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

This study presents the development and evaluation of tangible mathematics, investigating how these materials enhance grade 7 learners' engagement, understanding, and problem-solving skills in number and algebra. Following a needs assessment that identified rational numbers as the most challenging topic, this phase focused on designing and validating physical manipulatives grounded in established learning theories. The development followed a design-based research approach with iterative refinement cycles. Tangible Mathematics —including fraction circles, bars, tiles, and operational tiles manufactured from clear acrylic—were developed with systematic color-coding, clear fraction markings, and movable connections. Validation involved five mathematics education experts using Department of Education assessment rubrics, yielding exceptional scores across content quality (37.8/40), technical accuracy (16/16), and instructional design (22/24). Teacher feedback highlighted the materials' effectiveness in supporting concept visualization and improving attitudes toward mathematics, while recommending physical enhancements. Preliminary testing with 84 grade 7 learners showed significant performance improvements in the experimental group using the manipulatives compared to the control group. Both quantitative assessment data and qualitative classroom observations confirmed that the tangible materials successfully enhanced learner understanding, engagement, and problem-solving abilities in rational number operations. These findings provide a strong foundation for subsequent implementation of the tangible mathematics approach in grade 7 classrooms.