That was one of the very hardest things for me to deal with.I used to call them "big girl temper tantrums.". Kids are really hormonal at that age and the best way for me and my girl to deal with it was to send her to her roo until she could calm down and we could discuss the problem. If you stand there fighting and yelling....it just gets worse. They aren't rational during those times. It's hard but try to bite your tongue until everyone is calm. But I was very adamant that I was NOT going to have a loud conversation or argument that is just a waste of energy and oxygen.
As a parent - you have to remeber that these emotional times are going to happen but they are fleeting. Kids know when they are being unreasonable. I would just tell my daughter (who is 23 now and wonderful!) I was not going to be reduced to fighting and yelling. It solves nothing.
I look back now and realize now that most of it was so stupid and all the breath I wasted and wish I'd ignored more. I heard a child psychologist say once "if you want a behavior to go away ignore it and it will dissipate.". If you give your child attention when they scream - they leanr that really fast!! Good luck!