I have been introducing the order of operations in a new way to my kiddos to try to prevent these types of misconceptions.
The two triangles above are what I give my kiddos now. They paste both into their math journals to refer back to. Why two different organizers? Well, I think it illustrates the fact that division and multiplication (or addition and subtraction) are to be completed in the order they appear, from left to right. If students constantly hear the operations in a specific order, many of them will memorize that and inadvertently solve problems in that order. The use of two graphic organizers with the operations reversed in each section helps reinforce that equal weight is given to "MD" and "AS" in each step. I also usually have my kiddos draw an arrow from left to right in the three lower sections of the triangle just to make it a bit more clear.
In fifth grade, we do not have to learn about square roots, but I give my kiddos the graphic organizer with square root on it anyway. I read an interesting article a few years back about "rules that expire" which inspired me to create it this way. The basic idea of the article was that throughout a child's life, they learn things in math that continually "expire" as they go on. For instance, when you multiply by 10, just add a zero! Well, that "expires" in fifth grade when they begin multiplying decimals. 42.5 x 10 is not 42.50! Conceptual understanding clears this up, of course, but trying to avoid the rules that "expire" is very helpful, too. In this case, the order of operations "expires" when square roots come into play if the students have not heard about them before.
I love that the triangle shape takes the form of the problems as they are being solved, too! Each step along the way makes it smaller and smaller, until the work is eventually in the shape of a triangle.