Joanne Posted April 1, 2012 Share Posted April 1, 2012 We have standardized testing this week at the school I teach. I am covering some areas for my math class that we haven't gotten to yet. That class has a high percentage of doubters with regard to math. They struggle in advance of difficult topics. Do you have suggestions as to *why* when you subtract a negative, it is the same was adding the opposite? My own problem with math is I was taught the algorithim better never understood it. Suggestions how on to present the material? BTW - we do math according to level rather than scrict grade. This is a mixed class of 4 - 6 graders. Thanks! Quote Link to comment Share on other sites More sharing options...
Dana Posted April 1, 2012 Share Posted April 1, 2012 Number line illustration here. Quote Link to comment Share on other sites More sharing options...
GingerPoppy Posted April 1, 2012 Share Posted April 1, 2012 Number line illustration here. Thank you, Dana! I love the hot and cold cube story further down the page. Quote Link to comment Share on other sites More sharing options...
usetoschool Posted April 1, 2012 Share Posted April 1, 2012 (edited) The way my kids have understood it is to explain that the - sign means "the opposite" and that the + and - are not instructions to DO something, but symbols that tell you about the number itself. Which means all the addition and subtraction problems are just a list. 5-2 is just (an implied) +5 and a -2. In the case of subtracting a negative, 5 - (-2) it is just +5 and the opposite of -2. The opposite of (the opposite of or -) 2 is just a 2. If you use the number line and make a list and start at 0 you would move +5 and be at 5 and then from there 2 more. -(-2) is the same as +2. Start inside the parentheses and work out. What is the opposite of 2, it is a negative 2. Then you have one more opposite of, the opposite of negative 2 is +2. There are a couple of math rules about additive inverse stuff but if you just want them to understand the concept then just stop there. Otherwise you can read, I don't know, this one is as good as any: http://www.coolmath.com/prealgebra/06-properties/07-properties-additive-inverse-01.htm Edited April 1, 2012 by jcooperetc Quote Link to comment Share on other sites More sharing options...
Heather in Neverland Posted April 1, 2012 Share Posted April 1, 2012 This is how I explained it to my ds... If I owe the bank $1000 for a loan, it goes in the NEGATIVE column in my budget because it takes away from my net worth and that is a NEGATIVE thing! If the bank forgives half of my loan (subtracting 500 from the 1000 I owe), I now only owe $500 and that is a POSITIVE thing. :D This is, of course, long before I teach about interest rates. :tongue_smilie: Quote Link to comment Share on other sites More sharing options...
babysparkler Posted April 1, 2012 Share Posted April 1, 2012 This is how I explained it to my ds... If I owe the bank $1000 for a loan, it goes in the NEGATIVE column in my budget because it takes away from my net worth and that is a NEGATIVE thing! If the bank forgives half of my loan (subtracting 500 from the 1000 I owe), I now only owe $500 and that is a POSITIVE thing. :D This is, of course, long before I teach about interest rates. :tongue_smilie: :iagree: This is how I teach this concept. Quote Link to comment Share on other sites More sharing options...
Lucy the Valiant Posted April 1, 2012 Share Posted April 1, 2012 We use the money concept, too - If I owe someone $4, my balance is - $4. If another friend pays that debt for me and "TAKES AWAY" the - $4, I'm even. :001_smile: Quote Link to comment Share on other sites More sharing options...
StephanieZ Posted April 1, 2012 Share Posted April 1, 2012 The best way I've seen to explain this is from Art of Problem Solving (prealgebra). 1) Define additive inverse as: whatever you have to ADD to a thing to sum to zero. So, the (additive) inverse of 5 is -5, or the additive inverse of -5 is 5, etc. 2) Subtraction is defined as adding the additive inverse. So, 3 - 4 = 3 + (-4) because the inverse of 4 is -4 3 - (-4) = 3 + (4) because the inverse of -4 is 4 Make sense?? I loooove this approach. FWIW, AoPS has a similarly awesome way of looking at division. :) (Division is definied as multiplying my the multiplicative inverse . . . This makes dividing by fractions insanely intuitive and easy.) Quote Link to comment Share on other sites More sharing options...
nono Posted April 1, 2012 Share Posted April 1, 2012 Joanne, Maybe because it's just a mathematical example of a double negative being a positive? Don't not swim = Do swim ;) Quote Link to comment Share on other sites More sharing options...
Melissa in Australia Posted April 1, 2012 Share Posted April 1, 2012 I have always used this little graph thingy - + = - - + = - = + = + this is the way I was taught, some of my children write out the graph thingy in the front of their math book so they can look at it if they are getting confused. Quote Link to comment Share on other sites More sharing options...
Melissa in Australia Posted April 1, 2012 Share Posted April 1, 2012 Oh, the graph didn't post very well, basically it is positive negative equals negative, positive positive equal positive, negative negative equals positive Quote Link to comment Share on other sites More sharing options...
Liz CA Posted April 1, 2012 Share Posted April 1, 2012 Two negatives make a positive - mention that this is only the case in Algebra/Math. :001_smile: Quote Link to comment Share on other sites More sharing options...
BMW Posted April 1, 2012 Share Posted April 1, 2012 My kids grew up in Alaska and I homeschooled them there... We KNEW that if it was -10 degrees that it was 10 BELOW zero. If temperature dropped another 10 degrees, it was -20 degrees. Since we lived this, it was not difficult to understand. -2 and (+) another -2 meant that the temperature just dropped another couple of degrees and it was -4. -2 and +2 meant zero, of course, because we just go a couple of degrees HIGHER in temperature. I moved from Alaska and NEVER looked back... but now I am glad that at least it gave us a solid and working knowledge of negatives and positives as far as numbers went.... Don't know if this helps any, though... Quote Link to comment Share on other sites More sharing options...
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