We present fundamental ideas for a proposal for teaching fractions. The theoretical foundation focuses on the critique of the overemphasized use of geometric models, which are commonly found but difficult to correspond into reality. In contrast, we find theoretical support in Realistic Mathematics Education and Freudenthal's developmental research. As part of the research procedures, we proposed to students realistic problem situations involving real whole objects and special parts of them, allowing students to develop solution strategies through reflection and discussion. We observed the emergence of meaningful concepts and strategies; fractions expressing quantities and being logically placed on the number line, with multiple representations for each; and informal understanding of the density of this set of numbers on the number line.