Fairness, or the ability to distribute resources in a manner that accords with societally recognized principles of justice, is a hallmark of human cooperation. Young children rapidly develop the ability to enact fairness, but the cognitive underpinnings of this ability remain unknown. The present study investigated 4-7-year-olds’ acquisition of three principles of fairness -- equality (the principle that all parties should have the same), merit (the principle that those who work harder should get more), and starting opportunity (the principle that those who started with less should get more) -- in relation to their emerging cognitive control and memory for numerical information (numerical accuracy). Cognitive control predicted children’s equal sharing, whereas numerical accuracy predicted merit-based sharing. Children up through the oldest age we tested ignored starting opportunities. The results suggest that different principles of fairness may be underpinned by distinct cognitive processes.