How Many Each?

After a great day at EdCampOttawa, I came home to a roast chicken dinner (yes, my husband is a great cook) along with roasted veggies.  While helping himself to seconds, my 8-year old, Noah, complained that he hadn't gotten enough potatoes.  My husband said that he had cut 4 potatoes into 4.  The kids quickly figured out that there had been 16 potato slices.  I then asked how many we would each get if they were equally distributed among us (us being 6 people).  They tried 2 and counted up to 12, then tried 3 and counted up to 18 (in 3s) so they knew it was more than 2 but fewer than 3 pieces each.  Noah then said that it wasn't 2 and a half.  I asked him how he knew.  He got mad at me, screamed that he wasn't doing this anymore and stomped away from the table.  So I turned to Jacob, who is 6, and asked him the same question as I had seen him making gestures with his hands that looked like he was figuring it out.  He told us that if they each got 2 and a half pieces, that would be 15 pieces.  At some point my 10-year old said she had figured it out, but actually managed to not yell out the answer (good job, Isabelle!).  So back to Jacob.  We went back to knowing it was more than 2 pieces each which he told me would be 12 pieces. I asked how many pieces were left to be divided among us.  He said 4.  He wanted to give each kid 1 and the adults none, but I said we each had to get the same amount.  Then he thought Noah shouldn't get any since he had left the table.  With a little encouragement he said we could "chop, chop" the pieces into 3.  So how many pieces would that make?  12, he counted. And then he figured that once around the table was 6 so he could around the table another time and we would each get 2 of the cut-up pieces.  So 2 and two-thirds each.  Just as we were saying this Noah yelled from the next room - 2 and a half and one sixth each!  Yes, Noah.  Yes :)  Then he sat back down and finished eating.