“26 and 10 is 36, and 7 is 43.”
I do it this way mentally...
25 + 15 = 40.
1 + 2 = 3.
40 + 3 = 43.
looks like we don’t have a common core : )
And I did it differently.
I recognized that 17 is nearly 20.
I added 10 to 26 to get 36.
Then I added 10 again to get 46.
Then I subtracted 3 because 17 is not quite 20.
Sometimes I will just mimic the way done on paper. I glance at the units column and see that there is a carry.
Then I add 2 plus 1 plus the carry to get 4.
Finally, ignoring the carry I add 6 + 7 to get the 3, for an answer of 43.
The point being, I don't do it the same way all the time.
I recall an anecdote from a book by Richard Feynman, the Nobel prize winning physicist. He is with several other people who propose a math problem to him. As a result of some coincidental relationships in the numbers, he is able to do the mental calculation to generate an answer to several decimal places, impressing the people around him.
His was another example of the fact that a skilled person wouldn't necessarily use just one approach to making such a calculation.
Those of us who use such shortcuts to making calculations do so in order to save the trouble of doing the calculation on paper. If a person doesn't have the skills to do the paper calculation, then there will be little incentive to understand and retain shortcuts.
Educators have been struggling for generations to find some way to teach arithmetic and higher math to the masses. They have failed to improve on the necessity of having everybody learn the basics. Calculators allow people to be ignorant, they are not a replacement for knowledge.