This article describes sixth-grade students' engagement in two model-eliciting activities offering students the opportunity to construct mathematical models. The findings show that students utilized their knowledge of fractions including conceptual and procedural knowledge in constructing mathematical models for the given situations. Some students were also able to generalize the fraction model and transfer it to a new situation. Analysis of the students' work demonstrates that they made use of four fraction constructs--part-whole, operator, quotients, and ratio. The activities also revealed difficulties in the students' knowledge of fractions, some of which were overcome in the process of organizing and mathematizing the problem.