Make Math Moments Academy › Forums › Full Workshop Reflections › Module 4: Teaching Through Problem Solving to Build Understanding › Lesson 41: The Stage of Mastery › Lesson 41: The Stages of Mastery Action › Reply To: Lesson 41: The Stages of Mastery Action

I have middle school students who have not grasped the concept of what fractions/ratios are equivalent to 1. When I review this concept with them/reteach, I can see the stages of expertise as I go through it with them.
Stage 1: Many think 1 is the same as 1/4 or 1/5. They do not understand the rationship between a fraction versus a whole number.
Stage 2: They may understand that 1/4 and 1/5 is not the same as 1 but they don’t understand why and still give the same answer.
Stage 3: Student may realize that ratio is the same as a whole. They may visualize a pizza with 4 total slices and think 4/4 = 1
Stage 4: Student may know that 1/1 = 1 due to Automacy. Memorized, like multiplication facts.
Stage 5: Student can represent their thinking in may ways. A circle broken into 4ths show that 4/4 is the same as 1 whole . Fraction bars showing four 1/4 pieces is equivalent to 1 whole. There are many more strategies that could be shown.