This is a collection of 12 different division reasoning problems that require your students to understanding through written explanations. No, it doesn't mean your students are going to explain the long division algorithm by writing about the steps they took to solve the problem. First of all, who cares? Second of all, it doesn't really show a mastery of the concept of division; it only shows they have memorized the steps in an algorithm that is totally unnecessary to memorize in an age of calculators and computers.
These division problems use hypothetical relationships for your students to write about. For example, if I told you that ♥︎ ÷ ☁︎ = ✄, and ✄ > 1, what could you tell me about ♥︎ and ☁︎? Well, you would know that ♥︎ has to be larger than ☁︎, but you would also have to know that neither ♥︎ and ☁︎ can be equal to 0, but that also if ♥︎ was equal to 1, then ☁︎ would have to be a fraction or decimal. And that's only the beginning of the fun!
Yeah, I know these are really hard; you can give them to your "gifted" students, or just let everyone bang their heads against them. Some are easier than others, so feel free to "edit" which ones you want to subject your kids.
There are 12 different problems to cut out; students take a problem, paste them onto the answer sheet and then write about the problem. There is an answer sheet, as well solutions for all the problems, which you shouldn't really need, because this would really rock if you had your students "peer review" one another's solution.