Moon Motion

We watched the eclipse in the hot tub last night. Loi was enjoying it, but I was pretty sure the shadow was moving the wrong way. If you just run out in the cold and look for a second you wouldn't notice. We all know which way the moon moves, right? From left to right across the sky. So the right side of the moon should enter the shadow first. Not so, just the opposite. I spent the whole time trying to puzzle it out. No luck. Later, on the internet, I learned the moon actually moves right to left no matter what it looks to be doing! Who knew? They told us about the sun not actually rising, but not a peep about the moon. Odd.