Knowledge in History of Mathematics allows us to better understand how we reached the current knowledge, why not teach this or that topic and how to teach to be better understood by our young people. Nowadays, there are already teachers who use the History of Mathematics as a strategy to follow in the teaching and learning process. In order to help integrate History of Mathematics in a form of non-formal education, we proposed in "Ciencia Viva" project - Science in the Holidays for Young People 2015 - to introduce Fibonacci sequence in part of the Summer School of Mathematics of the University of Tras-os-Montes e Alto Douro. We have proposed interlinked tasks among themselves that involved the biography of Fibonacci, the sequence with the same name, their basic properties and its applications. In the experience developed with project participants, it was considered the task as a working set of proposals presented to the students and the whole activity of these proposals. In the activities, tasks were diverse, from tasks using the technology, through tasks involving students in the use of paper and pencil and manipulative didactic materials. Thus, there is provided a different approach to many issues of curriculum areas. First the students researched on the internet about the life and work of Fibonacci, following the various tasks. A large number of interesting curiosities and applications of these numbers to mathematical, physical, biological and engineering sciences are included. It also contains a wide variety of material accessible to college and even high school mathematics students and teachers at all levels. With the proposed tasks to the students of secondary school, we believe had contributed to establish connections between History of Mathematics and different mathematical topics, as well as, other areas of knowledge. This project was carried out in a collaborative environment in which students took an active role and culminated with the construction of a poster illustrating the investigated theme.