The teacher is a retard and needs to be fired. As does the idiot who hired the teacher.
More than not reasonable: IT’S COMPLETELY POINTLESS.
Such a test item measures absolutely nothing.
There’s the principle that when you hear hoofbeats, you should assume it’s a horse not a zebra. Why assume the pizzas were different sizes if you weren’t told that?
There have been several threads on this board (see examples below) complaining about trick math questions where the correct answer required you to make some assumption. And people generally complain how those questions are unfair and you shouldn’t have to make any assumptions to answer a question. You should just be able to take a question as it’s written and assume the words in the question are being used in their most obvious sense unless told otherwise.
That’s what this question did. It said take the question at its most obvious meaning, which is that the first pizza in the question is the same as the second pizza in the question. The student went looking for the trick in what wasn’t a trick question.
Why is Humpty Dumpty an egg?
Another “Is this riddle fair?” thread
Will Shortz’ Puzzler on NPR this morning
Frog riddle: does the answer make sense?
What does “times more” mean to you?
Is the answer to this math puzzle legit?
Can you solve this riddle?
Magician crossing bridge.
The teacher is absolutely wrong. It’s clearly possible for 4/6ths of one pizza to contain more pizza by weight, volume or other metric than 5/6ths of another, different pizza. The question stipulates that that is the case in this instance, and asks what circumstances must prevail for this to be so. The correct answer is that Marty’s pizza must be larger than Luis’s. (An honours student might have added that Marty’s pizza had to be more than 20% larger than Luis’s, but the question doesn’t explicitly require this level of detail in the answer.)
The teacher’s answer that “this is not possible” because it is possible, and common experience tells us so. Has this teacher never been to a pizzeria?
I still can’t figure out what the teacher is trying to test for in the question.
Is the class philosophy? Or math?
We were told that. We were told that 4/6ths of Marty’s pizza represented more pizza than 5/6ths of Luis’s pizza, from which it follows that the size of Marty’s pizza must be at least 120% of the size of Luis’s, which is the deduction the question invites us to make.
The question was not:
Who ate more pizza?
The question was:
How is that possible?
The second question actually invites lateral thinking. The first does not.
Deductive reasoning is a fundamental mathematical technique.
Or, to put it another way, your question poses a false dichotomy. Maths isn’t something different from philosophy. Maths is a particular branch of philosophy.
There are plenty of reasonable explanations for why Joe got home first: 1) he left earlier, 2) the bus had to stop repeatedly, 3) Joe can take a shortcut and the bus takes a roundabout path, so on and so forth… And phrasing it “is that possible” seems to be inviting explanations, rather than asking the person to give an answer of “no, because buses go faster than walking” (which is incredibly obvious and doesn’t need to be tested).
Because asking “how is this possible” leans towards the assumption that it is, and the idea is to reason how. Asking how it’s possible and then wanting the answer of “it’s impossible” is stupid. One pizza being bigger than the other is a completely reasonable explanation, certainly much more than there being a zebra in my vicinity.
I agree with Drunky Smurf - the teacher made a mistake, and instead of rewarding the kid for having half a brain, punished them. That is not something I would want teaching my kids - while making a mistake in test design is an excusable mistake, such things happen, reacting to it in such a way is poor form.
Is it only me, or does this whole pizza school question story seem improbable to anyone else?
To me, the student’s answer was the obvious one, the one which I would have sworn the test’s creator intended.
I propose that the teacher be given an 80% pay cut, immediately followed by a 90% raise. She should be perfectly happy with that, since 90% is greater than 80%.
Which is great, if we’re in a 400-level course discussing the finer points of mathematical reasoning. These are kids. In an educational system that doesn’t do all that well a job teaching them what fractions are to begin with.
How about we teach them arithmetic with fractions, and make sure they understand it, before we spend class time showing them that math is just a particular branch of philosophy?
I remember crunching through lists of problems when I learned fractions, and learning techniques like cancelling, finding common factors, stuff like that. Is that no longer a thing? At that point in my math learning, while I might find a particular word problem to be a pain in the ass, it would never occur to me to think that one of the premises in the word problem was flat out wrong.
The question is asinine. And makes me want to take the poor kid out for pizza.
If Marty also ate the spare 1/6 of Luis’s pizza, which would be a reasonable thing to do if Luis was going to leave it, then they both ate 5/6 of a pizza. If Marty’s pizza had extra pineapple on it, which makes his leaving some of it totally reasonable - who puts pineapple on pizza?, then his 4/6 plus Luis’s 1/6 would be greater than Luis’s 5/6.
Math is not zoology. There are no assumptions in math.
It’s certainly asinine to expect the teacher’s answer. But “How is that possible?” is a perfectly reasonable question - to which the student gave the best answer.
It should be spectacularly obvious (even to a silly teacher) that 4/6 of one pizza can be larger than 5/6 of a different pizza. Therefore, saying this isn’t possible is not only quite wrong - it’s also a failure to answer the question.
Maybe Marty’s pizza had more toppings! (The teacher is still wrong, though.)
All I’ve been able to find out about the overall test was that it was supposed to help the students learn to determine if an answer they had come up with was reasonable or not. An example given was that if you were adding two numbers together and the sum you came up with was smaller than the two numbers you were adding, you should be able to spot that this is not a reasonable answer. So the test was apparently supposed to help students learn to spot obvious mistakes in their math - for example thinking 4/6 of something is bigger than 5/6 of something.
Why assume the pizzas are the same size if you weren’t told that, either?
The thing is, this could have been a really interesting question if the teacher hadn’t gotten it so colossally wrong. When i delivered pizza, we had two sizes, 12" and 16". The 12" would be 113 square inches in area. 16" would be 201 square inches.
For the record, 4/6[sup]*[/sup] of a 16" would be 134 sq. in., and 5/6 of a 12" would be a shade over 94 sq. in. It would be very easy for Marty to have eaten more pizza than Luis, using real-world numbers.
If they’re trying to teach an understanding of math, rather than just number crunching, pizzas are a good example. 16" doesn’t sound that much bigger than 12", really. It’s just 4" more, 33% in terms of diameter. But in terms of area, which is what you want when it comes to pizza, it’s almost 78% bigger. That’s the kind of numerical intuition that would actually be helpful.
I still remember a math teacher back in junior high or so. He brought in a can of tennis balls and asked which was greater, the height of the can, or the distance around. Now, I knew that a can held three balls, so the height would be about 3 times the diameter of a tennis ball. But the distance around would be the diameter of a tennis ball times pi. A tennis ball can is tall and skinny. It doesn’t look like it’s farther around, but it is.
- Shouldn’t that be 2/3; what ever happened to reducing fractions to lowest terms?
Like when you add two negative numbers?