Now I have a headache. But these different methods are just ways you would do it if you had to do it without paper. These problems are complex enough to different ways but the different ways don't need to have names and rules. If I am doing maths and I want to check my answer I would automatically use a different way (there wouldn't be much point doing it the same way).
I have never seen everyday maths but I would have no trouble with "calculate x then verify your answer", I would have a problem with solve for x using method a, then method b, then method c.
Of course checking using a different pathway didn't come naturally to me when I was 8.
