This paper examines the implementation of unplugged tasks across different school settings developing computational thinking skills and concepts at upper primary school children in Spain without programming and without using electronic devices. The study is based on qualitative case study design. Across the three case studies/schools -- Waldorf-Steiner, conventional and innovative -- several themes and key tasks were emerged for unplugged computational thinking development. The evidence stems from observation field notes and interview transcripts with 152 participants. We collected 94 lessons in total, and we analyzed the data based on a predefined coding scheme and thematic content analysis. We conclude that the detected unplugged tasks demonstrate a great potential to develop computational thinking skills and concepts, even though the teachers are not fully aware of their development. The study highlights the need for teacher professional development on computational thinking teaching and learning. Also, we stress the need for computational thinking skills, concepts, and tasks integration into curriculum explicitly. Given the paucity of research on unplugged methods and computational thinking development in primary education, this study is promising to uncover some prominent issues for further examination and future research agenda.