This article describes a project in which students investigate the question: What dihedral angles between pairs of mirrors in a kaleidoscope result in perfectly symmetric images? The unit culminates with students building their own kaleidoscopes. This content aligns with parts of the Common Core's standards for fifth grade (classify two-dimensional figures), sixth grade (solve real-world measurement problems that arise in building the kaleidoscopes), seventh grade (construct triangles with mirrors), and eighth grade (describe rotations and reflections) (CCSSI 2010). Solutions and activity sheets for Mathematical Explorations are online at http://www.nctm.org/mtms.