The Internet is losing its mind about this confusing pizza math problem

Marty had a large and Luis had a medium...smart kid, too bad the teacher isn't as bright.

Or am I missing something?

There are different sizes of pizzas. They aren't all uniform. The kids answer is correct, and makes perfect sense.

Good answer from the student, kinda common sense for anyone that has had a pizza.

did not specify if the pizzas are uniform. So the answer "it's not possible" is technically wrong.

What you are missing is that the teacher did not write the question.
It is a standardized question.
And possibly that teachers can be wrong.

then it certainly is possible.

Let's give the teacher some dimensional insight into size.

...always eating a greater fraction of my pizza than anybody else around me.

And on those rare occasions when I don't order the largest pizza available, I just use the Banach Tarski Paradox to subdivide my small pizza and reassemble it into a large pizza.

https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox

and the best philosophy of life.

He ordered a pizza that was 10/6 normal size, two-thirds larger than any pizza meant to be eaten by mortal man.

Whether you are right or wrong is irrelevant. What's important is providing the answer they want. The sooner the kid learns this, the better off he'll be in the real world.

=/

You are qualified to makes hundreds of dollars an hour as a management consultant, and potentially thousands of dollars an hour if you work your way up to a partner.

You have to come up with some kind of meaningless strategy, which is usually built around some self-help style book that some psychologist who has never managed anyone wrote. This is the current bullshit de jour, that's been making the rounds at many large corporations:
http://www.gallupstrengthscenter.com/

First you attend an introductory seminar, then you read the book, then you take the test, then you receive an evaluation that tells you what your "strengths" are, then you attend coaching sessions taught by idiots working for consultants making hundreds of dollars per hour.

My results were inconclusive because I answered too many of the questions as neutral. When asked about that during the coaching sessions, I told them my biggest strength was recognizing bullshit, which as you can imagine went over like a lead balloon.

http://en.wikipedia.org/wiki/Now,_Discover_Your_Strengths#Criticism

Sharing none with the teacher, of course.

This is written as a solve for X problem, not a probability question. The X to solve is the comparative size of the pizza that will have enabled Marty to have possibly eaten more pizza than Luis.

It's like me asking a student "Marty is in Seattle, and Luis is in San Diego. The sky over Marty's head is grey. How is this possible?"
(BTW there is a huge "June Gloom" type overcast going on down here in San Diego right now, so it's pretty grey here...)

Haele

We don't care what the actual size of the pizzas in question were. The question just tests understanding of the concept that a small portion of a large thing can be larger in absolute terms than a large portion of a small thing. That's the sort of problem I solve all the time in economic decision-making, even in such prosaic choices as which size/weight of item to buy at the grocery story.

On Edit: reading further down the thread, I think you are more concerned about why we are trying to solve the problem or clean up the word problem presented than to just come out and say "the teacher was wrong". I can dig it.

So go ahead and ignore everything I've written below, because I just got my BS in Business and am still in the "present the proof of your argument" mode.

Your argument to me is that the problem is about recognizing and applying the differences between portion size to come to a conclusion. Deconstructing this requires a "solve for X", where in this case, the variable to the value that each number of portions the subjects have is determined by the volume of the whole pizza each subject has.
The constants are that 1) you have two participants, Marty and Luis, who have eaten a specified percentage of their respective pizzas, and 2) each pizza has six slices.
Therefore, Ockham's Razor would lead us to the realization that the variable required to solve for the situation presented is that the pizzas were of different size. The person solving the question must come to that conclusion, either by recognizing that this is where the most correct answer is to be found (the argument you are making with me), or by actually proving how Marty could have consumed more pizza than Luis by solving for X - the variable that affect the constants.
Is this a Algebra class or an Economics class?
I'm assuming Algebra because of the age of the student indicated in the story, but it could very well be a Marketing class, where the student is learning decision making or resource allocation strategies.

Now, the teacher's reaction to the answer was incorrect for either type of class, and the question was poorly written to encourage either recognition of variables or for presenting a proof to the situation.

Haele

Not a cloud in sight in Seattle today.

cities get less cloudy in alphabetical order...

should have specified, both pizzas were the same size before the ambiguous question.

It's a fact that pizzas come in different sizes; the assumption that they were the same size is purely your own. You're trying to introduce new facts to make the answer into something different from what it is.

If the question is worded correctly, the teacher's answer is logically correct. Anger or insults or internet tempests in teapots won't change that.

If the teacher wrote the test, then said teacher should take a lesson in rhetoric. Oh, and I'm not a fan of that kind of trick question anyway. If you want correct answers, the question must be clear.

The question as written explicitly states that it is assessing reasonableness (as you can see from the photo in the article), not seeking a quantitative answer. The teacher's answer is not logically correct at all because it relies on an unwarranted inference.

Consider another example: if I give you half the money in my wallet, you would have more than if Bill gives you all the money in his wallet. How is that possible when a whole is more than a half? Very easily; people often have different amounts of money in their wallets, and I have more than twice as much as Bill.

I think you are missing the point.

There's no end to the possibilities if you want to imagine in new facts afterwards, but what we're discussing is the correct response to the facts that were actually given.

so that the only correct answer could be the answer that the teacher wanted. You are freaking out at the thought of that for some reason. You want the kids answer to be the answer the teacher was looking for even though it was not.

So here are some facts:
1. The kids answer is currently correct.
2. If the teacher specified that the pizzas were the same size then they could get the answer that they wanted.
3. The question is stupid.
4. You are freaking out about this question.

Why would we want to change the question to validate the teacher's incorrect answer? This particular teacher is demonstrably incompetent, but some of you seem more interested in finding a way for the teacher to 'really' have been right than acknowledging the fact that the kid was write and the teacher was wrong. There is no evidence that the teacher is the author of the question, and even if this is the case the responsibility lise with the teacher. As written the question is sufficient and the kid's answer is 100% correct.

This matters because it's the kid's GPA that suffers when the teacher makes mistakes. I don't see why we should tolerate teachers who are less competent than the kids they are supposed to be instructing. Why people are defending the teacher's behavior or claiming that the question is somehow deficient is beyond me.

2. is not in evidence.

In fact the teacher did not write the question. It is a standardized question.

The teacher is stupid.

(assuming there really was a teacher and not just someone with a blank test, a couple pens and a camera.)

Also how would you write the question to make the point that you have to know the original size of each pizza as well as the fractions?

"how would you write the question to make the point that you have to know the original size of each pizza as well as the fractions?"

That is a real brain buster. How about prefacing the question with something along the lines of "Marty and Luis ordered the same size pizza..." Or is that too complicated?

But that is the opposite of what I asked for.
Telling someone something does not test if they understand that concept.

This question does show that it is important because one can't answer the question without understanding that you have to know the original size.

Your answer is too simple, not too complicated.

You asked:
"Also how would you write the question to make the point that you have to know the original size of each pizza as well as the fractions? "

I replied:
How about prefacing the question with something along the lines of "Marty and Luis ordered the same size pizza..."


Simple is exactly what I was aiming for. The teacher is a fool and simple solutions are the most fool proof solutions.

Being able to draw logical inferences correctly is such a useful skill that I feel obligated to help people who are having difficulty with it. It bothers me that the teacher in this story is wrong and is damaging the child's education by perpetuating his or her ignorance.

The question tells you that Marty ate more pizza, but the percent he ate was lower. There's no possible way his pizza could be the same size as the other one. This is a question that tests the student's ability to determine scale.

The question makes perfect sense as is. This is either fake or the teacher had major brain-fart. It is not a trick question at all. The basis of the question is, "How can something have a lower percentage of it taken away than something else, but still have more in total taken away?" It's because the item has to be bigger.

... then ate another 1/6 of his own. That scenario isn't excluded by the wording of the problem, it doesn't say they ate *only* the quantities specified. (If you eat 5/6, then you also ate 4/6, & 3/6 etc.)

It's also possible that Marty has been eating pizza every day for years while Luis eats it once a month. Clearly, Marty has eaten more pizza than Luis, regardless of how much they consume at any given point in time. It's another scenario not excluded by the wording of the problem, as it doesn't place a time constraint on the "pizza consumption" period.

There is a very simple explanation from the superficial paradox in the question; the pizzas were of different size, which is a matter of normal everyday experience for practically anyone in the US. Introducing irrelevqant new information to refine the problem is unnecessary when a simple explanation will suffice.

It's testing the ability of the student to form an answer outside the suggested parameters of the question.

"How is this possible?" It's not, given only the information set forth in the question. So the teacher was looking for "It's not possible".

But the student's answer WAS clever, and essentially answered the question correctly by saying "it's not possible unless I add or assume some additional facts".

I think the teacher should have given the student credit for a correct answer and creativity in expressing it - it would have been the cool thing to do, and would have encouraged that creativity. But some teachers are NOT cool, and instead are simply hard asses.

This teacher is a hard ass. Had some like that myself.

The assumption that the pizzas are of the same size is as much an assumption as the one that they could be different sizes, which latter is actually grounded in fact.

... the teacher WAS trying to be clever with a trick question, but worded it poorly. Kid wins.

On the plus side, my 9 year old nailed it in about 5 seconds. He said "Marty's pizza slices were bigger."

He's a lot smarter than I am.

So "it is not possible" is not an option.
You can't contradict or ignore the "given" information.
The teacher was just plain wrong.

There is some serious cognitive dissonance going on in this thread.

Of course, it gets into the realm of trick questions if you ask only, "How is this possible?"

A better phrasing would be: "Is this possible, and, if so, how?" That would keep the students on their toes to look for implicit assumptions (such as both pizzas being the same size) that they must discard to find the solution -- a very valuable lesson IMO.

On other occasions, however, a proposed task really is impossible. Euler gained accolades, and is credited with laying the groundwork for the field of topology, by proving that the Seven Bridges of Königsberg problem has no solution.

This is what happens when you teach to test instead of teaching to think.

4 and a 4.5 inch
8 and 9, 16 and 18, 25 and 28, ...

However, I guess it was multiple choice. In which case: it ain't gonna happen is correct.

The teacher's explanation is based on the question itself lying. That's nonsense. It's a word problem - you're supposed to be given completely accurate information. If not, the whole point becomes meaningless.

The question explicitly states that Marty ate more pizza. You cannot have the correct answer being that Marty didn't eat more pizza - that violates the rules set by the word problem.

There really is nothing to think about here. The question asks one thing, and the student answered it correctly.

Maybe Marty is Luiz' older brother and their mom gave him 2 slices to Luiz' 1 slice.

Perhaps apocryphal, as I think many attributed to him were.

"You better cut the pizza in four pieces because I’m not hungry enough to eat six."

It's impossible to know the answer without knowing what you're starting with in the first place.

Look, you're told as facts that the two kids arte different portions of their individual pizzas, but that the kid who ate the smaller portion of his nonetheless consumed more than the other. The inference that he had a bigger pizza to start with is the only possible conclusion that comports with the facts. In a word problem like this declarative statements are offered as facts and it is your job to figure out a fact that you were not given (ie Marty having a larger pizza than Luis did).

Maybe it seems very abstract or meaningless to you but there are many contexts where this sort of problem comes up all the time. Legal disputes very often turn on the ability to draw correct inferences from limited available facts, for example.

are mostly voting for Trump - well at least 5/6 of them.

to use a condom.

had this same worksheet and made the same answer. Unfortunately, this kid's teacher was just dumb or was just having a bad day and not paying attention.

Excellent answer!

what planet you are on

same size, which is not information included in the original question. So the kid is absolutely right. The teacher's answer is wrong.

Marty bought a pizza (so it was his) and he ate 4/6 of it. He then gave the leftover pizza to Luis (so it became Luis's pizza), and Luis ate 5/6 of that.

If the original pizza was cut into 36 slices to facilitate the calculation, Marty ate 4/6 or 24 slices. He gave the remaining 12 slices to Luis, who at 5/6 (or 10 slices) of what was now his pizza.

This solution leaves two uneaten slices -- one to give to the student to reward him for a correct answer, and one to throw at the numbskull teacher.

He also ate the remaining third, but it is true that he ate 4/6ths of the pizza.

Can we stop expecting teachers to be perfect? I've made a few mistakes. Oopsie!

I made a mistake in front of the class trying to solve a third quarter calculus problem. I also saw one of my grad level math teachers get a problem wrong once. But we aren't talking about advanced math here... this is like 3rd or 4th grade math/logic and the 4th grader just took his teacher to school

Look, of course everyone screws up. I messed up tying my shoelace this morning and had to spend 3 minutes unpicking the knot I carelessly pulled tight. But I didn't double down on my mistake and start telling everyone else they were tying their shoelaces incorrectly.

accept the premise that Marty's 4/6 is larger than Luis's 5/6. When the teacher says that is NOT possible, she is certainly wrong, both for this problem, since the question explicitly says that Marty's 4/6 is larger than Luis's 5/6, and in general, because 4/6 of something relatively large (say, a gallon of water) is greater than 5/6 of something relatively small (say, a cup of water).

Thus the student is right, the teacher is wrong, and the teacher is obviously embarrassed now.

She can apologize to the kid and give the kid the missed point, and everyone else can just leave her alone, since she was probably up late grading papers and preparing lessons after having parent-teacher conferences for several hours that evening or fulfilling some other time and labor intensive obligation for the school at no extra pay.

When we are tired, rushed, and overworked we sometimes make mistakes. Tired, rushed, and overworked is pretty much a chronic condition for most teachers, so it is a wonder they don't make more of these kinds of mistakes.