Okay, I just cannot explain this. Math experts, please help...

[LisaNY]

We're working on Foerster's Algebra, multiplying/dividing signed #'s. Basically, the formula is -1(X) is negative. Also, we are taught that an even # of negative signs yields a positive answer, and an odd # of negative signs yields a negative answer. Now, here's my question - My dd wants me to explain this visually, and I have no idea how to do that. (She's asking me to use bars like they do in Singapore, or some pictorial way of showing this concept.)

 

My thought is that you cannot possibly show that, but I'm sure one of the resident math experts can tell me otherwise. Any takers?

 

Thanks! :001_smile:

[Mrs. Readsalot]

I also had to do a visual to explain this to my son.

I found this website and it is great

Here is the link

http://www.mathsisfun.com/multiplying-negatives.html

[Nan in Mass]

I can think of several ways:

If you use the words "the opposite of" when you see a negative sign and explain that it means "switch directions", you can use a number line. If you are going in the positive direction as you count out 10, then -10 means count 10 in the opposite direction, and -(-10) means that you switch directions twice and end up going in the same direction as 10. This was how it was explained to me, many moons ago.

 

Singapore does some work with thermometers. Again, you have to use "the opposite of" for this to work, and it gets confusing because then you are using a mix of "opposite of" and "negative" so -(-5) is negative minus five degrees.

 

Singapore also uses money and the idea of checks, so if you take away an I-owe-you for $5 from your money box, that is the same adding $5 to your total because it is a double negative. They illustrate it by showing a box with the total amount of money in the box written under it. (This is in NEM1.)

 

Keys to Algebra uses a football field. I'm really fuzzy on the rules to football, so I can't explain it very well, but they related a negative to losing yards and somehow made a connection between the other team losing yards (other team is one negative and losing is the other negative hence the double negative) mean that your team gained yards. I think. The nice part about this system was that if you made a picture of a football field, you could superimpose a number line over top and it made the switch from game to variables by going from field to number line to real numbers to variables.

 

You might be able to do it verbally by explaining that negative means "the opposite of", like our English word "not", so -5 is "not five" and -(-5) means "not not five" which really means "five", just like "I don't not like icecream" means "I like icecream", but I don't like this method because it won't work for multiplication.

 

You can do it in a kinetic manner with a set of scales and using the negative to mean "take away" OR "opposite".

 

I think your daughter is quite right to insist on a picture GRIN.

 

Whatever you wind up doing, make sure you explain it in terms of a number line eventually and give her lots and lots of practice making it make sense to herself so she doesn't just memorize the rule and learn to solve the problems quickly by doing that. If she doesn't really get this now, she might hit a wall later on in algebra.

 

HTH

-Nan

[LisaNY]

THanks, Ladies! :001_smile:

[mooooom]

Maybe it won't help at all, but it is how I remember

 

In my head I always manipulated the actual symbols - two negative symbols make a positive symbol, three make a positive and a negative symbol.....

 

Weird, but it is how my brain works

[LisaNY]

Maybe it won't help at all, but it is how I remember

 

In my head I always manipulated the actual symbols - two negative symbols make a positive symbol, three make a positive and a negative symbol.....

 

Weird, but it is how my brain works

 

That's a cool way of thinking about it. :001_smile: