How to compare surfaces?

The paper presents the analysis of an experimental activity, based on the inquiry model, realised with 9-10 years old pupils. The experiment consists of three main phases: 1) submission of a worksheet, 2) individual interviews, 3) communication in class. The worksheet introduces the problem of the equivalence of figures with respect to their surfaces, in a context of ‘fences and sheep’. The pupil is asked to verify and to check his answers in a personal interview. The final discussion in the classroom plays a fundamental role in the experiment. The research reports a qualitative analysis of the results, with particular attention given to difficulties and misconceptions that emerged on the topic.