In my curriculum, one of the first few lessons in Algebra 2 Honors was about the subsets of real numbers. If I were teaching this again, I would use this interactive notebook page.
I always teach the subsets of real numbers using a diagram. It makes it SO much easier to understand. I’ve used this color-coded diagram in the past, and it works well.
I like to give my students the formal definitions and show them the notation. Since I had honors students, I would use the capital letter notation periodically so my students would get used to it. If I were doing this in class, I would give my students the definitions and verbally give them a few examples. Then, I would have them discuss with their partner to write down their own examples.
I usually follow up this short lesson with an activity or a little Algebra 1 review.