jaybird0827
Puritan Board Post-Graduate
My answer did not agree with that in the answer key, but I believe my solution to be correct. If interested, please take a crack at it before looking at my solution.
Math Problem
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toddpedlar
Iron Dramatist
I don't know what the answer key says but your solution is the same as mine - at least the final answer is. I'd have an extra factor in the first line (since the greens vary directly as the ratio B^3/W^2, rather than being equivalent to that ratio) - and you have a numerical error in an intermediate step. I'd say you get 17/20 for your work, Jay
Solus Christus
Puritan Board Sophomore
Solus Christus
Puritan Board Sophomore
I second Todd Pedlar's post.
But as a personal pet peeve, I think questions like this are nonsense. Perhaps I am ignorant of something, but I cannot possibly imagine an engineer, scientist, or mathematician requiring the skill of translating a complex sentence structure into a formula.
The problem can be taken in a number of different ways. Since there are no limitations given on the range of these variables (no mention of fractions, max/min, etc.), I believe it would also be legitimate to interpret it as two separate formulas: g = b^3 and g = 1/(w^2).
That interpretation meets the problem's requirements perfectly in my mind. G varies directly with the cube of B, and inversely with the square of W.
Most people, when making problems like this, simply do not take the time and care to be precise.
The only time such a grammar-to-formula translation skill could be required is when a researcher/teacher/etc. is intentionally obtuse in recording the actual formula. In the real world, I would simply want to tell him to write it properly and be done with the issue.
JohnGill
Puritan Board Senior
It's also for computer programming and modeling.
I saw that and shared your annoyance. I was thinking (in my typical rebellious fashion) that the problem could be called a nonsense problem because there were two independent equations with only one potential intersection, and that intersection could be arbitrary.
But then I played along and set it up as the solution presented did.
But I take issue with your opinion on the skill of translating a complex sentence into a formula. I think it is a good thing to have. Sometimes a problem cannot be easily described in words. Trying to get it into a formula forces you to think about relations of interacting things in different ways.
Think of Maxwell's "Deamons" or Einstein's light ride. These were essentially word problems that led to fundamental equations.
JohnGill
Puritan Board Senior
Brian Withnell
Puritan Board Junior
This is true, and I realized I overstated my case. It is a very necessary skill for those doing original research, especially theoretical work, and in some more limited sense could be valuable for non-researches to be exposed to in order to develop logical and analytical ability.
But, strictly in the case of a formula that is already known and can be easily expressed mathematically, if a person turned that into a sentence to give to me only for me to then unscramble it again....well, that would be incredibly annoying.
Brian Withnell
Puritan Board Junior
I check what you got, and I got the same (I did include a k for a constant, but it doesn't affect the result of your calculation ... it becomes part of the original value).
I might expect the solution key to give the answer using 1/3 in the denominator (the easiest mistake to make) which would yield 9/8ths (1.125 times as much).
I wonder why they would ask such a simple question. Low level math course? I'd expect this to be solved in high school Algebra II.
Is this for a course you teach?
-----Added 3/3/2009 at 12:09:05 EST-----
Got to ask ... if you were trying to instruct students in how to translate English language into math language, you would most likely want to make things simple (like this problem) so that you could limit the variables and access the students parsing and composition skills. Translation is not always straight forward and seldom as simple as this exercise.
If it were a physics course, you could use the equation for the gravitational attraction of two bodies ... the force between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them ... but then you don't have the powers in both numerator and denominator to see if they understand the inverse and direct proportionality principles.
I might expect the solution key to give the answer using 1/3 in the denominator (the easiest mistake to make) which would yield 9/8ths (1.125 times as much).
I wonder why they would ask such a simple question. Low level math course? I'd expect this to be solved in high school Algebra II.
Is this for a course you teach?
-----Added 3/3/2009 at 12:09:05 EST-----
Got to ask ... if you were trying to instruct students in how to translate English language into math language, you would most likely want to make things simple (like this problem) so that you could limit the variables and access the students parsing and composition skills. Translation is not always straight forward and seldom as simple as this exercise.
If it were a physics course, you could use the equation for the gravitational attraction of two bodies ... the force between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them ... but then you don't have the powers in both numerator and denominator to see if they understand the inverse and direct proportionality principles.
JohnGill
Puritan Board Senior
You slide-rule geek!
Brian Withnell
Puritan Board Junior
I am a high school math teacher. If you want to know what a high school Algebra II student is supposed to know at the end of the course, you can look here. If you look at AII.2 and AII.20, you can see this problem falls into those categories. It might be a little on the "apply and extend" because it combines both, but I'm sure we teach it.
jaybird0827
Puritan Board Post-Graduate
-----Added 3/3/2009 at 06:48:56 EST-----
Good catch, Todd. I have since updated my document.
Agree.
I agree with that conclusion - apparently what the person solving the problem for the answer key did. Question might be a good candidate for a multiple-choice item.
Actually no. Currently I'm not doing any teaching. Our prior discussion occurred during a 3+ week substitute teaching assignment that ended in December.
I had decided I needed to refresh my knowledge and skill in Calculus. As a prerequisite, I got out what had been our son's course in Saxon Advanced Mathematics. I just finished taking the entire course, self-study. A similar question appeared on one of the tests (I made some changes before posting it here).
-----Added 3/3/2009 at 12:09:05 EST-----
Makes sense to me.
I don't know what the answer key says but your solution is the same as mine - at least the final answer is. I'd have an extra factor in the first line (since the greens vary directly as the ratio B^3/W^2, rather than being equivalent to that ratio) - and you have a numerical error in an intermediate step. I'd say you get 17/20 for your work, Jay
Good catch, Todd. I have since updated my document.
Agree.
I agree with that conclusion - apparently what the person solving the problem for the answer key did. Question might be a good candidate for a multiple-choice item.
Actually no. Currently I'm not doing any teaching. Our prior discussion occurred during a 3+ week substitute teaching assignment that ended in December.
I had decided I needed to refresh my knowledge and skill in Calculus. As a prerequisite, I got out what had been our son's course in Saxon Advanced Mathematics. I just finished taking the entire course, self-study. A similar question appeared on one of the tests (I made some changes before posting it here).
-----Added 3/3/2009 at 12:09:05 EST-----
Makes sense to me.
That's just it - even with this simple exercise, the teacher/professor got it wrong in the way he asked the question. There are at least two legitimate interpretations of that sentence, and therein lies the problem with it. To make the problem clear takes a lot more care and attention than people realize.
As far as the skill of mathematical translation, I don't know if I accept that computer programming involves something similar. I've only taken introductory classes in a few different languages, and none of them remotely required use of a sentence like this. Using brackets, parentheses and different lines to make the meaning clear is FAR easier than spelling it out in an actual sentence.
Brian Withnell
Puritan Board Junior
Ah, that makes a lot of sense. Saxon (I have that book) does a lot of repetition of basic skills throughout, and what they do in the Advanced Math book is at a pre-cal, higher level Algebra (II+ ?) with some of their problems seeming to dip down and some right up there. This one I'm surprised they got wrong, but most publishers have college math students doing the solutions.
I remember you doing the substitute work, and I had a crazy idea that you were looking at teaching as a career (maybe you are?) and this could have been for a student teacher gig.
Good catch on finding the error.
Most people would figure they had done the problem wrong and go with the solution the book gave.
Skyler
Puritan Board Graduate
I came up with the same answer as you did. Different process, but same results.
Brian Withnell
Puritan Board Junior
I don't know as I'd say there were two ways of interpreting the language. I'd say the person that did the solution did it wrong. The real world does work in English, and you have to translate it to Math. One of my most rewarding projects I designed was a system that translated incoming toll free (800 number) calls to the appropriate 10 digit telephone number (800 numbers get translated to normal numbers as part of the service, and I worked for a company that sold an enhanced 800 service that translated the numbers based on a number of criteria). The English description was just that, English. What the software did was a bidirectional mapping of four dimensional hyperplanes to a directed acyclic graphs of decision nodes. I had to be able to work in the English and the Math in order to design a solution that would work. Anything where you are going to come up with an original design requires you to be able to bridge the space between the two worlds.
I was going to put in a rant about how lack of math education has wasted the minds of our youth. Sigh. I started teaching to help mitigate that loss of thinking skills, and I should just work to fix what I can.
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