Answers will vary. Some ideas: Students come up with the triangle inequality through data gathering and checking, but the teacher persists in asking them to explain why it should hold. That stretches students into not just the geometry content, but also the logical deductions. This course covered the triangle inequality, and several of the same ideas came up. One particularly interesting piece is at the beginning of the clip, when students use a geometric model to check if the sum of two lengths is greater than the third length. Many teachers rely on algebra and arithmetic more, and it's nice to remember that many students do have a sense of geometric reasoning as well.
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