Investigating symmetric dot patterns provides opportunities for foundational mathematical learning that is not restricted to multiplication alone. Students have opportunities to learn about the properties of symmetry, about the generalization of patterns, about writing and interpreting equations--all areas of study in grades 3-5. And symmetric dot patterns are commonly used in earlier grades to build skills in subitization. The evidence is clear: Symmetric dot patterns are a particularly powerful object for investigation, providing opportunities for foundational learning across PK-5. The software TileFarm provides a means for creating interesting and curious symmetric patterns for students to count. In this article, Matt Roscoe demonstrates how students' conceptual understanding of addition and multiplication can be powerfully supported through active investigation of symmetric dot patterns created using TileFarm. After briefly introducing the software, he shares the results of a classroom experiment in which second graders investigated objects that were created using TileFarm. Roscoe concludes by sharing the lessons he and a colleague learned in their informal research.