Nothing makes as much sense to a student as his or her own reasoning. And that is why a math class should give students the time and careful facilitation that enables this. The problem at hand was 4/3 + 5/2. Here is an account of a class in which this problem was tackled by students who had understood the need/reason for fractions to be of the same size i.e., to have the same denominators so as to be able to add them easily. However, they had not yet arrived at any particular method to achieve this.

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