This is one of those problems that makes more sense with context. The teacher had the students working on “reasonableness”, which is essentially “does the question I’m asking make sense?”. The students were probably instructed to ignore actually trying to solve the problem when presented with one, but instead explain why the question either does or doesn’t make sense.
In this case the student potentially misunderstood the task. The failure on the teacher’s part is wording the question in such a way that it actually has a reasonable solution, and isn’t necessarily an unreasonable question.
The teacher doesn’t need to write all of that to get the point across. They can speak to them on the side and say, “remember when we worked on reasonableness last Tuesday?”
This isn’t testing reasonableness. This is testing to see if a student understands that to properly compare fractions the wholes have to start as equivalent.
Source: I use questions similar to this every year because if I don’t get some real funky diagrams.
But… you can totally compare fractions without the whole being equivalent. You just have to know the size of the wholes. It’s just a poorly phrased question that has more than one correct answer when only one was intended.
Edit: also, it’s totally testing reasonableness, that’s literally the title of the question. Still poorly phrased though.
This is one of those problems that makes more sense with context. The teacher had the students working on “reasonableness”, which is essentially “does the question I’m asking make sense?”. The students were probably instructed to ignore actually trying to solve the problem when presented with one, but instead explain why the question either does or doesn’t make sense.
In this case the student potentially misunderstood the task. The failure on the teacher’s part is wording the question in such a way that it actually has a reasonable solution, and isn’t necessarily an unreasonable question.
The feedback should look totally different if that was the case though
The teacher doesn’t need to write all of that to get the point across. They can speak to them on the side and say, “remember when we worked on reasonableness last Tuesday?”
This isn’t testing reasonableness. This is testing to see if a student understands that to properly compare fractions the wholes have to start as equivalent.
Source: I use questions similar to this every year because if I don’t get some real funky diagrams.
But… you can totally compare fractions without the whole being equivalent. You just have to know the size of the wholes. It’s just a poorly phrased question that has more than one correct answer when only one was intended.
Edit: also, it’s totally testing reasonableness, that’s literally the title of the question. Still poorly phrased though.