A meaningful level depends on the child. "Half of five" may not be meaningful to the child if s/he cannot visualize the concept. Using cookies may encourage the understanding of "half," and later other situations (with things that do not easily divide in half, or without manipulatives, etc.) can be experienced and added to the child's repetoire of knowledge of "half." I am not saying we should never use abstract representations, we may just need to work up to them, depending on the child.