(no subject)

I gave my students a "project". The question is: how many different integer triangles with a given perimeter are there. I asked them not to search internet, and to do as much as they can themselves. I also warned them that this is an awfully difficult problem, and they might not end up with a nice proven formula. I suggested that  as a start they could find the number of triangles for a few "small" perimeters, and then see what else they could do. I said that I will grade the project as "pass"-"fail", "fail" being "did nothing." I knew that they are always willing to try a problem anyway, and there is no need to motivate (or frighten ) them wih a grade in this case.

I of course did internet search myself, but did not find anything 7 grade appropriate and complete.

I was amazed at what they did so far, and we have not even finished yet! And then I myself decided to search the web again, to see what else can be added to what they did, and what nobody did before.

Unbelievable! I saw my own daughter working on this problem in Math Circle, with James Tanton, when she was the age of my students !!!