I am in the middle of Lech Lecha with 7 yo, at the pasuk where Hashem tells Avram to look in all four directions. Since we spend two days on a pasuk, when we read it yesterday, I thought: "I should really print out a map of Israel and ask him to draw and label a compass rose. That way he will see why south is called desert and west is called sea." I mentioned it to him and he said, no thanks. Comes today, and I realize that I never printed out that map. While he is filling out a workbook page, I quickly printed out a map from http://www.daat.ac.il/he-il/maps/gvolot and he very agreeably drew a compass rose on it. He asked me to draw a circle, then he added the points. I reminded him that north is usually on top, then he copied the word from the pasuk. He added the rest, very nicely asked for help in writing the letters that he was not sure how to form, got every direction in the right spot. He already knew that desert is to the south and the Mediterranean is to the west. Once the compass rose was completed, he asked me if he could hang it up in his room. He placed it over his top bunk.
This is giving me a serious pause. This kid does not like projects and decorating and workbooks. He really did just bare minimum here, but it must have tapped into something, otherwise he would not care where his final result would be.
The unplanned and totally unschool-y moment happened when I was tucking in 9 yo. We agreed that he will do his mishna assignment first thing tomorrow morning. Lately he has been very interested in defining things precisely, so he wanted to know how early he should get started. I said that he can eat breakfast, get dressed and daven first. Next thing I know, he is manipulating these and trying to figure out how many combinations could there be: first get dressed, daven and breakfast, or first get dressed, breakfast and daven... He came up with five. I told him these are called permutations. He thought there were nine possibilities. I said that there are six, for three items. I mentioned factorials (he has read most of Life of Fred, I bet they are there somewhere). I also explained what they meant. Then he wanted to know what happens if you have four: get dressed, daven, eat breakfast, look at assignments. I explained that the number of possibilites is 4*3*2 and he figured out that. We got up to five items and he calculated that 5!=120
That was so unplanned, but all of a sudden, it was so vital to know, just how many ways are there to get things done.
Maybe that's a lesson for me, too.