Children build foundations for mathematical thinking in early play and exploration. During the preschool years, children enjoy exploring mathematical concepts--such as patterns, shape, spatial relationships, and measurement--leading them to spontaneously engage in mathematical thinking during play. Block play is one common example that engages problem solving. Children develop and work out a variety of logical and mathematical relationships in attempts to understand the physical problems they encounter when building with blocks. Such early engagement in mathematical thinking during block play correlates to later mathematical ability in middle school and high school as measured by standardized test scores, grades, or the number of advanced math courses taken in high school. Mathematical thinking during exploratory play in preschool builds curiosity and enthusiasm for mathematics as well as for the challenges of mathematical problem solving that carry over into the more formal and abstract study of mathematics in high school. In this article, the authors collaborate with a preschool teacher and her students to explore ways that children engage in mathematical thinking as they interact with adults using a simple mathematical curriculum tool. They explore what children do spontaneously with the materials and then describe the kinds of mathematical thinking children engage in during their exploratory play with Digi-Blocks--manipulatives that assist students from preschool through fourth grade in developing place-value concepts. Their purpose is to help preschool teachers see more clearly what their students can and do accomplish mathematically at a very young age.