This paper aims at the discussion of opportunities and challenges of using specific construction sub-problems as active parameters in the physical construction of digital parametric design models. To create an overview, a taxonomy of sub-problems for construction is introduced. By using prototypes as a physical interface for the digital model, the different sub-problems become an integrated part of the digital design process. By a reflective process the digital model is informed by the material parameters gradually.A case study is presented to discuss two different implementation strategies. The students acting in this study are presented with a combination of five sub-problems. Starting with these sub-problems, the student design a product digitally. By a reflective process, the object is materialized digitally and built physically.