Daughter's math homework (1 Viewer)

[P Boy]

This is the answer to this whole entire thread.Parentheses would tell you one thing. The LACK of parentheses tells you another. It's clear-cut.

You, my friend, are an example of why nerds get their lunch money stolen & get daily wedgies in elementary school.You may be right, but you won't admit that others can't see things as you do.

 

[Kleck]

-(5)^2 and (-5)^2 would be the best way to to do them both, -5^2 can really be interpreted either way.

This is not the sort of thing that gets to be "interpreted". It is what it is.

 

[Kleck]

If someone chooses not to accept the accepted definition, well, okay. I'm guessing they don't have a very high Erdos number.

Ummm, wouldn't you want a low Erdos number?

Yes, my error.

 

[John 14:6]

I was taught -5^2 = (-1)(5^2). But I'm seeing the point from the other side here. Why can't a negative number stand on its own?Is there some kind of world-wide math board that can settle this once and for all and declare a correct approach?

 

[PC Load Letter]

I was out yesterday so I missed getting in on this thread early.  I am not going to read all 10 pages because we have been down this road before.  I first saw this problem when my son was in middle school.  His teacher and I went toe to toe on this.  I even posted a poll on this last year: Here

Mr. Pack, I feel your pain, the answers are 57 and 54.  The teacher's thinking and all of you people who think like her are wrong.  I am 41 and graduated high school in 1982.  I was taught that -5**2 = -5*-5 = 25 and will always be that way.

I've seen several people justify the other line of thinking and I've seen books that do the same.  But, for my own sanity I asked a former boss of mine.  He is a computer programmer with a masters degree in math ... he said that -5**2 is +25 no way around it.

But -5^2 does not equal -5 * -5. (-5)^2 = -5 * -5. They are 2 completely different equations. When you asked your former boss did you write the equation down or did you ask him in words "What does negative 5 squared equal"? That is not the same as what the formula is saying. When you say "negative 5 squared" you are implying the formula to be (-5)^2 which equals 25. When you say "What is the negative of 5 squared" you are saying -(5^2) = -5^2 = -25

I actually sent him an e-mail with it typed out as -5**2.(I use -5 as an example, it may have actually been -4 in my e-mail. I don't remember exactly, but you get the point.)

Well if he said -4^2 = 25 then he needs his masters revoked.

 

[chet]

I was taught -5^2 = (-1)(5^2). But I'm seeing the point from the other side here. Why can't a negative number stand on its own?

Is there some kind of world-wide math board that can settle this once and for all and declare a correct approach?

I think Shick! and Carlton run that board too. They got that job with their high erdos numbers.

 

[(HULK)]

Dr. Math Explains it AllAccording to his interpretation, both ways are correct. In my view, however, my way is better. Either way, print this out and bring it to the teacher, and your kid should get credit for the correct answer

Squaring Negative NumbersDate: 02/19/2002 at 10:59:10From: Thanh PhanSubject: Squaring negative numbersHello,I would like to know: does -9^2 = 81 or -81?--------------------------------------------------------------------------------Date: 02/19/2002 at 12:38:08From: Doctor RickSubject: Re: Squaring negative numbersHi, Thanh.You really should be precise about what you are asking in this case, since (-9)^2 means -9 times -9, but the expression -9^2 could also be taken to mean -(9^2), that is, the negative of the square of 9, which is -81.When we're working with variables, if we see -x^2, we interpret it in the second way, as -(x^2), because squaring (or any exponentiation) takes precedence over negation (or any multiplication; -x is treated as -1*x. When you have numbers only, as in -9^2, it's not at all clear that we should treat it differently from -x^2. However, some will argue that it should, because -9 represents a single number, not an operation on a number. Thus, some will interpret -9^2 as (-9)^2, while others will read it as -(9^2).Because of the difference of opinion, I highly recommend that you put in the parentheses explicitly whenever this situation arises.- Doctor Rick, The Math Forum

 

[MrPack]

If the problem was meant to be read the negative of 5 squared, then it necessitated a parentheses.  Bottom line.

This is the answer to this whole entire thread.Parentheses would tell you one thing. The LACK of parentheses tells you another.

It's clear-cut.

I was leaning the other way last night, but after reading what smoo smoo wrote and now what hulk wrote, I am moving this way.Why isn't the -5 the base number?

 

[P Boy]

I was taught -5^2 = (-1)(5^2).  But I'm seeing the point from the other side here.  Why can't a negative number stand on its own?Is there some kind of world-wide math board that can settle this once and for all and declare a correct approach?

A negative number can not stand on its own in this kind of problem without parentheses for exactly the reason that -5^2 = -25. Parantheses are added to show attachment of the negative to the number which makes it negative, rather than an unwritten 0 before a subtraction sign. That is a truth in the mathematical world.

 

[Ditkaless Wonders]

So if I think that -5 ^ 2 = 25 was I mistaught back in the 70's, did I mislearn this back in the 70's, or has the convention on order of operations shifted in that time?Nevermind. Pony's post cleared it up. I think my initial algebra teacher in seventh grade may have needed an education. Fortunately most equations are written with redundant clarity. They may not be ellegant, but they are clear.

 

[(HULK)]

Google calculator's answer

 

[MrPack]

I have come to the conclusion that the way it's written, BOTH sets of answers are correct since it's not written very clearly.I still say -5 can be the base number here.

 

[Sam Quentin]

PB, it's great that your company always prevents confusion by including the parenthesis but not all companies are as careful as yours. Which is why kids need to be taught order of operation rules. The teacher is doing the right thing by giving these examples. It doesn't matter if kids get tripped up by them. They will learn from their (or their father's  )mistakes and fix them.

Hence the problem. That lies in who is reading the material, not that we knew what we meant when we performed the calcs. You can't count on the interpretation skills of the reader or checker - so you avoid confusion through written clarity.THAT would be much more important for the teacher to be teaching - adding parentheses for clarity, and leading by example. Providing & enhancing the clarity of written material is critical for anyone in the real world, rather than worrying about whether kids missed the fact that the negative is applied after squaring the number. As a mathematician, I would have placed the parentheses in the proper place before submitting the problem.

So, you'd teach them how to write math "properly", but ignore teaching them hoe to read it properly?

 

[(HULK)]

I have come to the conclusion that the way it's written, BOTH sets of answers are correct since it's not written very clearly.

I still say -5 can be the base number here.

Exactly.-5 is a number. Unless it is explictily defined one way or another, I see no reason to not read -5 as negative five.

 

[P Boy]

So if I think that -5 ^ 2 = 25 was I mistaught back in the 70's, did I mislearn this back in the 70's, or has the convention on order of operations shifted in that time?

It means you ought to stick to a profession that doesn't require anything more than adding years to jail sentences, which always are positive numbers unless you happen to be the one convicted, in which case they are most certainly negative.It also means you need to let your wife give your daughter help with her math homework in the future.

 

[rolyaTy]

I was taught -5^2 = (-1)(5^2). But I'm seeing the point from the other side here. Why can't a negative number stand on its own?

Is there some kind of world-wide math board that can settle this once and for all and declare a correct approach?

A negative number can stand on its own. (-5)^2

The rule is all about removing ambiguity

 

[Ditkaless Wonders]

Fortunately I took my revenge on my seventh grade algebra teacher by boning his daughter for a year in college.

 

[(HULK)]

So if I think that -5 ^ 2 = 25 was I mistaught back in the 70's, did I mislearn this back in the 70's, or has the convention on order of operations shifted in that time?

It means you ought to stick to a profession that doesn't require anything more than adding years to jail sentences, which always are positive numbers unless you happen to be the one convicted, in which case they are most certainly negative.It also means you need to let your wife give your daughter help with her math homework in the future.

You ought to read what Dr. Math said.

 

[NCCommish]

Dr. Math Explains it All

According to his interpretation, both ways are correct.  In my view, however, my way is better.  Either way, print this out and bring it to the teacher, and your kid should get credit for the correct answer

Squaring Negative Numbers

Date: 02/19/2002 at 10:59:10

From: Thanh Phan

Subject: Squaring negative numbers

Hello,

I would like to know: does -9^2 = 81 or -81?

--------------------------------------------------------------------------------

Date: 02/19/2002 at 12:38:08

From: Doctor Rick

Subject: Re: Squaring negative numbers

Hi, Thanh.

You really should be precise about what you are asking in this case,

since  (-9)^2 means -9 times -9, but the expression -9^2 could also be

taken to mean -(9^2), that is, the negative of the square of 9, which

is -81.

When we're working with variables, if we see -x^2, we interpret it in

the second way, as -(x^2), because squaring (or any exponentiation)

takes precedence over negation (or any multiplication; -x is treated

as -1*x.

When you have numbers only, as in -9^2, it's not at all clear that we

should treat it differently from -x^2. However, some will argue that

it should, because -9 represents a single number, not an operation on

a number. Thus, some will interpret -9^2 as (-9)^2, while others will

read it as -(9^2).

Because of the difference of opinion, I highly recommend that you put

in the parentheses explicitly whenever this situation arises.

- Doctor Rick, The Math Forum

Going to be siding with the good doctor here.

 

[P Boy]

So, you'd teach them how to write math "properly", but ignore teaching them hoe to read it properly?

Well, I'd keep hoes out of the classrooms unless you are teaching multiplication. But I would encourage enhancement of understanding of mathematical problems.Again, if this were a problem in the real world, it would be a subtration problem, not an add-a-negative problem. The -5^2 would be placed at the end of the problem, not the beginning.There's a distinct difference between understanding theory & practical application, and how each are perceived by experts and non-experts.

 

[rolyaTy]

I have come to the conclusion that the way it's written, BOTH sets of answers are correct since it's not written very clearly.

I still say -5 can be the base number here.

That conclusion is wrong, even though it doesn't make sense to you why it is Teachers give students those types of problems SPECIFICALLY to make sure they understand the difference between -5^2 and (-5)^2 , because there is a difference and it's important to know and to remember that they aren't the same. (Although apparently many people can go through their lives oblivious to this and not suffer from it).

 

[Clayton Gray]

If this were a poll, mark me down as

57

54

-5^2 = 25

Suddenly, I know why mediocre chicks win the babe bracket.

 

[Sam Quentin]

Dr. Math Explains it All

According to his interpretation, both ways are correct. In my view, however, my way is better. Either way, print this out and bring it to the teacher, and your kid should get credit for the correct answer

Squaring Negative Numbers

Date: 02/19/2002 at 10:59:10

From: Thanh Phan

Subject: Squaring negative numbers

Hello,

I would like to know: does -9^2 = 81 or -81?

--------------------------------------------------------------------------------

Date: 02/19/2002 at 12:38:08

From: Doctor Rick

Subject: Re: Squaring negative numbers

Hi, Thanh.

You really should be precise about what you are asking in this case,

since  (-9)^2 means -9 times -9, but the expression -9^2 could also be

taken to mean -(9^2), that is, the negative of the square of 9, which

is -81.

When we're working with variables, if we see -x^2, we interpret it in

the second way, as -(x^2), because squaring (or any exponentiation)

takes precedence over negation (or any multiplication; -x is treated

as -1*x.

When you have numbers only, as in -9^2, it's not at all clear that we

should treat it differently from -x^2. However, some will argue that

it should, because -9 represents a single number, not an operation on

a number. Thus, some will interpret -9^2 as (-9)^2, while others will

read it as -(9^2).

Because of the difference of opinion, I highly recommend that you put

in the parentheses explicitly whenever this situation arises.

- Doctor Rick, The Math Forum

Where in there does Dr Rick say that either is correct?Just because there is a difference of opinion does not mean that one way isn't the generally accepted real answer.

 

[rolyaTy]

So, you'd teach them how to write math "properly", but ignore teaching them hoe to read it properly?

Well, I'd keep hoes out of the classrooms unless you are teaching multiplication. B

 

[Clayton Gray]

Pack--pls print this out and give it to your daughter to bring to her teacher.

Trust me, the thought has crossed my mind.I sent these problems out to all the engineers here at work, and everyone but 1 came back with the right answers. They all came up with the same answer I did.

 

[P Boy]

You ought to read what Dr. Math said.

"Because of the difference of opinion, I highly recommend that you put in the parentheses explicitly whenever this situation arises."

- Doctor Rick, The Math Forum

I believe that the good Doctor's opinion is exactly what I've been championing here.

Thanks.

 

[Clayton Gray]

Not reading through this whole thing.

My mom is currently a math teacher, and I got an 800 on the math portion of the SAT.

It's a good thing -5^2 wasn't on the SAT.

-5 squared equals 25. If the problem was meant to be read the negative of 5 squared, then it necessitated a parentheses. Bottom line.

I'm here to correctly tell you that -5^2 is -25.

Because negative 25 is the negative answer, and 2 negatives = a positive; I can POSITIVELY tell you you're wrong. -5^2=25

Yep

 

[Sweet J]

You missed the post where Pack says his daughter originally answered the questions correctly but he told her they were wrong. She ended up changing the answers and now has a 99.9% in the class.

 

[lombardi]

Why, so that one day when the kid faces the problem in a completely acceptable, clear, and solveable form without parentheses, he can stare at it like a deer in the headlights?

There is only one answer to this problem, and the student should learn and understand that.

Okay, provide me with a real world sitiuation where the equation would be written in this form rather than as a subtraction problem.The real world & the world that we math nerds exist in are very different. Don't be so anal just to prove a point.

If someone said the equation for a parabola is y=-x^2, are you implying that thats the same as the parabola y=x^2?

Wow, now that blows my mind. I was so sure I was right and then I read this and I have to reconsider.That's what I get for going over to the dark side and agreeing with Smoo.

 

[Ditkaless Wonders]

So, you'd teach them how to write math "properly", but ignore teaching them hoe to read it properly?

Well, I'd keep hoes out of the classrooms unless you are teaching multiplication. But I would encourage enhancement of understanding of mathematical problems.Again, if this were a problem in the real world, it would be a subtration problem, not an add-a-negative problem. The -5^2 would be placed at the end of the problem, not the beginning.

There's a distinct difference between understanding theory & practical application, and how each are perceived by experts and non-experts.

GB eggheads for hire. Were it up to me to engineer stuff we would all be living in shallow depressions in the ground and walking everywhere we wanted to go.

 

[rolyaTy]

I don't believe teachers should use negative numbers. There are plenty of positive numbers to choose from.

 

[John 14:6]

This alludes back to an earlier post, but what would your answers be for these?4 x 2³ - 5² =2 x 3² - 6² =

 

[trout]

If this were a poll, mark me down as

57

54

-5^2 = 25

Suddenly, I know why mediocre chicks win the babe bracket.

Hey...in those polls, I always vote for the hottest chicks...I'm positive about that.

 

[Clayton Gray]

From the Prentice Hall "Middle Grades Math - Tools for Success" Course 2 - 1999 Edition, Page 157:

When you use an exponent with a negative numer as the base, it is important to use grouping symbols to avoid confusion.Example 3: Simply each expression.a. (-5)^4 = (-5)(-5)(-5)(-5) = 625b. -5^4 = -(5*5*5*5) = -625

 

[Dolfan]

I have come to the conclusion that the way it's written, BOTH sets of answers are correct since it's not written very clearly.

I still say -5 can be the base number here.

That conclusion is wrong, even though it doesn't make sense to you why it is Teachers give students those types of problems SPECIFICALLY to make sure they understand the difference between -5^2 and (-5)^2 , because there is a difference and it's important to know and to remember that they aren't the same. (Although apparently many people can go through their lives oblivious to this and not suffer from it).

Why are they different? Because you, and some math scholars say so?I say there is a difference between -5^2 and -(5)^2.

 

[playin4beer]

Can I incorporate two threads into one and quote "Tommy Boy" here???

My fellow nerds and I will retire to the nurdery with our calculators

 

[rolyaTy]

Why, so that one day when the kid faces the problem in a completely acceptable, clear, and solveable form without parentheses, he can stare at it like a deer in the headlights?

There is only one answer to this problem, and the student should learn and understand that.

Okay, provide me with a real world sitiuation where the equation would be written in this form rather than as a subtraction problem.The real world & the world that we math nerds exist in are very different. Don't be so anal just to prove a point.

If someone said the equation for a parabola is y=-x^2, are you implying that thats the same as the parabola y=x^2?

Wow, now that blows my mind. I was so sure I was right and then I read this and I have to reconsider.That's what I get for going over to the dark side and agreeing with Smoo.

The thing is though, that when you're talking about a variable, it's easy to see that the rule is right.But the argument is over when you have a specific number, like -5^2...whether negative five is the number being squared, or whether it's the opposite of five squared.

Because it's clear that when using a variable, you square first then invert, you should do the same with -5^2 to get -25. It'll save the kids trouble down the line when they get to math that uses variables.

 

[Clayton Gray]

Pack--pls print this out and give it to your daughter to bring to her teacher.

Trust me, the thought has crossed my mind.I sent these problems out to all the engineers here at work, and everyone but 1 came back with the right answers. They all came up with the same answer I did.

They aren't sanitation engineers are they?

 

[shadyridr]

What does this equation equal?-x^2+x=if x=5?

 

[P Boy]

I don't believe teachers should use negative numbers. There are plenty of positive numbers to choose from.

'90s education - anything to enhance the students' self esteem while accentuating the positive and ignoring (oops) de-emphasizing the negative.

 

[Smoo]

Please, somebody solve the following problems:5-*312*/46+*7Those don't make sense, right? You don't put two operators in a row?So why does this make sense?0--5The answer to that is clearly 5. You're subtracting -5 from 0, to get 5. Why is that?Oh right. Because the negative in front of the 5 is NOT an operator! It's PART OF THE NUMBER!

 

[(HULK)]

Why, so that one day when the kid faces the problem in a completely acceptable, clear, and solveable form without parentheses, he can stare at it like a deer in the headlights?

There is only one answer to this problem, and the student should learn and understand that.

Okay, provide me with a real world sitiuation where the equation would be written in this form rather than as a subtraction problem.The real world & the world that we math nerds exist in are very different. Don't be so anal just to prove a point.

If someone said the equation for a parabola is y=-x^2, are you implying that thats the same as the parabola y=x^2?

Wow, now that blows my mind. I was so sure I was right and then I read this and I have to reconsider.That's what I get for going over to the dark side and agreeing with Smoo.

There is a significant difference between how an interger is treated versus a variable.

 

[posty]

Simple...Now -5^2 is negative of 5^2 or -25...When I went to school, it was (-5)^2 or 25...My wife, who teaches 7th and 8th grade math, has to teach it the first way...

 

[trout]

This alludes back to an earlier post, but what would your answers be for these?

4 x 2³ - 5² =

2 x 3² - 6² =

4*8-25= 7But, had it been presented as -5^2 + 4*2^3 I would've said 25+32=57

 

[PC Load Letter]

From the Prentice Hall "Middle Grades Math - Tools for Success" Course 2 - 1999 Edition, Page 157:

When you use an exponent with a negative numer as the base, it is important to use grouping symbols to avoid confusion.

Example 3: Simply each expression.

a. (-5)^4 = (-5)(-5)(-5)(-5) = 625

b. -5^4 = -(5*5*5*5) = -625

Well that's all well and good for ^4 problems, but this a ^2 problem.

 

[Clayton Gray]

If the problem was meant to be read the negative of 5 squared, then it necessitated a parentheses.  Bottom line.

This is the answer to this whole entire thread.Parentheses would tell you one thing. The LACK of parentheses tells you another.

It's clear-cut.

I was leaning the other way last night, but after reading what smoo smoo wrote and now what hulk wrote, I am moving this way.Why isn't the -5 the base number?

Because it just isn't. I don't care what Dr. Maff wrote.

 

[rolyaTy]

I have come to the conclusion that the way it's written, BOTH sets of answers are correct since it's not written very clearly.

I still say -5 can be the base number here.

That conclusion is wrong, even though it doesn't make sense to you why it is Teachers give students those types of problems SPECIFICALLY to make sure they understand the difference between -5^2 and (-5)^2 , because there is a difference and it's important to know and to remember that they aren't the same. (Although apparently many people can go through their lives oblivious to this and not suffer from it).

Why are they different? Because you, and some math scholars say so?I say there is a difference between -5^2 and -(5)^2.

If you want your kid to succeed in math, teach them that -5^2=-25, if not, tell them to interpret math equations according to their personal preference.-5*4+2*(-5)^2=apple pie 2+2=candy

Hope that works for ya

 

[John 14:6]

Please, somebody solve the following problems:

5-*3

12*/4

6+*7

Those don't make sense, right? You don't put two operators in a row?

So why does this make sense?

0--5

The answer to that is clearly 5. You're subtracting -5 from 0, to get 5. Why is that?

Oh right. Because the negative in front of the 5 is NOT an operator! It's PART OF THE NUMBER!

Are these statements true?4 x 2³ - 5² = -5² + 4 x 2³

2 x 3² - 6² = -6² + 2 x 3²

 

[P Boy]

Well that's all well and good for ^4 problems, but this a ^2 problem.

 

[P Boy]

Are these statements true?4 x 2³ - 5² = -5² + 4 x 2³2 x 3² - 6² = -6² + 2 x 3²

Yes