What is Common Core 32 -12 and how can I solve it?

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I am trying very desperately to figure out this specific problem I don't need examples of other problems i need this very very specific problem before i loose my freaking mind. Please someone explain this and show me how it works I am extremely desperate. I am told this is some sort of key, I do not know this is not my math problems or work sheet, just information I was unfortunate enough to stumble on a meme. Absolutely no one can give me a straight answer, I have even asked a math teacher and he had no idea what this was.
 

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The first one is 32-12=20.
The second is 248*38=9386.
The methods used are subtraction by addition and lattice multiplication.
The lattice multiplication is sensible, while correct I do not see the reasoning behind the subtraction, that is not how I would do it.
 
the subtraction 'method' looks like hard work to me! Starting with 12, if you add, in succession, the numbers 3,5,10 and 2, you reach a total of 32. Hence the answer to 32-12 is equal to the sum of those numbers - 20. The choice of numbers to add seems somewhat arbitrary, save for the fact that the intermediate totals are round numbers - well, sort of. I'll stick with the traditional method!
 
Thank you guys, I am digging around looking for every spec of information on this, I can't believe this is being taught in schools now.
 
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