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Re: 8÷2(2+2)=?
Posted by: N-OS X-tasy!
Date: August 01, 2019 04:03PM
Quote
Janit
Quote
rz
There are two methods that are taught, each of which will give a different answer. So there is no "right" answer.

I fully expect to see this kind of question given to my son though. Ever since kindergarten, I've battled with his school over ambiguous things like this. One time, he was given a paragraph and asked "Which is the most important sentance in this paragraph?" He chose one. I chose a different one. My wife chose a third one. When I argued with the teacher, asking "How can a third grader be expected to correctly choose this, when two reasonable adults can't even agree?", I was told "It doesn't matter what choice they make, as long as they can describe why they chose their particular answer." I was dumbfounded. That's Common Core for you.

Actually, the teacher's approach is quite sensible. She/he knows that people will disagree, and she/he knows there is not one "right" answer. She/he is teaching and testing the ability to take a position and defend it with a cogent argument. This is a simplified version of the format of every essay question I was ever given throughout most of my education, and it is the basis for developing critical thinking. This is a proto- essay question suited to a third grader.

A better evaluation of the teacher would derive from asking how did she/he grade the answer, and was the feedback she/he provided appropriate for a third grader.

It is quite possible that your son did not understand the nature of the task, and responsibility for that confusion does rest on the teacher. However, if the teacher was lying, and actually did grade as though there was only one right answer, (the one she/he believed) then that was a serious problem.

Math is an OBJECTIVE science. For each properly stated expression like the simple one presented here, there is only one correct answer (exceptions include solving for polynomials and other non-simple scenarios). Anyone who teaches otherwise has no business teaching math, especially to students too young to understand on their own the danger of this approach.



It is what it is.
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Re: 8÷2(2+2)=?
Posted by: space-time
Date: August 01, 2019 04:37PM
if the multiplication sign is not spelled out, it is well understood by everyone here, right?

no one doubts that 2(2+2) =8, correct?

So let's re-write that expression

8÷2(2+2)=8÷2*(2+2)

it is the SAME expression

so tell me what is 8÷2*(2+2)

or better, tell me what is 8÷2*4
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Re: 8÷2(2+2)=?
Posted by: N-OS X-tasy!
Date: August 01, 2019 05:00PM
Quote
space-time
if the multiplication sign is not spelled out, it is well understood by everyone here, right?

no one doubts that 2(2+2) =8, correct?

So let's re-write that expression

8÷2(2+2)=8÷2*(2+2)

it is the SAME expression

so tell me what is 8÷2*(2+2)

or better, tell me what is 8÷2*4

You are failing to take into account the requirements of the distributive property, which says x(a+b) = xa +xb. Thus,

y÷x(a+b) = y÷(xa+xb), not y÷x*(a+b).



It is what it is.
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Re: 8÷2(2+2)=?
Posted by: bfd
Date: August 01, 2019 05:05PM
Quote
Janit
Quote
rz
There are two methods that are taught, each of which will give a different answer. So there is no "right" answer.

I fully expect to see this kind of question given to my son though. Ever since kindergarten, I've battled with his school over ambiguous things like this. One time, he was given a paragraph and asked "Which is the most important sentance in this paragraph?" He chose one. I chose a different one. My wife chose a third one. When I argued with the teacher, asking "How can a third grader be expected to correctly choose this, when two reasonable adults can't even agree?", I was told "It doesn't matter what choice they make, as long as they can describe why they chose their particular answer." I was dumbfounded. That's Common Core for you.

Actually, the teacher's approach is quite sensible. She/he knows that people will disagree, and she/he knows there is not one "right" answer. She/he is teaching and testing the ability to take a position and defend it with a cogent argument. This is a simplified version of the format of every essay question I was ever given throughout most of my education, and it is the basis for developing critical thinking. This is a proto- essay question suited to a third grader.

…maybe "more than one possible response" rather than "not one right answer…

Yes, if we knew for certain that the teacher was using that kind of strategy, posing questions where one knows that there are many possible answers that will come out in a classroom discussion is great - as long as the students leave understanding which one answer is correct and which possible answers aren't - as well as why… All too often though, students will get left with a serious misunderstanding that may never be corrected because the teacher really didn't finish up the lesson by making certain to clear up any of these common misconceptions. (see Thread: this one) As a result, too many people may inadvertently learn to defend mathematical nonsense, and that's not good for anyone.

As to the question about third graders and this topic, order of operations is a third grade Common Core math standard, but one would think that this particular question might really be a little too convoluted for third grade level. (or as Walter Sobchak might say, 8-year-olds, Dude …)



Edited 1 time(s). Last edit at 08/01/2019 05:09PM by bfd.
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Re: 8÷2(2+2)=?
Posted by: space-time
Date: August 01, 2019 05:14PM
Quote
N-OS X-tasy!
...

y÷x(a+b) = y÷(xa+xb), not y÷x*(a+b).


??? where does that come from? why do you assume that MULTIPLICATION should be done FIRST?


y÷x(a+b) = y÷x*(a+b)

Unless you show me another set of parenthesis like this, y÷(x(a+b)), which I didn't see in the original question.

Once again put that expression in Wolfram Alpha (a very reputable and well respected math software), in google, etc.
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Re: 8÷2(2+2)=?
Posted by: space-time
Date: August 01, 2019 05:17PM
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Re: 8÷2(2+2)=?
Posted by: Carm
Date: August 01, 2019 05:22PM
Quote
space-time
Quote
N-OS X-tasy!
...

y÷x(a+b) = y÷(xa+xb), not y÷x*(a+b).


??? where does that come from? why do you assume that MULTIPLICATION should be done FIRST?


y÷x(a+b) = y÷x*(a+b)

Unless you show me another set of parenthesis like this, y÷(x(a+b)), which I didn't see in the original question.

Once again put that expression in Wolfram Alpha (a very reputable and well respected math software), in google, etc.

[www.khanacademy.org]
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Re: 8÷2(2+2)=?
Posted by: Marc Anthony
Date: August 01, 2019 05:43PM
Quote
Carm
The answer is 1.
It’s funny how everyone suddenly forgets the distributive property and jumps to PEMDAS or BEMDAS.
8/2(2+2)
8/4+4
8/8
1

Using the distributive property is the more laborious way of doing it, however, both methods must arrive at the same answer, if done correctly.
Using the distributive method:
8/2(2+2)
(4)(2+2)
(4*2)+(4*2)
8+8=16



Le poète doit vivre beaucoup, vivre dans tous les sens. - Verlaine
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Re: 8÷2(2+2)=?
Posted by: rjmacs
Date: August 01, 2019 05:45PM
I love this forum.



rj
AKA
Vreemac, Moth of the Future
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Re: 8÷2(2+2)=?
Posted by: space-time
Date: August 01, 2019 05:57PM
Quote
Carm
Quote
space-time
Quote
N-OS X-tasy!
...

y÷x(a+b) = y÷(xa+xb), not y÷x*(a+b).


??? where does that come from? why do you assume that MULTIPLICATION should be done FIRST?


y÷x(a+b) = y÷x*(a+b)

Unless you show me another set of parenthesis like this, y÷(x(a+b)), which I didn't see in the original question.

Once again put that expression in Wolfram Alpha (a very reputable and well respected math software), in google, etc.

[www.khanacademy.org]

That part I understand. But why do you do the right side of the expression first, then the left side???

I think you failed.
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Re: 8÷2(2+2)=?
Posted by: Janit
Date: August 01, 2019 06:57PM
There is no right answer, because the question is incoherent!

JUST SAY NO!
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Re: 8÷2(2+2)=?
Posted by: Mike Johnson
Date: August 01, 2019 07:14PM
If Stephen Wolfram himself said its 16, it’d give me pause. But some dumb online parser that is confronted with a badly written expression, that is not actually Stephen fathermocking Wolfram.
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Re: 8÷2(2+2)=?
Posted by: space-time
Date: August 01, 2019 07:14PM
YES!
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Re: 8÷2(2+2)=?
Posted by: bfd
Date: August 01, 2019 07:38PM
Problems like this are good for bringing out some common misconceptions … but probably shouldn't be used with very young students (even for the sake of "challenge"). That's why a teacher's understanding of the mathematics underlying a given problem is most important - even at a primary level.
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Re: 8÷2(2+2)=?
Posted by: testcase
Date: August 01, 2019 08:10PM
The CORRECT answer is 16




Everyone who came up with a different answer; get over it. angry villagers smiley
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Re: 8÷2(2+2)=?
Posted by: space-time
Date: August 01, 2019 08:16PM
Quote
testcase
The CORRECT answer is 16




Everyone who came up with a different answer; get over it. angry villagers smiley

My answer is 42
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Re: 8÷2(2+2)=?
Posted by: Carm
Date: August 01, 2019 08:20PM
Quote
Marc Anthony
Quote
Carm
The answer is 1.
It’s funny how everyone suddenly forgets the distributive property and jumps to PEMDAS or BEMDAS.
8/2(2+2)
8/4+4
8/8
1

Using the distributive property is the more laborious way of doing it, however, both methods must arrive at the same answer, if done correctly.
Using the distributive method:
8/2(2+2)
(4)(2+2)
(4*2)+(4*2)
8+8=16

I concede. 16 is the answer. My previous answer was based on improper formatted question and the use of the division sign.

8
——— (2 + 2)
2
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Re: 8÷2(2+2)=?
Posted by: space-time
Date: August 01, 2019 08:57PM
Quote
N-OS X-tasy!
Quote
Janit
Quote
rz
There are two methods that are taught, each of which will give a different answer. So there is no "right" answer.

I fully expect to see this kind of question given to my son though. Ever since kindergarten, I've battled with his school over ambiguous things like this. One time, he was given a paragraph and asked "Which is the most important sentance in this paragraph?" He chose one. I chose a different one. My wife chose a third one. When I argued with the teacher, asking "How can a third grader be expected to correctly choose this, when two reasonable adults can't even agree?", I was told "It doesn't matter what choice they make, as long as they can describe why they chose their particular answer." I was dumbfounded. That's Common Core for you.

Actually, the teacher's approach is quite sensible. She/he knows that people will disagree, and she/he knows there is not one "right" answer. She/he is teaching and testing the ability to take a position and defend it with a cogent argument. This is a simplified version of the format of every essay question I was ever given throughout most of my education, and it is the basis for developing critical thinking. This is a proto- essay question suited to a third grader.

A better evaluation of the teacher would derive from asking how did she/he grade the answer, and was the feedback she/he provided appropriate for a third grader.

It is quite possible that your son did not understand the nature of the task, and responsibility for that confusion does rest on the teacher. However, if the teacher was lying, and actually did grade as though there was only one right answer, (the one she/he believed) then that was a serious problem.

Math is an OBJECTIVE science. For each properly stated expression like the simple one presented here, there is only one correct answer (exceptions include solving for polynomials and other non-simple scenarios). Anyone who teaches otherwise has no business teaching math, especially to students too young to understand on their own the danger of this approach.

I am actually surprised that you are so coherent here and yet fail to provide the correct answer. This does not compute.
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Re: 8÷2(2+2)=?
Posted by: DP
Date: August 01, 2019 09:03PM
I love this forum.

Me, too! Lots of time on members' hands... And fights are breaking out!

There is no right answer, because the question is incoherent!

How about changing how math is done and drop the parentheses? It's never used in the real world so just get rid of it!





Disclaimer: This post is checked for correct spelling, punctuation, and grammar. Any attempts at humor are solely the responsibility of the author and bear no claim that any and all readers will approve or appreciate said attempt at humor.
My name is DP, and I approve this message.
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Re: 8÷2(2+2)=?
Posted by: RAMd®d
Date: August 01, 2019 11:50PM
This is kind of like Thanksgiving, but without food.

(Not my Thanksgivings! I live by a Food not Fights credo.)




When a good man is hurt,
all who would be called good
must suffer with him.

Everybody matters or nobody matters.

You and I have memories longer than the road that stretches out ahead.

There is no safety for honest men except
by believing all possible evil of evil men.

We don’t do focus groups. They just ensure that you don’t offend anyone, and produce bland inoffensive products. —Sir Jonathan Ive

-An armed society is a polite society.
And hope is a lousy defense.

You make me pull, I'll put you down.

Mister, that's a ten-gallon hat on a twenty-gallon head.

I *love* SIGs. It's Glocks I hate.
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Re: 8÷2(2+2)=?
Posted by: MEG
Date: August 02, 2019 12:01AM
It's confusing because it's using numbers. Rewrite the equation with variables like:

a÷b(x+y)

The question is whether you think the problem as written becomes:

(a/b)x + (a/b)y

or

a÷(bx + by)

[edited to change spacing between the two versions]



Edited 2 time(s). Last edit at 08/02/2019 12:03AM by MEG.
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Re: 8÷2(2+2)=?
Posted by: Buzz
Date: August 02, 2019 12:38AM
OK, this has been just too f'ing much fun.

If we have two "correct" answers, 1 and 16, let's agree to average them and that the real, final correct answer shall now be 8.5.

OTOH, another old school wrinkle was/is to drop the parenthesis after solving what's inside, then proceeding from there according to whatever appropriate rules are in place. If more clarity was needed/desired because of any possible ambiguity over such rules, brackets should then be employed to afford the solution, since brackets didn't/don't disappear like the parenthesis did/do.

Way back when, we would have been presented with:

8÷2[(2+2)]=?

or

8÷[2(2+2)]=?

though both would have likely included the multiplier clarifier; 8÷2*[(2+2)]=? or 8÷[2*(2+2)]=?, or, 8÷2x[(2+2)]=? or 8÷[2x(2+2)]=?

Like I said, too much fun.
==
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Re: 8÷2(2+2)=?
Posted by: Janit
Date: August 02, 2019 07:28AM
Quote
N-OS X-tasy!
Quote
Janit
Quote
rz
There are two methods that are taught, each of which will give a different answer. So there is no "right" answer.

I fully expect to see this kind of question given to my son though. Ever since kindergarten, I've battled with his school over ambiguous things like this. One time, he was given a paragraph and asked "Which is the most important sentance in this paragraph?" He chose one. I chose a different one. My wife chose a third one. When I argued with the teacher, asking "How can a third grader be expected to correctly choose this, when two reasonable adults can't even agree?", I was told "It doesn't matter what choice they make, as long as they can describe why they chose their particular answer." I was dumbfounded. That's Common Core for you.

Actually, the teacher's approach is quite sensible. She/he knows that people will disagree, and she/he knows there is not one "right" answer. She/he is teaching and testing the ability to take a position and defend it with a cogent argument. This is a simplified version of the format of every essay question I was ever given throughout most of my education, and it is the basis for developing critical thinking. This is a proto- essay question suited to a third grader.

A better evaluation of the teacher would derive from asking how did she/he grade the answer, and was the feedback she/he provided appropriate for a third grader.

It is quite possible that your son did not understand the nature of the task, and responsibility for that confusion does rest on the teacher. However, if the teacher was lying, and actually did grade as though there was only one right answer, (the one she/he believed) then that was a serious problem.

Math is an OBJECTIVE science. For each properly stated expression like the simple one presented here, there is only one correct answer (exceptions include solving for polynomials and other non-simple scenarios). Anyone who teaches otherwise has no business teaching math, especially to students too young to understand on their own the danger of this approach.

And some of us are arguing over whether the expression in question is properly stated.
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Re: 8÷2(2+2)=?
Posted by: Sam3
Date: August 02, 2019 07:49AM
The problem is poorly written, it's ambiguously stated.

Period.

Either answer is correct, based on different interpretation of how it's written.

If this was given on a test, and the teacher marked either answer wrong, I would be miffed and, if necessary, would take it all the way past the principal to the school board.

Use brackets to clearly define what you are looking for.

The following is a quite lengthy read, when including all of the author's updates, but it is quite fascinating and clearly explains the issue.

[www.math.harvard.edu]
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Re: 8÷2(2+2)=?
Posted by: S. Pupp
Date: August 02, 2019 09:17AM
I'm changing my answer to MAVIC.
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Re: 8÷2(2+2)=?
Posted by: ztirffritz
Date: August 02, 2019 10:04AM
Popular Mechanics of all places, has a good treatise on this conundrum.

[www.popularmechanics.com]

According to them, it should be interpreted as:

8
--- = 1
2(2+2)



**************************************
MacResource User Map: [www.zeemaps.com]#
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Re: 8÷2(2+2)=?
Posted by: space-time
Date: August 02, 2019 11:09AM
If they could do advanced Math they would not be Mechanics.
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Re: 8÷2(2+2)=?
Posted by: Rick-o
Date: August 02, 2019 11:32AM
I'm no mathlete, and I actually hated math in school, but after a quick glance, I came up with 16.



Mr. Lahey: A lot of people, don’t know how to drink. They drink against the grain of the liquor. And when you drink against the grain of the liquor? You lose.

Randy: What the @#$%& are you talking about?
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Re: 8÷2(2+2)=?
Posted by: PeterB
Date: August 02, 2019 12:07PM
Quote
Rick-o
I'm no mathlete, and I actually hated math in school, but after a quick glance, I came up with 16.

Same here -- I was taught that parentheses should be done first, the rest done in left-to-right order, with multiplication and division having equal priority but both over subtraction and addition. Basically PEMDAS but not explicitly stated as such.




Freya says, 'Hello from NOLA, baby!' (Laissez bon temps rouler!)
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Re: 8÷2(2+2)=?
Posted by: bfd
Date: August 02, 2019 12:44PM
OK, it's about that time…

[vimeo.com]
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Re: 8÷2(2+2)=?
Posted by: space-time
Date: August 02, 2019 03:29PM
8÷2*(2+2) = ???

forget it space, it's macresource forum
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Re: 8÷2(2+2)=?
Posted by: N-OS X-tasy!
Date: August 02, 2019 05:57PM
Quote
S. Pupp
I'm changing my answer to MAVIC.

The sanest response so far. smiley-laughing001



It is what it is.
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Re: 8÷2(2+2)=?
Posted by: wave rider
Date: August 03, 2019 02:31AM
Gots to get the denominator settled before dividing it into the numerator. Answer is 1.



=wr=
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