I have a rectangle that grid mesh that I want to subdivide, however, all attempts resulted into the subdivided faces being proportional to the rectangle mesh, I would like to be able to have the rectangle mesh be made up of smaller squares, not rectangles; how would I do this?
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Use loop cuts to manually subdivide the first time. CTRL-R
Start by making a certain number of loop cuts across the short side. Just enough to know loop cuts on the long side will result in a square.

Then make the necessary loop cuts on the long side to complete the square (or close enough to it. In this example, I only needed one more on the long side

From there, you can subdivide normally and keep your square proportions. If you really want to get perfect about it, and the dimensions of your plane are conducive to it, you could calculate the number of loop cuts needed by subdividing the dimensions of your plane mathmatically. But usually not necessary.
Dale Forbes
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I thought of something in the meanwhile, just make a square mesh or quad, make it as large as I need it, then subdivide until satisfied, then delete faces on either of the short sides to trim it down to a rectangle, should be left with a rectangle made up of squares. -- frankly this seems like a hack, I wish (I knew of) more precise ways to control subdivisions. – Victor S Feb 21 '15 at 00:13