This appears to be taken out of context to stir up outrage. I'd be willing to bet that if we saw the rest of the page, the lesson here isn't "how to subtract" but "how to estimate"--simplify the math by rounding to numbers easier to work with, then see if the resulting answer is in the ballpark. 75 is a correct answer, just not to the question asked.
Sevesteen, a perfectly adequate way of determining whether an answer is reasonable is to do the math. If you wanted a demonstrated method without doing the actual subtraction, the question should have said so. The estimate also required doing subtraction, just of estimates of the actual numbers rather than the actual numbers.
If you want to test estimation (i.e, rounding) there are better ways to pose the question. The teacher was an imbecile.
Ruralcounsel, this is from a commercial worksheet on mental math, estimation and rounding. Based on the Googled copy I found, this isn't the best or clearest question on the page, but in context and at least giving the benefit of the doubt on the instructions given to the student the teacher's comments make sense.
Well, let's "estimate" then. 103 is pretty close to 100, only 3 away, in fact, so let's start by using 100 by rounding down. 28 is pretty close to 30, only 2 away, so let's round up to 30. Remove 30 from 100 and you're left (or, in today's more common vernacular of the illiterate, "your") with 70. Remember that initial difference of 3 between 103 and 100? Do you recall that gap of 2 between 28 and 30? Any idea what 2 and 3 together make? Yep, it's "5." Been that way for a while now, contrary to what "New Math" and "Common Core" advocate. What happens to "70" if you put that "5" with it? Golly gee, shazam, it's "75."
So, my "estimate" of the difference between 103 and 28 is "75." That it also happens to be the exact difference must be some sort of accidental dumb coincidence. Or, perhaps, what "generic technical staff" like engineers, designers, testers, service techs, etc. do damn near every minute of every day, and frequently with much, much larger numbers.
If the object of this test was to verify (and potentially improve) estimating skills it failed miserably in the language used to state the problem requiring solution (See: "you're" and "your," referenced above).
Nosmo, if I were the teacher and you showed your work the same way I'd give full credit...whether you stopped when you got to 70, or continued to 75. You used the tools that were requested. Doing the math on paper (with paper methods) is essentially using a rifle in a pistol match then complaining you didn't get full credit for bulls-eyes.
...if I were the teacher and you showed your work the same way I'd give full credit.
Were that the case, Sevesteen, I'd petition my parental units to allow me to change schools because this one only knows bullshit.
"Is 75 pages a reasonable answer for how many more pages Carole read on Tuesday than on Monday"
Effing A it's a "reasonable answer" because it's correct. If the question were "make a quick estimate of how many more pages Carole read on Tuesday than on Monday" then your approach - and the idiot teacher's - would be correct. BUT THAT IS NOT THE QUESTION THAT WAS ASKED. In fact, a "reasonable answer" could have been .75 with an exponent of 2 because that would also be a correct answer to the question that was asked. Or, 99,427,275 divided by 1,325,697 because that is also 75.
Then again, the way schools are going today, I'm surprised a "reasonable answer" wasn't "blue."
The issue here is language skills and communication ability, not math.
Sevesteen, Yes, I know what estimation is. Somewhere in my doctoral engineering program at MIT, I learned about estimation. In fact, I had a professor who claimed there were only four important numbers; zero, one, ten and infinity.
Estimation isn't what the question asked for. Nowhere in the question does the word "estimation" occur. The operative word is "reasonable."
You need to quit making excuses for ontological rigidness, denseness and stupidity on the part of the grader. Estimation only makes sense when a closed form solution is too difficult or time-consuming.
12 comments:
Common Core is an abomination.
I hope this is a joke.
This appears to be taken out of context to stir up outrage. I'd be willing to bet that if we saw the rest of the page, the lesson here isn't "how to subtract" but "how to estimate"--simplify the math by rounding to numbers easier to work with, then see if the resulting answer is in the ballpark. 75 is a correct answer, just not to the question asked.
Sevesteen, a perfectly adequate way of determining whether an answer is reasonable is to do the math. If you wanted a demonstrated method without doing the actual subtraction, the question should have said so. The estimate also required doing subtraction, just of estimates of the actual numbers rather than the actual numbers.
If you want to test estimation (i.e, rounding) there are better ways to pose the question. The teacher was an imbecile.
The answer was too correct!!
And that's elitist you know. Destroys equality!!
If only these teachers we're accountable to those who actually pay them.
Ruralcounsel, this is from a commercial worksheet on mental math, estimation and rounding. Based on the Googled copy I found, this isn't the best or clearest question on the page, but in context and at least giving the benefit of the doubt on the instructions given to the student the teacher's comments make sense.
For a more complete explanation:
...estimation is an important skill to learn. (Maybe not in this exact situation, but in general.) Suppose you’re buying groceries. You have four items in your cart that cost $1.99, $4.93, $6.03, and $5.14. If all you have is $20 in your wallet, is that enough to pay for the items? I think that’s a very realistic question. It would take you at least a little bit of time to add up those numbers individually and get an exact number. Would it answer your question? Absolutely. But you don’t need an exact answer.
The smarter thing to do would be to simply round the numbers. We should be saying to ourselves, “2 + 5 + 6 + 5 equals 18… throw in some tax… and I should still be under $20.”
Well, let's "estimate" then.
103 is pretty close to 100, only 3 away, in fact, so let's start by using 100 by rounding down.
28 is pretty close to 30, only 2 away, so let's round up to 30.
Remove 30 from 100 and you're left (or, in today's more common vernacular of the illiterate, "your") with 70.
Remember that initial difference of 3 between 103 and 100? Do you recall that gap of 2 between 28 and 30?
Any idea what 2 and 3 together make? Yep, it's "5." Been that way for a while now, contrary to what "New Math" and "Common Core" advocate.
What happens to "70" if you put that "5" with it? Golly gee, shazam, it's "75."
So, my "estimate" of the difference between 103 and 28 is "75." That it also happens to be the exact difference must be some sort of accidental dumb coincidence. Or, perhaps, what "generic technical staff" like engineers, designers, testers, service techs, etc. do damn near every minute of every day, and frequently with much, much larger numbers.
If the object of this test was to verify (and potentially improve) estimating skills it failed miserably in the language used to state the problem requiring solution (See: "you're" and "your," referenced above).
Nosmo, if I were the teacher and you showed your work the same way I'd give full credit...whether you stopped when you got to 70, or continued to 75. You used the tools that were requested. Doing the math on paper (with paper methods) is essentially using a rifle in a pistol match then complaining you didn't get full credit for bulls-eyes.
...if I were the teacher and you showed your work the same way I'd give full credit.
Were that the case, Sevesteen, I'd petition my parental units to allow me to change schools because this one only knows bullshit.
"Is 75 pages a reasonable answer for how many more pages Carole read on Tuesday than on Monday"
Effing A it's a "reasonable answer" because it's correct. If the question were "make a quick estimate of how many more pages Carole read on Tuesday than on Monday" then your approach - and the idiot teacher's - would be correct. BUT THAT IS NOT THE QUESTION THAT WAS ASKED. In fact, a "reasonable answer" could have been .75 with an exponent of 2 because that would also be a correct answer to the question that was asked. Or, 99,427,275 divided by 1,325,697 because that is also 75.
Then again, the way schools are going today, I'm surprised a "reasonable answer" wasn't "blue."
The issue here is language skills and communication ability, not math.
Yep, we're hosed... sigh
I can't possibly answer the question until someone defines the range of numbers that constitutes "reasonable".
If I'm reading a book then 250 pages a night is a "reasonable ". Number. Unless it's a highly technical manual. Then. 10.
So I would tell that teacher that any answer is reasonable based on the lack of needed detail
Sevesteen, Yes, I know what estimation is. Somewhere in my doctoral engineering program at MIT, I learned about estimation. In fact, I had a professor who claimed there were only four important numbers; zero, one, ten and infinity.
Estimation isn't what the question asked for. Nowhere in the question does the word "estimation" occur. The operative word is "reasonable."
You need to quit making excuses for ontological rigidness, denseness and stupidity on the part of the grader. Estimation only makes sense when a closed form solution is too difficult or time-consuming.
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