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Need help "teaching to the test" ;) Subtracting negatives......


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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!

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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 by jcooperetc
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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:

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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.

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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.)

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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...

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