This may sound kinda weird but hear me out.
When young kids transition to preteen and teen, especially girls, their bodies need tons of calcium, the lack of it can result in behavior like your describing. Our daughter went through that, we heard the rumor and guess what, it was a miracle. we made her take one in the morning and one at lunch, all of our friends did the same thing and man o man-it really made a difference.
I changed careers. But in all honesty my schedule has always been very hectic. This is on my short list of suspected issues though.
Thank you for your input. This gives me a good direction to start in.
Was there a major change in her life about 6 months ago? (Divorce, move, death of close family member, etc.)?
Kids do need to be taught ways of behavior. Otherwise they learn by experimentation. A tantrum gets me what I want, I will keep doing that, etc. And I have a feeling that being the youngest she is powerless and is looking for a way to get a bit more of what she wants - so do be aware of that. And I have known older kids to taunt the youngest just for the heck of it. Anyway, do give her perhaps a bit more attention. BUT
The rule is that when she starts a tantrum - she gets a short timeout. And the timeout does not start until the tantrum stops. She will go nuts for a while. Just keep repeating - "as soon as you choose to stop your tantrum, the timeout will start and 2 min later you can ..." Do not try to reason with her or talk with her while she is yelling. You are just playing into her hands.
Essentially, the rules for behavior modification are that there must be immediate, short, consistent consequences. Do not expect overnight miracles. It has taken her awhile to get to this point and it will take a while to relearn control. But she will.
I would also look into buying "Cool down and work through anger" or "When I feel angry". This is part of a series of books aimed at 4 to 7 year olds and meant to be read to them at night (several times) and then practiced. Kids do need to be taught how to deal with anger. You do not try and use these techniques while she is screaming. But once she stops or later on in the day - you can refer back to them or pull the books back out.
You can find them here - http://www.amazon.com/Cool-Through-Anger-Learning-Along/dp/1575423464/ref=pd_sim_b_5
Hope this helps.