This is the sequence I use in Intervention and I teach strategies, rather than number facts.
I find most of my students rely on their fingers for all number facts, and although it works for a few, fingers are not the answer for all number facts.
This resource can be used with my NUMBER FACTS SCREENER, also available FREE on my store site.
Start with adding Zero. This is usually easy and I haven't had a student who doesn't get zero at this level. As long as they can count you can start with the Count-Ons next.
I have added the sequence in the box to the right of the facts grid. I use lots of games to reinforce the strategies and if kids have used their fingers for years (and had little success) you will need to play lots of games to replace the finger-counting habit. While fingers can be accurate for adding 1, 2 or 3, there are better strategies for other facts.
I have many games at my store for you to consider and I am convinced that explicit teaching and games are the secrets to success.