolled in a public middle school. A preliminary study was carried out. Later, three students were chosen as a focus group to work on a model-eliciting activity called the Volleyball Problem, and the entire process was recorded on video. The mathematical thoughts that the students developed during the modeling process and their written responses were then qualitatively analyzed. The results obtained showed that the students were able to produce many new and different ideas. They were able to discuss various assumptions before reaching a conclusion and the activities helped them to think deeper and develop their mathematical thinking. At the same time, however, it was found that the students experienced certain difficulties during the model-eliciting process in terms of understanding, developing, and constructing an adequate model.