Whether sharing a collection of toys among friends or a pie for dessert, children as young as kindergarten age are keen on making sure that everyone gets their "fair share." In the classroom, fair-sharing activities call for creating equal-size groups from a collection of objects or creating equal-size parts of a whole and are generally used by teachers to support students in formulating ideas of unit fractions. Young children are successful at creating equal-size groups or parts of collections and wholes, an idea that Confrey and colleagues refer to as "equipartitioning" (Confrey et al. 2009). In contrast to breaking a collection or whole into unequal-size groups or parts, equipartitioning describes children's cognitive ability to partition a set of objects or a whole into groups or parts of the same size. In their work with children from prekindergarten through the middle grades, the authors sought to understand the ways that the children learned equipartitioning through fair-sharing activities and to chart these ways as they developed across the grades. In this article, the authors present the different strategies, justifications, names, and mathematical relationships that students used as they engaged in fair-sharing activities (Confrey et al. 2010). From these observations, they offer an outline of the ways children use this early understanding to build successively more sophisticated ideas of rational number. (Contains 3 tables and 1 figure.)