single player

I've tried plying Minecraft single player with out the internet on and it wont let me. We have an Xbox with Minecraft on it and it lags bad when we try both on the WiFi. i like playing by my self a whole lot more than other people. I know you have better things to do while updating but can you fix that as well? I wont have WiFi for a while so i cant play Minecraft with out it now.