The difficulties that primary students experience when dealing with real-world related word problems have been discussed extensively. These difficulties are not only related to complex, non-routine problems but already occur with respect to routine problems that involve the application of a simple algorithm. Due to difficulties with the comprehension of the text and the identification of the "mathematical core" of the problem, primary students frequently engage in a rather arbitrary and random operational combination of the numbers given in the text. In doing so, they fail to acknowledge the relationship between the given data and the real-world context. While traditional word problems often do not seem to provide a suitable context for the development of mathematical modelling skills, the use of Fermi problems in the middle and upper primary mathematics classroom can help to foster students' mathematical modelling strategies. In this article, the author explains how children in some German classrooms developed problem solving processes through working on challenging open style problems. (Contains 4 figures.)