Based on the first of these, I’d think that the student was mistakenly adding instead of subtracting. But how could that also explain the second mistake?

On the other hand, it’s hard to imagine that the student is subtracting in the second case, since they end up with a number that’s larger than what they started with.

Ideas?

• 2 wholes + 1 whole + 2 parts that fit together to for a whole = 4 wholes.
3 wholes + 1 whole + 2 parts that don’t fit together = 4 wholes and ignore the messy parts?

I could imagine a student saying that, and I could imagine testing that hypothesis with some other follow-up questions like what if it had been 3 1/2 and 1 1/2 instead of 3 1/2 and 1 2/3…

Who drew the fractions, the student or the task-giver?

• The pictures were part of the problem. As in: I gave it to them.

• Michael Paul Goldenberg

Well, the other day all sides of right triangles were equal regardless of the numbers, so why not have all fraction problems equal 4?

• We’re certainly cataloging some weirdo mistakes on this site.

I can’t decide whether I like the inexplicable mistakes or not.

• Michael Paul Goldenberg

Well, without being able to speak with the students in question, it’s an even bigger challenge. I’m impressed with some of the explanations folks have offered here for various things that I certainly missed. But there are times when I wonder if students are using buggy algorithms, making minor oversights, or just pulling numbers out of some very strange random number generator.

• Yeah.

In this particular case, I can tell you that this student was working with a partner, and they both signed off on this. These kids aren’t hopelessly confused, and they did a lot of tough problems correctly. I’m inclined to think that this goes in the category of “fast mistakes,” mistakes that happen instantly and aren’t always rationally explicable.

I’d say that, each time I look at these problems, I’ve noticed in myself a tendency to group the wholes together. That gets you the 4.

• Susan

I would be concerned about the drawings. If these are subtraction problems why are students drawing the minuend? Wouldn’t the starting group be sufficient as subtraction requires removing a part to determine the remaining part? Not understanding the operation may also cause students to group all the parts into four wholes.

• I ‘d go along with @maxmathforum ‘s evaluation, adding that, once they’ve decided to add rather than subtract, students may be justifying their thinking by remembering that similar fractions (with like denominators) CAN be added (1/4 + 3/4 = 4/4 = 1), but dissimilar fractions CAN NOT (1/2 + 2/3 = not allowed; ignore; nothing to be done about this; our hands are tied in this matter), leaving only the four wholes.