I am starting order of operations with my students tomorrow and Tuesday. I prefer not to just jump into algorithms with students without hooking them in or giving them some kind of real-world reason they are learning a new skill.
Before teaching, my understanding of order of operations was the some people made some rules, decided that multiplication had to be done before addition and we all just blindly follow. Who "they" were was unclear to me.
When we teach order of operations by just giving an expression and asking students to evaluate it, that is essentially what we are teaching: We are saying that these are just some rules you need to memorize.
However, as I tell my students, in the real world there aren't signs that make you solve a math problem before you enter a room. Or you don't have to prove you can multiply before you take your driver's test. Instead, math comes up and you have to be able to take all you have learned and decide what is useful in that situation.
So instead of telling students the order of operations, I introduce them to real life situations and ask them to write numerical expressions that tell the story with numbers. Then I ask them to evaluate those expressions using the knowledge they have of where the expression came from. My students learned order of operations last year without exponents, so they are not completely new to it.
I have created a presentation on Google Slides that will be the lesson I do with my students.
Use it if you would like. If you would like to make changes to it, go to File and then Make a Copy for yourself to save to your Google Drive.