"Big Math for Little Kids," a comprehensive program for 4- and 5-year-olds, develops and expands on the mathematics that children know and are capable of doing. The program uses activities and stories to develop ideas about number, shape, pattern, logical reasoning, measurement, operations on numbers, and space. The activities introduce the mathematical ideas in a coherent, carefully sequenced fashion, and are designed to promote curiosity and excitement about learning and doing mathematics. The program produces playful but purposeful learning of deep mathematical ideas, and encourages children to think about and express their mathematical thinking. Throughout the program, great emphasis is placed on the development of mathematical and mathematics-related language. Our observations suggest two broad questions for future research: What kinds of competence can children develop in the context of a rich mathematics environment? In what ways can mathematics learning promote language and literacy?