What’s Goin’ On In Room 133

Posts Tagged ‘number line’

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!