I thought I'd have a simple object lesson to introduce fractions to the younger children. But the older family members had to throw some philosophy into the equation. Austen & Shakespeare said 8-9 respectively because they wanted me to cut it into pieces to share with everyone in the family. Hypatia said 10 - then she admitted that she didn't have a reason for choosing that number other than it was close to the other numbers chosen. Aristotle said "five - because when you cut into it, the star shape has 5 parts". That got me thinking and I said "Three - because the core, the flesh, and the skin". Then there was a discussion of whether the stem and the bud counted as a part in this sense and how the bud was the flower that had dried up. As we examined it, we noticed that there were 5 petals. Then we discussed how those were both fibonnci numbers - 3 & 5. Washington chose "Six - because 5 parts plus 1 apple makes 6. Wilberforce said "two - because it is on the second level of the food guide pyramid".
After laughing about the interesting and varied perspectives, I said OK. Think of this apple as the number 'one'. If we were to cut this apple in half (as I slice it into two halves) - what number would you give it. There were a few comments like 10 - double the 5 parts - no 9 becuase the stem is only on one side. We observed the seed that got sliced in half and the tube like channels that fed the apple to grow. Finally we continued on the dicussion of fractions that I had intended in the first place. ...
YEAH! My kids are thinking out of the box - which means my lessons don't go as smoothly as planned but they are alot more effective at teaching them how to think.
