These are valid tricks for solving math problems, but there are two problems with it. First, you shouldn't impose one method for solving problems. If there are other tricks people can use, let them. If they want to do it the long way, let them. Some bureaucrat picking one specific algorithm for breaking down problems is absolutely not helpful.
Second, it fundamentally misses the actual math learning part. Mental math is absolutely not what math is about. Solving arithmetic problems is not what math is about. This sort shit is what leads people to say stuff like "I liked math until they started putting letters in it!" It's just totally wrong. Math is not about plugging in numbers to get an answer. It's about understanding the operations themselves. "You can just use a calculator" is a completely valid statement but, in my experience as a teacher, not having a full grasp on algebra leads to not even putting numbers into calculators correctly.