This paper describes three conceptual areas in physics that are particularly important targets for educational interventions in K-12 science. These conceptual areas are force and motion, conservation of energy, and geometrical optics, which were prominent in the US national and four US state standards that we examined. The four US state standards that were analyzed to explore the extent to which the K-12 science standards differ in different states were selected to include states in different geographic regions and of different sizes. The three conceptual areas that were common to all the four state standards are conceptual building blocks for other science concepts covered in the K-12 curriculum. Since these three areas have been found to be ripe with deep student misconceptions that are resilient to conventional physics instruction, the nature of difficulties in these areas is described in some depth, along with pointers towards approaches that have met with some success in each conceptual area.