This article doesn't talk about the first major step. Playing Over-the- Break. This is the first hard thing a beginning clarinetist runs into. "How do I play an A and then a B over the break? It seems like the air wants to stop going through the horn or all that I get are squeaks, ahh!" What do you teach them? "COVERED" fingerings are magic! Seriously, this is huge for middle school. I like to call these "Covered A" fingerings. Basically what is done is once a student plays an A, A# or even a brief open G [use sparingly, base using this on the sound] in the mid register, and are going to jump the break and not go below that G they can put their entire right hand down on the clarinet. The right hand should finger the first note they'll play over the break [B, C, C#,D, Eb, E] only in the right hand. Then the student can just move their left hand into position to play over the break and nail that note. Covered A fingerings allow for less movement to hinder the airstream or produce leeks in the pads of the finger against the key holes. I would start to teach over-the-break just going from A [covered] to B back and forth. Then you can go from A# to B. Then A to C, A# to C, A to C#...etc Good Luck!
Another important thing to remember is air- the student must be blowing consistently and not "backing off," otherwise it's so much harder to make a sound up high. Finger position is important, but without proper air support it's nearly impossible to make a good sound! The student should blow using his or her diaphragm and should try to keep the air consistent.