I just got my second iOS device. Notification nightmare, please help!

I am sure there is a very simple explanation to this, but I just can't seem to figure it out and it is really annoying me. Yesterday I purchased an iPad mini and put it on the same iTunes account as my current iPhone 5, synced them together. I'm logged into the same services (iMessage, Facebook, Twitter) on both devices and I keep receiving the same notifications twice, once on each device.

Does anybody know how to stop this? On one hand I like that they sync across the devices, but getting notifications from both at the same time is incredibly annoying. Is there a way for it to know what device I'm currently using and send it there? That sounds like the ideal solution but I just hope there is SOME sort of solution (that doesn't require a jailbreak)

You guys seem to know your stuff so hopefully you can help me out!