Intelligent tutoring systems (ITSs) are commonly designed to enhance student learning. However, they are not typically designed to meet the needs of teachers who use them in their classrooms. ITSs generate a wealth of analytics about student learning and behavior, opening a rich design space for real-time teacher support tools such as dashboards. Whereas real-time dashboards for teachers have become popular with many learning technologies, we are not aware of projects that have designed dashboards for ITSs based on a broad investigation of teachers' needs. We conducted design interviews with ten middle school math teachers to explore their needs for on-the-spot support during blended class sessions, as a first step in a user-centered design process of a real-time dashboard. Based on multi-methods analyses of this interview data, we identify several opportunities for ITSs to better support teachers' needs, noting that the analytics commonly generated by existing teacher support tools do not strongly align with the analytics teachers expect to be most useful. We highlight key tensions and tradeoffs in the design of such real-time supports for teachers, as revealed by "Speed Dating" possible futures with teachers. This paper has implications for our ongoing co-design of a real-time dashboard for ITSs, as well as broader implications for the design of ITSs that can effectively collaborate with teachers in classroom settings. [This paper was published in: "Proceedings of the International Conference on Learning Analytics and Knowledge (LAK '17)," ACM, 2017.]