Addition on a Number Line

>> Professor Perez: Hey!
This is Professor Perez again.
Today, we're going to do some addition.
And we're going to do addition on a number line.
But, we can't get started without our student of the semester...and that's Charlie.
He better be ready to go!
Hey Charlie, you ready to go?
>> Charlie: Yeah...
>> Professor Perez: Yeah, you better be!
Okay, here we go Charlie!
Right there!
Now, Charlie, what is 6 plus 3?
Tell us how you do 6 plus 3.
>> Charlie: Six...plus...
>> Professor Perez: Okay, well, we're going to do 6 plus 3 on a number line right here.
That's right.
Now, we're adding.
Now, Charlie, when you add on a number line, which way do you go?
Do you go to the right or do you go to the left?
Which way, Charlie?
>> Charlie: To the right.
>> Professor Perez: To the right!
That's right.
We move to the right with addition.
Okay, now, in this lecture, we're only going to be adding positive numbers.
Later in the semester, we will get to adding negative numbers
and also subtracting negative numbers, okay?
So for right now, let's do a simple problem here 6 plus 3.
Charlie, where do we start on this number line?
>> Charlie: 6
>> Professor Perez: At the 6.
And we move which way?
>> Charlie: To the right
>> Professor Perez: How far?
>> Charlie: 3
>> Professor Perez: And where do you end up?
>> Charlie: 9
>> Professor Perez: At 9, there you go.
Don't forget to circle your answer there!
Very nice, Charlie.
Okay. Let's try another one here.
Now, here is negative 6 plus 3.
Where do we start this time, Charlie?
>> Charlie: Negative 6.
>> Professor Perez: That's right.
Right there.
Okay, now which way do we move?
>> Charlie: To the right.
>> Professor Perez: How far?
>> Charlie: 3.
>> Professor Perez: And where do we end up Charlie?
>> Charlie: Negative 3.
>> Professor Perez: Negative 3.
And that is our answer, negative 3.
Very nice, Charlie!
Okay, don't forget to circle your answer.
Now, here we are...0 plus 5.
Where do you start, Charlie?
>> Charlie: 0
>> Professor Perez: That's right, and move which way?
>> Charlie: To the right.
>> Professor Perez: How far?
>> Charlie: 5.
>> Professor Perez: And what's your answer?
>> Charlie: 5.
>> Professor Perez: There you go!
All right, Charlie, let's do another one here.
Negative 4 plus 5.
Where do we start?
>> Charlie: Negative 4.
>> Professor Perez: Negative 4.
Right here.
Now, we're going to move right, right?
We're going to move right 5.
Now, Charlie, what can you tell me about your answer?
>> Charlie: It's positive?
>> Professor Perez: Okay, why is it going to be positive?
>> Charlie: Because we're going to pass the zero!
>> Professor Perez: That's right, we're going to cross the zero.
But notice here, we go to zero...how many spaces have we moved?
>> Charlie: 4
>> Professor Perez: And we still have...how many more to go?
>> Charlie: 1 more.
>> Professor Perez: 1 more.
And so our answer is positive 1.
There you go!
Don't forget to circle your answer.
Let's do another one.
Now, negative 9 Charlie, don't get scared!
Now where do we start this time?
>> Charlie: Negative 9.
>> Professor Perez: Negative 9.
And we've got to move right...how far?
>> Charlie: 11
>> Professor Perez: 11.
Now, Charlie, we're starting at negative 9.
How far do we have to move to get to the zero?
>> Charlie: 9.
>> Professor Perez: Okay, 9 spaces.
Okay, now, how many more do I have to go?
>> Charlie: 2.
>> Professor Perez: 2 more.
That's right.
Okay, notice, the 9 plus 2 is the 11.
Now, where do we end up at Charlie?
>> Charlie: 2.
>> Professor Perez: 2 and so negative 9 plus 11 does give you a positive 2.
Okay, let's do one more.
Let's start way over here at negative 10.
Now, Charlie, we're going to move right 18 units, so, let's start at negative 10.
Now how far do I have to move to get to the zero?
>> Charlie: 10.
>> Professor Perez: Okay, let's do that.
And we've moved 10 spaces.
Okay, let's take a break!
Phew! Okay, break's over, Charlie!
Now, how many more do we have to move?
>> Charlie: 8.
>> Professor Perez: 8 more, that's right, Charlie, so we move the 8.
And now we've moved 18 total to the right and so what's our answer?
>> Charlie: 8.
>> Professor Perez: That's right, it's 8.
Don't forget to circle your answer there!
Very nice, Charlie!
Now, here's a question.
This is getting ready for...getting you ready for Beginning Algebra.
What number do you add to negative 5 to get 2, Charlie?
Remember, negative 5 is here and 2 is over there so...think about this Charlie.
What do you think the answer is?
>> Charlie: 7?
>> Professor Perez: Okay.
How many of you agree with him?
Yeah, you've got a lot of people that agree with you Charlie.
Okay, let's see if he's right!
Okay, so if we're at negative 5 and we move right 5, we're at zero, right?
Remember, we're trying to go from negative 5 to get to 2.
Now, how many more do I have to move, Charlie?
>> Charlie: 2?
>> Professor Perez: 2 more.
Okay now, here we go.
We start at negative 5 and to get to 2 we had to move a total of how many spaces, Charlie?
>> Charlie: 7.
>> Professor Perez: 7.
So, here's our answer.
What number do you add to negative 5 to get 2, Charlie?
>> Charlie: 7.
>> Professor Perez: 7.
That's right.
Okay, now, in Beginning Algebra, you're going to be asked this very same question, okay?
But you're going to be asked in this manner here.
Negative 5 plus x equals 2.
That equation there is actually asking you, "What number do you add to negative 5 to get 2?"
And what's our answer, Charlie?
>> Charlie: 7.
>> Professor Perez: It would be 7.
So, x would be 7 in that equation.
You're going to get to those types of equations, Charlie,
when you get to Beginning Algebra...that's IF you make it through this class!
Yeah, you'll do fine if you just keep up with the homework and pay attention in class!
All right.
So, here's another problem, Charlie.
What number do you add to negative 8 to get 7?
Okay, let's do it on the number line.
We're going to start at negative 8 and we're going to move to the zero.
How many spaces do we move, Charlie?
>> Charlie: 8.
>> Professor Perez: That's right.
8. Now, take a break!
Phew! Okay, now, how many more do we have to move, Charlie, to get to the 7?
>> Charlie: 7 more!
>> Professor Perez: 7.
That's right.
And so, when you look at this, we moved 8 and we moved 7 more.
Now you have to do an addition problem.
Charlie, how much is 8 plus 7?
>> Charlie: 15.
>> Professor Perez: Okay, it is 15, that's right.
Very good.
So, to answer this question, "What number do you add to negative 8 to get to that 7?"
what's your answer?
>> Charlie: 15.
>> Professor Perez: 15.
Very nice!
That's because negative 8 plus 15 equals 7.
Now, again, in Beginning Algebra, you'll be asked this equation.
Which basically, that equation is asking you this question.
What number do you add to negative 8 to get 7?
x is the unknown number.
And so what's our answer, Charlie?
>> Charlie: 15.
>> Professor Perez: x equals 15.
Very nice!
Anyway, so, we'll take a break and come back and do part two of our addition lecture.
Anyway, Charlie?
Get some rest, do your homework problems, and we'll see you again soon and you too!