While manipulatives have played an important role in children's mathematics development for decades, employing tangible objects together with digital systems in the classroom has been rarely explored yet. In a transdisciplinary research project with computer scientists, mathematics educators and a textbook publisher, we investigate the potentials of using tangible user interfaces for algebra learning and develop as well as evaluate a scalable system for different use cases. In this paper, we present design implications for tangible user interfaces for algebra learning that were derived from a comprehensive feld study in a grade 9 classroom and an expert study with textbook authors, who also are teachers. Furthermore, we present and discuss the resulting system design.