REAL Fractions Objectives
Students should work with the fraction circles until they figure out the ASMD rules for fractions on their own from seeing the connection between the problems they work and the answers they get. Taught this way, the students "own" the rules and learn that they instead of just their teachers are smart.
Students should also learn to sketch fraction circles being added, subtracted, multiplied, and divided. From these sketches, they should be able to remember the ASMD rules for fractions they once figured out if they forget them — a certainty for most students.