I like to start the student off right away learning how to play complete songs. I've developed a library of songs along with backing tracks that add something new with each level.
I will also teach scales, note reading and playing lead along with music theory. Also I will help you with songs you would like to learn within your skill level. Most of all it's a fun way to learn and keep you going. I take the same approach when teaching Bass Guitar as well. Most musicians become very good at playing because those are the ones who enjoy playing and have fun doing it!
Piano lessons require more of a structured approach than guitar. I like to use the Edna Mae Burnham piano courses to get students started.
With piano there are two paths, one is sight reading and the other is band style. I teach both styles in the course. Band style is very important if you wish to just play your favorite songs...unlike guitar though, the sight reading I feel is very important to learn as well. Both styles can be a lot of fun! As with guitar I always keep the focus on fun and the joy of learning.