Implicit in much of comparative and international education research is that education is a creature of the nation-state, shaped largely by economic, political, and social forces defined by national boundaries. However, in federal nation-states, primary and secondary schooling is the juridical responsibility of the constituent states, not the national government. We make the case in this article that in comparative education analysis, there is persuasive support in political theory to consider subnational state comparisons in federalist nations and that such comparisons can yield valuable insights for improving education in the federal nation-state as a whole. We focus on one federal country, Brazil, and on the possible differences in the "effectiveness" of state education administrations in delivering education. We measure state effectiveness by students' mathematics achievement gains on a national test in 1999-2013. We also examine the possible reasons why gains differ greatly in states with similar demographic characteristics.