Socioeconomic status (SES) is associated with childhood cognitive achievement. In previous research we found that this association shows neural specificity; specifically we found that groups of low and middle SES children differed disproportionately in perisylvian/language and prefrontal/executive abilities relative to other neurocognitive abilities. Here we address several new questions: To what extent does this disparity between groups reflect a gradient of SES-related individual differences in neurocognitive development, as opposed to a more categorical difference? What other neurocognitive systems differ across individuals as a function of SES? Does linguistic ability mediate SES differences in other systems? And how do specific prefrontal/executive subsystems vary with SES? One hundred and fifty healthy, socioeconomically diverse first-graders were administered tasks tapping language, visuospatial skills, memory, working memory, cognitive control, and reward processing. SES explained over 30% of the variance in language, and a smaller but highly significant portion of the variance in most other systems. Statistically mediating factors and possible interventional approaches are discussed.