#6-LOW D: Natural sharpness & thinness; then corrected.
(Also true of low C#). Correct both of these with use of the trigger mechanism (or ring) by lengthening third valve tubing and opening throat to more "oh" shape.
#7-TOP SPACE E: Natural flatness; then corrected.
In this instance the correction is executed by lipping up the note. Students will eventually learn how to "lip a note" but initially they fail to recognize the degree of flatness of top space E. (Also true of fourth line D.) Therefore, use this excellent method of making them aware of top space E flatness: Ask each student to play the note with the normal fingering (open) and then produce the same note using first-second-third valve combination.
The immediate result is that the student recognizes just how flat the natural tendency of top space E really is. Though you would not generally ask students to use this alternate fingering, it is a very useful, in-tune possibility. Furthermore, it will aid the students in better understanding how to "lip up" a note; when they return to the open E fingering, they will automatically adjust pitch upward.
#8-HIGH A: Pinched sharpness; then corrected.
The high register of the trumpet is not really much out of tune in the sense of natural tendencies, but the tendency of most students is to pinch these notes quite sharp:
To aid the student in hearing pitch, which is closer, ask him to play a high A using third valve instead of the normal first and second. The pitch will be lower and from a comparative standpoint will encourage him to reduce pinching in an attempt to match pitch. From an ear standpoint, I would recommend making the student aware of the tone quality difference in the high range as compared to the middle range. If the student attempts to match the tone quality of the middle range while playing in the high register, he will automatically play with better intonation.