We usually see programs/teachers/classrooms accomplishing this through “table setting” when children are asked to distribute the cups and napkins, etc.  This is a good example of how the distribution of these items asks that children consider “how many” children there are, “how many” of each item they need, if they have “too much,” or “too little,” and what they might need to do to correct the situation.

There are other opportunities you can seize throughout the day that will give more children a chance to distribute items.  Items that need to “go home” are often put into backpacks or cubbies which is a perfect way children can “distribute.”  Children can give out “classroom mail” and books for independent reading.  Other children can collect the books and distribute them back onto the book shelf.  Ask children to “hand out” items at group time and then mix it up by asking, “Can you bring over enough instruments so that each child gets one?” or “Make sure that everyone gets 2 books so they can choose which one they want to look at.”  This way you allow the child to use her internal mathematical thinking strategies to problem solve.