The international architecture of the last decades has examples of works and architectural projects presented graphic from the two-dimensional unfolding of three-dimensional folded surfaces. These valuable individual experiences have not represented generalized strategies that can be transferred to the professional practice and to architectural education. This article uses results of more than 10 workshops (with Unfolding and Folding methodologies) developed in Chile, Argentina and Brazil to build up a pedagogy for the project that makes it possible to investigate the spatial and material properties of folded compositions in Architecture. It proposes to review and update project instruments through the incorporation of Parametric Design; 3D origami software and Digital Manufacturing.