It used to be that Math was lots of number crunching but Elementary Math has changed –my theory is the advent of the calculator and Google. Homework can no longer be a page of straight division problems as they can be Googled for the answer and even for all the steps involved!!!
I came across this working on homework with a 4th grader. Is it 9 divided by 2? or 9 divided by 4? Both have a remainder of 1.
See the diagram below for these two ways of interpreting division (albeit division without remainder).
Here is another example:
13 can also be grouped by quotition division see above with 3 groups of 4 with remainder 1. This method will yield the same Math results EXCEPT for problems like 12 divided by 5 which is 2 remainder 2. But divide 12 by 2 and we get 6 not 5 remainder 2 b/c the remainder goes in one more time (same goes for divide 21 by 6 is 3 R3 but 21 divided by 3 is exactly 7 not 6 R3.). So be aware that division these days is about interpretation and not computation.
Math Confidence by Robin the Math Lady 