The advice column in yesterday’s paper had a question from a woman who wrote to complain about her child’s teacher. The question ran something like this: “Mary ran four laps, John ran two times more than Mary. How many laps did John Run?” The teacher claimed that the correct answer was 6, but the child (and the mother) insisted that the correct answer was 8. The columnist agreed with the mother and said the only thing to do is to use the incident as an illustration that the teacher is not always right. What think you, O Dopers? Poll to follow if I can make it work
You left out “12.” “Two times more than four” is four plus twice four, or 12.
It could be worse. The same careless kind of speech uses “Five times less” to mean “one fifth.” Damned lazy construction, and ambiguous as blazes.
I voted 6. I don’t see a way of interpreting that question to get 8. Even if you assume the times means multiplication, you are then saying you are multiplying by “more than Mary”. What does that mean?
Likewise if the question said, John ran two times what Mary ran, that couldn’t be interpreted in a way other than the times meaning multiplication.
To me they both mean the same thing … Twice what Mary ran … Two times what Mary ran … Two times more than Mary ran … All the same thing.
How can ‘what Mary ran’ and ‘more than Mary ran’ mean the same thing?
If I was searching for some shred of ambiguity, I guess I could maybe see the 12 interpretation.
It’s a badly worded question. In ordinary speech then an exchange like this:
MARY: I ran around the track four times!
JOHN: Ha, I ran around the track two times more than you did!
would readily be understood by me to mean that John ran two more laps than Mary had, or six (4+2) laps.
However, in the context of a math problem it seems understandable that a child would take “two times” to mean “multiply by two”, especially if this is the only place in the problem where the word “times” appears. If the problem said “Mary ran four times, John ran two times more than Mary” or “Mary ran four laps, John ran two laps more than Mary” then it would be more obvious that this was meant to be an addition problem and not a multiplication problem.
Ambiguous question, and another vote for 12. Darned showoff kids…
The statement is way, way too far meaningless.
“Two more times around the tract”
“Two times as many”
And: the “12” answer is as logical as the “6”.
If I were the teacher, I’d accept 6, 8 or 12, as long as the pupil could defend their answer. Assuming, of course, that there was no instruction on the top of the test or given orally that said something like, “Use addition to solve the following.”
I find that in most of the “Common Core Math” (which isn’t Common Core) that gets people on the internet in an uproar has this sort of context to it, but not in the report.
The question is ambiguous, and that’s what I voted, although that “Colorless green” option was very attractive.
What we (or, more specifically, the parent) should be asking is: Who wrote that question?
“Half again” is the one that befuddles me. Six is half again as many as four? I think?
It’s very poorly worded - but in this context my first instinct would be to interpret “two times more” to mean “two times as many”.
“Two times More than Mary ran” means exactly the same thing as “two times more than what Mary ran.”
It’s just like how “I couldn’t care less” and “I could care less” mean the same thing.
Natural language isn’t scientific notation.
Yep. That one, at least, is relatively straightforward. Half of what you started with, added to what you started with.
Yet another reason the wording is off:
Mary ran 4 laps, all at once. John ran some unspecified number of laps, then took a rest, and ran some more laps. Wait, he ran two times more than Mary – so he must have taken a second rest, and run another set of laps.
Me, I’d try to second-guess the fellow who wrote the question, and figure that he probably meant that John ran two more laps than Mary. But it’s awkward, non-parallel sentence construction, and ambiguous.
I read the question to mean that John ran two more laps around the track than Mary ran.
I would think if they wanted the answer to be 8, they would have said, “John ran twice as many laps as Mary.”
I voted that it was an ambiguous question because it was poorly worded.
To me, “two times more” most clearly means “twice as much” in this context. But I can see how in a different context it could mean “an additional two”. But the clearer way to say that would be to drop the “times”.
“Mary ran four laps, John ran two times more than Mary.” - John ran four multiplied by two.
“Mary ran four laps, John ran two more than Mary.” - John ran four plus two.
Now if you had worded it “Mary ran four times around the track, John ran two times more than Mary.” then I would feel you’ve changed the context enough that “two times more” most clearly means “an additional two”.
My HS Physics teacher was a cool guy.
We had had the discussion of how incandescent vs florescent lights.
He had a Q: Which type uses a filament?
He wanted: Incandescent
Correct answer: Both.
The fluorescent tube has small filaments across the ends - it works by running an arc between the two.
He accepted both.
That question at least had a correct answer.
The OP lacks even that.