What’s Goin’ On In Room 133

Posts Tagged ‘positive numbers’

Homework: page 78 ques 25 – 30; 36 – 41, 48 – 53 and page 83 ques 18-31. Also study Concept Summary on page 82.  Due Thursday, guys!

Alright, sports fans, I mean, uh, colleagues, we have spread joy to the maximum and brought gloom down to the minimum by weaving our way through the positive and negative sides of our number line.  We have added (+ve plus +ve = +ve, -ve plus -ve = -ve, and if they are different signs, it depends on which one has the greatest absolute value).  We have subtracted using number line, absolute value and the ultimate weapon THE ADDITIVE INVERSE…you know, 4 – 2 = 4 + (-2)?   Yeah, that one. 

And now we have just multiplied these guys (+ve X +ve = +ve; -ve X -ve = +ve, and if the signs are not the same, it’s a negative).  Same with division: like signs dividing each other, the answer is positive; unlike signs dividing each other, it’s negative. 

So where is all this going?  Where are we headed?  What strange new worlds are we likely to power through with this knowledge besides census taking and temperature watching and profit calculating?  Well, my friends, we are heading for…a NEW world…a world where positive and negative exist as brothers…a world of two dimensions and four quadrants and an infinite number of pairs…a world of planes and coordinates and a view, just over the horizon, of the masters who have gone before…a world known by many names, but here we call it the Coordinate Plane.

Cue the music: “Have faith or pandemonium liable to walk upon the scene!”

Remember that song, colleagues?  Sorry, uh, might be a bit before your time, as they say.  Ask me about that tomorrow.

Anyway, we have accomplished much on our number line.  We have always known that the sum of 2 + 3 = 5, but now we know why as we start out at zero and move to a given coordinate on our number line (positive 2), and, always going to the right to add, we move three spaces and read the new value (5).   And we know that when we are adding negative numbers we remember that they behave, well, negatively.  So instead of adding and moving to the right, they add and move backwards to the left.  (Remember my moonwalk?  Michael Jackson couldn’t have done it better…)

We have used absolute value with absolute certainty as we added our integers, both positive and negative.  We have seen that, when adding two numbers, the number with the largest absolute value is the one that determines what sign the answer will be: positive or negative. 

We have practiced and practiced and we shall practice again.  You have worksheets on the adding and subtracting of integers, and you are asked to examine the relationship between the two operations.  That is because, my dear colleagues, we are entering new territory.  We are entering a world where proof exists in the mind….a world where addition rules and there really is no such thing as subtraction…it is the world of…the Additive Inverse.  And life as we know it will never be the same!  (Cue the music: “Don’t mess with Mr In-Between!”)

Once again, we peel another layer off of the things we already know.  The simple number line is now just like a ruler.  No, not like King Solomon – like a measuring ruler!  And we know that ruler extends out to infinity on the positive side – and on the negative side. 

We already knew that numbers on our number line increase from left to right – and now we are reminded that they decrease from right to left!  We see positive numbers on the right side of zero, and we see negative numbers on the left side of zero.  The set of numbers that are on the right side of zero are the same set of numbers on the left side zero; it’s just that the right side is positive and the left side is negative.  Looking at them, it’s almost like setting up a mirror right at the point of zero, huh?  

Well, we saw that, on the number line, the distance between any number and zero is called the number’s absolute value.  And since we are talking about the distance from point A to point B, this absolute value is always a positive number. 

Makes sense?  Check this out.  The absolute value of 6 is equal to the absolute value of -6.  That’s because the distance between 6 and 0 on the positive side of the number line is the same as the distance between -6 and 0 on the negative side of the number line.  The only difference is that one is on one side of zero and the other is on the other side of zero.  Going in opposite directions, yes, but the distance is still the same. 

Can you dig that?  Positively!  So check out the practice session we laid out today on page 59, questions #1 thru 19.  More practice to come when we meet again – absolutely!