The present study aims to improve the quality and the effectiveness of Science Education in early grades along with the goals of UNESCO's emerging agenda for sustainable development and the 4th goal about quality in education. It examines the interaction between formal and non-formal education in designing and organizing complete educational programs directly connected with science education curriculum and utilizing innovative tools targeting to an attractive and rich context for science education. According to the second Science Centre World Summit (SCWS, 2017), museums promote scientific knowledge which is considered a pure cultural component and as such it is studied under the prism of cultural historical activity theory. Activity Theory is used in this research as a theoretical framework for the design and analysis of educational activities, with an emphasis on active and interactive learning processes. It is a predominantly socio-cultural theory offering a broad scope of design and implementation for linking science with culture and society. The educational program developed, "Thunderbolt hunt", is different from the usual educational programs offered because, although it cultivates scientific method skills, it is implemented in the Archaeological museum of Ioannina which constitutes a non-formal learning environment of general interest. The process of designing such programs is based on a number of principles and on numerous fields: the socio-cultural theory of activity, the science education and the museum education. The museum thus becomes a facilitator of scientific knowledge while at the same time functions as a dynamic meeting place for students with their social, cultural and historical environment. The preliminary results of the study are presented in this paper.