What do you think would happen if terrorist took over a grade school in the United States?
It is impossible to know what would happen in such a situation. There are many variables that would have an impact. For example, if the terrorists were like those who committed the 9/11 attacks, what would happen is that many of the children at the school would die. The terrorists would not be interested in negotiating. All they would want to do would be to kill as many victims as possible. This seems like the most likely outcome today because terrorist attacks have not been aimed at anything other than simply killing and injuring people.
If the terrorists were trying to achieve something more than killing, thing would be different. For example, let us imagine the terrorists were holding children hostage and demanding that large sums of money be transferred to accounts that their organization could access. In that case, what would probably happen is that the authorities would stall while trying to devise a way to kill or disable the terrorists while keeping casualties among the hostages as low as possible. The government would not want to simply give money to the terrorists. This would make further attacks likely. They would try to negotiate and to pretend to need more time to comply with the terrorists’ demands. As they did so, they would be planning an attack on the school to rescue the hostages. I imagine that they would go ahead with the attack rather than let the terrorists go free with the money. They would try their best to minimize deaths among the children, but they would attack anyway.
However, this is simply speculation. We do not know what the government would do and the government is certainly not going to announce what it would do.