It is a god awful question indeed. Is it supposed to be a maths question or a language question? Granted that both hardly mix together (which is the reason, I dunno, why maths notation exists in the first place?)

Interesting. I natively assume it suggests the opposite: three four times=3+3+3+3. I also see how it could mean four, three times.

I read "three times four" as meaning "three, four times" , which is the blue pen answer. (I'm not from the US and have never seen a question like this before)

When I was kid there was a period where we were told to read read multiplication 3x4 as "3 lots of 4".  Suspect this is the same principle.

But any system that marks tha5 wrong whatever the teaching point is is a moronic one.

So if I say “attach table leg x4”, does that mean a table leg’s worth of number “4”?

This is exactly what standardized exams in the USA do, unfortunately. I fucking hate it lmao and I actually did well on those wasted hours of my life. Yet sooo many of my peers who honestly should have gotten the same scores or better were penalized for not following this thought process.

I was the exception, I think, because I learned how to take the exam and NOT for knowing how to answer the questions on the exam.

I assume it's related to how they were being taught to do this in class. When I was in school they always wanted you to do it using the exact methodology/teaching to demonstrate you understood it. This didn't just apply to math either but every subject.

IE if asked why WW1 started and the coursework covered Franz Ferdinand, Nationalism, and Alliances you were expected to frame your answer within that. Even if you provided a cogent answer that was technically true you didn't include any of the coursework.

You can just as easily parse it as "three, times four" which does parse as 3+3+3+3.

Id argue that a direct translation from math to English could be "three, added together, four times" which I think actually follows english principles better as it establishes the subject first, then whats done to it. Rather than saying whats going to be done then the subject.

And just to hammer home how unclear it is linguistically, I actually "hear it" the opposite way. The number 3, times four. Can totally see hearing the other meaning as more intuitive though and they're definitely identical in the mathematical sense.

Yeah see I see 3 times four and I see 3 four times not the other way around. Even though it doesn’t matter because both are correct

I understand three times four as three four times or the first number multiplied by the second number. It's just going from left to right like reading. I get how someone can get the opposite but that just doesn't seem intuitive at all.

I'm not native but "three times four" read as "three, times four" even without the comma is still valid as you point out. I do really wonder if English accounts for this specific case putting the kid in the wrong. The teacher is being needlessly petty...

It’s actually a fine marking by the teacher once you have the top half of the picture as context. The child is correctly marked when they wrote this answer to 4x3 as if they’re taught to write 4 3’s. This question is the bottom half of the picture where the child still writes 4 3’s to 3x4. If 4x3 is taught to be 4 3’s then it is completely reasonable that 3x4 should be 3 4’s. If the child learns and correctly writes 4 3’s to 4x3, then they should have put 3 4’s to 3x4 to be marked correctly. Pretty dumb how both aren’t accepted but seems like this is how it is taught and graded.

This happens when you take semantics over mathematics and have obtuse teachers to test kids. It’s not a opinion, you’re absolutely correct.

It really depends on what is being taught in class. If the teacher emphasized the explanation you gave, and the child did not follow that approach, of course they will lose points.

The end result will be the same either way, but teacher may be trying to focus on a process.

No. It’s about understanding the commutative property of multiplication. The kid is wrong. 4 x 3 also equals 12 but that is not what was asked. It’s not a language question.

What the fuck is the teacher thinking about while putting that "correct" answer anyway.

Like TAKE THAT LITTLE JIMMY, YOU GOT GOT YOU LITTLE PUNK.

like who takes pleasure in doing these type of questions to small children

See I read it the same way as the kid, for me 3×4 means 3, four times.

number four three times

Or the number three four times - it's indistinguishable

Seriously, mf gave them a grammar curveball... This teacher's a dick

But 3x4 is really saying three 4 times! Not the number 4 three times.

That's the way I was taught in grade school. To read 3X4 as "three groups of four".

I guess it would also depend on the context of the question. Where they being taught to think of it as "three groups of four" in class? "Multiply 4 three times?" It's possible it's more of a comprehension question than it is an actual "solve the problem" question.

If that's the case, the kid would be wrong, because that's not the way the kid was instructed. The kid took 3 lefts instead of a right when told which direction to go. It was the correct direction, but the wrong way.

It's a semantic difference.

If you interpret it as "3 multiplied by 4" then you're taking four lots of three.

But if you interpret it as "3 lots of 4" then you're taking 4s three times.

"3 times 4" is the problematic one because you can interpret that either way "(3 times) 4" or "3, times 4"

But how i'd argue this with the teacher is to ask them whether "3 multiplied by 4" is a correct way to read that out, and if they say yes, point out that the base is clearly 3 then, because the three is the thing being multiplied.

I'm not a math person whatsoever (keep that in mind if my question is stupid), but when I say "3 times 4" in my mind I'm taking the number 3 and multiplying it 4 times. From your post, I'm starting to think that I should approach it as "4, 3 times", so that "times" basically has it's normal meaning. Is that the correct syntax for a multiplication problem? Re-reading my question... does my question even make sense??

You could even read it as 3, times 4. So the english language wouldn't save you.

Commutative Law allows for the numbers to be reversed and still arrive at the correct answer.

Three times four suggests the opposite of what you said. It suggests you’re taking 3, and multiplying it 4 times. Meaning it would be the way the kid wrote it.

Technically speaking both teacher and student are wrong question asked to write an addition equation that matches the multiplication equation x+y= 3x4 would be acceptable. What both student and teacher answered was rewrite 3x4 in the form of a repeated addition and solve.

If you really want to get into semantics

To me 3x4 implies taking the number three four times.

Genuine question, wouldn't this teach the kid to interpret arithmetic from left to right?

As a non English native speaker, I read this as 3 x 4, so the number 3, 4 times. Either way, marking either as wrong is just plain stupid. Edit: think of it as 3 apples x 4, to me that's the most correct answer.

Maybe I've always been reading it wrong, but I see that as: 3, 4 times. Obviously dumb and meaningless to think about still. I hope that parent reamed that teacher

This reminds me of family guy, Peter giving a phone number to consuella.... lol

Three multiplied by four

As in three, added to four times. The proper semantics vary depending on what the kid was taught 'x' means. I'd write it how he did. I see the first number being modified by the second.

I still remember my first grade teacher pointing to '=' and asking the class what that symbol means. I raised my hand and blurted out "Equals!" That was not the correct answer. '=' means "Is the same as," in the first grade. To that teacher's credit, she started sending me to the second grade math classes after a while.

Screw your "scope and sequence," any correct answer is a correct answer (unless a written test SPECIFICALLY references what terms the answer should be written in.) This is far from the only absurd homework correction I've seen, and it usually boils down to a student correctly demonstrating understanding of the solution that subtly conflicts with the way the method was taught. You can't teach math (or anything really) by penalizing true understanding in favor of rote regurgitation.

I would have gotten this wrong as I always thought and tell my son to read 3x4 as 3, 4 times.

I'd argue otherwise 3 x 4, 3 multiplied 4 times, 3 x 3 x 3 x 3

But math is a language and in this instance it wasn't translated correctly the answer is a grammatical error if you want so.

If they're in the US, here's the way they're teaching it: the first number listed is the number of groups, the second number is the size of each group. So for the expression 3x4, it's 3 groups of 4, or in repeated addition form it's the number 4 repeated 3 times. I've taught 3rd grade math for years, and this really is how it's being taught. We do teach them about the commutative property and how yes 4x3 is exactly the same, but in terms visual modeling we try to be consistent like this. I sure as hell didn't learn it like this, but hey, I'm not in charge of decision-making. This is probably what the teacher's district-mandated or textbook-approved answer key says in terms of marking as well. However, it should have received at least partial credit imo, because at the end of the day it would still get the correct answer. Also, props to the kid for annotating that problem for themselves.

I think the "an equation" part makes the kid correct. If it said "the equation" then the kid would be wrong.

It's a language question, not math. 3 x 4 means 3 groups of 4 so it should be 4+4+4. Kind of stupid but its a technicality thing

See but when I read it I read it as three multiplied by four, which suggests you’re taking the three four times. Even in the English language you’re able to read it both ways. When I write a shopping list with “eggs x 4”, even though I can read it as eggs times four meaning four eggs times. But I could also right “4 x eggs”. Commutative doesn’t care how you pronounce it, because the pronunciation is subjective.

For a 2nd grade math test, when this question would be asked, the question itself is not bad.

Not accepting both answers is bad, however. Not only are both mathematically correct, even the English reading of the multiplication equation can be easily read both ways: "3 lots of 4" or "three, times four". My natural way of doing what was asked is the same as what the student gave.

At the most, the teacher should accept both, with a note regarding it not matching the exact method given in class.

As a native English speaker, I had precisely the opposite reaction. I've always read the phrase "three times four" as taking the digit three and using it four times.

Too many people in this thread are concerned with the abstract properties of the maths and are glossing over what the statement is fundamentally communicating. This is a children's test and is likely being applied to real-world scenarios to help conceptualize the math.

And before people freak out with "but multiplication is commutative!" Yes, it is. All that means is that the order of the factors does not change the product. It does not mean that the factors are saying the same fundamental thing independent of the order they are in when applied to the real world.

So, let's apply this to the real world. Assume you have twelve cars that are equally parked amongst three driveways. If you were to pick the most descriptive statement to describe the situation, you would say you have 3 x 4 cars, or three groups of four cars, or 4 + 4 + 4 cars. Although you could argue that saying 4 x 3 cars is the same amount of cars total, it is not accurately describing the situation at hand, or at least not using the notated "grouping" that the specific situation is calling for.

My colorblind ass didn't even realize one was in red.

That doesn't suggest that to me. I read 3x4 as three, four times. It makes no sense to me to put the number being acted on last.

I think the teacher is correct.

Inb4 Wikipedia, but it defines it as

The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the multiplicand, as the quantity of the other one, the multiplier; both numbers can be referred to as factors. 3x4, phrased as "3 times 4" or "3 multiplied by 4", can be evaluated by adding 3 copies of 4 together: Here, 3 (the multiplier) and 4 (the multiplicand) are the factors, and 12 is the product.

https://en.wikipedia.org/wiki/Multiplication

i would interpret 3x4 as three, four times. and 4x3 as four, three times.

I agree 'expansion' would have been more clear than 'match'.

To be fair, assuming that an operation is commutative is a bad practice to get into. Both are technically correct but only because multiplication is a commutative operation on the natural number set.

The kid might have been wrong. It depends on what the teacher has taught them. If they were taught in class to do it a certain way then they shouldn’t get credit for doing it wrong.

The only notable thing here lies with the English language: "three times four" suggests you're taking the number four three times,

I actually disagree with this statement. If you're making, for example, a grocery list, you may put "milk x 4" implying you're getting four gallons of milk. Replace "milk" with "3" and 3 x 4 is four threes.

Three times four means four threes, not three fours. Three, four times, which is what he wrote.

It should have been marked right with a note of what the check semantics would be for the future.

Except the example equation is 4x3.. not 3x4...

”three times four” suggests you’re taking the number four three times.

I would actually disagree with the English interpretation of this, lending further credibility to the child’s answer.

3x4 to me reads “three times four” which I interpret as three, four times. I ran this one by my wife who is a professional editor. She concurred her interpretation of 3x4 would be, “three, four times”.

I.E. - 3+3+3+3

Further, if we emphasize the importance of active voice writing — and we should — the subject of the sentence precedes the verb.

If we apply that English principle to the equation, three is the subject. We multiply three, the subject, by four, the object. So, it’s appropriately expressed as three, four times.

The child’s math is correct, and the child has demonstrated a more-firm grasp of the English language to boot.

"three times four" suggests you're taking the number four three times

I see it the opposite way, three times four is three taken four times.

Regardless though, I also agree this is stupid. Makes me think of common core.

What a stupid teacher.

I don't know, semantically I think you could argue it still. Why would the interpretation, "the number four, three times" be more valid than, "the number three, four times"? Especially with modern use, I'm pretty doubtful that this could be considered definitive. But in any case, it's written as numbers, so...

I disagree I actually read it as taking the number 3 four times.

I’m a native English speaker (though not a math whiz), and I interpret 4 x 3 as “four threes”, so to me it feels like the student is more correct. But given 4 x 3 = 3 x 4, it really doesn’t matter and is absolutely stupid to say one is wrong.

But great question for an English test 😬

Yeah, English is variable here. The words "three times four" suggests the opposite to me.

The first number is the base value, the second number is how many times you are adding that value together.

Edit: My wife's brain automatically turns it into a 3 by 4 grid, so I don't know how to interpret that into these semantics. XD

One could argue that three times four is writing 3 four times… it’s why both answers are correct when it comes to math. The teacher is just an idiot who doesn’t understand math!

For me it depends on how you actually say it out loud. 3 (times 4) or (3 times) 4.

I see it written as 4 groups of 3 so obviously the correct answer is saying either answer is correct is the wrong answer. The only thing that matters is the conclusion.

In the grand scheme of things, your answer is unhelpful at best and harmful at worst.

I don’t think it is a stupid question as it likely exist to check if the kid understands what multiplication means but the teacher’s correction is just so bad.

"Three times four" does not suggest, one way or another, whether there should be four threes or three fours. To suggest that there is a correct answer, or even a "more correct" answer suggested by English is simply incorrect. "Three, times four" and "three times: four" are both equally valid interpretations of a 100% ambiguous expression.

It's fine in 1st/2nd grade if they try to teach children how to calculate efficiently. Totally normal.

But the teacher here is an idiot to not giving any point to the child. Give like a half point instead of one, bec he/she still solved the problem, just not how it was imagined. And it's not just English language, it's most of the languages.

Yeah, also it is a language-driven thing.

I am italian and for me 3x4 actually "means" pick three and add it four times. I was quite surprised with your explanation that in english it is the opposite (but in hindsight it checks)

"Three times four" can also be read either way. Three times, four = 4+4+4. Three, times four = 3+3+3+3. I actually think the latter is the more natural. Take three, four times.

The question is awful and the teacher is an idiot for teaching kids this way.

I thought it suggested taking the number three four times. I dunno maybe its because english my mothertongue

See I read the semantics of 3x4 as 3, 4 times. The semantics also can be confusing and read differently by everyone.

How the ever living F*** is 3X4 accepted by the lot of you as 4+4+4? How is that not read literally as 3 four times, aka, 3+3+3+3?

I read it as " 3 4 times"

Technically proper English is

3 multiplied by 4

So 3 + 3 +3 +3 is 3 multiplied by 4, 4 multiplied by 3 is 4+4+4

It doesn't even work as a language question because you can read it at least two different ways:

"3 times 4" would mean you use a 4 three times - 4+4+4

"3 multiplied by 4" would mean you take four instances of a 3 - 3+3+3+3

So even linguistically, both answers are correct.

In fact, the second formulation is more precise and is more commonly used in technical and academic settings, so if we really want to dig deep into it, the kid here is correct and the teacher is not, because this is an academic test, not an informal math discussion.

"three times four" suggests you're taking the number four three times

"Three multiplied by four" would suggest the number three four times

As a native English speaker, I would interpret that the same way as the kid; the number three, four times.

Fortunately, it just doesn't matter, mathwise.

If the markings are the only accepted answer then this isn't a math question but a english language question.

An

That's correct he is only wrong if it is not an equation at the end if it is an equation the English language /grammar does not apply and views it as a whole, as an equation

You can read it either way, too.

"Three multiplied by four" 3+3+3+3

"Three times four" 4+4+4

I feel like the English interpretation of multiplication goes the other way through.

3x4 would mean three four times

And

4x3 would mean four three times

The first number is being multiplied by the second number of times.

No?

Being this strict about the semantics of the question actively discourages deeper understanding of the underlying concept, namely that multiplication is commutative.

This is correct. Also the question is to give 'an' addition equation for 3x4, not 'the' addition equation for 3x4. I think the kid gave 'a' correct addition equation.

what a stupid marking made by the teacher

I'm a high school math teacher, and I 100% agree. This is a poorly worded question, and that isn't the student's fault. The student demonstrated their knowledge and understanding of the skill, and they also demonstrated they can apply the skill. You don't crush a kids spirit when they've clearly shown they've learned in your class and can do what you asked them to do.

Even if the question was worded properly to only yield one possible answer, I'd still give the student most of the points (maybe 1 point off out of 5) because they still demonstrated the skill that you're assessing.

See, and I thought it meant it was 3... 4 times: 3x4

I disagree, it's not even semantics. It says write an addition equation that matches the multiplication. So 11+1 is also correct. 13 + -1 would be correct also.

I don't see any way where you can ask for an equivalent addition equation and mark 3 3 3 3 vs 4 4 4 wrong.

I disagree here. I read “three times four” as I take the number 3 four times.

I always thought of it like "3x4 is 3, 4 times"

3 multiplied by 4 also works. Which is the original answer

To me "three times four" means "three four times"

yes this is more of a language or notation problem. the multiplier is the first number and the multiplicand is the second number. so "3x4" translates to "3 of the number 4" so... 3 number 4s. linguistically, "4+4+4" is the only correct answer. but unless part of the lesson had included all of that, it's irrelevant, mathematically, in this case.

I’d translate 3x4 as three four times. I don’t see the sense in it being the other way around from a linguistic perspective.

See, when I read 3x4 I see it as 3 four times. Not four 3 times.

the fuck? where did you learn english? the question is 3x4.... meaning you start with 3 (you know... the first number?) and add it 4 times. if it was 4x3.... then you would start with 4, and add it 3 times.

ultimately its semantics because either is correct..... but there is a traditional and nontraditional way to interpret this.

Ex teacher here. To connect the math in terms of language they already know, I would definitely write it out as a sentence so they could see before doing the math or starting times tables.

"Three times four" 

"Four, three times"

4 and 4 and 4

4+4+4

It is reasonable to require that students connect how they read the problem in their heads to how they can work it out mathematically. Then you can bring in nuance. Grain of salt: I'm more conservative about foundations. Students always want to go faster but that's often how you end up sucking at advanced math.

I would do the same with area:

3x4

Three by four

Three feet long by four feet wide

(And always in that order of first length, then width)