At a camp I attended we would sing the song through, then begin to omit sections but still do the motions.

You push the damper out,
you pull the damper in,
the smoke goes up the chimney just the same.
Just the same, just the same.
The smoke goes up the chimney just the same.

[hand motion]
you pull the damper in,
the smoke goes up the chimney just the same...etc.

Quite funny as a little kid.