Researchers have generated a powerful framework that identifies three aspects of noticing students’ mathematical thinking: attending to, interpreting, and deciding how to respond to student thinking. Previous research has tended to focus on evaluating how well teachers engaged in noticing, and how well they connected the different aspects of noticing. We describe a complementary way of studying the connections between different aspects of noticing, one that stresses the content of teachers noticing. We report on a study in which participants were shown depictions of students reacting to the launch of a complex task. Participants then chose among a variety of possible interpretations and teacher responses. We found that participants displayed patterns in how they decided to respond to specific interpretations. We describe some of these patterns, as well as similarities and differences between secondary and elementary mathematics teachers. We argue that developing non-hierarchical categories for interpreting and deciding how to respond to student thinking, and describing patterns linking them, reflects how teachers engage in noticing and support teachers in learning how to notice more effectively.