This week I was on the phone with my mom discussing the difference between teaching math conceptually verses procedurally. She argued that some math procedures have no conceptual base.
My arguement was that the nice thing about math is that everything you do is based on a counting concept. So, she brougt up multiplying negatives, arguing that this rule has no conceptual base.
I disagreed....give an example of what my proof was by posting the reason why
-2 * -2 = 4. Show the math if you can
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First put it into English terms, if you say i'm not not going to the store, it mean I AM going to the store. This applies to the mathematical terms too. -12 * -$700 = $8,400. You can think of it as taking away a negative number 12 times.
ReplyDelete-Jesse
Like Jesse said we can put this in English terms to understand this. If you say, "I do not not eat" you really are eating. Here is an example of why two negatives equal a positive in math. The tank of a truck has 30,000 liters, and 1,000 liters are taken out every day. What was the level 3 days ago?
ReplyDeleteWe know the tank has -1,000 every day, and we need to subtract that 3 times (to go back 3 days), so the change will be:
-3 × -1,000 = +3,000
So your answer is you had 33,000 liters 3 days ago.
Simon Bellido
A negative * a negative equals a positive because it is going on a different direction than negative (positive). However multiplying -2 times 2 would be a continuation in the same direction thus equaling
ReplyDelete-4. Whereas -2 times -2 is a different direction which makes it equal 4.
Alex Goncalves
Like Alex said, a negative times a negative equals a positive. -2 X 2=-4 because the signs are unlike. When the signs are alike, it is always positive. When the signs are different, the sign is always negative.
ReplyDeleteBrendan Mulligan
To me, I think math things like multiplying negatives is both conceptual and procedural.
ReplyDeleteHow it’s procedural:
Multiplying Numbers with the same sign rule:
The product of two positive numbers or two negative numbers is positive.
Ex. 5 times 2= 10 -5 times - 2= 10
Multiplying Numbers with different signs rule:
The product of a positive number and a negative number or a negative number and a positive number, is negative.
Ex. 3(-6) = -18 -3 Times 6 = -18
How it’s conceptual:
One example as Jesse said was using it in English terms. “She didn’t not buy 5 apples” meaning she bought 5 apples.
Another example is what happens in real life. If you lost $5 on a stock and your losses double, that means you lost $10 (-5×2). If your losses negative-double, that means you gained $10 (-5×-2).
A third example is an example made by me. It’s an interesting one and kind of confusing. Let’s see if u know what I’m talking about. Stand up and pick any spot in a spacious room. You know north and south. In this case, north equals or is like positive numbers. South equals or is like negative numbers.
Face north. Walk forwards. You are now walking north or towards higher positive numbers. Go back to that spot. Face north and turn around and walk forward. You are now walking south or towards negative numbers. Go back to that spot. Face north. Walk backwards. You are walking South again towards the higher negatives. Go back to that spot. Face north. Turn around AND walk backwards. Where are you going? You’re heading North to big positives by doing the equivalent of a negative (turning around) times a negative (walking backwards).
Mark Soriano