Basic Addition Introduction to addition. Multiple visual ways to represent addition.
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- Welcome to the presentation on BASIC ADDITION.
- I know what you're thinking:
- "Sal, addition doesn't seem so basic to me."
- Well, I apologize.
- I hope I --
- Hopefully, by the end of this presentation,
- or in a couple of weeks, it will seem basic.
- So lets get started with,
- I guess we could say, some problems.
- Well, let's say I start with an old classic.
- 1 + 1
- And I think you already know how to do this.
- But, I'll kind of show you a way of doing this,
- in case you don't have this memorized,
- or you haven't already mastered this.
- You say, well, if I have
- (Let's call that an avocado.)
- If I have 1 avocado,
- and then you were to give me another avocado,
- how many avocados do I now have?
- Well, let's see. I have 1 ... 2 avocados.
- So 1 + 1 is equal to 2.
- Now, I know what you are thinking:
- "That was too easy."
- So, let me give you something a little bit more difficult.
- I like the avocados. I might stick with that theme.
- What is 3 + 4?
- Hmm. This is, I think, a more difficult problem.
- Well, let's stick with the avocados.
- And in case you don't know what an avocado is,
- it's, it's actually a very delicious fruit.
- It's actually the fattiest of all the fruits.
- You probably didn't even think it was a fruit --
- even if you [have eaten] one.
- So, let's say I have 3 avocados.
- 1, 2, 3. Right? 1, 2, 3.
- And let's say you were to give me 4 more avocados.
- So let me put this 4 in yellow,
- so you know that these are the ones you're giving me.
- So how many total avocados do I have now?
- That's 1, 2, 3, 4, 5, 6, 7 avocados.
- So 3 + 4 is equal to 7.
- And now I am going to introduce you
- to another way of thinking about this.
- It's called the number line.
- And, actually, I think this is how I do it in my head,
- when I forget -- if I don't have it memorized.
- So [on the] number line, I just write all the numbers in order,
- and I go high enough just so I can --
- [so that] all the numbers I am using are, kind of, in it.
- So, you know the first number is 0,
- which is nothing.
- Maybe you don't know; but now you know.
- And then you go to
- 1 (one)
- 2 (two)
- 3 (three)
- 4 (four)
- 5 (five)
- 6 (six)
- 7 (seven)
- 8 (eight)
- 9 (nine)
- 10 (ten)
- It keeps going,
- 11 (eleven)
- So, we're sayng 3 + 4. So let's start at 3.
- So I have 3 here.
- And we're going to add 4 to that 3.
- So all we do is we go up the number line,
- or we go to the right on the number line, 4 more.
- So we go 1 ... 2 ... 3 ... 4.
- Notice, all we did
- is we just increased it by 1, by 2, by 3, by 4.
- And then we ended up at 7.
- And that was our answer.
- We could do a couple of different ones.
- We could say, what is --
- What if I asked you what 8 + 1 is?
- Hmmm. 8 + 1.
- Well, you might already know it.
- 8 + 1 is just the next number [after 8].
- But if you look at the number line, you start at 8,
- and you add 1.
- 8 + 1 is equal to 9.
- Let's do some harder problems.
- And, just so you know,
- if you're a little daunted by this initially,
- you can always draw the circles,
- you can always do the number line,
- and, eventually over time, the more practice you do,
- you'll hopefully memorize these,
- and you'll do these problems in, like, half a second.
- I promise you. You've just got to keep practicing.
- Let's say....
- I want to draw the number line again.
- Actually, I have a line tool;
- so I shouldn't give you all of those ugly looking lines
- that I've been giving you.
- Look at that. Look at that. That's amazing.
- Alright, let me see.
- Oh. Oh. Yeah, look at that.
- Okay. So, that's a nice looking line.
- I'm gonna feel bad to erase it later on.
- So let me draw a number line.
- So let's do a hard problem.
- What is --
- I'm gonna do it in different colors now.
- 5 + 6
- So if you want, you can pause the video and try this.
- You might already know the answer.
- And the reason why I say this is a hard problem
- is because the answer [is] more [than the]
- [number of fingers you have on your two hands].
- So you can't necessarily do it on your fingers.
- So let's get started with this problem.
- Actually, my phone is ringing.
- But I'm going to ignore the phone,
- because you're more important.
- So. Okay. Let's start start at the 5.
- So we start at the 5.
- And we're gonna add 6 to it.
- So we go: 1
- We're at 11!
- So 5 + 6 is equal to 11.
- Now I'm gonna ask you a question.
- What is 6 + 5?
- Well, we're now going to see that, OK?
- Can you switch the two numbers
- and get the same answer?
- Well, let's try that.
- I'm gonna try it in a different color,
- so we don't get all confused.
- So let's start at 6.
- Right? Ignore the yellow for now and add 5 to it.
- 1 ... 2 ... 3 ... 4 ... 5.
- Ah. We get to the same place.
- And I think you might want to try this
- on a bunch of problems.
- And you'll see it always works out --
- that it doesn't matter in what order you --
- "5 + 6" is the same thing as "6 + 5."
- And that makes sense.
- If I have 5 avocados and you give me 6,
- I'm gonna have 11.
- If I have 6 avocados and you gave me 5,
- I'm gonna have 11 -- either way.
- Let's do a couple of --
- Since this number line is so nice,
- I wanna do a few more problems using it.
- Although, as I use it,
- I'm sure I'll just continue to confuse you,
- 'cause I'll write so much on top of it. But --
- Let's see. I'll use white now.
- What is -- What is 8 + 7?
- Well, if you can still read this, 8 is right here.
- Right? We're gonna add 7 to it.
- 1 ... 2 ... 3 ... 4 ... 5 ... 6 ... 7.
- We go to 15.
- 8 + 7 is 15.
- So hopefully, that gives you a sense
- of how to do these types of problems.
- And more than, I guess this --
- and you're gonna learn multiplication in a little bit.
- But these types of problems are,
- when you're getting started off in mathematics,
- these kind of require the most practice.
- And, to some degree, you have to start memorizing them.
- But, over time, you know, when you look back,
- I want you to remember how you feel
- while you are watching this video right now.
- And then I want you to watch this video in, like, three years.
- And remember how you felt when you're watching it now.
- And you're going to be, "O my! This was so easy!"
- 'Cause you're gonna learn so fast.
- So, anyway, I think you have an idea.
- If you don't know the answer
- to any of the addition problems,
- that we give you in the exercises,
- you can press the "Hints," and it'll draw circles,
- and then you can just count up the circles.
- Or, if you want to do it on your own,
- so you get the problem right,
- you could draw the circles,
- or you could draw a number line, --
- like we did in this presentation.
- I think you might be ready to tackle the addition problems.
- Have fun!
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