(This is not dissimilar to the fact that learning to read and sugarhouse casino parking cost write numbers -at least up to 100- is easier to do by rote and by practice than it is to do by being told about column names and the rules for their use.).
They go beyond what the students have been specifically taught, but do it in a tricky way rather than a merely "logically natural" way.
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Students have to be taught and rehearsed to count this way, and generally they have to be told that it is a faster and easier way to count large quantities.
If you are rude or irresponsible, dont be surprised if no-one trusts you to watch their kids.
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It is much more feasible to figure amounts of things on paper (or in a calculator) than to assemble the requisite number of things we are talking about in order to add, subtract, multiply, or divide them, especially when we are talking about large numbers.
Although children should not be taught arithmetic only mechanically, there are some mechanical skills that can be relatively easily learned by children, and that are important or necessary for seeing more "interesting" number relationships.