Rigorous college-and-career readiness standards require significant shifts in typical mathematics instruction. Many schools and districts employ coaches to support instructional changes. Although there is evidence that coaching programs can support teaching improvement, research has yet to identify high-leverage coaching practices. In collaboration with a network of state leaders and coaches, our research team refined a model for math coaching and documented the practices coaches employed in one-on-one work with teachers. Analysis of videotaped coaching conversations and teaching events suggests that model-trained coaches improved their capacity to use a high-leverage coaching practice--deep and specific prelesson planning conversations--and that growth in this practice predicted teaching improvement, specifically increased opportunities for students to engage in conceptual thinking.