We use data from Washington State to examine two stages of the teacher pipeline: the placement of prospective teachers in student teaching assignments; and the hiring of prospective teachers into their first teaching positions. We find that prospective teachers are likely to complete their student teaching near their college and hometowns, but that prospective teachers' student teaching positions are much more predictive of their first teaching positions than their hometowns. This suggests that student teaching assignments may contribute to the "draw of home" in new teacher hiring. We also find that more qualified prospective teachers tend to student teach in more advantaged districts, suggesting that patterns in student teaching assignments may contribute to the inequitable distribution of teacher quality.