I am doing a home remodeling project. I am finishing some attic space into a small bedroom. The partition walls are 2x4 construction with standard R-13 faced insulation. I am wanting to add some extra insulation between the heated and unheated areas of the attic. I am thinking of adding some rigid foam board insulation. What do you think? Where would it be applied, to the heated or unheated side of the wall?