We know from Bach's first biographer, Johann Nikolaus Forkel, that Bach always started his students with four-part figured bass exercises. Figured bass is a shorthand method of musical notation where the bass note is given and the student has to realize the upper parts. At first Bach would supply the bass lines and the student would fill in the alto and tenor parts. Eventually Bach's students would have to write their own bass lines and add all the remaining voices. Most of all Bach wanted each separate voice used to be a complete melody in itself.
Bach compiled two notebooks, which today are published as a single one, for his wife Anna Magdalena. Because both notebooks are arranged by order of difficulty, scholars can get an idea of how Bach instructed his keyboard students. The first part of the notebook is devoted to simple keyboard pieces and figured bass exercises and Bach's own compositions are included later in the notebook. The notebook was a family effort; the music is copied in his own hand, his wife's hand, and that of his two of his children, Carl Philipp Emanuel and Johann Christian.
Bach wrote fifteen two-part and fifteen three-part compositions titled inventions. Bach uses the word "invention" to describe a musical theme that could be the basis for an entire composition. The aim of the inventions was to teach the pupil a singing style of playing the keyboard and also to have him acquire knowledge of composition through example; as Bach wrote, "above all arriving at a cantabile manner in playing, all the while acquiring a strong foretaste of composition." According to Bach's pupil, Heinrich Nicolaus Gerber, Bach started him with the inventions and gradually moved on to his more advance compositions such as the "Well-Tempered Clavier."
After a student had satisfactorily mastered the easier pieces, such as the inventions, Bach would give his student keyboard suites. Bach wrote two sets of compositions which he titled suites, the "French Suites" and "English Suites." Each suite is primarily made up of 4-6 dance movements such as the allemande, sarabande, gigue and minuet. Because the "French suites" are the less complex of the two, Bach would presumably assign his students movements from those before proceeding to the "English Suites."
Bach composed two sets of preludes and fugues for his students. A fugue is an imitative type of composition and Bach is generally accepted as the greatest master of this type of composition. A fugue starts with a subject, which is a single melodic line. After the melodic line is "stated" in its entirety a second melodic line enters while the original melodic line is stated a fourth-higher in pitch. According to Heinrich Nicolaus Gerber, Bach would only give his students selections from the "Well-Tempered Clavier" after they had mastered many of the inventions and suite movements.