The grounding of cognition in embodied actions has resulted in both theoretical formulations of encoding of information and instructional applications of these encodings. Actions on objects typically occur within matched formats: physical actions on physical objects, virtual actions on virtual objects, or mental actions on mental objects. Instead, I explore the theoretical and instructional implications of a 3 × 3 taxonomy that creates nine combinations of physical, virtual, and mental actions with physical, virtual, and mental objects. Following a description of each combination, I discuss the implications of the taxonomy for generic characteristics of instruction that apply across representational formats and taxonomic differences in which format matters. I then compare the proposed taxonomy to three other recent taxonomies including a taxonomic analysis of encoding that defines encoding as a relation between two entities (an iconic, motoric, phonetic, or semantic code) in which information in the first entity is used by the second entity. A comprehensive theory of manipulatives will require specifying the interconnections among theories that range from a small grain size in which the representation of actions differs from the representation of objects to a large grain size represented in embedded/embodied theories of cognition.