So how do we do it right? Well, ask “What does the periodic table mean? Where does it come from? What is the requisite prior knowledge?” Then find the answer. That answer tells you how to properly teach the table. You can find answers in A Short History of Chemistry by Isaac Asimov and some brief background info in “Evolution of the Atomic Concept and the Beginnings of Modern Chemistry” by Dr. Michael Fowler. Also, search on “history of the periodic table.” Then present it all systematically to students over the course of years.
Teaching the periodic table of elements in elementary school or even junior high school is inappropriate and a violation of logic — of hierarchy, context, and the nature of concepts. The fact that a lot of places do shows how messed up the school system is, and how poor the epistemology we are taught. Yeah, we think we are doing some good — no criticism of parents here! we are doing the best we can based on what we know! — when we are teaching our kids the periodic table before we learned it, but it turns out to be a bad idea.
Students memorize a bunch of names, and that is all. They learn names and positions, and maybe some properties, but it’s all just like Pokémon: a big fiction having nothing to do with reality. You’d be better off teaching them Pokémon because at least they know it’s fiction. What they know about the periodic table, they think is real knowledge.
You can tell this is true, because once they start asking “why” about the periodic table, you find you cannot answer. “Why are all these letters in the same row?” “Why are all these letters in the same column?” “What do you mean by “react”?” “What do you mean by “valence electrons”?” “Atoms? What’s an atom? How do you know what they are and what they do and where they are?” Kids do not have the knowledge to make sense of it. They do not have the requisite prior learning. So please don’t teach the periodic table out of order, just as you would not try to teach calculus before you teach algebra, or teach advanced dance or martial arts moves before the basics. Try it in gymnastics, and someone is going to get hurt!!