Computational thinking is nowadays being widely adopted and investigated. Educators and researchers are using two main approaches to teach these skills in schools: with computer programming exercises, and with unplugged activities that do not require the use of digital devices or any kind of specific hardware. While the former is the mainstream approach, the latter is especially important for schools that do not have proper technology resources, Internet connections or even electrical power. However, there is a lack of investigations that prove the effectiveness of the unplugged activities in the development of computational thinking skills, particularly for primary schools. This paper, which summarizes a quasi-experiment carried out in two primary schools in Spain, tries to shed some light on this regard. The results show that students in the experimental groups, who took part in the unplugged activities, enhanced their computational thinking skills significantly more than their peers in the control groups who did not participate during the classes, proving that the unplugged approach may be effective for the development of this ability.