At School :

"I did division today in school"..he announced
"That's nice. How do you do it"? I asked
"Three of us sat and shared the thousands, hundreds,tens and units between us"

Arav has just given an excerpt version of the work that he must have completed in school. What struck me was that he has understood the core concept of the word division and that he is only four and a half. Montessori materials enables a student to explore infinitely. Though initally the numbers (i.e 56+57 or 20/5) would be provided by the teachers, eventually students create their own problems and arrive at the solutions.