More and more schools are acquiring advanced manufacturing equipment. Activities that incorporate the use of this equipment for the purpose of teaching some academic content can either be designed or redesigned for other educational purposes as well. This article describes how the authors extended an activity that was initially designed to help students learn science and engineering through reconstructing historical inventions to create opportunities for middle school students to learn mathematical modeling in an authentic context. In the case described in this article, the original purpose of the "Solenoid Invention Kit" was to help students understand the connection between electricity and magnetism. However, the kit was extended to address mathematical modeling and problem solving through the "Deriving Ampere's Law" task. An ancillary outcome was that students experienced the benefits of teamwork and persistence. These examples illustrate that 3D printing can be used in schools to address a variety of educational goals.