This study developed AI-integrated instructional materials for elementary grades 5-6 aligned with Korea’s 2022 Revised National Curriculum and evaluated their impact on students' AI core competencies and integrative thinking. Following the ADDIE process and analyzing national policy documents, we organized ten topics suitable for the elementary AI framework. The materials were implemented in a Grade 6 class in Gyeonggi Province, with pre-and post-surveys measuring AI competencies (understanding, ethics, socio-emotional) and integrative thinking (problem-solving, critical, and creative thinking). Paired-samples t-tests revealed significant increases in both subdomains of integrative thinking. These findings suggest the materials promote balanced development in AI conceptual and ethical awareness while strengthening mathematics-grounded integrative thinking through data interpretation and modeling. This study contributes a practical design model, lesson resources, and assessment criteria for upper elementary AI-mathematics integration.