If it had been two more times, I would have said 6.
But two times more, makes me think first of multiplication, so I’d say 8, but at the same time accepting that there is some ambiguity.
Upthread someone said it would be readily understood in everyday conversation as 6. I’d dispute that. I think two people listening to that statement might come to a different answer and not realize that there was another way of parsing the sentence.
I would say that the correct answer is 12 (two times four, more than four), but that it would be easily confused for 8 (more than four, specifically two times four). 6 is just wrong.
And no, the teacher is not always right. This has nothing to do with Common Core, and has always been the case. I’ve certainly had a few times when a student has pointed out my mistakes to me. If that happens, I score both my answer and the correct answer as correct.
I think if the language describing Mary’s run was different, like:
“Mary ran around the track four times, John ran two times more than Mary.”
or alternatively:
“Mary ran four laps, John ran two laps more than Mary.”
The repetition of “times” or “lap” would make the meaning much less ambiguously “6”. The only ambiguity is due to the fact that “times” can also mean multiplication as well as “instance of something happening”.
Since the OP says the original question “went something like” what we are given, rather than “exactly was”, I can’t say whether the exact original wording was better than presented or not.
Yes…
I think 12. If John had run 5% more than Mary, he would have run 1.05 meters for every meter that Mary ran. If he ran 100% more, he would have run twice hers.
But that is because I take “times” to mean multiplication. In the context of a school math word problem, I think that meaning is to be preferred. If instead “times” meant “events” as in “how many times did they run around the track”, the answer would be 6.
This word problem is both ambiguously worded, and based on a concept of “how much more” that is often confused in common speech.
But teacher, I did use addition. Multiplication is just repeated addition so I added it three (for 12 or two for 8) times.
And if you understand that, then you’ve understood a good concept in math. It may or may not be the concept we’ve been working on in class.
As your reward, you get to write the next math quiz for the class. Any ambiguous questions will come off your score. Go!
This.
That’s not how I’m parsing it. It’s made up of two segments, each with optional words:
(two times/two times more than) (Mary ran/what Mary ran)
two times = two times more than
Mary ran = what Mary ran
I actually said it would be readily understood by me to mean six (4+2). This being the SDMB, I fully expected that if I just said “readily understood” then someone would claim that either they or some hypothetical person might have understood it differently. But I would not personally take an everyday conversational claim that someone had performed an action “two times more” than someone else to mean anything other than +2.
The question is ambiguous.
“Mary ran four laps, John ran two times more than Mary. How many laps did John Run?”
If two times more means 2x then John ran 8 laps. But if it’s meant that John ran two additional laps more than she did, then it’s 6. I have no idea how 12 might be arrived at.
This is how I’d interpret it. Word order matters, and “[number] times…” suggests multiplication (particularly in a class dealing with basic arithmetic). Regardless of how you interpret it, it’s awkwardly worded.
since “times” is term used in math the question is ambiguous.
I don’t understand why the teacher doesn’t accept answers that fall with the ambiguity of the question.
Agreed. We can’t weigh in on how the question should be interpreted without knowing its precise wording.
And I agree with those who said that 12 is a legitimate answer, at least the way the OP worded it. If John had run 25% more than Mary, that would have been five laps (4 + (4*0.25)).
Mary went out on Monday and ran four laps around the track. John went out on Tuesday, Wednesday, and Thursday and ran one lap around the track on each day.
“Mary ran four laps, John ran two times more than Mary. How many laps did John Run?”
The answer is three.
Thusly:
Yeah, afterwards I figured it out.
I voted for ambiguous. I understand how both 6 (4+2) and 8 (42) would be arrived at, but like many of the responses, I think the most direct interpretation is actually 12 (4+24), even though I also think that’s the least likely intended interpretation. IMO, when it comes to word problems, because they can sometimes be ambiguous, as long as they can make a reasonable case for their interpretation and can get the correct answer for that interpretation, then it ought to be marked correctly.
The only exception I’d make to that is if there’s clearly a pattern based on the lesson, all the problems fit that pattern, and even if an alternate interpretation is reasonable, it leads to a clear inconsistency, then I think I’d just say the kid should get a second chance to do the problem. Even in that, I think it’s hard to know what the right pattern might be. Kids might be doing word problems based on simple addition and not have covered multiplication yet, at which point the teacher’s interpretation is consistent. If the kids have covered simple multiplication or multiplication-like concepts, then the kid’s interpretation might make more sense. Besides, really, 2*4 is harder than 2+4, so why not just give the kid the benefit of the doubt and avoid the word “times”, or similar words that might be be construed to mean an unintended operation, in future word problems.
Having written and reviewed more than my fair share of technical publications, I hate ambiguous language like that. When reasonable people disagree about the meaning of what someone has written, then that person has done a poor job of expressing himself.
“X is 2 times more than Y” is ambiguous. That said, most non-technical folks who don’t think very hard about these things tend to interpret “X is 2 times more than Y” to mean the same thing as “X is twice as much as Y.”
I’m with the child and the mother. It is this word (bolded) that removes 6 from the possible answers.
John ran two times more than Mary