I taught for a number of years when my wife and I lived in South Dakota. There were very few piano teachers, and I felt that I was qualified enough to teach young children, at least for the first couple of years.
They would range in age from about 5 to 12. If they were beginners, I would just start by having them get familiar with the layout of the keyboard, notice that there were groups of two black keys and three black keys. Then I would show them that they could play something "pretty" just by improvising on the black keys alone. I would play something else pentatonic below.
Depending on age, when they were ready, I would introduce them to middle C and the D and E above, so they could play "Mary had a little lamb", always with myself accompanying them so it sounded more impressive. F and G, and Beethoven's "Ode to Joy" would follow, and the left hand would get in on the act with its lone "G" below middle C.
I generally used the Piano Pageants method by the composer Donald Waxman, as it was by far the most interesting in terms of the little pieces being "real" compositions; I highly recommend it. After going through two or three of those books, we'd graduate to pieces by Kabalevsky and Tansman, etc.
Also there was a book called "The Joy of Jazz" edited by Denis Agay, which I myself enjoyed as a child. I was generally asked to provide some sort of Christmas music arrangements, and sometimes the kids would bring in simple arrangements of popular movie tunes, etc. Last but certainly not least, I was eventually "obligated" to arrange a simple version of the opening section of "Für Elise", as I must have had 20 kids ask for it.
I figured that it was in general a good idea to coordinate piano playing with reading the notes off the page, as aside from improvisation, in the West that's how music is most efficiently communicated, at least its framework.
There's probably a lot that I don't remember, since it's been at least 25 years!
