Classical poetry is central to aesthetic education and cultural inheritance in China's K-12 education, and web-based instructional videos have become a primary learning resource. However, existing production pipelines either require costly teacher-guided editing or generate videos automatically without systematic instructional design, leading to unclear logic, shallow explanations, and limited contextual adaptation. We propose PoemDirector, a multi-agent framework developed with a national K-12 educational platform partner that unifies context-adaptive instructional mode selection, hierarchical explanation, and end-to-end video generation. A Director Agent analyzes each poem, selects a pedagogically grounded instructional mode from a teacher-co-designed library, and coordinates specialized agents to produce a complete instructional video from a poem title alone. We further establish a multidimensional evaluation framework, refined by literary and education experts, to assess instructional quality and poetic presentation. Experiments show that PoemDirector substantially outperforms commercial baselines and approaches human-crafted video quality across multiple dimensions. The resources are publicly available at https://github.com/ai4ed/PoemDirector.