Old math: Add the 1s column, if it’s greater than 9, carry the 1, add it to the tens column, add the 10s column, carry the 1 if needed.
New math: Add the 10s, add the 1s. If adding the 1s is greater than 9, repeat.
New math is the way most people add numbers in their head. Makes mental math and paper math consistent. Old math is easier for dealing with more than 2 digit numbers.
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