Math Question (1 Viewer)

[chet]

My daughter did a graded homework assignment and got docked some marks in the following way.  I looked at what she did and don't think she should have lost marks--what am I missing?

I don't have the exact question, but she was asked to expand some polynomials, collect terms, and then factor.

So she after expanding and collecting, she was left with something like:

56x^2 + 5x -6

Everything was correct until then.  She then factored the above and only wrote the answer:

(8x + 3)(7x - 2)

The teacher took off marks and wrote, "How did you get to the final step?"  There were at least two and possibly three instances of exactly the same scenario where she was penalized.

I am not going to go and fight with the teacher for a homework assignment but I am genuinely :shuked: as to what the intermediary step should be.  I think it's like asking someone to factor 15, and marking them wrong when they write 3 * 5.

 

[IvanKaramazov]

That is weird.  I can't conceive of what the "missing" step would be either.

 

[zamboni]

I'm guessing there was an intermediary step that was taught in determining why to use 8x7 for 56 rather than, say 14x4. 

 

[IC FBGCav]

http://depts.gpc.edu/~dunmol/PDFHandouts/stepsinfactoring.pdf

 

[zamboni]

Ah yes, I seem to remember the FOIL method: http://www.dummies.com/how-to/content/how-to-factor-a-polynomial-expression.html

 

[joffer]

My daughter did a graded homework assignment and got docked some marks in the following way.  I looked at what she did and don't think she should have lost marks--what am I missing?

I don't have the exact question, but she was asked to expand some polynomials, collect terms, and then factor.

So she after expanding and collecting, she was left with something like:

56x^2 + 5x -6

Everything was correct until then.  She then factored the above and only wrote the answer:

(8x + 3)(7x - 2)

The teacher took off marks and wrote, "How did you get to the final step?"  There were at least two and possibly three instances of exactly the same scenario where she was penalized.

I am not going to go and fight with the teacher for a homework assignment but I am genuinely :shuked: as to what the intermediary step should be.  I think it's like asking someone to factor 15, and marking them wrong when they write 3 * 5.

i'm sure that's not important.

 

[Short Corner]

try the AC method

multiply 56*6 = 336

you want to find factors of 336 that have a diference of 5 (21 and 16)

break up 5x into 21x -16x.... 56x^2 -16x + 21x -6  then group terms

(56x^2 - 16x) + (21X - 6) .... 8x(7x - 2) - 3(7x - 2) ...(8x-3)(7x-2)

 

[BobbyLayne]

First

Outer

Inner

Last

Don't be shy about sending her to a state school, Chet.

 

[Kanil]

First

Outer

Inner

Last

Don't be shy about sending her to a state school, Chet.

Don't be a dummy.  It's First, OutSIDE, inSIDE, Last.

 

[gianmarco]

My daughter did a graded homework assignment and got docked some marks in the following way.  I looked at what she did and don't think she should have lost marks--what am I missing?

I don't have the exact question, but she was asked to expand some polynomials, collect terms, and then factor.

So she after expanding and collecting, she was left with something like:

56x^2 + 5x -6

Everything was correct until then.  She then factored the above and only wrote the answer:

(8x + 3)(7x - 2)

The teacher took off marks and wrote, "How did you get to the final step?"  There were at least two and possibly three instances of exactly the same scenario where she was penalized.

I am not going to go and fight with the teacher for a homework assignment but I am genuinely :shuked: as to what the intermediary step should be.  I think it's like asking someone to factor 15, and marking them wrong when they write 3 * 5.

Although others have already answered what those middle steps are, I think it's obvious that SOMETHING has to be done to go from 56x^2 + 5x -6 to (8x + 3)(7x - 2).  Whether it's easy or not or whether or not she can do it in her head is irrelevant.  For someone who hasn't learned how to expand polynomials, you have to learn some method or step to get from Point A (56x^2 + 5x -6) to Point B ((8x + 3)(7x - 2)). 

It's obvious her teacher wanted her to show her work in that step to make sure that she is probably: 1)  doing it herself  2)  doing it the way she was taught/the right way  3)  doing it correctly.  It's not anywhere near as simple as factoring 15 into 3*5 and I'm sure you know this.  Basic principle in virtually every mathematics class (and many science classrooms) is showing your work, especially when it's new subject matter.  Even though many things can be done in your head (especially for brighter students), it doesn't mean you can skip writing them down.  Consider it a lesson learned for her so that she doesn't do it in the future.

 

[Short Corner]

Although others have already answered what those middle steps are, I think it's obvious that SOMETHING has to be done to go from 56x^2 + 5x -6 to (8x + 3)(7x - 2).  Whether it's easy or not or whether or not she can do it in her head is irrelevant.  For someone who hasn't learned how to expand polynomials, you have to learn some method or step to get from Point A (56x^2 + 5x -6) to Point B ((8x + 3)(7x - 2)). 

It's obvious her teacher wanted her to show her work in that step to make sure that she is probably: 1)  doing it herself  2)  doing it the way she was taught/the right way  3)  doing it correctly.  It's not anywhere near as simple as factoring 15 into 3*5 and I'm sure you know this.  Basic principle in virtually every mathematics class (and many science classrooms) is showing your work, especially when it's new subject matter.  Even though many things can be done in your head (especially for brighter students), it doesn't mean you can skip writing them down.  Consider it a lesson learned for her so that she doesn't do it in the future.

The A-C method I used above works the first time every time and basically makes the quadratic virtually have a lead coefficient of 1 which simplifies the problem.  The other method when you havemultiple possible factors for the first term is usually called 'guess-and-check'

 

[pecorino]

Some teachers require students to introduce new linear terns in the middle to create two terms with a common factor and then finally factoring it completely after that. It's silly that the teacher would require it and they should be reprimanded. Or at least buy them a drink because they need to lighten up.

 

[Short Corner]

Some teachers require students to introduce new linear terns in the middle to create two terms with a common factor and then finally factoring it completely after that. It's silly that the teacher would require it and they should be reprimanded. Or at least buy them a drink because they need to lighten up.

I don't think it's silly at all.  It is a method of FOILing in reverse and the alternative is to guess-and-check.

 

[bostonfred]

How certain are you that she's not cheating? 

 

[pecorino]

I don't think it's silly at all.  It is a method of FOILing in reverse and the alternative is to guess-and-check.

The whole overemphasis on factoring is ridiculous and having kids learn methods like this is sill and a waste of time. It's why so many folks don't really know what math is about anyway. The better alternative is to type the polynomial into some piece of technology and if it's factorable then the machine will do it. The example given in this problem is so unlikely to ever be encountered "in the wild" and is so contrived as to be ridiculous. I would prefer that if a student were to be given the problem to factor this polynomial, that the kid would ask "why?" Some do and they get shot down by their teachers who probably couldn't adequately answer their question anyway. </rant>

 

[Short Corner]

The whole overemphasis on factoring is ridiculous and having kids learn methods like this is sill and a waste of time. It's why so many folks don't really know what math is about anyway. The better alternative is to type the polynomial into some piece of technology and if it's factorable then the machine will do it. The example given in this problem is so unlikely to ever be encountered "in the wild" and is so contrived as to be ridiculous. I would prefer that if a student were to be given the problem to factor this polynomial, that the kid would ask "why?" Some do and they get shot down by their teachers who probably couldn't adequately answer their question anyway. </rant>

So because a small minority of teachers are ill prepared to answer why, factoring is over emphasized?  Should kids notlearn to add or subtract as well since they can punch that in to  a machine?  Just because you can't point to a problem 'in the wild' that mirrors this one doesn't mean that this is a building block for attacking problems they will encounter.  Pigeon hole your kid into things she just has to punch into a machine and she will be working the register at McDonalds.

 

[Hooper31]

My daughter did a graded homework assignment and got docked some marks in the following way.  I looked at what she did and don't think she should have lost marks--what am I missing?

I don't have the exact question, but she was asked to expand some polynomials, collect terms, and then factor.

So she after expanding and collecting, she was left with something like:

56x^2 + 5x -6

Everything was correct until then.  She then factored the above and only wrote the answer:

(8x + 3)(7x - 2)

The teacher took off marks and wrote, "How did you get to the final step?"  There were at least two and possibly three instances of exactly the same scenario where she was penalized.

I am not going to go and fight with the teacher for a homework assignment but I am genuinely :shuked: as to what the intermediary step should be.  I think it's like asking someone to factor 15, and marking them wrong when they write 3 * 5.

Plausible reason? The teacher may have shown the class an intermediate step that the teacher expected to see. Or maybe not and the teacher is just a typical math nazi. I can think of a couple of things they may have expected to see. The big X and four square method works very well in this scenario so that a student doesn't have to try and complete multiple operations in their head. The average student isn't good at it. Here's an example of what I'm talking about. 

http://media.showmeapp.com/files/32104/pictures/thumbs/76132/last_thumb1319814991.jpg

Factoring binomials is one of those algebra skills that puts the majority of students on their ### and makes them despise algebra. No, I don't think it's a necessary skill for most people. I think we make students take far too much algebra. I would prefer students focused on statistics. 

EDIT: Almost forgot, nobody likes math. 

 

[Short Corner]

Plausible reason? The teacher may have shown the class an intermediate step that the teacher expected to see. Or maybe not and the teacher is just a typical math nazi. I can think of a couple of things they may have expected to see. The big X and four square method works very well in this scenario so that a student doesn't have to try and complete multiple operations in their head. The average student isn't good at it. Here's an example of what I'm talking about. 

http://media.showmeapp.com/files/32104/pictures/thumbs/76132/last_thumb1319814991.jpg

Factoring binomials is one of those algebra skills that puts the majority of students on their ### and makes them despise algebra. No, I don't think it's a necessary skill for most people. I think we make students take far too much algebra. I would prefer students focused on statistics. 

EDIT: Almost forgot, nobody likes math. 

This essentially a visually aided guess-and-check.  The A-C method is much better.

 

[Hooper31]

This essentially a visually aided guess-and-check.  The A-C method is much better.

It's a better method for those that can do several operations in their head. From my experience that's a small slice of our population. When you ask someone to "find factors of 336 that have a difference of 5" you're not being reasonable when you're talking about all students. I agree that method I displayed is visual, but it's much easier for the majority of students to access. I've taught all levels of mathematics. I can assure you that my calculus students aren't drawing an X and using a four square box. They're doing the calculations in their head.

 

[Short Corner]

It's a better method for those that can do several operations in their head. From my experience that's a small slice of our population. When you ask someone to "find factors of 336 that have a difference of 5" you're not being reasonable when you're talking about all students. I agree that method I displayed is visual, but it's much easier for the majority of students to access. I've taught all levels of mathematics. I can assure you that my calculus students aren't drawing an X and using a four square box. They're doing the calculations in their head.

This is exactly what you are doing when your quadratic has a leading coefficient of 1.  It reduces the number of pairs of factors you have to consider.  If the lead coeff. is one, that is the calculation that calculus students are doing in their head.

FWIW... I didn't learn the A-C method until I started teaching.  Would have save me a lot of time factoring along the way.

 

[bushdocda]

Some weird French math step, maybe.