Alla ricerca di una strategia di classificazione degli sviluppi piani dei parallelepipedi rettangoli

It is referred on a didactic experience in which pupils aged 11-14 face problematic situations which are to them completely new and which concern the plane developments of solid figures.The activity carried out has enabled the pupils to: i) have the chance and the motivation to make conjectures; ii) acquire good skills in connecting space to plane and refine their spatial intuition; iii) use with awareness, in a "concrete" context, geometric trasformations and their proprerties; iv) use in a spontaneus way notions connected to topological transformations; v) face in a concrete way activities - even complex ones - of the logical combinatorial kind (classifications, partitions, identifications) for the realization of a double-entrance table.Among the results achieved by the pupils we underline the following: a) the developments of the cube are exactly 11; b) the developments of the right-angled parallelepiped having the three dimensions different are exactly 54; c) the developments of the right-angled parallelepiped having the two dimensions equal are exactly 29; d) the developments of the right-angled parallelepiped (in both cases (b) and (c) can be divided into 11 classes corresponding to the 11 developments of the cube.