From my seat, it sounds to me like you don't know that prof very well. If that's the case, your rec isn't likely to be super strong anyway. But if you're dead set on having him write one, I suggest that you propose sitting down over coffee or going to his office hours so you can explain your story. If he is agreeable, you can help him understand it in the best possible light. If not, you may want to rethink that prof entirely, because this doesn't seem like something that you should leave to chance.
It is pretty normal to provide your professor with a transcript. I personally would explain that your grade sink is not characteristic of how you feel you are as a student overall and just provide a short brief reason and show that your grades did come up back up after that period.
Comments
From my seat, it sounds to me like you don't know that prof very well. If that's the case, your rec isn't likely to be super strong anyway. But if you're dead set on having him write one, I suggest that you propose sitting down over coffee or going to his office hours so you can explain your story. If he is agreeable, you can help him understand it in the best possible light. If not, you may want to rethink that prof entirely, because this doesn't seem like something that you should leave to chance.