I begin by drawing a very simple progression on the board, like so:
This is the "game board." In the course of the drill, I'll play these chords on the piano. I'll vary the sequence of chords to make several reasonable progressions: in addition to the I-IV-V-I cadence, I can play a simpler cadence:
or a plagal motion:
With each chord, the students' job is to recognize what I've played and respond by arpeggiating through the top three voices with solfege syllables. So, if I play the tonic, the students respond by singing
(This is in a moveable-do context, obviously, which emphasizes scale-degree identity.)
Occasionally, errors are made. Usually, this means that the students sing the correct notes with the wrong syllables, guessing incorrectly that my IV is a V et cetera. In the give-and-take rhythm of the exercise it is easy to say "nooo, that's a IV, let's sing it correctly" and reiterate the chord.
The presence of the upper three voices on the board forces the students to learn good voice-leading connections between the harmonies and creates a uniform correct answer for group drilling. (It is also essential, I've found, to make the exercise work at all, since most beginning students cannot do this kind of manipulation in their heads.)
As the lesson progresses, the progression on the board can be modified. My initial voicings were probably the easiest to arpeggiate through, since they begin on the very comfortable tonic scale degree. The following progression it a bit more challenging:
Students can also be asked to arpeggiate from top to bottom, to produce only the "alto" or "tenor" voice etc., or even to create "broken" patterns like middle-top-bottom. The final challenge would be to erase the visual reference and force the students to perform the arpeggiations from memory.
I find that the exercise is effective in small doses (ca. 10 minutes at a time), and can often be trotted out to clarify the harmonic underpinnings of a particular melodic passage. Some students recognize it as an essential building block to tonal mastery and practice similar arpeggiations on their own, while others seem to view it as merely an idiosyncratic diversion.