This is exactly how they are teaching math (in second grade) these days. As far as the division idea goes, my daughter calls it parsing. Take a handful of.. (I like Mancala stones) and then divide it up between the members of the family, lets say 4. Your result is the number everyone gets and the leftovers.
For addition, they are learning tricks like 5 + 5 = 10, add 1 to one side and subtract one from the other and you get the same result, 6 + 4 = 10, 7 + 3 = 10, etc.
I have more "tales from second grade" if you are interested, you know where to find me.
And dont forget to go out with your kids and inhale some fresh air and sun along with all the math facts! 🙂