A while back I stumbled on teacher's website that advocated a different way to teach factorization. Rather than jumping straight to factorization practice, the teacher first had their student's practice finding pairs of numbers with a given product and sum. That is, they would give them tons of problems of the form:
If $a \times b = 2$ and $a+b=3$, then what are $a$ and $b$?
Rather than teaching them a method for finding $a$ and $b$, the goal was to get students to 'see' how a given sum and product can be formed. The idea was that when the students were introduced to factorization, they would have extensive experience with one of the basic skills required, and they could focus on understanding the conceptual structure.
The thing is, I can't find the website again. Is there a standard name or reference for this kind of method?