We share a subset of the 41 underlying strategies that comprise five ways of reasoning about integer addition and subtraction: formal, order-based, analogy-based, computational, and emergent. The examples of the strategies are designed to provide clear comparisons and contrasts to support both teachers and researchers in understanding specific strategies within the ways of reasoning. The ability to categorize strategies into one of five ways of reasoning may enable teachers to organize knowledge of student thinking in ways that are useable and accessible for them and provide researchers with sufficient information about the strategies and ways of reasoning such that they can reliably build on this work. [For the complete volume, "Exploring the Integer Addition and Subtraction Landscape: Perspectives on Integer Thinking. Research in Mathematics Education," see ED612853.]