The Number Line
"Positive and Negative Integers"
Take a trip down the number line with our rapping integer! In this song, he teaches students about positive and negative integers, absolute value and adding and subtracting integers. The video gives a helpful visualization that aids students’ understanding of positive and negative. It also uses negative numbers and absolute value in a real-world example of owing money.
I’m an integer, yeah you found me,
Sitting on the number line, all my friends around me.
Like a roller coaster I go up and down,
But I always have value, I never clown.
Maybe you’re measuring a mountain’s height,
If you add to me, then I slide to the right.
If you subtract from me, then I slide to the left,
Yeah, I was more, but look at me, now I’m less.
I could go to 0, that’s a number too,
Maybe I’m at sea level, see, that’s nothing new.
If we dive like the best who ever lived,
I’m less than 0, so you know I’m negative.
So -8 is less than -6,
And -6 is less than 6, you get the pics?
I’m on the number line, find me on the number line.
To the right when it’s hot in the summertime,
To the left when it’s cold in the winter,
My value’s absolute, I’m a winner. (x2)
People tell me, “There’s something about you,”
They’re impressed with my absolute value,
The distance from me to 0 on the number line,
So my absolute value is positive every time.
The absolute value of 23 is 23,
The absolute value of -3 is 3.
Let’s say the number line is my bank account,
I have 90 bucks, that’s what I’m giving thanks about.
If I spend 110 dollars on my credit card,
Now I’ve got -20 bucks, man times are hard.
The absolute value of my debt is 20,
I owe the bank 20 bucks, now get ready.
If I spend 30 more, man I’m out of luck,
-20 minus 30 that’s -50 bucks.
If I pay the 50, then I’m back at 0,
I don’t owe them any money, they don’t owe me money either.
I’m on the number line, find me on the number line,
To the right when it’s hot in the summertime,
To the left when it’s cold in the winter,
My value’s absolute, I’m a winner. (x2)
Integers are positive or negative whole numbers. Zero is also an integer, though it is neither positive nor negative.
The number line is a line with all integers on it. It extends forever in both directions. But we obviously don't draw the whole thing. We just draw arrows on the left and the right to show that the line actually keeps going on and on.
Numbers get bigger as you go right and get smaller as you go left.
Zero is a number. Don't let anyone tell you otherwise. In fact, it is an even number, since it can be divided by 2. But it isn't positive, and it isn't negative.
Don’t get confused by the fact that 8 is bigger than 6. When you’re dealing with negative numbers, everything is opposite. -8 is to the left of -6 on the number line; so it is smaller. And what is smaller than -8? -9 or -10 or -25 or any other number to the left of it on the number line.
Here's a way to remember how numbers work on the number line: turn a thermometer on its side, with the high temperatures on the right. As the temperature gets higher, it goes further to the right, and when it gets colder, it goes to the left. 0 isn't the coldest temperature. -8 is even colder. And -20 is even colder still.
Absolute value is a number's distance from 0 on the number line. It is represented with tall lines around a number that look like this: |x|
So the absolute value of 3 looks like |3|
So the absolute value of 3 looks like |3|
All negative numbers have positive absolute values. The absolute value of -8 is 8. Here are some more examples:
|-9| = 9
|14| = 14
|-82| = 82
Absolute value is always positive. What's the only exception? The absolute value of 0 is 0. And as we said, 0 is not positive or negative.
|-9| = 9
|14| = 14
|-82| = 82
Absolute value is always positive. What's the only exception? The absolute value of 0 is 0. And as we said, 0 is not positive or negative.
If you take a number (like 90) and subtract a larger number from it (like 110) you'll always get a negative number.
90 – 110 = -20
90 – 110 = -20
If you have -$20 in the bank, how much do you owe the bank? You don't owe them -$20, you owe them $20. So this question is actually asking for the absolute value. And |-20| = 20
If you have a negative number and you subract from it, you're going to get a number that looks bigger. But it's actually smaller, since smaller numbers are further to the left on the number line.
-20 – 30 = -50
-50 is even less than -20. You now have even less money. In other words, you owe the bank even more cash. But if you pay the bank back, you can get back to zero.
-50 + 50 = 0
-20 – 30 = -50
-50 is even less than -20. You now have even less money. In other words, you owe the bank even more cash. But if you pay the bank back, you can get back to zero.
-50 + 50 = 0
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