Find Number of Feet - critical Thinking

[Deleted member 4993]

Ok. Sullivan did not say to use pi or 3.14.
In that case, using 3.1415 leads to

C = pi•16

C = 3.1415 • 16

C = 50.264 inches

Then 4 • 50.264 inches = 201.056 ft

You forgot unit at the last step.

Was it explicitly mentioned in the problem that the wheel was a circular wheel? If you assumed that you should declare it.

Was it explicitly mentioned in the problem that the wheel was rotating on a flat plane - without slipping? If you assumed that you should declare it.

 

[harpazo]

You forgot unit at the last step.

Was it explicitly mentioned in the problem that the wheel was a circular wheel? If you assumed that you should declare it.

YES, IT IS A WHEEL, A REGULAR EVERYDAY WHEEL.

Was it explicitly mentioned in the problem that the wheel was rotating on a flat plane - without slipping? If you assumed that you should declare it.

YES, OF COURSE ROTATING ON A FLAT SURFACE.

Khan, this basic math, brother. Am I right or wrong?

 

[Deleted member 4993]

YES, OF COURSE ROTATING ON A FLAT SURFACE. (rolling without slipping)

Khan, this basic math, brother. Am I right or wrong?

This is basic math and your answer was excellent for a 12 yr. old student facing this problem for the first time.

However, it is not "complete" answer for a self professed middle aged student with multiple (3?) degrees.

This - critical thinking - is exactly what is missing in a lot of the students attending our high-schools and aspiring to be engineers, scientists, doctors, etc. Unlike some of us - I lay the blame at the feet of the guardians of the students at home. Thinking - about unspoken assumptions and consequences of those assumptions - should be a way of life for "inventors" of our society.

Would you be able to do the following extension of the problem:

Due to sudden impact with a stationary object, the circular wheel has become "slightly" but perfectly elliptical. The length of the major axis of the elliptical wheel is 16.25" and the length of the minor axis is 15.75". Assuming the wheel is rolling on a flat-surface without slipping - along a straight line, will this wheel travel different distance compared to the circular wheel? If it is different - what is the % change compared to the perfectly circular wheel?[edited}

Disclosure: I had to pull down my CRT math handbook to attack this problem. However, you can get the formula to use (with approximation) by googling around.

Problem-solvers should know the implied assumptions and always interrogate assumptions. That is how we make progress....

 

[JeffM]

Subhotosh, my friend, I must respectfully disagree in two respects.

The idea that our children are so woefully educated is because of incompetent parents rather than because of incompetent teachers is profoundly wrong. Undoubtedly there are bad parents, parents who neglect or mistreat their children, but such parents are rare. Few parents do not try their best to care for their children. A parent should ensure that a child gets enough to eat, but that does not mean that every parent should be a farmer. We do not blame the parents if the gas main breaks and the children are cold; instead, we expect the gas company to get experts out in the cold who can fix the break without blowing up the neighborhood. The difference between the gas company's employees and school teachers is that gas explosions are very rare but the number of woefully educated students is in the millions.

Many parents do not have the mental capacity to solve problems such as you have posed: should we forcibly sterilize such people on the grounds that they lack the competence to be an engineer. Many more parents do not have the education even to begin to attack such a problem. Perhaps we should fine them for spawning offspring when they are so benighted.

We require parents to educate their children by sending them to school. It is not the parents' fault that the schools are staffed by half-wits and administered by quarter-wits.

Second, I believe engineers are under-appreciated, often to a shocking degree. The people who dominate our national communications, the media, the lawyers, and a large portion of the entertainment industry, are skilled with words and with appeals to emotion. We would still be living in caves if only such people existed. So it is not surprising that engineers are frequently defensive. But to decide that the "inventors" of society are a technological elite is going way too far.

EDIT: Actually, it is partially the parents' fault that the schools are so bad. If I were the parent of a public school student, I'd be inciting people to riot. People should not be so naive as to believe that the public school system is anything more than an intellectual Ponzi scheme.

 

[Otis]

A few, quick reactions.

… Undoubtedly there are bad parents, parents who neglect or mistreat their children …

Personally, I would not conflate abusive parents with parents who don't take enough interest in a child's schoolwork.

… We do not blame the parents if the gas main breaks and the children are cold …

I would, if those children remained cold for months or years.

… [several] parents do not have the education [to help with math homework] …

I once read that 4 out of 5 parents have resources and options available, when students fall behind in class. I'm not sure if that's still true (or if it ever was, as a general claim), but I think Subhotosh's point is that parents could do better.

… the "inventors" of society are a technological elite …

I had a different take. I agree with both views: many parents ought to take a more active role, and schools ought to be better funded and managed. (Personally, I really dislike public education's one-size-fits-all approach.) Universities still lament that too many high-school graduates
arrive unprepared for college. I know two teachers in public school (grade school and middle school). In casual conversation about education issues, each of them mentioned to me that it's not easy to get parents to come to the school for teacher-parent conferences.

And the entire orchestra plays on …

\(\;\)

 

[Deleted member 4993]

Subhotosh, my friend, I must respectfully disagree in two respects.

The idea that our children are so woefully educated is because of incompetent parents rather than because of incompetent teachers is profoundly wrong. Undoubtedly there are bad parents, parents who neglect or mistreat their children, but such parents are rare. Few parents do not try their best to care for their children. A parent should ensure that a child gets enough to eat, but that does not mean that every parent should be a farmer. We do not blame the parents if the gas main breaks and the children are cold; instead, we expect the gas company to get experts out in the cold who can fix the break without blowing up the neighborhood. The difference between the gas company's employees and school teachers is that gas explosions are very rare but the number of woefully educated students is in the millions.

Many parents do not have the mental capacity to solve problems such as you have posed: should we forcibly sterilize such people on the grounds that they lack the competence to be an engineer. Many more parents do not have the education even to begin to attack such a problem. Perhaps we should fine them for spawning offspring when they are so benighted.

We require parents to educate their children by sending them to school. It is not the parents' fault that the schools are staffed by half-wits and administered by quarter-wits.

Second, I believe engineers are under-appreciated, often to a shocking degree. The people who dominate our national communications, the media, the lawyers, and a large portion of the entertainment industry, are skilled with words and with appeals to emotion. We would still be living in caves if only such people existed. So it is not surprising that engineers are frequently defensive. But to decide that the "inventors" of society are a technological elite is going way too far.

EDIT: Actually, it is partially the parents' fault that the schools are so bad. If I were the parent of a public school student, I'd be inciting people to riot. People should not be so naive as to believe that the public school system is anything more than an intellectual Ponzi scheme.

I have to "fight" with you on both points.

Second point first. I said - "Problem-solvers should know the implied assumptions and always interrogate assumptions." I did not mention - implicitly or explicitly - "engineers" anywhere here. In my opinion, everybody is making a living by being a "problem-solver". That includes poet to pottery-maker.

As to the first point, I'll just give a personal anecdote. My grandmother - who did not graduate from eighth grade in India - instilled critical thinking in my mind. Critical thinking starts with thinking beyond the immediate "question". Whenever I complained some did me so wrong - she would gently (sometimes not-so-gently) persuade me to think about the wrong-doer perspective. "May be s/he does not think it is wrong" - and so on. At that time I really did not like this change of perspective - but now I realize a coin when flipped can fall on head or fall on tail or roll under the sofa (never to be found again). As my sons were growing up, I had noticed most my neighbors "trusted their kids" and did not care about their HW. I think there is subtle confusion between trusting and not-caring. My brother and I got pestered by my "illiterate" Grandma about our HW - before going to any evening "fun" activities. Then of course "the more educated" male members came in and made sure that we completed those HWs correctly (It was my job to make sure my brother's "productions" were correct). I claim - to induce critical thinking, no formal education is needed.

Otis said that "the education system is one-size-fits-all". I do not agree with that either. I was forced to take poetry, social-studies, history (Indian and World) all through high school. I took it like bitter medicine - do not quite "see" how it is going to help me - but I'll take it because I have to. Now I am glad I did. I can carry-out intelligent conversation with most of the strangers. This is a great education system - we need to be able to use it and care for advancement of our "species" (however it may be defined).

 

[Otis]

… I was forced to take poetry, social-studies, history (Indian and World) all through high school …

That's not what I had in mind, Subhotosh, when I wrote one-size-fits-all. I don't like how public schools teach and evaluate students as though everybody is identical. Exampes: You get B+ on exam, and I get C- only because I think differently (eg: need extra 10-15 min, but otherwise can answer the same as you). Or, I learn successfully in my assigned group, but you struggle because your group ignores your questions and belittles your ideas. Some students are auditory learners and need to express thoughts out loud or listen to music when working but punished for doing that in class. Other students are punished for thinking independently (i.e., not allowed to approach problem from their different, yet valid perspective).

I thinks there's room in public education for more flexibility, regarding differences between individuals. The USA is wealthy in many ways, yet public education of children consistently ranks low compared to other great nations. Maybe part of the reason why is because we don't acknowledge uniqueness of individuals in school as much as we could.

?