Nice lesson. For some reason I usually think of the half-steps you need to make a major scale more as the numbers in between instead of the larger pattern or as keys on the keyboard. I think a list of the notes like you did might make it easier for someone who doesn't know the keyboard to learn. They don't have to try to remember what's a black key or a white key, just how many spaces over. I've tried explaining scales to people with just a piano keyboard and they always get hung up on focusing on the keyboard instead of the relationship of the notes. I wonder if a Janko keyboard might help. I'll have to try it. :)
Nate, When you have your major scales down, the way you are doing it is the way to go. I am teaching under the assumption that most people have not memorized their major scales. In a private lesson, I would ask them to figure things out by using the major scales and if they did not know the scale, I would have them use their knowledge to recreate the scale using either I w w h w w w h or the circle of fifths. It is more time consuming in the short run, but if it makes them realize their lesson money is being spent on remembering major scales which inspires them to learn the major scales, then they can use your shortcut in the future. In the long run, it is a shorter process. Also, thanks Tooka and all my supporters.