The hypothetical learning progressions presented here are the products of the deliberations of two working groups of science education researchers, each group also including a state science curriculum supervisor, organized by the Consortium for Policy Research in Education (CPRE),with support from the National Science Foundation. Their charge was to produce hypothetical learning progressions describing the pathways students might be expected to follow as they acquire deep understanding of two of the core learning goals set by the National Research Council's (NRC) Committee on a Conceptual Framework for the New K-12 Science Education Standards. The goals in question address students' understanding of the structure, properties, and transformations of matter in the physical sciences and of the flow of matter and energy in ecosystems in the life sciences. These two core goals were chosen because a good bit of research has been done on children's learning in these areas, some of it carried out by members of our working groups. These hypothetical learning progressions are intended to inform those who are working on the new national science standards, to serve as tools for those charged with developing curriculum and assessments to implement the new standards, and to encourage others to undertake the theoretical and empirical work needed to fill important gaps in our knowledge about learning progressions.