Discussion in 'Debate & Marathon Threads Archive' started by DrivingPigeon, Apr 6, 2015.

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1. ### DrivingPigeonPhenom

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Apr 6, 2015

Yesterday my family was at my grandma and grandpa's house for Easter when my dad decided to give us a math problem to solve. He said that he saw it on facebook with a note that said "50% of people will get this wrong." He said that he's shown it to "hundreds" of people, and young people get it wrong because of the "new math" that we're learning these days. He said that he gave it to a high school math teacher, who looked at it for a long time, and got it wrong.

Before showing it to us he said that my grandma and aunt would get it right, but my husband and I would probably get it wrong, because we were taught this "new math." I thought that was pretty entertaining, because my husband and I were the only 2 in the room with a college education, and my husband is an electrical engineer. He graduated 3rd in his class from a top engineering school, and has taken the highest level math classes offered.

This is the problem that he gave us: 7 + 7 / 2 x 8 - 6

What do you get for an answer? What do you think my dad thinks the answer is (hint: he's wrong )?

3. ### comabaCohort

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Apr 6, 2015

29

Did he get 50?

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Apr 6, 2015

29

5. ### DrivingPigeonPhenom

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Apr 6, 2015

Yes!

My husband and I both got 29, and my dad kept telling us that we were wrong, because of the "new math" that we were taught. We tried to explain order of operations, but he kept telling us we were wrong and that the problem was so simple. I'm embarrassed for him, because he's obviously showing this to a lot of people (he bartends on the weekends), and he doesn't even know the right answer.

The best part was his rant about how kids these days are taught math in such weird ways. He also went off on a rant about how kids aren't taught history anymore in schools. It was so difficult for me not to say anything, but I really didn't want to get into it.

6. ### czaczaMultitudinous

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Omg. Sounds like my MIL. FIL is a retired hs math teacher and administrator. He now is an adjunct and teaches math remediation at a small college. My MIL pontificates on common core ALL THE TIME and how her girlfriend retired because the standards drove her out and how good teachers are leaving(more like she was eligible for retirement and pension funding threats being what it is, she went...) MIL wouldn't be able to do that math problem. FIL would.

7. ### MikeTeachesMathDevotee

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Apr 6, 2015

It's especially difficult being a math teacher under common core. You have to deal with all kinds of stupid opinions.

8. ### brosPhenom

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Apr 6, 2015

The answer is 29 because the way it is written, there are no parentheses to define how it should be done.

So it becomes:
7+((7/2)*8)-6

9. ### czaczaMultitudinous

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Bros,why did you feel you needed to google for the answer? Aspects of order of operations are taught as early as grade 3.

10. ### swansong1Virtuoso

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Apr 6, 2015

Common core has not changed order of operations, to the best of my knowledge. I would have figured it out the same before and after CC.

11. ### czaczaMultitudinous

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:thumb: good old PEMDAS!

12. ### DrivingPigeonPhenom

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Apr 6, 2015

Exactly. I'm so tempted to send my dad the Khan Academy video on order of operations, along with an explanation of its origin. I'll think I'll just let it go, though. :thumb:

13. ### lucybelleConnoisseur

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Apr 6, 2015

I always see these "math" challenges on facebook. I think they're silly. If anyone really wanted someone to solve that they would put parenthesis on the freaking thing!

*LB's rant over*

I also got 29 easily. For a second I thought you all were saying that was the wrong answer and I was like whhaaa?

14. ### stephenpeConnoisseur

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Apr 6, 2015

When I read it like this
7+7
2x8-6

I get 14 divided by 10 or 1 2/5

15. ### czaczaMultitudinous

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You aren't applying order of operations.

7 + 7 / 2 x 8 - 6

You'd do 7/2 first=3 1/2

Then multiply by 8. 8x3 1/2 = 28

Then 7+28= 35

Subtract 6. 35-6=29.

16. ### TeacherGroupieModerator

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Apr 6, 2015

Um, it's not quite that simple.

Had the expression been written with the obelus or standard division sign, ÷, like this,

7 + 7 ÷ 2 × 8 – 6 ,​

then, yes, the order of operations goes forth as czacza indicates and the result is 29.

But the symbol that's in play isn't ÷, it's /. Whether that symbol is called "slash", "diagonal", "solidus", or "virgule", it's not ONLY a division sign: instead, it is used in an inline fraction (that is, a fraction that is typeset as one line) to separate the numerator from the denominator.

As Wolfram Mathworld notes with a less spectacular example, is that the resulting expression IS still ambiguous: we don't know just how much of what's before / is intended to be numerator nor how much of what's after / is intended to be denominator. That is, our 7 + 7 / 2 × 8 – 6 contains a fraction, and, according to math's rules of punctuation, that fraction really and truly COULD be any of the following:

7
8

7 + 7
_ 2

___7___
2 × 8 – 6

7 + 7
2 × 8

___7___
2 × 8 – 6

__7 + 7_
2 × 8 – 6

Using any of these vertical fractions disambiguates matters in a hurry, but they are more than slightly a pain to produce. To see how I did these, choose Reply-With-Quote. The fractions will look extremely untidy. The typographical untidiness goes far toward explaining why the solidus even exists distinct from the obelus.

On behalf of my mathematician friends, let me beg everyone please when writing math to provide such parentheses as are necessary to make things clear, and to avoid using / or solidus unless you actually do intend a fraction. (Typing an obelus on a Mac is pretty easy: it's Option-/. I expect that it isn't much harder on a PC.)

17. ### DrivingPigeonPhenom

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Apr 6, 2015

Uhhh...I didn't know how to do the division symbol. I thought about explaining that the / was in place of the division symbol, but I assumed people would just figure it out. And they did.

But thanks for all of that.

18. ### czaczaMultitudinous

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:lol:

I've never thought about a keyboard not having the 'division sign', but good we understood what you meant.

19. ### TeacherGroupieModerator

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It can be disconcerting when a story turns out to be less cut and dried than one thought, yes.

Turns out, by the way, that the notation that we all grew up with for long division is really rather recent - enough so that the sign for it (which looks like it was cobbled together from a left parenthesis attached to a horizontal line, because it WAS cobbled together from a left parenthesis attached to a horizontal line) doesn't have its own name. See http://jeff560.tripod.com/operation.html.

20. ### vickilynMagnifico

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Apr 6, 2015

Wow, I thought I was the only person not seeing it as clear cut, and now I can understand why. I truly thank you.

21. ### brosPhenom

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Apr 7, 2015

Order of Operations might be taught that early now. I was taught it in eighth grade (Pre-Algebra, or at least that was what was taught at the time).

Because I couldn't figure that out mentally. Last time I had to do any kind of rigorous mental math was my neuropsych eval in 2010, before that, sometime in high school when we weren't allowed to use calculators.

If I were to try to solve it without a calculator, I would proceed as follows:
7+7/2*8-6
PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)

No P or E. so lets do M, as that is what comes first.

2*8

16
7+7/16-6

There's D

7/16 = 7/16

7+7/16-6

There's A
7+7/16 = 7 7/16

7 7/16-6

Now there's S

7 7/16-6

1 7/16

Yeeeeah

I have no idea how or why you can change the order of operations like that. It is PEMDAS, not PEDMAS.

alt+0247 (on the numpad) ÷ for windows users.

22. ### TeacherGroupieModerator

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Oh, and on a PC I bet Alt-/ (that is, Alt plus lower case question-mark) would work to type the obelus.

23. ### MikeTeachesMathDevotee

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Apr 7, 2015

PEMDAS and PEDMAS are the same thing. It's "multiplication or division, whichever comes first".

24. ### 3SonsConnoisseur

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I see M/D as essentially the same operation (albeit, inverse of each other). Similar with addition/subtraction.

The way I did the problem is by treating 7/2 as a fraction, multiplying it by 8 to get 56/2, and then dividing 56 by 2 to get 28 (in fact, you'd get the same answer, perhaps easier mentally, by dividing the 8 by 2 first to get 4, and then multiplying the 4 by 7). Then I add 7, and then subtract 6 (though I *could* have combined the +7 and -6 together and just added one).

Personally, I don't see the question as ambiguous. If there aren't parentheses, the 7+7 is NOT intended to be grouped over the 2 (it may be because of my background in computer programming, where formula HAVE to use the virgule and the computer will quite clearly use the OoO as defined within its math guts, to do the problem).

25. ### czaczaMultitudinous

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Aspects of order of operations are taught in grade three. NOT all of PEMDAS. For example, third graders solve word problems requiring them to use multiple operations and write equations to solve. They are also using beginning algebra concepts in some activities. Definitely 4th and definitely in 5th, students are pretty much using PEMDAS as shown here (albeit with the regular division sign in most cases)

A bit off topic, but did you take any math in college, or as part of teacher preparation? I transferred my license from Virginia so I'm unclear of what Praxis are required in our state, but do NJ teachers take the math Praxis as part of certification?

26. ### 3SonsConnoisseur

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Not sure this has anything to do with common core, but maybe it should:

A bat and ball cost \$1.10.

The bat costs one dollar more than the ball.

How much does the ball cost?

27. ### czaczaMultitudinous

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PEMDAS is not exclusively common core, nor is problem solving. Both types of math concepts existed way before CCSS.

28. ### gr3teacherPhenom

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Apr 7, 2015

It should really be:
P
E
MD
AS

Basically, multiplication and division are done in order, as are addition and subtraction. You work from left to right, doing them in the order they come up.

29. ### amakayeEnthusiast

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Apr 7, 2015

I didn't know it didn't have an official name. When I was in elementary school, it was called a "division box", and that's the same name that the math series I teach uses (in another region of the country, interestingly).

30. ### czaczaMultitudinous

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Just for fun I call it the goesinto sign! As in 4 goes into 28 :lol:

However, I teach my kids how problems are set up in different ways and how to navigate through and problem solve regardless of how an equation is set up.

31. ### Ms.BlankCompanion

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Apr 7, 2015

hmy:

Bros, I really don't mean to be offensive here, but someone else asked what I'm thinking...how did you get through a bachelor's program AND and teaching credential program without ever hitting (and fully comprehending) the order of operations? Even if you DID first approach them fully at eighth grade, you've had more than enough time to master the concept. Could this be a component in your troubling job search? Are you teaching something to do with this during demo lessons, have a reference who is telling prospective employers that your math foundation isn't solid, SOMETHING? Just a thought, maybe something to look into... The others are right, the schools I work in are working with the full range of order of operations in fifth grade, with smaller parts of this concept being taught all the way up until then (meaning this is something that you, as an elementary school educator, should be very familiar with...I am NOT saying that just because now they are working with it in elementary, that means you should have learned it in elementary...please don't twist my point around).

Honestly, I'd be furious if I had sixth graders come to my classroom after having a fifth grade teacher that taught them that multiplication MUST come before division and addition MUST come before subtraction...because it doesn't work that way. It would be a LOT of reteaching on my part. Order of operations is a HUGE concept...one that is built upon and used well into high college level math (and the rest of one's math schooling and career). It's important. Without a proper foundation, the kids will suffer greatly.

32. ### MikeTeachesMathDevotee

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Apr 7, 2015

Let x = the cost of the ball
Therefore, x + 1 = the cost of the bat

x + (x + 1) = 1.10
2x + 1 = 1.10
2x = 0.10
x = 0.05

Therefore, the ball costs 5 cents and the bat \$1.05.

My knee-jerk reaction was 10 cents .

33. ### amakayeEnthusiast

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I also thought 10 cents at first, then realized the bat would be \$1.10. The article was interesting, considering it might be evidence of an aversion to thinking and reasoning to check a problem. That's definitely something I notice in my students...

34. ### czaczaMultitudinous

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Kids who aren't yet using algebraic thinking could solve this using a guess and check strategy. I guarantee I have at least three kids who could work through the bat and ball problem merely based on perseverance and good number sense.

35. ### a2zMaven

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They can only do so if they know how to comprehend the question which is a language and/or reading task that depends on a good understanding of grammar.

They have to understand that "a dollar more than the ball" doesn't mean a dollar. Those that don't comprehend language well and don't understand the comparison in that phrase will struggle to be able to do guess and check.

36. ### stephenpeConnoisseur

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All of our 5th grade teachers are teaching order of operations this year, We spent a lot of time on it. So wasnt my answer actually right with the slash instead of the other sign.

37. ### czaczaMultitudinous

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Read the OP's response to the question regarding the slash. Those of us who teach math basically interpreted the slash as 'divided by'.... But then again, I'd be hard pressed to know the rules to volleyball.

38. ### czaczaMultitudinous

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I guarantee I have at least 3 in my class who have the background knowledge and skills to solve the bat and ball problem. No doubt.

39. ### ChristyFModerator

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Wow....I don't view order of operations as life altering. I teach the location of the states, but I don't look down on someone who doesn't know them. By the way, when I was taught order of operations many years ago, I was taught that there was no varying. I completely understand the relationship between multiplication and division as well as adding and subtracting, but I was taught that PEMDAS was carved in stone, no reordering. Every text I taught out of said the same. It's only been in the past 2 or 3 years that I've learned different. I'm sure that means I'm lacking some how, but its not something I can change, so I live without shame. Personally, I have a problem with those type of posts, created to shame those who don't know the answer. I was an honor student in school, graduated college with honors, and continue my learning. Just because I may know some random fact/skill doesn't make me better than someone who doesnt.

40. ### czaczaMultitudinous

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ELA and math tend to be the tested , and asked about on interviews, subjects ( think standardized tests, assessments and screenings further on in life...where the 50 states are tend to be a bit of a parlor trick or questions Jeopardy, sadly , unless it's your area of expertise/ certification/job requirement)... Regardless of what we think, math and ELA are the 'big' areas in tems of elementary content....in middle school and above, all content areas just become more competitive. Regardless, Schools are looking for teachers who KNOW THEIR SHIP . Basic math operations are not considered a 'random' skill. And if someone wants to teach elementary, they betterhave a firm grasp on the content without having to google the most fundamental skills (PEMDAS being one). Teachers should KNOW what they are required to teach. I know where the counties in my state are because that's what I teach...I'm not required to know the twelve pairs of cranial neves ( I could guess a rough stab at them though)..but in terms of 'whats important' in school, there definitely is an emphasis on the 3 'R's...

And PEMDAS has ALWAYS viewed multiplication/division and addition/subtraction as inverse and equal operations. Without parentheses or other notation if what order to prioritize, inverse operations are threatened in a left to righ following PEMDAS

41. ### ChristyFModerator

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Everyone is most definitely allowed their own opinion. As I stated, I understand order of operations. However,I think telling someone it could be part of why they can't get a job is over the top. It's one math skill. My point wasn't in debating PEMDAS, nor in discussing "parlor tricks". it was to point out that maybe some perspective should come into play. By the way, in your school, I'm sure I'd be viewed as the fluff teacher; since I spend my day teaching science and social studies. However, at my school, I'm viewed as a valuable member of the staff and those kids do more thinking, problem solving, writing, collaboration, reading informational text etc with me than the ELA teacher. And they will be much more prepared to be well rounded citizens.