Theories of cognitive control suggest that goal representation is both amodal and specialized. The GLAM-PS (Glamorgan Problem Solver) Cognitive Architecture has no specialised goal representation or goal handling. In addition, GLAM-PS, a distributed production system theory, does not use amodal representation (it is an embodied/grounded architecture). The current paper demonstrates that it is, nevertheless, possible to model ‘off-line’ and abstract problem solving within GLAM-PS. A model of linear equation solving is presented. The processes used by the model to solve equations are described in detail, with a particular focus on the way control of thought and action is achieved. Instead of goals, the model’s problem solving is guided by the use of naturally occurring control states derived from existing internal and external representations. The conclusion that specialized goal representation isn’t needed may also apply to architectures using amodal as well as modal representation (e.g. J. R. Anderson’s ACT-r, 2007).