Recognizing and using mathematical structure are key components of mathematical reasoning. The authors believe that one productive way to support students' use of structure is by identifying opportunities to address structure in the context of what teachers are already doing, rather than developing additional tasks or new curriculum materials. The authors have found that the topic of reasoning about number systems in general, and integers in particular, provides rich opportunities for students to look for and make use of structure. When students extend their understanding of numbers to new domains (e.g., from whole numbers to integers), they have opportunities to identify and use underlying structures and generalizations of arithmetic by deciding how operations should function (or reflecting on how operations do function) and which properties remain true within expanded number systems. This broad view of structure within the context of integer arithmetic is the focus in this article. The authors present reasoning about integers, which provides students with rich opportunities to look for and make use of structure.