Seeking more effective mathematics instruction, this author decided to incorporate Cognitively Guided Instruction (CGI) into first-grade classroom lessons. Students in CGI mathematics classrooms are prompted to use their prior knowledge to solve new problems, establish cognitive structures to which new learning can be connected, and be driven by student inquiry. These strategies include: (1) direct modeling (physically representing the numbers), counting strategy (representing the action in the problem by physically keeping track of the number of groups and counting up the number in each group using skip counting); (2) derived fact (no longer modeling the action in the problem but making use of what the student already knows about facts); and (3) recalled fact (knowing the fact without needing to represent the action). (Contains 6 figures.)