FriedClams Posted January 28, 2013 Share Posted January 28, 2013 From Horizon math we learned the the PEMDAS: Parenthesis Exponents Multiplication Division Addition Subtraction We used the mneumonic "Pretty Earings May Dangle and Shine". We're now using Saxon Algebra 1/2 and they emphasize the right to left for anything after division... Here's the rub... And an example: 7 + 5 x 3 - 2 x 4 + 5 x 3 I say - No P No E M: 7 + (5x3) - (2x4) + (5x3) 7 + 15 - 8 + 15 No D A: 7 + 15 - 8 + 15 (7+15) - (8+15) 22-23 S: -1 Saxon says: No P No E M: 7 + (5x3) - (2x4) + (5x3) 7 + 15 - 8 + 15 No D A/S left to right: 7 + 15 - 8 + 15 (7+15) --> 22 22 - 8 --> 14 14+15 --> 29 I feel like a idiot. LOL!!! Which one is correct? (And like all incriminating posts - I'll totally remove this later and hope all evidence of my stupidity is forever erased from the www... LOL!!) Quote Link to comment Share on other sites More sharing options...
Chrysalis Academy Posted January 28, 2013 Share Posted January 28, 2013 It's multiplication and division - on the same level - left to right then addition and subtraction - on the same level - left to right so in your example, you go through it on the last pass, and do the adding & subtracting as you hit it, left-to-right order. You would have done the same thing on the previous step had there been any division. Quote Link to comment Share on other sites More sharing options...
Arboreal TJ Posted January 28, 2013 Share Posted January 28, 2013 (7+15) - (8+15) This should be 7+15+(-8)+15. In my head I would add 15+15=30 then 7-8=-1. Finally 30-1=29 Quote Link to comment Share on other sites More sharing options...
Classic Mom Posted January 28, 2013 Share Posted January 28, 2013 Think of the list as: P E M and D- right to left A and S-right to left Equals=29 Quote Link to comment Share on other sites More sharing options...
regentrude Posted January 28, 2013 Share Posted January 28, 2013 That's why PEMDAS is a horrible and misleading way to remember order of operations! It suggests that multiplication precedes division and that addition precedes subtraction, but neither is the case: multiplication and division are of the same level, and addition and subtraction are of the same level as well. So when you get to. 7 + 15 - 8 + 15 you may NOT insert parenthesis like you did here A: 7 + 15 - 8 + 15 (7+15) - (8+15) but must simply go left to right: A/S left to right: 7 + 15 - 8 + 15 (7+15) --> 22 22 - 8 --> 14 14+15 --> 29 Saxon is correct. Quote Link to comment Share on other sites More sharing options...
AngelBee Posted January 28, 2013 Share Posted January 28, 2013 I got this wrong too. Hug Quote Link to comment Share on other sites More sharing options...
FriedClams Posted January 28, 2013 Author Share Posted January 28, 2013 Y'all rock. Thank you. I knew Saxon was correct, and Horizons elementary math likely never got too complex - but I am old and I can't remember what I made for breakfast, much less math last year, so I'm out of luck! LOL!! Thanks to everyone! Quote Link to comment Share on other sites More sharing options...
blondeviolin Posted January 28, 2013 Share Posted January 28, 2013 This should be 7+15+(-8)+15. In my head I would add 15+15=30 then 7-8=-1. Finally 30-1=29 This, exactly. Quote Link to comment Share on other sites More sharing options...
AndyJoy Posted January 28, 2013 Share Posted January 28, 2013 When I go over PEMDAS with my tutoring students I draw two small arrows pointing to the right under MD and AS to help them remember "together from left to right." Quote Link to comment Share on other sites More sharing options...
Dana Posted January 28, 2013 Share Posted January 28, 2013 When I go over PEMDAS with my tutoring students I draw two small arrows pointing to the right under MD and AS to help them remember "together from left to right." I generally write it out as (1) Symbols of grouping (2) Exponenets (3) Multiplication and division as they appear from left to right (4) Addition & subtraction as they appear from left to right. IF I write PEMDAS, I do so as P / E / MD / AS. I warn them I'll try to catch them & we do examples where we have division before multiplication. I also explain order of ops as working by "shortcuts" (exponents as shortcut for repeated multiplication; multiplication as shortcut for repeated addition). And as early as possible, I say we don't have subtraction, only addition, so we'd read 5 - 8 as "5 plus negative 8". Definitely makes things easier with coefficients. Testing on this in my cc class on Wednesday. I just know I'll catch a number of them... sigh. Quote Link to comment Share on other sites More sharing options...
regentrude Posted January 28, 2013 Share Posted January 28, 2013 There is a much easier way to remember order of operation taught in European schools, where division is denoted by the symbol colon : and multiplication by the dot. We simply learn that dot-operations (multiplication and division) take precedence over line operations (+ and -). This does not falsely suggest a ranking between mult/div and add/subtr. Quote Link to comment Share on other sites More sharing options...
kiwik Posted January 29, 2013 Share Posted January 29, 2013 We use bedmas (b for brackeds). It is not that hard to remember that it could just as well be bemdsa. Just don't overthinj. :-) Quote Link to comment Share on other sites More sharing options...
kiana Posted January 29, 2013 Share Posted January 29, 2013 Some people are now advocating using GEMS -- grouping, exponents, multiplication, subtraction -- and remembering that multiplication/division are the same operation, as are addition/subtraction. Quote Link to comment Share on other sites More sharing options...
Dana Posted January 29, 2013 Share Posted January 29, 2013 Some people are now advocating using GEMS -- grouping, exponents, multiplication, subtraction -- and remembering that multiplication/division are the same operation, as are addition/subtraction. If they can get it in the texts the schools use, maybe a change will be made. I'm frustrated with all the poor math knowledge right now (had a class last night when teaching fractions and prime factorization with just a TON of whining, "Do we have to do it that way?" Argh.) I especially wish we had teachers who actually KNEW math teaching math. The misconceptions I have to try and correct get so frustrating (especially with the whining). I don't like the start of semester. Quote Link to comment Share on other sites More sharing options...
kiana Posted January 29, 2013 Share Posted January 29, 2013 I especially wish we had teachers who actually KNEW math teaching math. Some states are moving towards having "math content specialists" in elementary, as we already have reading content specialists. I wholeheartedly approve -- for a classroom situation, where the teacher has many students and cannot just say "hold on while I ask the hivemind", but needs to come up with multiple explanations for multiple levels of misunderstanding "on the fly". Quote Link to comment Share on other sites More sharing options...
regentrude Posted January 29, 2013 Share Posted January 29, 2013 I especially wish we had teachers who actually KNEW math teaching math. This. IMO, the most crucial difference to countries that perform better in math and science is that they have teachers who actually KNOW their subject, and that teachers without this expertise are not allowed to teach. Quote Link to comment Share on other sites More sharing options...
alef Posted January 29, 2013 Share Posted January 29, 2013 I like this mnemonic: Pandas Eat Mustard on Dumplings and Apples with Spice--it's designed to emphasize that Multiplication and Division go together (not one before the other) as do Addition and Subtraction. Quote Link to comment Share on other sites More sharing options...
skimerinkydo Posted January 29, 2013 Share Posted January 29, 2013 I just found the idea to use "GEMS" and I think it will work better and I am going to try it with my daughter this afternoon. The acronym is just easier to remember. Also, my children tend to get confused and not realize they can group multiply/divide and add/subtract. Learning that concept now will help them later. Here is a website with a GEMS drawing to make it more visual http://axisofreflection.blogspot.com/2012/10/gems.html (scroll down) Quote Link to comment Share on other sites More sharing options...
Forgiven Posted January 30, 2013 Share Posted January 30, 2013 I don't think this is a matter of order of operation but of understanding what -8 is. Either way would work as you can add or subract in any order and should come up with the same number. So when you have 7 + 15 - 8 + 15, it's really ALL adding. the -8 is really -1X8. That's how you should look at all negative numbers. So with the first method or doing additions before subtractions, if you want to break it up like you did, you'd get 7+15=22 for the first calculation and -8+15=7 for the second calculation. Add those together (remember, that "minus" sign is really a negative 1 multiplied by the 8, so it's all addition really), and you get 22+7=29. Now for the second way (Saxon), you would add 7+15=22, then subtract the 8 (this is really adding a negative 8), which gives you 22-8=14. Then you would add 14 to 15 to get 29. I don't think there's anything wrong with either order of operations, just that you need to look at a minus sign as a negative number, not as a cut and dry minus. Angie Quote Link to comment Share on other sites More sharing options...
hsmamainva Posted January 30, 2013 Share Posted January 30, 2013 I went to school in high school in the ( *cough* ) 1970s and I was taught "Please Excuse My Dear Aunt Sally." I taught the same phrase to all of my kids, too. If that's easier for your kids to remember than the one about pandas :) Quote Link to comment Share on other sites More sharing options...
kiana Posted January 30, 2013 Share Posted January 30, 2013 I went to school in high school in the ( *cough* ) 1970s and I was taught "Please Excuse My Dear Aunt Sally." I taught the same phrase to all of my kids, too. If that's easier for your kids to remember than the one about pandas :) The only problem with this is that (as shown by the OP) it can easily lead to confusion and students falsely thinking that addition comes before subtraction, and multiplication before division. That's why people are trying to come up with newer mnemonics which eliminate that confusion. Quote Link to comment Share on other sites More sharing options...
misty.warden Posted January 30, 2013 Share Posted January 30, 2013 The only problem with this is that (as shown by the OP) it can easily lead to confusion and students falsely thinking that addition comes before subtraction, and multiplication before division. That's why people are trying to come up with newer mnemonics which eliminate that confusion. I don't think it's the wording of the mnemonic that causes the confusion, rather not having it ever explained that addition and subtraction are effectively the same operation (with the understanding that subtraction is adding a negative number) and multiplication and division are the same (with division being multiplication by a fraction). The panda thing doesn't make any sense to me personally but whatever gets the job done for each person is "right" for them as long as they understand the reason why it works. Quote Link to comment Share on other sites More sharing options...
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