This paper describes a simple hands-on and visual-method designed to introduce physics students of many age groups to the topic of quarks and their role in forming composite particles (baryons and mesons). A set of puzzle pieces representing individual quarks that fit together in ways consistent with known restrictions of flavor, color, and charge are depicted. The employment of the pieces in modeling familiar particles, such as protons and neutrons, as well as other, less familiar hadrons, is shown. Included are notes describing the process of creating the puzzle pieces, followed by some suggestions for their use in educational settings.