my phone is connected to the internet but it keeps saying check your internet connection and won't load pages

It happens no matter where I'm at. At home I'm in the bedroom next to the router and it still does it. If my wifi is off shouldn't I still be able to get on the internet? It doesn't matter if my wifi is on or off that message that says please check your internet connection keeps popping up on the screen and pages won't load . Also sometimes for a couple days at a time Facebook won't refresh.