Creating classroom exercises consumes substantial teacher time, requiring educators to balance pedagogical soundness with student engagement while adapting materials for diverse learners. Through formative interviews with ten K-12 teachers, we observed that educators increasingly turn to AI tools for exercise creation, yet struggle with prompt design, fragmented workflows across multiple applications, and significant verification overhead. From these interviews we synthesized a three-phase workflow model describing how teachers conceptualize, transform, and finalize educational content. Building on these insights, we present CAT-AI, an AI-assisted authoring system that embeds structured parameter specification, unified WYSIWYG editing, and transparent confidence indicators to support teachers throughout exercise creation without requiring prompt engineering expertise, disrupting workflow, or extensive manual verification.