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User

Joined: 13 Sep 2007
Posts: 2

 Posted: Thu Sep 13, 2007 12:37 pm    Post subject: Teaching negative/positive integers (add/subtract) Right now we are at a point in the curriculum where my DD needs to learn and understand how to add/subtract negative integers. The lesson in the book is rather confusing (using a football analogy) so I am looking for ways to teach her this concept. Anyone have some tips, websites, ect.?
ncmom
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Joined: 13 Jul 2007
Posts: 321
Location: Eastern NC

 Posted: Thu Sep 13, 2007 1:32 pm    Post subject: My son started this a couple of years ago. The first thing I did was made a number line up and put in on the wall. As far as teaching it. Well I told him to ignore the + sign. All numbers are positive unless they are negative. If you are doing an addition problem and the bigger number is pos. and the smaller neg. It is essentially a subtraction problem. The knowledge of how you get this will have to eventually be understood to do more complicated problems but I found this was a good place to start. Good luck! Here are a couple of sites that help us: http://www.mathsisfun.com/positive-negative-integers.html http://www.math.com/school/subject1/lessons/S1U1L11GL.html http://www.factmonster.com/ipka/A0876848.html
Lily
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Joined: 10 Jun 2007
Posts: 427

 Posted: Thu Sep 13, 2007 3:07 pm    Post subject: I was taught with credit cards. If the shirt you want is \$45, but you only have \$30 on you, how much do you have to put on the credit card if you want the shirt? Or, hey, if you're getting a rebate of \$30, how much is that going to take off your credit card bill of \$100? Putting it in real world perspective helped a lot (and tamed my credit impulses as an adult!)_________________"The greatest sign of success for a teacher... is to be able to say, "The children are now working as if I did not exist." - M. Montessori Proud non-member of the HSLDA
Theodore
Moderator

Joined: 06 Oct 2005
Posts: 2122
Location: Missouri, US

 Posted: Thu Sep 13, 2007 11:30 pm    Post subject: All you have to do is reverse both the sign and the problem type. If you're subtracting a negative, change it to a positive and add. If you're adding a negative, change it to a positive and subtract. You don't really need to know why that works - it's enough to know that it does._________________
Bob Hazen
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Joined: 28 Oct 2005
Posts: 28

MariaMiller
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Joined: 29 Sep 2007
Posts: 1

 Posted: Sat Sep 29, 2007 2:25 pm    Post subject: Some good real-life MODELS for integers are: - temperature in a thermometer - altitude vs. sea depth - earning money vs. being in depth. When first teaching integer operations, tie them in with one of these models. I'll take for example the temperature. Assuming n is a positive integer, the simple rules governing this situation are: * x + n means the temperature is x° and RISES by n degrees. * x − n means the temperature is x° and DROPS by n degrees. It's all about MOVEMENT — moving either "up" or "down" the thermometer n degrees. For example: * 6 − 7 means: temperature is first 6° and drops 7 degrees. * (-6) − 7 means: temperature is first -6° and drops 7 degrees (it's even colder!). * (-2) + 5 means: temperature is first -2° and rises 5 degrees. * 4 + 5 means: temperature is first 4° and rises 5 degrees. These simple situations handle adding or subtracting a positive integer. Practice those first, until kids are familiar with these cases. The remaining cases to handle ar adding or subtracting a negative integer: * (-2) + (-5) would mean: temperature is first -2° and you "add" more negatives so it gets even colder. The last case is least intuitive one: * 1 − (-5) or subtracting a negative integer. I personally just remember the little rule of "two negatives turns into a positive". Some people explain it this way. In (-7) − (-3) you can think that you have 7 negatives at first, and you "take away" three of those negatives, leaving -4. This rule of "two negatives makes a positive" might seem counterintuitive at first, but it is needful so that many principles of mathematics can continue to apply (for example distribuitive property). This is continued at: http://homeschoolmath.blogspot.com/2007/09/tips-for-teaching-integers.html See also an excellent treatise of integers vs. submarine depth at Text Savvy: http://www.textsavvyblog.net/2006/06/adding-and-subtracting-integers.html And my article: http://www.homeschoolmath.net/teaching/integers.php Maria Miller
twiggybumble
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Joined: 25 May 2007
Posts: 27

 Posted: Wed Oct 24, 2007 10:39 am    Post subject: My son is learning about this right now. I just drew a simple number line on the board with the zero, and several places in both directions. Then I would pick a place, say -4, and ask him to add 2. Then I would move 2 in the direction of the positive numbers, winding up at -2. My son is a visual learner, and this worked well for him. Good luck!
Bob Hazen
Moderator

Joined: 28 Oct 2005
Posts: 28

 Posted: Wed Dec 26, 2007 6:45 am    Post subject: clarification on "two negatives make a positive" On an earlier post in this thread, MariaMiller wrote: "1 − (-5) or subtracting a negative integer. I personally just remember the little rule of 'two negatives turns into a positive'.... This rule of 'two negatives makes a positive' might seem counterintuitive at first, but it is needful so that many principles of mathematics can continue to apply (for example distribuitive property)." Remember that the context of Maria's remark is the subtraction of a negative number. BE CAREFUL: what she wrote here does not apply to the addition of two negative numbers. For example, -13 + - 5 = -18, yes. My concern here is that I've seen kids take the rule "two negatives make a positive" and apply it (against all common sense, of course) to the above problem, resulting (incorrectly) in, "-13 + -5 is two negatives, and two negatives make a positive, so -13 + -5 is +18." The problme here is that Maria's rule doesn't apply here - but kids can easily make the mistake of thinking that it does!!! What Maria's rule of "two negatives make a positive" applies to would be: -subtracting a negative number, where you end up writing the subtract/negative sign twice in a row: 3 - -5 = 3 + 5 = 8. -multiplying a negative times a negative: -3 x -5 = +15. But it doesn't apply to adding two negative numbers: -3 + -5 is not equal to +8. I know Maria would agree with this. Hope this helps! Bob Hazen_________________Bob Hazen's Algebra for Kids
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