This study aims to describe the Realistics Mathematics Education (RME) approach in increasing the independence of students' mathematics learning in the material area and around square and rectangle. This type of research was classroom action research. The subject of this study were fourth grade students of Elementary School consisting of 29 students. Learning devices in this study were Learning Implementation Plans and Group Worksheets while the instruments used in this study are observation sheets of student learning independence, teacher observation sheets, questionnaires, and interview guidelines. The results of the study showed that the RME approach that was packaged by giving problems in the form of written or unwritten stories that enabled students to find different solutions/answers and using manipulative media could improve student learning independence with the average student categorized well.