<![CDATA[This study develops and validates a Hypothetical Learning Trajectory (HLT) integrating everyday life science contexts within Realistic Mathematics Education (RME) framework for teaching social arithmetic to seventh-grade students. Through design research methodology involving three students with varying mathematical abilities, the research examined how contextually rich learning activities scaffold students' progression from informal to formal mathematical reasoning. Results demonstrated significant improvements in conceptual understanding across all ability levels, with most substantial gains observed among lower-ability students (143.8% improvement). Qualitative analysis revealed students' transformation from procedural memorization to conceptual reasoning, with contextual barriers rather than cognitive limitations identified as primary impediments to mathematical understanding. The HLT successfully facilitated students' development of meaningful connections between mathematical procedures and real-world applications, particularly in profit-loss scenarios and taxation calculations. These findings indicate that RME-based contextual integration creates effective pathways to conceptual mastery, offering inclusive learning opportunities that address persistent gaps between classroom mathematics and practical application. The research contributes to both theoretical understanding of mathematics learning trajectories and practical instructional design for meaningful mathematics education.]]>
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