Since Bloom's initial work on competencies in 1956, various competency systems have been designed and used to assess students' competencies. Different pedagogical researchers and stakeholders prefer different systems. We have been collaborating with them. Such systems are essential for the adaptation by adaptive intelligent tutoring systems. Now, this paper presents how ActiveMath integrates several competency systems to bridge the gap between different competency systems and thereby facilitating the reuse of learning objects across system boundaries. The combination of competency-related data is achieved by mapping a new competency system to the internal one.