Visual Preschool Piano
Visual preschool piano is a method that always works, given the age of the students. I use many methods to teach kids piano, not just numbers, and not just notes. The most effective method I've found is simply to show them visually what to play.
For all the difficulties that younger kids have with mental abstractions, they are very good visually and make good observers. Watch them with a video game or at sports. They know where to look.
Piano Is Easy
Abstractions Don't Work
Numbers, notes, pages, books, they are all meaningless abstractions to a five year old. But the white keys of the piano? They are buttons, quite tangible to such a child. They make a pleasant sound (or noise) and are fun to push down.
I've taught hundreds of four year olds, even younger, usually the youngest of a group of siblings who watched their older brothers and sisters play, and now wants their turn. What's the first thing I do with such a child? I find out what song they know and love. It is almost always Twinkle, Twinkle.
Take Their Fingers And Move Them
I gently take their index finger and play 1 1 5 5 for them. "You have to find the distance between 1 and 5." I move their finger over and over, 1 1 5 5 1 1 5 5 1 1 5 5 1 1 5 5. Sooner or later they get it, and realize they have just learned the first line of Twinkle Twinkle. Ask them to play it while you sing.
Keep Adding Numbers
Now ask them where six is. Ask, "Play 1 1 5 5 6 6." The rest of the song follows this scenario depending on the age and abilities of the child. All this has taken 5 minutes at most. Their "lesson" is done. Next week, I will ask for exactly the same thing, see if they remember, and, if they do, add more. Never criticize if they have forgotten: it's in there somewhere.
Just try again with humor, as if the mistake and forgetting never happened. You might not get further than this song, or you may be able to show them more songs. As long as they are coming to the piano happily, you have a viable student.