Where does it say God's plan is un-changing? We assume his plan is rigid, fixed without form or flexibilty built in. Have you ever seen a river flow? God's plan is that a river must flow from the highland to the ocean. The course of that river changes many times over the course of time, yet God's plan is achieved. And you will see this when you fly a plane over the ground, and actually see where the river used to go and where it goes now. Change is built into us as it is into his plan.
God's plan is like a system of roads and streets, he has it all laid out. We assume his plan is a series of one-way streets, which are not connected.
We assume God's plan is rigid and isn't interactive. There are software games in which the players
interact with each other and with the software, yet all the details and options are planned and known by the creator ahead of time. Why is God's Software so hard to understand how it might work? Why can't our free will be built into his plan?
If you want to see and understand God's plan look at his creation and it's design.
RO 1:20
For since the creation of the world God's invisible qualities--his eternal power and divine nature--have been clearly seen, being understood from what has been made, so that men are without excuse.
You are walking in the forest, and it gets late and dark. You start to look for shelter, and find a cabin. It's very cold, but you are also hungry. You have a choice; light a fire or light the stove. The problem is you only have one match, and can only light one item, what do you light first?
Our limited knowledge of the problem forces us to a conclusion. A conclusion which is not correct. Such is God's Plan, our limited knowledge moves us to wrong conclusions.
So why do we pray? 
In order that God will give us another turn, an extra card, additional lives, one more chance, more powers, a secret move, the code to unlock the treasure, last minute escape, and countless other options he hasn't show us yet. And to chat with the maker of the game. Regardless of what he gives us the game is under control.
