This paper offers examples of how connecting concrete and abstract ideas through physical and digital modeling could enhance students’ learning and creativity. We intend to emphasize the educational purposes of these examples and discuss some teaching possibilities in which mathematical and technological competencies of students are developed through physical and digital manipulatives, particularly designing a mathematical puzzle task digitally to be 3D printed. We outline examples for such experiments and share our observations on how these activities could improve students’ geometric vocabulary and understanding of transformations. In addition to learning mathematics, we create opportunities for students to work collaboratively to develop a basic understanding of geometric modeling and to creatively solve a range of problems that naturally emerge during the digital to physical transition process. We believe that developing such learning environments and scenarios, and preparing teachers to be able to utilize alternative resources in their classrooms, could open new opportunities for learning geometry, enhance students’ creativity and help to cope with technology challenges.