I usually just do some scales, once I start getting warmed up I start with say low F or lower and do octave jumps up.. F-F G-G and so on till I get up to around Bb in the staff, and if im lucky I can get up to the D sometimes..
Then I usually play things i have from memory or are on my stand, or just fool around a bit before we start with full band warmup.. helps me to warm up beyond the 1 octave Bb scale we do. :-p
Daily warm-up routine that I use always begins with long tones(starting in middle range C, whole-note=60, going down by half-steps and returning to C.) After long tones, tongueing exercises, lip slurs, octave slurs, M6th slurs in upper range(starting on 4th space G to high E), then scales. I have found that to get that clear focused sound, long tones are the answer. For method books I use the Kopprash and Etudes for Trombone by Rochut(down an 8ve and as written).
MW 5450
MW 2182
Loud LM-3
G&W Bora SS
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I've tried to develop the practice habits of some of my young stundents. Generally, I have only a few bits of advice:
1) Practice is not some mindless activity; bring your full intellect to bear during it and the time will pass quickly. In particular, if you have a problem with a passage and keep making mistakes playing it, don't simply repeat it until you get it right. Find SOME way to read it correctly the first time, evein if it's playing at sub-human tempos. You wouldn't practice driving nails by hitting your thumb repeated with a hammer, would you?
2) Allocate your time wisely--know what you want to accomplish and how long you want to spend on it. Progress can come slowly, so be content with small victories.
3) Long tones and other "practice by rote" routines may be useful as a warm-up, but only if you use the very same routines before a performance. Othewise, why use them as preparation to practicing when you don't use them as preparation to performing?
4) Number of hours spent practicing is no measure of accomplishment. Use whatever time you have wisely to extend your capabilities. If you play Bordogni bel canto studies every time you practice without thinking about them and listening, you've done more damage than good. I find it amazing that most players who play Bordogni regularly are completely unfamiliar with the original vocal versions and their accompaniment.
5) "Practicing" is also time spent off the horn. If you're working on a Bach sarabande, you're wise to research how a sarabande was danced in Bach's time (did you know that it began as a fast dance? Interesting story being that). If you're playing an operatic excerpt, it's good to know the words to the excerpt and the plot of the opera and the circumstance where the piece in question occurs in the action.
Edgar Meyer mentioned at a recent master class that he isn't a fan of the "by rote" practice routine. He said that he was better served by doing something conscious, like playing Bach slowly, listening for subtleties. I think he has a point.
My .02 only (and I wish I followed my own advice more)