I know what you mean, treecritter, but if the child in question has worked through from the beginning, they used to have ten, rove seven and count what's remaining, then they moved on to really understanding, and then they moved on again to tricks like estimation. Surely if the child's showing their steps for estimation, that should count for showing your work?
Like, once you've understood division as a sharing of equal parts and have moved on to having memorised the facts to use as tools in more complex problems you're allowed to say "10 divided by three is three with one remainder, bring the 2 down, twelve divided by three is four" instead of "I have ten blocks and give one each to Carol, Bob and Ranjit, three times. At the end I still have one left over". KWIM? We use Singapore math and each new type of problem is introduced with objects (sharing apples between three friends), then blocks (sharing blocks between groups), then numerals (dividing). They are not expected to use the apples between friends once they have mastered the chapter and moved on.
