Why School Supplies? Why "break the pencil in half"

I started looking over my blog and realized, that I never truly explained why I use the phrase "for the child that breaks the pencil in half." When we were planning to go to Jamaica, I researched the country and found out that the children had relatively little in terms of school supplies. Once we picked the hotel, I arranged with one of the members of management to provide enough school supplies for one class. I was told that there would be 20 children in the class. So I proceeded to collect enough backpacks, pencils, school supplies, even supplies for teachers. Enough for 20 children. Once we were there I was told that while there were 20 children in a class, this was a one room school house and that there were a total of 50 children. All between the ages of 3 and 5. I cried when I realized that I did not have nearly enough supplies to go around. One of the local men saw me crying and said,
"Please, don't cry. We are grateful for whatever we receive. When I was growing up, if a child next to me did not have a pencil, I would cut the pencil in half and then we each would have one. That is the way of Jamaicans."
Imagine how happy I was to find out that we had enough pencils to give each child one of their own.

I started thinking about this. How many children would do this? How many communities are genuinely grateful for such supplies. Where do I find the children or child that will "break the pencil in half." ?