Many teachers are using the Five Practices model to guide them in orchestrating whole-class mathematics discussions that focus on understanding: (1) anticipate an array of possible student-generated solution strategies to a mathematical task before implementing the lesson; (2) monitor students' work as they grapple with the task; (3) select a subset of the student-generated solution strategies to be shared and discussed during the whole-class discussion; (4) sequence the selected student-generated solution strategies in a coherent way; (5) connect the solution strategies in ways that will highlight important mathematical ideas. Although the selecting and sequencing practices seem especially critical, they might be difficult to learn. The author wanted to better understand the thinking behind the selecting and sequencing decisions that teachers make so that she could help prepare future teachers. During one semester of a mathematics methods course for elementary school teachers, she worked with twenty-three preservice teachers (PSTs) on a set of selecting and sequencing solution strategies activities. The PSTs' rationales for the ways they selected and sequenced solution strategies could be grouped into three categories. The purpose of this article is to describe these three categories and to show how one of them has the potential to translate into a more productive whole-class discussion than the others.