I have been using this screener for a while now, and while it is short and quick, it will give you an idea of which students will need further diagnostic assessment and who doesn't.
I rely on teaching strategies, rather than number facts in isolation, so the screener is based on mastery of strategies and it doesn't matter if a student doesn't use the particular strategy if their number facts are correct, but it is the place to start if they are incorrect.
I have added a Class Overview so you can group your students according to skill levels and you'll know who to test further at this point.
The screener complements my ADDITION FAMILIES POSTER and they are both FREE on my store site.
I recommend teaching the addition strategies explicitly at the same time as you teach the related subtraction facts. I have added the Count-Backs as a separate item because counting back is a specific strategy when subtracting 1, 2 or 3 (but not any more than that).
You'll need to replace ineffective addition strategies and it makes sense to play games over and over. Games avoid the boredom associated with worksheets and they add some fun to learning maths.
There's plenty of games in my store for you to consider once you know what skills your students need to work on.