This article presents an observational study of teacher-student interaction in fourth-grade small group sessions introducing an algorithm for solving remainder divisions. The groups are segregated by arithmetic achievement. Teacher and student input is analyzed with reference to a cognitive analysis of the task. A quantitative analysis compares amounts of teacher and student input at specific, cognitively significant points in procedures across groups. This analysis shows that there are qualitative differences both in solution strategies that evolve in the course of the lesson and in the extent to which the teacher-student interaction focuses on two "critical constraints" that are central to acquisition of this procedure. A subsequent analysis of transcribed protocols from the small group sessions discloses interactional mechanisms that can account for these differences. Much of the teacher's input is characterized as an unpacking of the necessary procedure by calling in subprocedures which take the students' responses as arguments and by specifying subprocedures lower down in the goal hierarchy when students failed to produce adequate responses. The interactive mechanisms combine with students' background knowledge to result in the group differences detected in the quantitative analysis.