This article describes an inquiry-oriented real analysis classroom in which students were guided to discover mathematics for themselves. To support student inquiry, the framework of "five practices" from K-12 education was used. To illustrate this framework, two case examples are given from actual discussions that took place in this classroom. These examples focus on student construction of sequences of functions, both the space-filling Z-order curve and the Cantor staircase function. The article closes with practical guidance for other instructors who would use the five practices in their higher-level mathematics courses.