Reply To: Lesson 4-1: The Stages of Mastery Action

[Lizann “Lizzie” Herrera]

I reached out to a teacher this week to see if I could try some things with his students. He is in the beginning stage of introducing fractions to his 4th graders. He mentioned that he wants them to understand the relationship between fractions and division. Because students are just being introduced to Fractions, I chose the prompt: What is 1/2 of 24. This is how I see the different stages:

Stage 1: Students count one to one but are unclear when they have reached 1/2.

Stage 2: Students count one to one making two piles of the same amount each.

Stage 3: Students break the array in two groups of 12.

Stage 4: Students divide 24/2 or multiply 1/2*24 to get 12.

Stage 5: Students can represent 1/2 of 24 as 1 group of 12 or 2 groups of 6.

Stages-of-Expertise-Fractions.png 307 KB Image File — Click to view

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