Developing Tangible Mathematics: Design and Validation of Rational Number Manipulatives for Grade 7

Abstract– This study reports the design and validation of tangible mathematics materials for enhancing grade 7 students' understanding of rational numbers, identified as the most challenging topic in a preceding needs assessment. Using design-based research methodology with iterative refinement, we developed acrylic manipulatives (fraction circles, bars, tiles, and operational pieces) featuring systematic color-coding and movable connections. Validation by five mathematics education experts yielded exceptional ratings for content quality (37.8/40), technical accuracy (16/16), and instructional design (22/24). Teacher feedback confirmed the materials' effectiveness for concept visualization while suggesting physical enhancements. Preliminary testing with 84 students demonstrated significant performance improvements in the experimental group using manipulatives compared to controls. Both quantitative data and classroom observations confirmed enhanced understanding, engagement, and problem-solving abilities with the tangible approach. These findings establish a strong foundation for implementing tangible mathematics in grade 7 classrooms, addressing the critical transition from concrete to abstract mathematical thinking.