Taking advantage of pedagogical opportunities afforded by new technology requires appropriately designed lessons. This article reports on the use of "lesson study" to research principles for the design of a lesson aiming to take advantage of multiple representations. The lesson, for year 10 students who had personal access to TI-Nspire, focused on quadratic functions. Following observation of nine different classes and teachers, four key principles emerged: focus on the main goal for that lesson (despite the possibilities offered by having many representations available); identify different purposes for using different representations to maintain engagement; establish naming protocols for variables that are treated differently when working with pen and paper and within a machine; and reduce any sources of cognitive load that are not essential.