Developing methods of automated inference that are able to provide users with compelling human-readable justifications for why the answer to a question is correct is critical for domains such as science and medicine, where user trust and detecting costly errors are limiting factors to adoption. One of the central barriers to training question answering models on explainable inference tasks is the lack of gold explanations to serve as training data. In this paper we present a corpus of explanations for standardized science exams, a recent challenge task for question answering. We manually construct a corpus of detailed explanations for nearly all publicly available standardized elementary science question (approximately 1,680 3rd through 5th grade questions) and represent these as "explanation graphs" -- sets of lexically overlapping sentences that describe how to arrive at the correct answer to a question through a combination of domain and world knowledge. We also provide an explanation-centered tablestore, a collection of semi-structured tables that contain the knowledge to construct these elementary science explanations. Together, these two knowledge resources map out a substantial portion of the knowledge required for answering and explaining elementary science exams, and provide both structured and free-text training data for the explainable inference task.