Adding & subtracting with negative numbers

[freeindeed]

What are your best ideas, activities, and games for teaching this concept to a sixth grader? Thanks!

[Dana]

For addition, think money. Poistives are money you have, negatives are money you owe.

So -5 + (-3) means you owe 5 and you owe 3, so you'd owe 8, so answer is -8

5 + (-3) means you have 5 but owe 3, so you have 2, so answer is 2.

This seems to keep signs correct and avoids the confusion I see when using the formal definition with absolute value. I see too many students get addition and multiplication rules confused.

 

For subtraction, I say it isn't an operation... Only addition.

We just take the sign as part of the number.

 

So 6-2 means 6 + -2, don't rewrite, but think of it like that... Have 6, owe 2. Same answer we had when we saw things as subtraction.

-4 - 3 would mean owe 4, owe 3, so net is owe 7 and answer is -7.

We do run into a problem when we have two signs...

6 -(-3)

We can handle it two ways.

One is to use the definition and rewrite... a-b = a + (-b ). This gives 6 + 3.

The other is if you've already talked about negative numbers and -x has the same absolute value as x but is on the opposite side of 0 on the number line, then you see -(-3) as + 3 and just be sure to include the sign.

 

This is what I normally do with my students and it worked with my son.

You can also play around with using a number line for a more concrete approach.

[Chrysalis Academy]

Is it a girl? My dd just read the integers chapter in Kiss My Math and loved it. She talks about them as "mintigers" of different tastes, with postitive being very good tasting, and the more negative the number, the worse it tastes. The whole thing was kinda goofy to me, but my dd loved it and it totally clicked for her.

[Mom-ninja.]

We're doing that right now. In MM is explains it with money and number line as explained above. Ds is getting it, yet he still makes mistakes when doing the problems. It isn't automatic for him yet. He has to think about and walk through it.

[JudoMom]

Prealgebra Blastoff.

[TracyP]

CLE introduces negative numbers using a thermometer. For example, (-8) - 5 = (-13) would be shown as 8 below zero and the temp drops 5 degrees. Not really any different than a number line, but it seemed more relevant. Of course, that could be because we live in MN. ;)

[freeindeed]

Thanks all!

[happypamama]

Money, and the concept of owing it, made sense to my daughter. I remember my dad teaching it to me using red and black checkers; one was positive, and the other negative, and they canceled each other out.

 

With DD, we also talked about how negative means opposite, so two negatives mean the opposite of the opposite, so they cancel each other out; that also made sense to her.

[mathmarm]

Starting on the ground level and running up and down stairs. If you run down 7 steps and up 5 steps, you are still 2 steps below ground level.
If you live someplace where it is cold, then a thermometer reading activity makes a lot of sense. You can also use examples of putting things in the freezer, room-temperature and the oven.
Money is one of the most common-sense ideas for the typical 10 and up crowd, if you have a negative number you're in debt, if you have a positive number you are fine. I like to use the negating the opposite idea also, for some girls who consider themselves good at language, but bad at math, this makes a good deal of sense.

[mandymom]

Love this explanation of subtracting negatives from the Kiss My Math website:

 

http://www.kissmymath.com/downloadable/Sparky-Subtracting-Negatives.pdf

 

My younger dd hates math, but loved the book. It's got some really creative ways of explaining math concepts to pre-teen girls.

[RootAnn]

My younger dd hates math, but loved the book. It's got some really creative ways of explaining math concepts to pre-teen girls.

 

I checked that book out of the library thinking it would be helpful. DD#1 hated the constant references to boys & froo-froo girly stuff. She couldn't get into the math explanations because of the other "stuff" that annoyed her. I had hopes! :glare:

[Chrysalis Academy]

 

I checked that book out of the library thinking it would be helpful. DD#1 hated the constant references to boys & froo-froo girly stuff. She couldn't get into the math explanations because of the other "stuff" that annoyed her. I had hopes! :glare:

 

 

I know exactly what you mean, and it annoys me for the same reason, and dd is not a froo-froo girly girl or into boys at all, but for whatever reason, the math explanations are really clicking. Whatever works!!!

[Mommy Grommy]

We've been using negative numbers when playing games. DS likes to make up games where you lose points, and it was a natural way to introduce negative numbers. "Oh no, I have zero points and I just lost another point! Now I have -1 point!" Or "You have -5 points and you just lost another 3 points, now you're at -8!" The competition aspect of the negative numbers really resonates with DS. It gives him a way to more thoroughly beat his opponents! :laugh: :glare:

 

This is the game that started it all for us, by the way: Tetris Link. Everyone starts with zero points, but you can lose points and end up with a negative number. There is a little sliding counter that you move up or down depending on how many points you gain or lose in your turn. It makes the number line seem so intuitive.