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Daughter's math homework (1 Viewer)
- Thread starter MrPack
- Start date
But I would have missed it too. 
SkyRattlers
Anti-aliai
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'sAnd I respectfully disagree. As an engineering firm participating in real world problems where we do in fact have to submit calculations & drawings to local jurisdictions, I can state that it is company policy to ALWAYS use parenthesis to avoid ambiguous interpretations of signs & quantities.The negative sign out front is ambiguous - especially to a child learning operations.I disagree. The problem as written has a very clear and definite meaning. There is no ambiguity here.
The teacher should have used either -(5^2) or (-5)^2 to avoid any confusion. While you are correct about the proper order of operations on this problem, it is borderline a trick question with the placement of the negative sign without any parenthesis. I'm not sure we ought to be teaching sneaky tricks to kids - we ought to be teaching them proper use of mathematical processes. In fact, the problems should have been written as subtraction problems rather than adding negative problems.
And as an addition, I'll add that I was a teacher of math & physics for 12 years before getting my engineering degrees & opening our own company. I never would have used a confusing question like this in class or on a test. Your goal as a teacher isn't to try to trip kids up.
)mistakes and fix them.
Smoo
Fear the Beaver
Wrong. And your continuing to assert this as divine truth is getting mildly irritating. The base number in this problem is -5. -5 is a number, all on its own. If you want to spedify that it's an operation, you need to do so explicitly, using parentheses.-5^2 = 25 exactly follows the order of operations, because there's only a SINGLE OPERATION.
IvanKaramazov
Footballguy
No, that's the thing. It's accepted by everybody that multiplication is done before addition, so I don't need to specify that through parenetheses. As this thread has shown, it is NOT understood by everyone how to interpret -5^2, so you need to include parenetheses to specify exactly what it is you're saying. This is very similar to communicating in English. If I go in front of my students and say "Mathematicians tend to think Platonically," that statement has a clear, unambiguous meaning, but my students won't understand what that meaning is. They'll walk away thinking I said that mathematicians are all virgins. If I want to say that mathematicians like to reason abstractly, I should have just said that rather than use a phrase that I should have known would be easily misinterpreted.
Likewise, I promise you that if I told my students to calculate 4x2^2, 95+% of them would get it right, while if I told them to calculate -5^2, half of them would approach it one way and half would approach it the other way. That's not really their fault as much as it is mine for failing to say what I meant to say.
Mjolnirs
Footballguy
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.
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.
NCCommish
Footballguy
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The mathematician will argue that parenthesis are not needed in that problem any more than they are needed in (3 + 2) - 1.
(HULK)
(Smash)
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.-5^2 = -5 * -5 = 25This is the way of things. The teacher is wrong.In middle school, I had a teacher that taught that all rivers flow south. When I objected, I got detention. This teacher is wrong, and I hope for your child's sake that she is more open to critism.
shadyridr
Footballguy
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
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Whatevaman15
Footballguy
As a university math student, I can assure you guys that -5^2=-(5^2). Its the negative of 5-squared. Just like -x^2=(-x)^2. Did you guys used to write parabolas opening down as -(x^2)+3x+5 or whatever, rather than just -x^2+3x+5?
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.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
It's a good thing -5^2 wasn't on the SAT.
Dolfan
Footballguy
I only made it through the first few pages of this thread, but this post kind of sums up the argument I disagree with.Sure negative 5 is negative 1 times 5, but what does that have to do with the price of beans in China?
This might really blow your mind but negative 5 is also positive 25 divided by negative 5. And it is also negative 3 minus 2. And a whole lot of other things. When solving a problem though, it is just a number. A unique, single number called negative 5.
Using the logic by some in this thread, look at how I can screw up another problem:
16 * 10
Now I'm going to tell you that 16 is not really 16. 16 is really 8 + 8.
This gives us 8 + 8 * 10
Following Order of Operations, we get 8 + 80 = 88.
Isn't the correct answer 160?
I just don't get the whole idea of saying negative 5 is really -1 * 5
It's not. It's simply -5
Otis
Footballguy
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.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.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
Okay, I'll rephrase:The negative sign out front is ambiguous to most people without advanced skills in mathematics.The negative sign out front is ambiguous - especially to a child learning operations.I disagree. The problem as written has a very clear and definite meaning. There is no ambiguity here.
but here goe.......
Smoo
Fear the Beaver
No, the base number is -5. Self-contained numbers don't require parentheses.All this thread has established is that the powers-that-be in math have established by consensus that negative numbers are not to be considered actual numbers, merely as positive numbers with an operation on them. That doesn't make them right, it just makes them bullies with a stupid idea.
Otis
Footballguy
But this is not an advanced concept. We are talking fundamentals. Which is precisely why the question is actually a very good one for a young math student.Okay, I'll rephrase:The negative sign out front is ambiguous to most people without advanced skills in mathematics.The negative sign out front is ambiguous - especially to a child learning operations.I disagree. The problem as written has a very clear and definite meaning. There is no ambiguity here.
PC Load Letter
Irregardless.
OK.. for the last effing time....
Negative 5 is, by definition, 5 times negative 1.
You do multiplication AFTER exponents.
PERIOD.
This is the same reason why -6/-3 = 2
... the -1's cancel out and you're left with 6/3.
Negative 5 is, by definition, 5 times negative 1.
You do multiplication AFTER exponents.
PERIOD.
This is the same reason why -6/-3 = 2
Code:
(-1)*(6)--------(-1)*(3)
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Good point.
I'm here to correctly tell you that -5^2 is -25.-5 squared equals 25. If the problem was meant to be read the negative of 5 squared, then it necessitated a parentheses. Bottom line.It's a good thing -5^2 wasn't on the SAT.
Whatevaman15
Footballguy
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?
I was with you until you said it was a stupid idea.
PC Load Letter
Irregardless.
No offense, but remind me never to go over any bridges or into any tall buildings in Wisconsin.
Because negative 25 is the negative answer, and 2 negatives = a positive; I can POSITIVELY tell you you're wrong.I'm here to correctly tell you that -5^2 is -25.-5 squared equals 25. If the problem was meant to be read the negative of 5 squared, then it necessitated a parentheses. Bottom line.It's a good thing -5^2 wasn't on the SAT.
-5^2=25Where in everything that I have added to this thread have I made any implication like the one you are asking me about here?While most people will have at least some confusion about the negative placed in front of a number at the beginning of an equation, through my experience they'll have much less confusion about a negative placed in front of a variable.And everything I've written applies to interpretation by people - often people who may not hold advanced mathematical knowledge, not about mathematical truths.While something may be obvious to you, because you are well versed in math & understand it well, the point is that not all people are like you in that regard. Why not make the small effort to clarify a math problem by making exactly two more small marks on a piece of paper, especially for better understanding by a neophyte?
Mjolnirs
Footballguy
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.)
