As educational settings increasingly integrate artificial intelligence (AI), understanding how AI tools identify -- and adapt their responses to -- varied educational contexts becomes paramount. This study examines conversational AI's effectiveness in supporting K-12 mathematics education across various educational contexts. Through qualitative content analysis, we identify educational contexts and key instructional needs present in educator prompts and assess AI's responsiveness. Our findings indicate that educators focus their AI conversations on assessment methods, how to set the cognitive demand level of their instruction, and strategies for making meaningful real-world connections. However, educators' conversations with AI about instructional practices do vary across revealed educational contexts; they shift their emphasis to tailored, rigorous content that addresses their students' unique needs. Educators often seek actionable guidance from AI and reject responses that do not align with their inquiries. While AI can provide accurate, relevant, and useful information when educational contexts or instructional practices are specified in conversation queries, its ability to consistently adapt responses along these evaluation dimensions varies across different educational settings. Significant work remains to realize the response-differentiating potential of conversational AI tools in complex educational use cases. This research contributes insights into developing AI tools that are responsive, proactive, and anticipatory, adapting to evolving educational needs before they are explicitly stated, and provides actionable recommendations for both developers and educators to enhance AI integration in educational practices.