[Numeracy 154] Re: The double negative language-math link

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Claire Ludovico and/or TJ DeLuca tjdclaire at cox.net
Fri Feb 12 00:57:44 EST 2010

There is always above and below sea level...
I use bank accounts as the most likely exposure of my students to
negative numbers...and the minus a negative example is when one finds a
charge (funds subtracted) that has been (incorrectly) imposed by the
bank that is then removed (taken away) from your balance...or in other
words, they returned your money to you.

I once had to introduce integers to a group in a very limited amount of
time. I made up a story about the positive tribe and the negative
tribe...both very warlike but only with the other tribe, never with each
other. Positives, of course, carry two spears, negatives only one.
They have very strict rules of warfare: only one positive may fight a
negative ...no ganging up...and when they fight (so sad) both die. They
can hang out with their own kind, of course, no problem. (Addition)

Subtraction: They are also both very greedy...so in their wanderings in
the woods, if they should spy a new spear laying on the ground (the
minus sign) the positives, who have a spear in each hand, must throw
away their two spears in order to pick up the new spear (and thus become
negative) and the negatives, who carry only the one spear, can reach
down and pick up the new spear...and become positive. Then those former
negatives can hang out with positives (and vice versa) but can no longer
face their former kind without "war" breaking out.

Miraculously, the two tribes can marry (multiply) and the /product/ of
their union depends on their signs (multiple marriages allowed (perhaps
each parent "gifts" the same number of spears as he/she carries)...count
the negative signs: odd number, the "children" are negative, even number
(two spears again) the "children" are positive.) Divorce (division) is
quite possible and the rules are the same as for multiplication.

I don't know if my students always get why I tell the story (but then
they don't always get the rational explanation.) As I said, I usually
back up the problems with bank account analogies. But the spear story
helps sometimes if you have a negative (or minus sign) outside
parentheses and you can talk about shooting the spear through the
parentheses and changing the sign of everything inside.
Also, my students were looking at the problem yesterday: (-6) - (-1) = ?
I was able to say," If you have six negative guys and you take away one
of them, how many are left?" They got it.

On 2/11/2010 8:17 PM, Denney, Brooke wrote:


> Michael:


> I disagree with your statement that, "negatives carry meaning in

> mathematical, but not physical (reality) terms"; after all, it is

> winter in the Midwest and negative values mean something in my reality

> when we are talking about wind chill factors and really cold

> temperatures (perhaps living in a really warm climate you may have

> forgotten). Also, negative numbers are used when discussing the

> grade of the road (i.e., positive or negative grade). Does anyone

> else have examples of negative numbers used in reality?


> -Brooke



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