We present a teaching methodology to answer the question 'How can we link teaching with research in our engineering courses?' Due to the combination of hybrid Problem Based Learning with Research Tutored/Oriented Teaching, the methodology enables the students to acquire the skills of 'problem solving', 'working in teams', 'analytic', 'written communication', 'planning my own work', 'organization', 'learning more deeply', 'tackling with unfamiliar problems' and 'innovation'; the last two are directly related to the Scientific Research Process and are considered important for modern engineers. We apply the methodology in the course 'Ecological Modelling of Surface Waters' that we teach in TUM and NTUA following the teaching sequence 'Scope of modelling -- Background knowledge -- Simple model -- Tutorial -- Real case'. Due to its simplicity, the proposed methodology can be easily applied by University researchers, who are usually not familiar with the theoretical aspects of learning.