It's really not normal for babies movements to be reduced. It's a common misconception that they run out of room later on, I've also heard people say babys have lazy days and or sleep for 80% of the day, this isn't true either, they wouldn't sleep for longer than 90 mins so any longer without movement needs to be checked.
Visit www.countthekicks.org
They are a charity aimed at educating pregnant women in fetal movements to reduces unnecessary stillborns. Definitely worth a read.
See this I'm confused about some places say yes it's normal others no... My baby has quiet days but he still always moves at some point. If your worried I'd call your doctor/midwife and ask then what they think
Get any reduced movements checked out. Chances are all is well but better to be safe than sorry.