In dynamic matching problems, priorities often depend on previous allocations and create opportunities for manipulations that are absent in static problems. In the dynamic school choice problem, students can manipulate the period-by-period deferred acceptance (DA) mechanism. With a commonly used restriction on the schools' priorities, manipulation vanishes as the number of agents increases, but without it the mechanism can be manipulated, even in large economies. We also check manipulation in large finite economies through a novel computer algorithm, which can check every possible manipulation by examining all the different matchings that a single player can induce.