Singing chromatic and whole-tone scales (the ultimate test for accurate chromatic calibration!)
By concentrating on the ear rather than the voice, you accomplish much more than simply warming up! After the minor melody exercise have your singers ascend the chromatic scale a cappella singing "doo-doo" while you conduct quarter notes in an Andante tempo. Ask them to sing the octave up and down first (or a 1-3-5-8-1 arpeggio), to establish the aural destination (I suggest the "D-D" or C#-C# octave - relatively comfortable for all voice parts).
The first time they will over-shoot or under-shoot the octave after those twelve notes! Sing the octave again. Repeat the chromatic scale up in quarters. Work until they can sing an accurate chromatic scale up and down, ending on the same pitch with which they began.
Remind them to sing softly (mp dynamic).
When they can sing the chromatic scale accurately up and down at a steady tempo (all quarter notes) have them sing up with quarter-notes, down the chromatic scale in 8th notes, then back up in triplets, and down again in 16ths. Don't change the tempo - make the singers do the subdivisions with good ensemble. It's not easy to do the chromatic scale accurately at a rapid tempo, but they will get it.
The most important skill for singers is the ability to sing and hear the difference between half-steps and whole-steps . . . which leads to the next step: the whole-tone scale. This scale has only six tones. Sing the octave again, then repeat as above . . . up the whole tone scale in quarters, down in 8ths, up in triplets, down in 16ths. The Whole-tone scale takes a bit longer to learn, but you will be surprised how quickly it sinks in!
Singing minor and major arpeggios:
Conclude with singing minor arpeggios up and a major arpeggio down (start around B, since it's easy for all voice ranges). Remember, you must be able to demonstrate this! Each shift up a half-step must be done without the piano.
If this becomes easy, you can work on arpeggios with all minor thirds (diminished) or major thirds (augmented).
Some Advanced Techniques:
Once your singers can sing the minor melodies shifting down by half-steps accurately, the chromatic and whole-tone scales, and minor/major arpeggios, challenge their tonal memories as follows: Sing to them a different five-note minor melody, ask them to sing it back . . . then ask them to "audiate" the melody (i.e. hear it silently in your head), then say "OK, sing the 3rd note when I conduct it." Might not work at first . . . try again. Then try shifting the five-note down by a whole step, or up by a half-step. Then "audiate in that tonality, and sing the 4th (or 2nd) note on my cue." You can also create five-note melodies based on the whole-tone scale using these tonal memory exercises. Even more advanced: sing a 5-note melody, have them sing it back, then - in silence - ask them to shift down a whole step plus a half-step and audiate in that tonality . . . then "sing the 3rd note when I conduct you!" If they can do this their tonal memories are STRONG!