thanks for the links...

Thanks to Understanding at mindtangle.net for commenting on how the hypotenuse problem was used at a department meeting. Here's a copy of my reply:
I really appreciate your comments--
I'm hoping these 'innocent' little exercises will stimulate dialogue about HOW to develop problem-solving skill and reasoning. Most of us view problems such as these as math contest problems applicable only to the few. If I ask my 'basic' class this question and do not characterize it as an 'honors' problem, would they be willing to try it? I've done it! I do know they could guess 6 and 6 for the sides, we could compute the hypotenuse, then move on to 5 and 7, 4 and 8, etc. I would model the use of a table to record the data and then suggest letting one leg be 5.9, asking them to determine the other, then applying the Pythagorean Theorem. I've already shown this group how to use the STO key on the ti-83 to enter different pairs of values for A and B, then enter a formula like SQR(A^2+B^2) into the home screen. Press ENTER to see the result. Use STO again to enter new values, then 2nd ENTER a few times to retrieve the formula, etc. I had 2 of these students teach the STO method to my BC Calculus class! Betcha think I'm fabricating this story!
BTW, it's great that you used this question for staff development. Thanks again, encourage your teachers to look for my daily Problem of the Day! I welcome constructive comments.
Dave Marain