Socioeconomic (SES) gaps in academic achievement are well documented. We show that a very similar gap exists with respect to genetic differences measured by a polygenic score (PGS) for educational attainment. The genetic gap increases during elementary school, but only among the low SES children. Consequently, the high PGS children experience the largest achievement growth over the school years, even if they are born in socioeconomic disadvantage. While the SES gaps are partly due to selection into different environments, the high PGS children are simply better at extracting resources from a given environment because of higher conscientiousness and other predispositions.