There should be no need for using written methods to add two 2-digit numbers. That’s the theory and by year 4 children are beginning to have to put this into practice.
Also remember that most of us do a mental calculation in a different order than doing it in writing.
For example: 27 + 35.
I start with the tens and add 20 and 30, then add the 7 and finally add the 5.
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