Beginning students
I use Faber Piano Adventures All-in-One Adult method books--Levels 1 and 2--with beginning students. These books, in addition to Faber Adult Classics Levels 1 and 2 and Faber Adult Popular Levels 1 and 2, provide the beginning student with a solid foundation in note reading, time signatures (3/4, 4/4, and 6/8), accidentals, basic rhythm and note values, and an introduction to the foundations of good piano technique.
The beginning student will be introduced to one octave major scales. A scale book is essential. I recommend Faber Piano Adventures Scale and Chord Book 2.
Intermediate students
When students complete Faber Piano Adventures Levels 1 and 2, they are considered early intermediate. At this level, lessons focus primarily on repertoire. While I mainly recommend and assign classical pieces, students are welcome to pursue working on pieces outside of the classical repertoire. All intermediate students will be working in a leveled repertoire book series--either Succeeding with the Masters Festival Collection or Keith Snell Essential Piano Repertoire. These books introduce the intermediate student to classical pieces from four periods: Baroque, Classical, Romantic, and Contemporary.
Intermediate students will continue to work on scales--both major and minor (natural minor and harmonic minor)--with a goal toward playing all scales in four octaves.