This day, while stressful, provided numerous learning experiences for both parent and child. The parent can observe the meltdown, discern the cause, and decide whether it is legitimate or not. In some cases, such as the broken table, it is legitimate. The child was blamed but innocent. This does not make the meltdown proper behavior, but it does warrant a valid reason as to why the 7 year old boy is extremely upset. Nobody likes to be blamed for something they didn't do. On the other hand, the case of the checking math problems is totally inexcusable. When the teacher (or parent) instructs the child to do something, there should be no tantrum meltdown. If the child does not understand, they can ask for help and explanation (but should not interrupt until the parent is done instructing.) After that, they need to practice the problems and checking on their own. It is practice for making sure you write down the right answer and do the math correctly. In such a case, the meltdown should be disciplined because it is unwarranted behavior.
The fifth (and final) meltdown of the day (at least to my knowledge) involved a friend coming to play. Both the 3-year-old and 5-year-old wanted to play with the visitor, but neither girl wanted to share their friend. Thus ensued much screaming and crying and complaining from each girl as they tried to defend their side and claim to the visiting girl. In such a case, it is more difficult to discern the proper method of approach. I would have separated all the girls. The visitor would have to play by herself until the sisters could play together. I understand the need for siblings to have time alone to play with their friends, but there should also be much camaraderie and sharing between all of them. No one likes to feel left out.