The default behavior of my shell window is to create tabs. I can switch between those tabs but only one tab can be visible at a time.
Is it possible to open multiple shells in the same window? E.g. have a window split 4-ways with each pane running it's own instance of a shell. I would prefer this over tabs since I can run my shell window full-screen at see 4 shells at the same time.
terminator can do exactly this. It is available in the software center.
It is probably worth mentioning separately that byobu is very close to being native Ubuntu. Though it is an offshoot of screen, it is the project of Dustin Kirkland, one of the Ubuntu core developers.
His posts on byobu can be seen on his blog. .
As @EvilPhoenix pointed out, it does some cool things by default.
One of the links that Dustin has on his site is a review from Vincent Danen. It describes byobu as
Here's Dustin and an actual byobu:
Of course, whether or not you like byobu is a personal taste thing. (I tend to use terminator more often, myself.) But it is pretty cool, and worth a plug.
screen (not installed by default) is some kind of a window manager for text mode that can split your shell window into multiple regions each displaying another shell. If you like working with a shell screen is for sure worth having a look at.
tmux has a lot more functionality than screen and is highly customizable. Tmux Github page