Cross-posted from here.
The best “trick” for small-integer addition is, well, to just memorize your single-digit addition facts (while conceptually understanding that addition is ultimately just “counting up” and the order doesn’t matter).
Yeah, it takes some up-front work to memorize them, but it’s really not that much work, and once you can recall these automatically, addition in general becomes super easy, comfortable, efficient, and fast.
On the other hand, if you don’t memorize them, then your limited working memory will continually get hijacked and wasted on low-level processing, which will make it difficult to build more advanced skills of which single-digit addition is a component. At best, you’ll take longer to learn/execute more advanced skills and have an elevated error rate while executing them; at worst, you’ll experience total cognitive overload and not be able to learn/execute more advanced skills at all. Everything becomes super hard, uncomfortable, inefficient, and slow.