Research on teachers' noticing of student mathematical thinking has typically focused on how a teacher attends to, interprets, and determines a response to an individual student contribution in isolation from the broader mathematical classroom context. This research focus is not nuanced enough, however, to fully account for the complex noticing required of a teacher engaged in responsive teaching. To support teachers in enacting responsive teaching, it is important to have a way to distinguish high-leverage student contributions from among the many contributions available to a teacher. We draw on a previously developed framework to help teachers identify such contributions, those referred to as a mathematically significant pedagogical opportunity to build on student thinking (MOST) (Leatham in Journal for Research in Mathematics Education 46:88-124, 2015). We conceptualized a productive response to a MOST--what we call building on a MOST--that involves the teacher using a coordinated combination of moves to engage the class in collaboratively developing a sense-making argument about the significant mathematics inherent in the MOST. Rather than a single act of noticing, building requires the teacher to engage in an iterative, dynamic, and relational noticing process as students contribute their ideas to the sense-making discussion. It is this ongoing noticing that allows the teacher to keep the discussion focused on making sense of the MOST. In this article, we use this responsive teaching practice and the iterative noticing it entails to unpack a nuance of teacher noticing--what we call noticing with respect to.