The trade first method in math is a method in which to show students a non-traditional method of solving subtraction with regrouping (or borrowing) problems in math.

I find it interesting you describe it as non-traditional. I learned this method more than 50 years ago. I suppose somebody gets paid big bucks for creating a "new" method whereby you regroup all columns before subtracting any, rather than regrouping each column before subtracting it.