The paper reports on a collaborative project involving Italy and Hungary, within theEuropean Project PDTR, and presents an analysis of its implementation and outcomes. The work stemmed from a problem about the exploration of regularities, proposed by John Mason, scientific advisor of the project. We start from the preliminary analysis of the problem carried out by the two teams, present reelaborated versions, planning of the activities and modalities for implementing them in the classroom in the respective countries, discuss the outcomes of the experiment, final reflections made by experimenting teachers and general ones made by the teams about the materials elaborated during the activities.