This paper analyses different types of movable models that can be used for learning purposes related to Geometry within Architectural Graphics scope. Their use is considered both as finished objects, to be shown and manipulated, and as a hands-on activity, to be carried out by the students, with a pedagogical approach close to constructivism. The objectives of their use include the recovery or intensification of haptic and visual aspects, as an aid to enhance the understanding and exploration of the properties and possibilities of geometric surfaces. It also aims to promote reasoning and deductions about the key elements of curves and surfaces and the links between them, based on the analysis of their variations. Current availability of visual programming languages for the definition of virtual movable models would allow that reasoning. The methodology involves the study of historical models made with different approaches and their possible application in current teaching conditions. Variable arrangements and pieces of built architecture related to them are also considered. The results of the research point to the existence of a wide range of doable examples, albeit with adaptations to the means available, and to a very positive impact of their making.