[決賽] 相似性和比例推理（2） [Final round] Similarity and Proportional Reasoning (2)
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[決賽] 相似性和比例推理（2）
[Final round] Similarity and Proportional Reasoning (2)
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Big Concept: Similarity and Proportional Reasoning
Topic: Real-world Applications of Indirect Measurement
Bloom's Taxonomy: analyze, apply
Learning Goal: Use similarity properties (e.g., AA or SAS) to construct mathematical models for solving indirect measurement problems, and generate at least TWO distinct real-world examples.
Key Learning Points: Similarity criteria (AA, SAS), Proportional segments, Shadow-based measurement, Pinhole imaging.
Note: Challenge for Contestants: The contestant must drive the AI to produce two separate applications—one in landscape measurement (e.g., using shadow ratios to find building height) and one in optical physics (e.g., pinhole camera imaging). The focus is on the AI's ability to create a realistic spatial model for each.
學生背景
Student Persona
Grade: 9th Grade Focus Time: 12 minutes Background Knowledge: Has: ratios, similarity criteria (AA, SAS). Lacks: trigonometric functions, coordinate geometry. Has not applied similarity to indirect measurement contexts such as shadow-based height estimation or pinhole imaging geometry. Note: Challenge for Contestants: The contestant must drive the AI to produce two separate applications—one in landscape measurement (e.g., using shadow ratios to find building height) and one in optical physics (e.g., pinhole camera imaging). The focus is on the AI's ability to create a realistic spatial model for each.