In kindergarten we teach the basic concept of fractions. We teach them 1/2 and about fair share. I read the book Bears Berries. Then we each got paper berries that we had to share evenly among two bears on a page. The students picked this concept up quickly. So I had the students make a bear and two plates from construction paper. Then I gave them some berries and they had to share them evenly.
Later the students got with a buddy and I gave them a piece of bread that they had fair share with. So the students had to carefully tear the bread in half.