Background or Context: Teachers knowing their students is consequential for students' participation and learning. Evidence in mathematics education points to the ways that knowing the details of students' mathematical thinking supports teacher and student learning. What it means to know students and what teachers learn about their students are situated in the everyday practices of schooling. Purpose, Objective, Research Question, or Focus of Study: This study investigates how teachers characterized their students mathematically and how they considered meeting students' needs in math class. Research Design: This qualitative study focused on interviews conducted over four years with 61 teachers of kindergarten through second grade across two school districts. Conclusions or Recommendations: This study found that rather than describing what they knew about the details of their students' mathematical thinking or detailing specific tasks, tools, or teacher moves that supported their students, many teachers characterized students in ways that were in line with practices that organize districts, schools, and classrooms. Our data raise questions about the ways in which the structures and common practices of schools are shaping teachers' descriptions of their students in mathematics, and the corresponding classroom practices then engaged.