Author Topic: A math problem.  (Read 8968 times)

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MOM21SON

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Re: A math problem.
« Reply #75 on: November 02, 2012, 03:24:21 PM »
I haven't taken math since 9th grade and no desire to.  So I am one of the dummies that doesn't know basic math and came up with 1.

I would love to know how some came up with 3.5.

Well, 3.5 isn't right, but here is what I suspect the faulty logic was:

6-1x0+2/2=?

6-1 =5.
"Zero is nothing.  So ignore it."***
5+2 =7
7/2 = 3.5


*** This was probably either an actual thought, or the person got mixed up with the rules about multiply by zero and 1.  Possibly confusing it with the exponent rule?  In other words, I'm not quite sure what their logic on this step was, only that I'm pretty sure that's the way the rest of it went.

Now if the problem looked like this:

   6-1^0+2
---------------  = ?
         2
Then 3.5 would be the correct answer (Do exponents first, 1^0=1.  Then 6-1+2 =7. Then 7/2 = 3.5).  So maybe they just misread the multiplication sign and screwed up the order of operations on division?



Thanks to the last 2 posters.  He has now seen his mistake and corrected himself and came up with 7.

I used to make a lot of mistakes on the simplest parts of math/chem/physics problems in high school. Something that helped me a lot was restructuring the way I wrote my math notes when reducing equations. I'd write every version immediately beneath the prior version, with each part lined up vertically, so that it was easier to notice when I'd transposed something, flipped a sign, etc. This helped me a lot in avoiding small errors.

Thank you.  I will share this with him.  I am very surprised he missed it.  He got 100% in Algebra honors last year in a class with students that were 2 grades ahead of him.

Geometry honors is not going so well.  However, engineering is going very well, so I don't get it.

For what it's worth, geometry is kind of a different type of math - it takes a different way of looking at things than the number crunching with algebra.  I know a lot of students who did well in algebra and struggled with geometry and just as many that struggled with algebra but did well with geometry.  Knowing that you have to approach it differently seemed to help a lot psychologically. 

Do you know if his geometry is proof based?

Does that mean done on the computer?  If so, no its not.

Seraphia

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Re: A math problem.
« Reply #76 on: November 02, 2012, 03:33:51 PM »

For what it's worth, geometry is kind of a different type of math - it takes a different way of looking at things than the number crunching with algebra.  I know a lot of students who did well in algebra and struggled with geometry and just as many that struggled with algebra but did well with geometry.  Knowing that you have to approach it differently seemed to help a lot psychologically. 

Do you know if his geometry is proof based?



Absolutely. I did really well in Algebra. But the further into Geometry we got, the more lost I became. I can solve for x pretty well. But proving that a triangle = a triangle just bewildered me.

Proofs always make me think of the novel "If on a Winter's Night a Traveler" because I can't tell where it's supposed to go, or why I would want to go there anyway.
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Slartibartfast

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Re: A math problem.
« Reply #77 on: November 02, 2012, 03:39:15 PM »
PastryGoddess, you have an oops, I think.  In 6 - 0 + 1, you can't reduce that to 6 - 1, it would be 6 + 1.  The - is attached to the 0 (it's the same as saying 6 + -0 + 1.  So you would get 7 instead of 5.


since when can 0 be negative?  Please explain or link to a page explaining.  Since addition comes before subtraction I added 1 to 0 then subtracted 6 from there. 


http://www.math.com/school/subject1/lessons/S1U1L10DP.html

0 doesn't need to be negative to follow this. "6-0+1" is just "take nothing away from 6 and then add 1".  Zero operates the same way as any other number.

Ah I see.  It was the - in front of the 0 that threw me off.  Thanks for the clarification Iris :D

Part of the problem here is a persistent typo - it's 6 - 1 x 0 + 2 / 2, not 6 - 0 + 1 + 2 / 2.

CluelessBride

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Re: A math problem.
« Reply #78 on: November 02, 2012, 03:49:55 PM »
Proof-based is an approach for teaching math.  I'm having trouble coming up with a definition (math pedagogy isn't my area of expertise by a long shot!).  Basically it involves teaching/learning through proving mathematical statements.

So instead of a question like "Find the area of the triangle"  you would have a question like "Demonstrate that the two triangles are similar".  So it's not enough to know/be able to find the answer, but you also have to explain your logical path to that answer - you prove it.

Like Seraphia, it took me a while to get the point of it.  But in a way its a set up for more advanced mathematics.  I only asked because if your son is struggling with proofs, I suspect a little bit of tutoring or after hours help would go a long way in helping him understand and do well in geometry.  Once the concept of "proofs" gets solidified, a lot of the other geometry concepts finally click into place. Based on my experiences tutoring high school students, it seems many classes don't spend enough time making sure students understand proofs, and then the students just give up and assume they aren't good at geometry.  It would be akin to mistakenly thinking a student was bad a literary analysis when in actuality the student never learned how to read properly.

 


MOM21SON

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Re: A math problem.
« Reply #79 on: November 02, 2012, 03:58:49 PM »
Thank you Clueless for your imput.  His teacher basically says the same thing, once he gets it, it will all click.  I have to praise his teacher, she has helped by doing little things, such as he now sits next to a student his age VS sitting by a 16 or 17 year old that he is afraid to ask for help.

Lynnv

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Re: A math problem.
« Reply #80 on: November 02, 2012, 04:13:05 PM »

For what it's worth, geometry is kind of a different type of math - it takes a different way of looking at things than the number crunching with algebra.  I know a lot of students who did well in algebra and struggled with geometry and just as many that struggled with algebra but did well with geometry.  Knowing that you have to approach it differently seemed to help a lot psychologically. 

Do you know if his geometry is proof based?



Absolutely. I did really well in Algebra. But the further into Geometry we got, the more lost I became. I can solve for x pretty well. But proving that a triangle = a triangle just bewildered me.

Proofs always make me think of the novel "If on a Winter's Night a Traveler" because I can't tell where it's supposed to go, or why I would want to go there anyway.

I had loads of trouble with geometry too (and ours was proof based).  Solving algebra problems was simple in comparison, for me.  I liked trig and even calculus (though calc was definitely my limit).  But geometry was always a tough one for me.  I just couldn't do proofs very well.  Probably the same reason that I do well with a straight-up math problem (like the one here), but less well with a story problem. 
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MrTango

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Re: A math problem.
« Reply #81 on: November 02, 2012, 04:55:15 PM »
6 - (1X0) + (2/2)
6    -  0   +   1
6     -       1
        =5

This is not quite correct.

Your first step (multiplying and dividing first) is fine, but in your second step, you need to do addition & subtraction from left to right, so the six minus zero is done before adding the one.

jedikaiti

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Re: A math problem.
« Reply #82 on: November 02, 2012, 05:13:07 PM »
Thanks to the last 2 posters.  He has now seen his mistake and corrected himself and came up with 7.

I used to make a lot of mistakes on the simplest parts of math/chem/physics problems in high school. Something that helped me a lot was restructuring the way I wrote my math notes when reducing equations. I'd write every version immediately beneath the prior version, with each part lined up vertically, so that it was easier to notice when I'd transposed something, flipped a sign, etc. This helped me a lot in avoiding small errors.

Thank you.  I will share this with him.  I am very surprised he missed it.  He got 100% in Algebra honors last year in a class with students that were 2 grades ahead of him.

Geometry honors is not going so well.  However, engineering is going very well, so I don't get it.

Don't stress it too much - in HS, I got kicked out of honors algebra, but took to geometry like a fish to water. I didn't take ANY math in college (the first time), but on the second go-round I managed to survive Calcs 1-3, linear algebra, and differential equations. :-)
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nyarlathotep

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Re: A math problem.
« Reply #83 on: November 02, 2012, 05:23:59 PM »
Yep, it's 7.

In the UK, we remember it using BODMAS. I was really confused about the Aunt Sally mnemonic until I remembered that M and D were basically interchangeable.

Iris

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Re: A math problem.
« Reply #84 on: November 02, 2012, 05:38:47 PM »

For what it's worth, geometry is kind of a different type of math - it takes a different way of looking at things than the number crunching with algebra.  I know a lot of students who did well in algebra and struggled with geometry and just as many that struggled with algebra but did well with geometry.  Knowing that you have to approach it differently seemed to help a lot psychologically. 

Do you know if his geometry is proof based?



Absolutely. I did really well in Algebra. But the further into Geometry we got, the more lost I became. I can solve for x pretty well. But proving that a triangle = a triangle just bewildered me.

Proofs always make me think of the novel "If on a Winter's Night a Traveler" because I can't tell where it's supposed to go, or why I would want to go there anyway.

I had loads of trouble with geometry too (and ours was proof based).  Solving algebra problems was simple in comparison, for me.  I liked trig and even calculus (though calc was definitely my limit).  But geometry was always a tough one for me.  I just couldn't do proofs very well.  Probably the same reason that I do well with a straight-up math problem (like the one here), but less well with a story problem.

See I love, love, love doing proofs because if I get stuck or am wrong it's always for something silly like not noticing the extra triangle so to me they're like sudoku on fun crack. However, it's 20 years since I've had to do an exam in it so there's no pressure, which may make the difference. Also, without proofs maths is just a bunch of people making up stuff. Proofs are absolutely the cornerstone of mathematics. I read one time that at one stage you couldn't be admitted to study theology if you couldn't follow the proof that square root of 2 is irrational because that was considered the basic amount of logic and abstract reasoning that you needed to have to start with.

Mom21son - sticking my teacher nose in where it doesn't belong for a moment, if the setting out you typed above for this problem was your son's setting out that may be part of his problem with geometry. In most advanced maths setting out becomes really important because it's hard to organise your thoughts if your notes aren't organised first. It honestly is worth the effort and I know many 14 yos think that quicker and shorter is better. If his teacher is encouraging him to try a different setting out tell him to listen, she probably learnt the hard way :)
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MOM21SON

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Re: A math problem.
« Reply #85 on: November 02, 2012, 06:14:19 PM »
Thanks Iris!  They are actually refusing to drop him from the class, due to his mandated state testing scores.  He is doing better since the seat move.  He has a great attitude and wants to do well.  He is just upset because he has his first ever D and did not make the honor roll for the first time ever.

His teacher is very supportive and understands his frustration.

Acadianna

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Re: A math problem.
« Reply #86 on: November 02, 2012, 06:37:19 PM »
The correct answer will not be posted until tomorrow night.  It is causing quite a stir on the FB radio stations page.  Anyone game?

6-1x0+2 divided by 2=?

I have no symbl on my keyboard for divide that I can see.

Is it

6 - 1 x 0 +2 2 =

or

6 - 1 x 0 + 2
--------------- =
        2

That is important.  I read it as the second way and got 4.  If it's written the other way than the answer is 7.   This is why math has rules.

I agree-it does make a difference if it is written the second way rather than the first.  I stand by my 7, but will agree that it should be 4 if it was written the other way.

I never even thought of the second as a possibility.  The nature of the problem (learning order of operations) makes me think that it was probably written the first way, but that is just an assumption on my part and could be completely wrong.

When written the second way the fraction bar is actually both an operation symbol and a grouping symbol (like parantheses). It says to perform all operations in the numerator, and then divide.

We even teach a new mnemonic in math classes -- GEMDAS, with the "G" standing for "grouping" (to include parentheses, brackets, and the fraction bar).

MOM21SON

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Re: A math problem.
« Reply #87 on: November 02, 2012, 06:39:19 PM »
Here is the answer from the station.


To get the answer, the trick is the order of operations (multiplication and division first, addition and subtraction second). Multiplication and division happen at the same time, not one after the other. Same with addition and subtraction. Which is why 7 is the correct answer.



ilrag

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Re: A math problem.
« Reply #88 on: November 02, 2012, 06:59:58 PM »
The "trick" is to follow the rules of math?  ::)

MOM21SON

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Re: A math problem.
« Reply #89 on: November 02, 2012, 07:11:57 PM »
Obviously not everyone, me included knows the rules of math.  I thought it was fun.  But I see that not all did.