The 2030 Agenda for Sustainable Development sets up education as a fundamental tool to educate and raise awareness of the importance of sustainable development; thus, education in schools must fulfill this purpose. Regarding to Primary Education in Spain, legislation establishes that sustainability must be addressed in a transversal manner, although it is explicitly mentioned in the curriculum as content to be addressed by the social sciences subject. Given that, in practice, textbooks are one of the most used tools by teachers, in this paper, we analyse the treatment given to sustainability by the activities of the textbooks of social sciences in Primary Education of the main Spanish publishers, from two perspectives: analysis of cognitive complexity and study of the subtopic regarding sustainability addressed in each activity. For the analysis of cognitive complexity of activities, Bloom’s taxonomy (six cognitive categories) and Costa’s questioning levels (three levels of questioning) were used. The results reveal an abundance of cognitively simple activities, along with a shortage of cognitively complex activities. The most addressed subtopics are environmental problems and recycling.