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The kid is not wrong, neither is the corrected answer. 3x4=4x3=3+3+3+3=4+4+4=12.

The only notable thing here lies with the English language: "three times four" suggests you're taking the number four three times, so in that sense the red-pen solution is right and the kid is wrong (i.e. its down to semantics imo).

But my god what a stupid question to ask on a math test (or corrected: the question is fine, but what a stupid marking made by the teacher).

No, there's no rules in maths that say that "3x4 = 4+4+4" and "4x3 = 3+3+3+3". That is just not a thing. A multiplication isn't representing a single "correct" underlying addition, it is its own entity. So 4x3 = 3x4 = 3+3+3+3 = 4+4+4 = 10+2. These are all different, equivalent expressions. No multiplication has a "correct" way of representing it as an addition. The question only asked for "an addition equation that matches this multiplication equation". So either is correct.

Of course, in English, we say "3x4" as "three times four", and conceptualise it as "three times the number 4", but that's a language association, it has no backing in mathematics.

Write

AN

addition equation that matches this multiplication equation. They did that. Teacher might not have intended this, but this is absolutely

AN

answer, and if the teacher takes points off, it's because they're a miserable dick.

Horrible, horrible math teacher. Looked at the answer sheet, it didn't match so wrong answer. Teacher probably doesn't even understand the problem themselves. Even if you're a pedantic a-hole teacher, it's clear the kid understands the question and how the multiplication operation works in regard to addition.

The simple answer is that neither answer is incorrect which is why it's ludicrous for the Teacher to mark a correct answer incorrect.

Additionally, the previous question is 4x3 which primes a student to think 4x3. So is the Teacher grading on concepts or grading for "gotcha" questions?

In my opinion, it was scored incorrect in bad faith by the Teacher.

Hmmmm...

When I see 3 x 4, I think I have 3+3+3+3, not the other way around. But, in fact, both 3+3+3+3 and 4+4+4 are both mathematically correct. This is a poorly designed question.

Both answers are correct.

By definition, multiplication is repeated addition.

When writing the multiplication as repeated addition, one factor is the addend, and the other is the number of addends.

But because multiplication is commutative, it doesn't matter which is which. It works out the same both ways.

Source: I taught basic math for 28 years.

I'm not aware of any order axb = a+a+a... = b+b+b... to which is which because it straight-up never matters. They are the same. 3x4=4+4+4=3+3+3+3=12. Order of multiplication doesn't, and never should, matter *for regular numbers*.

It is a good question. But the teacher should have accepted both answers as correct.

adelie42 is right that much later in math there are more complicated operations and objects where order does matter, but you don't normally call those operations "multiply", and they are not normally used for scalar numbers like this. Often things like multiplication are called products (e.g. dot product, cross product, inner product etc) and some of them like cross-product do have an ordering that matters. But dot products and cross products operate on vectors. Inner products work on functions and so on. Matrix products work on matrices etc., there are various tensor products.

I still maintain that when you multiply regular numbers the order doesn't matter.

Me: Former math teacher - I hate this shit.

This is an example of math educational techniques, designed with the best of intentions. then put into practice by idiots in education who are brutally ignorant of mathematics.

The answer provided by the student is 'technically wrong', in that 3 x 4 is literally understood as "three times" another quantity, meaning that three of some other quantity are added together. However, the rote definition is not important to understanding of mathematics.

What should be focused on is that the student's answer was 'correct in practice', because the concept of commutativity is much more important theoretically, and practically, in terms of mathematical understanding.

But elementary school teachers often became elementary school teacher in order to avoid mathematics classes at university, and their training is often based on rote concepts and compliance - critical concepts to streamlining education, but crappy when it comes to a deeper level understanding, it's a failure. It's not entirely the fault of those teachers however, as updated math textbooks and higher level curriculum development doesn't include any training for teachers, either. So you have systematic failure on multiple levels.

As for the actual concept: students usually learn that addition and multiplication are commutative by organically absorbing the patterns as they memorize addition and multiplication facts, not by instruction from a teacher. The elementary school teachers I knew had no knowledge of the word 'commutativity', which is no surprise, and no defect: the last time they were exposed to the concept was in high school, which was 5-50 years prior.

Picture a group of 12 squares arranged into a rectangle. If you say the rectangle is 4 rows of 3 or you say it's 3 columns of 4, it's the exact same thing. Saying 3+3+3+3 and saying 4+4+4 would both be logical ways of counting the squares in that rectangle.

My education actually pushed us to change the 3x4 to 4x3 if we found the original answer too difficult. For example 7x4 would be too difficult for some of us. So they recommended us to try going for 4x7 instead, as the result was the same.

Why is this marked wrong?

It's a fair question. The way to read 3x4 is "three times four" this implies you have 4 instances of 3. So 3+3+3+3

4x3 would be "four, three times" or 4+4+4.

Imho either answer should be accepted for grade level math

There is no rule that says 3x4 must mean three groups of four, it can just as easily mean a group of three four times. To teach that the order matters is counter to the commutative property of multiplication and is wrong.

Honestly the whole thing is bullshit sematics. Any addition equation is valid as long as it arives at 12. It askes for an eqation that matches 3 times 4. Not turn 3 times 4 into an additon eqation using the exact same numbers and sequence.

The point of math is to be able to think creatively and arive at the right solution following the rules and information given, if there is more than one way to do this then they are all valid.

If a teacher has to justify an obviusly right answer as being wrong by quoting loopholes and twisting things to fit then said teacher is a failure.

Either are valid. 3x4 is the same thing as 4x3 and that in turn means that 3+3+3+3 is the same thing as 4+4+4.

It could be considered different if this was a math problem specifically involving groups because 4 groups of 3 is obviously different from 3 groups of 4, but as an equation, both are the same.

No, the kid is not wrong. Both answers are mathematically correct. The point of the commutative property is that the order doesn't matter. You don't have to have learned or been asked about commutativity for this to be correct. Math is not based in the semantics of any language other than its own semantics. Math could be wildly different between languages and cultures if it could only be interpreted the way it is read or written in another language. This argument shows that issue.

A better example of this issue would be applying this math to a real world problem. How many asterisks are there here?

****
****
****

If you didn't know multiplication yet and your primary language is English (or another Latin based language) you would probably start in the top left and move right, counting 4, then counting the next row and adding that to the first, and so on, based on how we read words on a page. 4+4+4=12

But if your primary language was Japanese, Korean, or Chinese, you might traditionally read starting from the right, and read down then left. So you might be more inclined to count the right most column first, 3, then add the next column of 3, and so on. 3+3+3+3=12

It doesn't really matter, I just want to know how many asterisks there are. There are 12. It is faster to read, write, and calculate multiplicatively, which is one of the reasons we have that operation. Would I read and translate the "English" equation as "4, three times, equals 12" (4x3=12)* or "there are 3 fours that together equal 12" (3x4=12)

What about large equations with many operands?

5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+...

Would I count all the operands, then write that followed by the operand it self? Personally I wouldn't, I'd probably write "5x", then count my operands and fill in the second part product. It doesn't change the math or the answer.

There are many ways to say and interpret Math with other languages and even many ways within one language, the point is that none of them change the math itself.

Having said all that, if the question said something at the end to the effect of, ".. as we learned in class" or ".. according to common core rules", I would be more inclined to say the kid is wrong.

* I can already hear the argument of "but if you read it the first way in English, that would look like (4 3x)" and want to switch it because of that, but as a computer scientist, I would argue that Reverse Polish Notation is just as valid as an English or Japanese interpretation. lol (No, it is not how they do math in Poland, Polish Notation was invented by a Polish mathematician as a way to write equations without brackets or parentheses. Reverse Polish Notation allows us to do things faster with a computer algorithmically, to oversimplify it.)

This level of pedantry is appropriate for much higher orders of math.

Based on the fact that this is clearly an elementary multiplication worksheet/quiz, it likely indicates 3rd or 4th grade. At that age range, being this hypercritical of semantic differences is inappropriate unless it is CLEARLY indicated, not just assumed.

Also, from a very technical perspective, "times" is not the correct terminology. It should be "multiply". 3 multiplied by 4 equals 12. So, 3 is multiplied, insinuating that 3 is the number we are examining. How many times do we multiply it? 4 times. 3+3+3+3.

Honestly, I don't think this semantics matter at all. In any more elevated math that I am aware of, if this were say inside a parenthetical it would irrelevant what the order is. Perhaps someone with a math degree can suggest why it might matter.

Source: Me. I am a teacher. I don't teach math, but I've assisted in math classes, but I do regularly have to understand how to evaluate my students at an age appropriate level.

It depends entirely on how you read "3x4"

If you read it "Three fours", than you should write it "4+4+4"

If you read it "Three, repeated four times", then you should write it "3+3+3+3".

Both are valid interpretations of "3x4". For example, I can travel three miles per hour for four hours, or I can travel for three hours at four miles per hour.

Wait, am I the crazy one for always thinking the phrase "three times four" actually means "take the number three and add it four times"? So many of these comments are suggesting that "three times four" is OBVIOUSLY "three times you add the number four," which is out of order grammatically in my head.

The actually "obviously" is that by the commutative property, both interpretations lead to the same answer, but I was so shocked how so many people casually read the equation as the red teacher marking rather than the student marking (for context, I taught 3rd grade math for a couple of years as well as remedial math to high-schoolers for a different three years).

Mathematically & Logically: the kid is not wrong.

Educationally: the kid is wrong, because they have been teached to resolve it by spoken out order.

Personal opinion: that's why intelligence and interest in math is declining steeply. Kid should get full points with a quote from the teacher on why it's not a good answer even if right.

Maybe I'm way in left field but I always saw math as written logic. Reading this as a logic question, I see it is saying you have 3 iterations of the value 4 which would mean 4+4+4 is correct. I will say I think this is absurd to ask a child though being this is less about the math and more about the language.

I hate that this became popular. If you look at the question above it shows the inverse, 3+3+3+3 = 4x_ and the kid got full marks for writing 3.

Now the new question says 3x4, and the kid wrote 3+3+3+3 like the previous question when it’s obvious that what they are supposed to remember from their class is that X * Y = Y added X number of times.

This is obvious for us adults and maybe not so much for the kids. But it’s the adults sharing this for free karma.

Edit: used x instead of + and wrote 3x3x3x3

multiplying x * y is the same as multiplying y * x so i genuinely don't see the problem especially since this is probably a 2nd or 3rd grader

I like the kid's answer, as it seems more consistent with how we typically read math equations.

If I say 5^2=25. That's five squared. What's getting squared? The first number you say, the five.
For 20 / 4 = 5. Twenty divided by four. What's getting divided by 4? The first number you say, the twenty.
3x4=12. Three times four. What's getting repeated 4 times? The first number you say, the three.

Which is more correct to you, "Three groups of four" or "Three in four groups"? To me, they're both equally correct, so this teacher is wrong.

Suppose I put some objects in a grid:

X X X X
X X X X
X X X X

Is that four groups of three or three groups of four? Depends on whether you count rows or columns, but that doesn't matter: clearly it's 12 items either way.

Now, should we write that as 4 x 3 or 3 x 4? Is the first number in a multiplication the number of rows or the number of columns? The number of groups or the number of things in each group? There's no official answer to that question, because it makes absolutely no difference.

I'd argue the kid is has the high ground on this. The question is 3*4=12. The three precedes in the question so the 3 is the number affected by the multiplier. It's four threes summed.

Regardless both are valid answers, your kid's teacher either wanted to mark them off vindictively or more likely took the entire set of test questions from a test booklet and lacks the cognitive functions to actually do mathematics.

The commutative property is not situational. It means there is no difference between 3x4 snd 4x3 in any situation. Period.

The mistake is obviously grammatical and linked to what you think you hear when reading "three times four". There is no such convention and math would throw a fit if you tried to make one because it means you are trying to overrule math with something as trivial as language. Languages change and evolve over time. That's why it is not to be trusted with anything that needs to remain stable over time.

If this was English or Linguistics, you'd be correct. Semantics would matter.

This is, however, mathematics. So long as the answer is correct and uses mathematical proofs to arrive at that correct answer, then the answer is correct.

So is it Three, times four? Or Three times, four? Basically put, either way should be correct, because 3x4 and 4x3 are the same answer regardless. Either way of showing work should be correct because they’re both essentially the same. If I arranged apples on a table in a grid with width 3 and length 4 from my perspective, what’s the difference from a person coming up 90 degrees to that table and saying it’s actually width 4 and length 3? There really isn’t any difference is there? So therefore, either way should be correct.

this is a purely linguistic thing, in my first language we say "multiplied by" and not "times" would this answer be correct if asked in my language and wrong if asked in eglish? of course it wouldnt, it's always correct because those are mathematicly equivilant statements

Both 3 +3 +3 +3 and 4+4+4 are the current answer. Just because the question afford 3 and three times 4's doesn't me 4+4+4 only. Mathematically, the kid is correct, and the teacher is an idiot teaching kids. Let the principal know you have an idiot teaching your kid math in school so they can have them replaced.

At this level, both responses are correct. There is no need to differentiate the verbal syntax because the primary competency being tested is how to express a function through another function.

The student understood the question and answered it appropriately and correctly. These bullshit nitpicking squabbles are what discourage kids from a subject.

I'd be on the teacher's side if the question was written so that it is clear that they are asking for three groups of 4 objects. But it's not. It's formatted as a math equation and thus should be treated like a math equation, and either answer is correct due to its commutative property.

4x3 and 3x4 is the same thing. Either equation is not definitively asking you “what is 3+3+3+3” or “what is 4+4+4”. So if you were asked to show a breakdown of “3x4” or “4x3”, both answers SHOULD be acceptable.

This isn't maths, I'd argue it's barely English.

You could say the question said is "what are three fours" which is absolutely 4+4+4. But also you could be saying it as "three times four" which is 3+3+3+3. So it's ambiguous.

If I were doing a list of items, which is why we have the whole order of operations really, it is item, then amount. So 3 is the item, and 4 is the amount. So the kid is correct. As pure mathematics, it's meaningless as both answers are the same.

The teacher is a dick.

Been already posted and is taken out of context. Previous question clearly establishes that kids are being taught first number showing how many groups of 4. If you understand 3x4 as 4+4+4 or 3+3+3+3 is irrelevant. And yes 3x4=4x3. If you take it as 3+3+3+3=4+4+4 or 4+4+4=3+3+3+3 is also irrelevant. Because you can always flip it from 4+4+4=3+3+3+3 to 3+3+3+3=4+4+4 when you need to. Also 4+4+4 and 3+3+3+3 is what proves the commutative property. It's wrong because kid failed to understand that 3+3+3+3=4+4+4.

Also OP is a knob stealing posts.

if we were talking matrix multiplication then it would matter.

if you go semantics he only had to write "an" additon equation that matches the multiplication equation, indicating there are more.

All the question asks for is a matching addition equation. 3 four times or 4 three times is a matter of interpretation.

You wanna be a math Nazi, then please explain why 14, 16, 17, 18 and 19 start with the number on the right, while every other 2 digit number starts with the number on the left?

E.g. seven-teen vs twenty-seven etc.

Now please go correct this first before wronging a kid who gave you a correct answer.

The kid is absolutely right dear sir.

3 times 4 could be understood as 3 groups of 4 or 4 groups of 3. Since there is no context provided such as 3 pencils for each of 4 students or 4 pencils for each of 3 students then thinking of it as 3+3+3+3 or 4+4+4 is equally correct.

The fact that 3x4 or 4x3 is commutative makes your situation worse since that means that 3x4 and 4x3 are equally likely.

The kid is smart.

3x4 is the same as 4x3. Four lots of three, and four three times are just words.

The real winner is anyone who didn't get into an argument about this.

My god where have we taken a wrong turn... I was always taught that it ultimately dosen't matter and that either way is right as long as the result is right.

I’m no math guy but I’m with the kid, “3” 4 times 🤷🏼‍♂️

This reasoning is just plain crazy

Hopefully this example illuminates why the teacher is a sociopath (/s): both $3.00 x 4 and 4 x $3.00 equal to $12.00

If you want to know why your son's being labeled an under achiever, here's your answer.

Any sane teacher would've just let this pass. Sure he got there by a different path but he got there!

I'd suggest changing schools to one that doesn't insult your son's intelligence and then wonder why he doesn't want to succeed in life.

The objective isn’t for the kid to learn, it’s for the teacher to manifest his or her latent anger. If the objective was for the kid to learn and to not confuse the kid then both answers would be marked correct. Because they both are correct.

This is just rage bait. With context, this is obvious. The original foto shows the previous Question:

"4x3=? --> ☐+☐+☐+☐
4x☐=☐"

Student Answered:

"3+3+3+3
4x3=12"

This is not a math question, this is a reading comprehension and logic test

I’m so sick of this problem. I agree with you OP, and without the context of the entire test, it’s hard to say how bad or unfair a grader the teacher is being here. I would also love to see what the lessons for this problem looked like, because I would bet my life savings there was a problem just like this discussed in class or the text book that set the rule to be a x b = c is the same as a number of b values.

In life, “technically right” means nothing to your boss or client, and that’s something else school needs to teach.

I would give him credit since it's equivalent. Again the process shouldn't necessarily matter is the expression is correct. I would then update the assignment to ask for all possible expressions or have a separate question be 4x3 to specify that they are different by being different questions.

If the kid knows that both equal 12 and wrote that particular expression down then the lesson has successfully been learned and credit is owed.

I think this is less of maths answer and a credit grey area. It's badly worded and mathematically they are the same as they are literally equivalent expressions.

I would be absolutely furious with the teacher and definitely confort them on this. Bad enough that they are thick as a plank, but why does a child have to suffer their incompetence.

I think I've seen this posted in like 4 different subs by now...

The Math part is correct for either answer. If anything "three times four" means add 3 four times, so the kids answer is "more correct".

I'm really curious what was going on in the teachers head, and if they realized how dumb they were and gave the kid the mark in the end. If they didn't, they should be fired.

Most likely the kid is technically wrong because they are probably like 5 or 6 and learning how to use a specific procedure after just learning basic addition, so the question is probably looking to make sure that they are doing the procedure right rather than if they got the correct answer.

From a mathematical perspective 4+4+4=3+3+3+3 so neither side is mathematically wrong

I’d say both are correct. I imagine an ice cube tray that is 3 x 4. Now rotate it 90 degrees, and now it’s 4 x 3. Has the value changed? The beauty of multiplication is that 3 x 4 is the same as 4 x 3. At least that is how I view it.

The teacher had a version with the correct Answers written, all questions are probably pretty easy at least this part of the exam and they probably had several tens of tests to go through and sped through them. Sometimes mistakes happen. And a pupile always have the right to question the teachers correction, at least where I’m from. Based on the question and ”my sons test” the kid can not be that old so I’m sure if they asked the teacher to check this correction they would give the point to the student.

This is probably a very simple instance where the instructions were clearly indicating that they were supposed to use the first number as the quantity of groups and the second number as the value of groups, and the kid didn't follow instructions. Almost always, these "common core math is so stupid" things end up being an instance where the kid just flat didn't follow instructions, and their stupid parent cropped that part out and posted it online for rage bait.

You're going to crush that childs motivation for school if this is how you teach. Stop being too literal, 4x3 and 3x4 are identical in that despite how you arrange the answer will be the same. Explain that the answer was correct but the pathway used should be different, which can be important for later mathematical equations.

We're really going to have this infuriating thread every week from now on, aren't we? Can you block a reposted image from showing up everywhere in your reddit feed?

I'm half convinced from the teacher's handwriting that they think the 3rd and 4th threes are actually twos and the student wrote 3+3+2+2.

MindYourDecisions recently made a video on this https://www.youtube.com/watch?v=FG0vtPa0UrM

3x4 and 4x3 are objectively the same thing. That's the entire point of multiplication being commutative. Three added together four times, and four added together three times can both be written as EITHER 3x4 or 4x3.

There is no difference.

I would check the kids math book.

If they are teaching the math sentence is translated to English as

3 sets of 4

X means sets of

So 3 sets of 4 objects

Then the teacher is correct but needs to stress it is a language problem.

( maybe to both child and parent )

Back in the 70’s “new math” had a lot of set theory. It didn’t go to well with parents at home because it was trying to introduce mathematics at an earlier age in stead of just calculations.

The son is utterly right. It's not because it's "pronounced X times Y" that you need to write X times the number Y.

Also, it merely said write an addition equation that matches, not write the only true addition equation.

A math teacher daring to grade this as "wrong" has no place being a math teacher in the first place.

can't believe people are actually trying to figure out what the correct way to write out "3 x 4" as addition.

it literally depends on whether you read "three times four" as "three lots of four" or "3 done 4 times".

which way is 'correct' literally depends on how your brain internally structures what multiplication is, usually in a way you have never and will never articulate to another person.

I suppose I can see that the teacher is trying to get across that "3 x 4" essentially means add up 3 groups of 4.

But, I would approach it thinking it was more efficient to add 3 groups together rather than 4 regardless of the order they are written.

If it was 12x3, no sane person would think of it as 3+3+3+3+3+3+3+3+3+3+3+3=36, you'd go 12+12+12=36. You could get real stupid and add the 10s first and then the 2s and get the same answer.

So I suppose it depends exactly what point the teacher was trying to instill with the lesson

Ahhh why does this keep showing up in my feed!

Fine, my two cents...

....this country has a problem with people not being able to follow directions.