There is a growing consensus that AI literacy requires a holistic lens, including not only technical knowledge and skills but also social and ethical considerations. Yet, providing holistic AI education for upper-primary students remains challenging due to the abstract and complex nature of AI and a lack of pedagogical experiences in schools. Against this backdrop, this study employs a design-based research (DBR) methodology to develop pedagogical solutions and theoretical knowledge. Drawing upon theories about AI literacy and learning sciences, this study proposes a novel pedagogical approach, namely, the embodied constructionist approach. This approach, by integrating embodied analogies and constructionist making, forges a cyclical "understand"-"make"-"reflect" process. Through this process, students gradually comprehend the conceptual, technical, and ethical dimensions of AI, towards holistic development in AI literacy. This approach was implemented and fine-tuned in authentic classrooms with 107 sixth graders over two years. During the implementation, a variety of qualitative data were collected from classroom observation, video-recording, student interviews and artifacts, and debriefings with the teacher. Using a case studies method, this study uncovered the overall learning progress demonstrated by the class in AI knowledge, skills, and ethical and critical reflections, as well as the reflections and struggles experienced by individual students. This study offers an age-appropriate pedagogy to promote inclusive, holistic AI education in the crucial, yet under-examined upper primary context. It highlights the potential of integrating AI literacy and computational thinking (CT) in K-12 education, while contributing to theoretical knowledge about embodied cognition and constructionism in the context of AI education.