Nice lesson! I think soon you’re going to start to see some big improvements (if you keep practicing the way you do). We talked about a lot of things so I’m just going to go over some of the points I made.
Warm up: Do these! The one warm up I mentioned was slurring from G to C and then chromatically descending (F#->B, F->Bb, etc..) Treat these as long tones with a slur in the middle. Soft gentle playing will allow the body to warm up at a proper pace. Warm up the physical body – mouth, lips, abs, air, etc.. – AS WELL as the mind. Go into it knowing what you will achieve in the practice session. Get to a positive & analytical mentality as soon as you play your first note. That will allow you to play more relaxed & for longer because you’re having fun.
Slurs: These are coming along nicely. I think you can master the 4 note slurs and quickly move along to 5 notes. Remember all the ways we approached the high note and decide for yourself which is the best method. Rest on the C and with logic (&patience) you will figure out a way to get upstairs that works the best for you. It’s either going to be air from your gut, pressure from your tongue, or clenching down on your lips – which we both know doesn’t work. If tonguing helps you get the higher notes then use the tongue to get familiar with how the note feels then slur there.
Patterns: Write out diatonic triads in the key of C, and label each triad with what degrees of the scale are in them. Ex: C triad (C,E,G) would be 1 3 5, etc… If you write them out they will start to make total sense. If you have time, write them out in another key too. Your choice.
The other pattern is 3rds. You know these. Get 3 or 4 keys together for next lesson.