Just sent you the homework. In addition to writing some root-position triads and seventh chords, you get to label some first inversion chords using the "slash chord" system used in pop and jazz notation, and write some first-inversion chords as well.
Remember, a first-inversion chord is one where the lowest note sounding (and/or written) is the third of the chord. We call the lowest note sounding the "bass" note, so we also say, "the third is in the bass."
In the slash chord notation system, the chord is labeled just as we have been doing, followed by a slash, then the note in the bass. For this assignment, the third is always in the bass.
So a C major chord in the first inversion is written as C/E. It actually makes a lot of sense.
A G7 chord (G-B-D-F) in the first inversion (B-D-F-G) is written as G7/B. Or if you have superscripting easily available, G 7/B.
Videos!
Writing first inversion triads and seventh chords:
Clarifying slash chord notation:
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