Exactly, it’s just the commutative and associative properties!
In this article I’m talking about elementary school math and they don’t tend to introduce those laws formally until pre-algebra, so I didn’t mention it. In my mental math articles geared for adults on addition and subtraction, I talk more about the laws of math that allow us to do these tricks.
Learning how to use these properties with numbers can help reinforce this topic when they attempt the same properties in algebra.
As student move up towards middle and high school math they are slowly introduced to mathematical notation preparing them for, if they choose, advanced mathematics.