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Stella M
03-28-2011, 11:08 PM
Dd is subtracting negative numbers. We know that two negatives make a positive ie 3--1 is the same as 3+1. But I don't understand why ?!

Can anyone either explain it to me or direct me somewhere with an explanation of 'why' ? Ta.

dbmamaz
03-28-2011, 11:28 PM
The best way I can explain it is probably looking at a number line. If you put a mark at 3 on the numberline, if you add 1 to it, you move 1 spot to the right, and land on 4. But if you had subtracted 1, you would move one spot to the left, and land on 2. If you add a negative number, that is the same as subtracting the same number, right? So if you add -1 to 3, instead of moving 1 spot to the right, you move one spot to the left. You do the opposite. Its the same thing w subtracting a negative, you do the opposite - subtracting a positive number, you move to the left, but subtracting a negative number, you move to the right.

Another way to think of it is this. 3 - 2 is the same as 3 + {(-1)x(2)}. Does that make sense?

So 3 - -2 is the same as 3 + {(-1)x(-2)}

are you clear that -1x-2 = 2?

You can also think of it as a balance beam. If i have 3 one-ounce disks on a scale, and I want to add a negative ounce, well, thats the same as taking an ounce away. The total weight will get smaller. If i want to take away the negative weight, i have to put that ounce back. Taking away a negative weight would make the total bigger. Ok, that might be the worst explanation yet!

Better try khan academy - free and awesome videos starting w basic math.

Stella M
03-29-2011, 12:00 AM
Actually, the balance beam explanation helps :) I can picture it so now I can hopefully explain it. I'll head on over to Khan academy too. Thanks!

my2monkeys
03-29-2011, 09:17 AM
Maria Miller from Math Mammoth also has helpful videos on youtube you may want to check out.

dbmamaz
03-29-2011, 11:08 AM
glad something i said made sense! I asked my husband, who has 4 math-related degrees, how he would explain the concept . . . he said he wouldnt. A lot of help that is!

Stella M
03-29-2011, 08:27 PM
Well, the Khan academy vid was great at explaining how to do it but still not the why! I used the balance beam explanation to explain it to dd this morning and she said she got it.

dbmamaz
03-29-2011, 08:39 PM
Cool! Out of curiosity, I asked my 7 yo. He said everything is just opposite with negative numbers. So i guess thats not really a why.

farrarwilliams
03-29-2011, 09:18 PM
Saying it's opposite is sort of a why - if you look at a number line it's not the same, it's a mirror image, which is, indeed backwards.

I also have trouble bending my head around negative numbers though. The why is really important though...

Stella M
03-29-2011, 09:55 PM
I just don't like dd being able to do something but not able to articulate why, kwim ? That's how I ended up failing high school maths :( I like being able to have a picture rather than a numerical explanation for the 'why', which may be dumb, I don't know, I'm a maths failure! So 'mirror image' makes sense to me because I'm thinking of an Alice in Wonderland type thing where everything on that side of the mirror is opposite to what it is here, so of course two negatives will turn into positives...don't suppose there are any maths curriculums that um, explain things that way ?

OK, with the little Alice story, dd is sure she's got it.

dbmamaz
03-29-2011, 10:02 PM
actually there are a lot of math story books to explain ideas. I'm pretty sure there was one about negative numbers. You know, that living math site i'm always talking about . .. idk.

But i think being able to picture it is important. I mean, at least being able to understand it past just the words that explain it. I found math easy until it got to things I couldnt picture . . . although my husband started trying to say something to our 7 yo about the rate at which speed is changing and somehow i remembered that that was calculus. I remembered it with enough confidence that I was able to say "You want to explain calculus to him?" and he looked positive for a moment and then faltered and said, "ok, maybe its too complicated." I'm usually so afraid of looking dumb in front of my husband i'm afraid to say anything about math. I'm always sure he thinks i'm explaining things wrong to the boys. but he's the only man i liked who wasnt intimidated by MY brain, so its a good thing overall.

farrarwilliams
03-29-2011, 11:06 PM
I'm pretty sure there are negative numbers included in The Number Devil by Hans Magus Enzenberger. You know, I think I may have misspelled his name, but I'm feeling too lazy to look it up. Melissa, that's a good middle school age math fiction book. And there might be a Penrose book that has negative numbers - I'm not sure. I don't love Penrose as much as some math aficionados.

I think some kids can understand it from the abstract but others need a concrete reason. This morning we were introducing multi-step problems with addition and subtraction. Mushroom had already done it a couple of weeks ago and had simple accepted when I showed him that the parenthesis meant do this part first. He was intrigued by how the problem could come out differently if you did it in the other order, but he accepted it immediately. BalletBoy threw a fit about it and kept arguing with me. Finally, I realized he needed to know WHY you would make such a rule. So I had to make a concrete image of it - (9-5)+2 is you've got nine cookies, but then Daddy eats five of them and to say sorry he gives you the last two from the jar - now many do you have? But 9-(5+2) is you have nine cookies - first you eat five of them and then you realize Daddy ate two more - now how many cookies to do you have? He listened to my stupid cookie story, nodded and then did the rest of the page without any issues.

dbmamaz
03-29-2011, 11:20 PM
Yeah, Orion frequently needs that kind of explanation Raven hasnt so far . . .but he hasnt gotten that far of course. he is, tho, a much more abstract thinker

SueEllen Grieves-Curl
03-30-2011, 06:41 AM
http://www.youtube.com/watch?v=sEU5uaf-Tu4&feature=related

I think this would help

Stella M
03-30-2011, 04:55 PM
We tried The Number Devil a few years ago but maybe it was too early; might give it a go again. Dd is showing a flickering of interest in maths - she's always done fine with it but in a bored sort of way - now she's doing some algebra and 'likes' it...so I should really try and fan the flicker into a flame. Or is a flicker good enough ?

I'm with BalletBoy - I'd need the cookie story too :)

Lying awake last night wondering if the minus of arming Ghaddafi in the past and the minus of arming the rebels in the future will cancel each other out and make a positive for Libya...that's my kind of math :)

SueEllen, thanks for the link, I'll check it out.