**ABSTRACT**

Problem solving and number sense are two of the core subjects on which strong emphasis is given in contemporary mathematics curricula of compulsory education. In this study, we examined fifth and sixth grade Greek students’ number sense concerning the mental calculation with rational numbers and specifically fractions and percents. We attempt to analyze the behaviors of fifth and sixth graders in mental calculations with fractions and percent examining the performance of students, categorizing the mental strategies used by them. Despite of the educational importance of these two mathematical areas – problem solving and number sense in mental calculations with rational number – there are not studies which examine directly the relation of students' performance in these two areas. This study has shown that the majority of students use rule-based strategies in operations with fractions and percents. Another result is that the students’ strategy choice (number sense or rule based) relates to their performance in problem solving.