IPhone with no SIM card draining battery?

I got a new iPhone and decided to give my old iPhone to my 3yr old daughter to use for apps and music. We thought it would be smart to take out the SIM card. I don't remember the exact reasoning now. But since we've done that the battery on the phone is really poor. It only lasts 30-60 minutes. Could this be because we took out the SIM card? Or is there another setting we could be adjusting so its not using so much battery power? Or could it just be that I got a new phone just in time and the battery is just going. Any help is appreciated

Nothing to do with the sim.
goto settings and turn off all notifications and, blutooth, 3g, everything not needed should be off.