http://serc.carleton.edu/spaceboston/2011activities/57580.html#discussion http://serc.carleton.edu/spaceboston/2011activities/57580.html#post18301 You would want to make clear that measuring two triangles with rulers may demonstrate that the rule is true for those two (and only within the accuracy of rulers and graph paper), but it does not form a proof that it's true for all right triangles. If you measured five, would it be a proof? 100? It's a good opportunity to discuss this.
It's a very good idea to show them the flame example, and to draw a picture of the light rays that make things upsidedown when viewed through this "camera obscura." Here's the NAtional Geographic article I was talking about:
http://ngm.nationalgeographic.com/2011/05/camera-obscura/oneill-text

Thanks again, Jan, beautiful work.]]> Lindy Elkins-Tanton 1312497840 http://serc.carleton.edu/spaceboston/2011activities/57580.html#post18301 http://serc.carleton.edu/spaceboston/2011activities/57580.html#post18321
I appreciated the many specifics you included that will make your activity clear enough to other teachers that they can carry it out. I like the idea of moving gradually from smaller to larger (and then extreme) measurements by going from the classroom objects to the tree. If it is possible to actually try out some of the ideas the students come up with for measuring more extreme distances, I think that would be great to do. I'll look forward to hearing how this activity goes when you carry them out this year, and hope you will make it available to other teachers.

Ellen
]]> Ellen Doris 1313181000 http://serc.carleton.edu/spaceboston/2011activities/57580.html#post18321