Because they spent an entire math class period earlier that week explaining to the students what “reasonableness” was going to mean on their next math test, and in the context of (I’m guessing 3rd or 4th grade) arithmetic the important thing they’re trying to teach is that 5/6 is a larger fraction than 4/6. I agree that the question could be worded better (change the last two sentences to “Marty says he ate more pizza. Is this possible?”) but I strongly suspect that the missing context from their class - or maybe even at the beginning of the test - explains enough to get the answer the teacher was looking for here.
Yes, one kid starting with a larger pizza changes the situation, but fundamentally that’s an algebra question, not a “learning fractions” question.
Well yes it is a learning fractions question. Pizza is not a number. Pizza is not a specification of size. It is absolutely crucial for understanding fractions, that a fraction of anything but two numbers will be factored by the size or whatever metric of that thing.
In the same wake you learn that “5” is not an answer to a typical physics calculation, as the unit is missing.
You could argue that it’s reasonable to assume that all pizzas are the same size but there are many pizza places that offer different sizes. You could as well argue that this is an attempt to make the kids think outside the box and come up with this explanation. How big a fraction is depends on how much the whole is is a good message you can’t learn too early. Understanding statistics is in large parts this. Many people will throw around percentages of pooling questions without ever questioning the pool of people asked.
I agree that the idea they were teaching was “is it reasonable for 4/6 to be larger than 5/6”, but it was too sloppy to be in a word problem with cultural context. Sometimes if you’re the teacher and a kid stumbles onto a loophole this big, you have to take the L and update your materials for the next year. Just add, “Marty and Luis ordered small pizzas at Joe’s,” and this goes away. This feels like the question writer had been in a groove with drafting more abstract problem sets, and didn’t do a good job when shifting gears into the word problem section.
Because they spent an entire math class period earlier that week explaining to the students what “reasonableness” was going to mean on their next math test, and in the context of (I’m guessing 3rd or 4th grade) arithmetic the important thing they’re trying to teach is that 5/6 is a larger fraction than 4/6. I agree that the question could be worded better (change the last two sentences to “Marty says he ate more pizza. Is this possible?”) but I strongly suspect that the missing context from their class - or maybe even at the beginning of the test - explains enough to get the answer the teacher was looking for here.
Yes, one kid starting with a larger pizza changes the situation, but fundamentally that’s an algebra question, not a “learning fractions” question.
Well yes it is a learning fractions question. Pizza is not a number. Pizza is not a specification of size. It is absolutely crucial for understanding fractions, that a fraction of anything but two numbers will be factored by the size or whatever metric of that thing.
In the same wake you learn that “5” is not an answer to a typical physics calculation, as the unit is missing.
We can understand the context of the curriculum goals and still realize that the question was asinine and the teacher is a dipshit.
You could argue that it’s reasonable to assume that all pizzas are the same size but there are many pizza places that offer different sizes. You could as well argue that this is an attempt to make the kids think outside the box and come up with this explanation. How big a fraction is depends on how much the whole is is a good message you can’t learn too early. Understanding statistics is in large parts this. Many people will throw around percentages of pooling questions without ever questioning the pool of people asked.
I agree that the idea they were teaching was “is it reasonable for 4/6 to be larger than 5/6”, but it was too sloppy to be in a word problem with cultural context. Sometimes if you’re the teacher and a kid stumbles onto a loophole this big, you have to take the L and update your materials for the next year. Just add, “Marty and Luis ordered small pizzas at Joe’s,” and this goes away. This feels like the question writer had been in a groove with drafting more abstract problem sets, and didn’t do a good job when shifting gears into the word problem section.