How to teach long division video at YouTube
The video and the article do not delve into the "why" long division works, but suggest a specific sequence of teaching long division. It should also make the process of finding the remainder within long division more transparent to students.
Please read my article from this link: How to teach long division
What about teaching why long division works?
I feel the algorithm of long division AND why it works presents quite a complex thing for students to learn, so in this case I don't see a problem with first learning the algorithmic steps (the "how"), and later delving into the "why". Trying to do both simultaneously may prove to be too much to many students.
However, once your student has a basic mastery of how to do long division, it is time to also study what it is based on. To learn more about that, please see:
Long division as repeated subtraction
Why long division works (based on repeated subtraction)
Why long division works—a comparison with sharing money (bills) (video)
The Cookie Factory Guide to Long Division by Denise
