Initiate a Debate
Ask the class what is 5+12? What is 12+5?
Can we agree that 5+12=12+5?
What is 3x4? Can we agree that 3x4 is another way of writing the number 12?
I am going to write something on the board. Tell me if you Totally agree, somewhat agree, somewhat disagree, or totally disagree...
Have students get in groups and say, "give me a knock down reason why you think you are right."
The students that I imagine
The choose your own adventure - This student says, "If you decide to multiply first it can work, if you work left to right it doesn't." This is pretty easy to counter, ask them to try both ways on just one side of the equation. You get that 5+3x4≠5+3x4, "That seems ridiculous doesn't it? So which one should we choose?"
The reader - We read a book left to right, so we read math sentences left to right as well. This student gets that we need to have a common way to solve all math problems, but does not quite understand the separate operations. (This is the student that I need help with!)