First in order with increased difficulty leading to mixed additions.
You should introduce them to the simplicity and pattern of adding 10's before introducing them to the rule of adding 9's by first adding by 10, then subtracting 1.
Mention to the student that when the sum is 10 or higher, the answer lines up with the right digit under the addition, and the left digit to the left. This is an important concept to understand which normally won't be noticed unless it is taught.
When covering the addition by 5's, also be teaching choral skip counting by 5's, as well as counting be 5's adding nickels as part of learning money, and by counting by 5's while teaching the minutes of the clock as part of teaching time.
Do not discourage counting using their fingers. As they move forward encourage the counting of fingers in their head, to the eventual memorization of these facts.
Encourage the memorization of facts, especially the addition of pairs (2+2, 6+6, etc.), as these can be used as the foundation of figuring out their adjacent sum. i.e. 6+6=12, therefore 6+7=(one more)13.