The authors explore how children's play can support the development of the foundations of mathematics learning and how adults can support children's representation of--and thus the "mathematization" of--their play. The authors review research about the amount and nature of mathematics found in the free play of children. They briefly discuss how children develop different types of play and describe ways adults can support and guide each of these to encourage an understanding of mathematics and to enhance children's mathematical skills. The authors' activities described in this article and the time to prepare it were partially funded by grants from the Institute of Education Sciences (IES) in the U.S. Department of Education and from the National Science Foundation (NSF).