4 is 4. It cannot be both 4 and not 4 at the same time and in the same relationship.
This seems obvious to us as humans. We can acknowledge that 4 is 4, even as our inner child may want to ask, "yeah but what about 4 as 2+2?" to which, we'd say, "what about it?" the essence of 4 or 4-ness is still the same whether we think of 4 as 4, four, or 2+2. The essence of the number is what we understand to be true even while we learn in prealgebra the different forms of the number 4. Being comfortable with 4 and expressing it in different forms is part of our goals. This is the heart of number sense or number theory. The exploration of the numbers by understanding their essence and how the essence of a number manifests itself in various forms is a worthy goal for high school mathematics. We can see how a number is both constant and changing at the same time.
In the golden age of Greece, Aristotle proposed four causes that produce change. The formal cause (what is this thing? the ideal), material cause (what is the thing made of?), efficient cause (who made it?), and final cause (why was it made? purpose). So we might ask, how does this apply to number? A number, 4 for example, is a representation of 4-ness that is unique and does not change, this is the ideal 4, the formal cause. A 4 is made out of it's factors (latin for someone who makes. Our language, philosophy and mathematical worlds are colliding!), the material cause. Onto efficient cause and we discern that the idea of 4 was in fact built into creation, we just discovered it, so it was made by God (which is one reason why it is important to study). Finally, the final cause: Why was the number 4 made? What purpose does it serve? Like everything else made by God, it's purpose is wrapped up in glorifying the creator. The same creator who made you also made the number 4, and He revealed this number to you to bring another layer of understanding to your God reflecting image of Himself. How cool is that? By diving into the four causes we learn about God, His creation, and our place in His order, which leads us to glorify Him all the more. What greater calling can there be in this life?
Philosophical theories abounded in the ancient world for hundreds of years before Aristotle formally put forth his theory of causes of a item. I think we can afford to spend a few years exploring these in the world of numbers. In true teacher form (pun intended), I'd like you to try exploring these four causes with a circle!