The development of students' argumentation competence is one of the major aims of science education and everyday problems, such as decisions on the consumption of tap water or bottled water, which may be suitable contexts to encourage it. Citizens consider of interest certain controversies associated with the bottled water consumption as an alternative to tap water, which has a significant effect on several aspects of their daily lives. Deciding whether or not to drink bottled water can be used as an interesting context for science teaching activities. To make appropriate decisions on this issue, students must know how to argue with scientific rigour. This paper presents an assessment of the degree of performance of 14/15-year-old students in scientific argumentation within this context. A specific rubric has been designed for each of the assessment activities used, and the Rasch model has been applied to analyse the degree of difficulty that each of the essential elements of an argument (evidence, justification, and conclusion) has for the students. Thus, evidence is generally shown to be the most difficult element of the argument for students followed by justifications and finally conclusions. The analysis procedure used can help to establish a sequence of argumentation activities within a particular context. Finally, the results obtained can be used in teaching to prepare the appropriate assistance according to the argumentation activity at hand.