My boy was quite the active one at that stage also (he is now much more cramped and can't move around as freely). At 27 weeks they are active and have lots of room to be so. So, you will feel it and yes it's normal. I totally know what you're going through!! My baby would put his head under my ribs and just hang out there, so I would gently move it because it can be painful!! It's a GREAT sign that she is moving alot. It means she's safe and doing well. Now my son is head down (ready for birth) so what he likes to do now is strech his legs out straight and you can literally see the bulge of his feet on the side of my belly. I tickle his feet and he moves them around. It's so fun that I get to play with my baby already. You have a lot to look forward to.
Blessings for a safe and healthy pregnancy!!