## Marilyn Burns

The fourth graders I’ve been working with this year have recently been learning about fractions. Last week I began a lesson by drawing two representations on the board (as shown above) and writing a question.

I gave the students about five minutes to do a “quick write” to answer the question and explain their thinking. I collected their papers without commenting on them, and then I began the discussion.

The conversation lasted for about 45 minutes, and a variety of arguments emerged. It was obvious to some students that the blue representation was 5/4, but others weren’t sure about that.

- Some students explained that each small blue shaded square was one-fourth and there were five of them, so that was 5/4.
- Some reasoned that since the green representation was 4/5, the other had to be 5/4.
- One girl argued vehemently that the representation on the left, the blue one, was 5/8, not 5/4, explaining that there were eight squares and five of them were shaded in.
- A boy countered by arguing that if the two blue squares were touching to make one rectangle, it would be 5/8, but they didn’t.
- Others thought that both of their arguments could make sense.
- It seemed clear to most of the students that the green representation on the right was 4/5, which caused some to think that maybe neither representation showed 5/4.

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