If the fabric is folded in half and you put down a pattern piece and cut it out, not only do you end up with two pieces of that pattern, but you end up with two opposite or mirrored pieces. Think of it like this: if you’re cutting out a sleeve, you’d want a right sleeve and a left sleeve. If you simply move that side bodice piece over and cut out another with it right side up, you’ll end up with two left (or right) side bodice pieces. And you can’t just flip the piece over (using the wrong side) if there’s an obvious right side of the fabric. (As far as the sleeve reference, your notches will only match up one side and you’ll essentially be putting in a sleeve backwards if you just go with it anyways.) This is cutting technique is done when there is not enough fabric to fold the fabric in half or if it’s recommended that you cut on a single layer, such as trying to match a design or working with textured fabric like velvet.
As far as marking the fabric pieces, whether a marking should be on the right side or the wrong, really depend on the type of marking. I would say that I make most of my markings on the wrong side of the fabric. There are exceptions such as pleat lines or placement markings like a patch pocket placement. The only way to know for sure is to read through the directions to know if you need to see the mark on the right side or the wrong side during that step of assembly. Hope this helps!
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