Posted on 03/10/2015 5:48:37 PM PDT by MNDude
My daughter has this problem-solving question for her homework. I'm feeling kind of dumb on this one. What do you think is the correct answer?
Mrs. Feltner wants to put a border on a baby blanket. The area of the blanket is 12 square units. Which shows how many units of materials she needs for the border?
A 12 units B 14 units C 15 units D 21 units
Okay, let’s try to save the question:
Baby blankets are rectangular with length to width ratio approximating the golden mean (1+sqrt(5))/2 ). Since A is infeasible, and the length to width ratios needed for a perimeter 15 or perimeter 21 unit blanket are further from the golden mean that that needed for a perimeter 14 blanket, the answer is B.
(Having length to width ratio approximating the golden mean *is* a property baby blankets typically exhibit, while having exact integer length and width in “units”, which should be empirically on the order of a foot is not.)
No. It’s not a fine problem for a child to solve because the child is being taught sloppy and unrealistic thinking: shapes all have sides of integer lengths, unwarranted assumptions can be made to make a problem come out nicely. Rot like this in the grade school curriculum is part of why kids struggle with math.
Try this one! Very simple.
Take a wooden 3” Cube paint it. Then cut it into 1” cubes.
How many cubes have just/only one side painted?_____
How many cubes have just/only two sides painted?______
How many cubes have just/only three sides painted?______
Your problem’s answer is 14 units, link
http://wyattsallstars.wikispaces.com/file/view/Lesson+13-8+practice.pdf
They are working on perimeters?
6,12,8. (?)
Of course, the customer might have ordered a long blanket, say 9.19493 units long by 1.30507 wide. In that case, the correct answer is D: 21.
Or maybe the customer had in mind an aspect ratio closer to 2.26. In that case, a 5.18614 by 2.31386 blanket would fill the bill and require a border of 15 units, answer C.
Or maybe the customer wants something special, say a circular blanket. In that case, the blanket needs to be 3.90882 wide, with a border measuring 12.27992 units. That answer doesn't appear.
The problem is improperly specified. Teach fails!
Has anyone considered how much you need if you cut the border on the bias?
I used to have a college Physics professor who gave multiple choice tests. Invariably, one question had no right choice. And he would then throw out that question - even when we’d write the correct answer! Drove the class nuts.
You made up your own description of what the border should be. It could as easily be a cording, no width at all.
The answers are units, not square units. The question is asking for the perimeter.
Ok. My little brother who wrote for houghton-mifflin and is now and actuary says its a stupid question. So I concede.
He said it reminded him of the people he worked with who knew nothing about the subject of their story problem.
You win.
One in the center received no paint.
Thanks, for playing.
First of all, I consider myself an equal opportunity integer/non-integer type of guy. I have used both of them without reservation for many years.
Alas, but 3.4641016... units per side (approximate square root of 12 actually equals 11.99999999...) will not get you 12 or 12.0 square units. Therefore, I assume you are using “new math” or “common core math”, in which case your solution would be correct.
In new math, 11.999999... is the equivalent of 12.0 because you feel it is so. Feelings really count in new math. One would not want to slight the problem solver by requiring an exact answer that could denigrate their self worth. In fact, 13 or 15 would be appropriate answers if one felt strongly. However, if one felt excessively strong a 12 or 16 answer would also be acceptible.
In common core math, the problem constraint (12.0) would be considered “socially unjust” and could be ignored if desired. The ultimate “right” answer would have to be the answer derived by “group think”. If you could convince the others in the group that 15 was the socially just answer then 15 would be declare the “correct” answer. If other groups came up with different answers, that would be considered OK.
The real problem with these two approaches, although they support social justice and individual freedoms, is that there are flaws when applied in “reality”. Consider a brain surgeon, nuclear physicist, lawyer or judge, etc. who uses that logic in their day to day business. Consider that we have observed this line of thought already in the Supreme Court’s decision on CommieCare.
Nope. On a 2x6, the perimeter would be 16
On a 1x12, the perimeter would be 26.
Me too. I have a BS in mathematics, and a PhD in physics, and use advanced math in my software development projects every day.
Alas, but 3.4641016... units per side (approximate square root of 12 actually equals 11.99999999...) will not get you 12 or 12.0 square units.
Alas, but if you think that the "exact" answers are "correct" you are living in a dream world. In reality, you cannot measure -- let alone cut -- a piece of cloth to more than three significant digits. So the "3x4" piece of cloth is no more a whole number than the 3.464 fails to be.
Therefore, I assume you are using “new math” or “common core math”, in which case your solution would be correct.
Therefore, I assume you don't know what significant digits are, in which case most of what you think you know about real world measurements is wrong. They are discussed elsewhere on this thread. Educate yourself.
In new math, 11.999999... is the equivalent of 12.0 because you feel it is so.
IN ALL MATH 11.999999... means an 11 followed by an infinite number of nines. 11 followed by an infinite number of nines is an abbreviation for:
11 + limitN→∞∑n=1N 9(1/10)n
IN ALL MATH, that limit is 12. Has nothing to do with feelings, new math, common core, or anything else. It is a simple fact of our number system that some numbers have more than 1 infinite decimal expansion. I refer you to any book on elementary analysis [usually called advanced calculus] where this is proved.
Consider a brain surgeon, nuclear physicist, lawyer or judge, etc. who uses that logic in their day to day business.
Any physicist who used 3.4641016 as a measured quantity in anything but the most highly refined measurements would, in fact, be laughed off the planet, and at least one (and probably all of the) referee(s) of his paper would tell him it's 3.46. [Except in quantum electrodynamics, and a few other applications.] The same applies to 3.000000 which is 3.00 in any household measurement you want to discuss. 3.00 x 4.00 does not equal the pure number 12. It equals 12.0: Three significant figures. That's all you get, and that number is the same as 12.05 and 11.95, and arguing about it makes you a pedant, but it doesn't make you right.
Even in pure mathematics, the perimeter of a cloth is not well defined. Perimeters almost invariably have fractional dimensionality and not the linear dimensionality most people learn.
For the seamstress, it might well be 14[.0 ONLY!], but to a bacterium crawling around the edge, it might well be 100 feet [because bacteria have to crawl not straight across the ruler's edge, but up/down/across from fiber to fiber], and to a photon flicking around the perimeter of a charged static cloth from the electrons in one atom to the next, it could be 100 meters.
Contrary to your sentiments, I am not on board with touchyfeely. I think most of our math education in this country is a disaster, and has been so since about 1964, when most of these hideous concepts found their way into the curriculum.
That is exactly why I don't accept the answer of 14. It is false to claim that the answer is 14. The truth is that this is a completely under-specified problem. Even if you assume that the dimensions must be rectangular, there are an infinite number of correct answers to this question, and that is the answer that a person who believes in rigorous mathematics should insist on. [Consult a book on modern algebra in which the general theory of the solutions of linear equations is discussed for details: a system of two equations in three unknowns doesn't have "one" answer. It's rigorously proved. It's what God knows to be true.]
It is a mistake to believe that poorly posed questions have answers. They don't. Because they are not really questions at all.
If you used a slide rule and got 11.9 995 275 003 984 9 you have a slide rule about 1012 feet long. [You gain 3 digits of precision for every three orders of magnitude increase in the length. An ordinary slide rule is a foot long, and is accurate to about 3 places. I am spotting you the final "9" just to be kind.]
That means that if you moved the slide at 99.9% of the speed of light [a highly dubious proposition, but certainly not out-of-line with the other accomplishments you've claimed on this thread, like cutting cloth to nine significant figures...] it takes about 1000 seconds to move the rule, and 1000 seconds from the slider position on the rule to come back to you to read off the answer. So each multiplication, division, and square root takes about 2000 seconds. I will again spot you a couple of operations and not count the additions and subtractions, so I count at least 6 operations. That's -- generously -- 12000 seconds to run the whole thing through a slide rule.
That's three hours and 20 minutes of planet-busting labor. I'm just going to say that I'm skeptical...
I don’t think anyone took into account the width of the border...
If the border is 2 inches wide, don’t you have to take 4 inches off the total figure (unless if you are sewing the the horizontal and vertical intersections on top of one another.
“It is a mistake to believe that poorly posed questions have answers. They don’t. Because they are not really questions at all.”
If so, why did you bother answering or posing your approximation to the problem?
I used TWO slide rules.
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