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CCSS.Math: , , ,

Let's think about
different ways that we can represent the number 675. So the most obvious
way is to just look at the different place values. So the 6 is in the
hundreds place. It literally represents 600. So that's 600. I'm going to do that
in the red color-- 600. The 7 is in the tens place. It represents 7 tens, or 70. And then the 5 in
the ones place. It represents 5. So let me copy and paste
this and then think about how we can regroup the
value in the different places to represent this
in different ways. So let me copy and
let me paste it, and maybe I'll do
it three times. So let me do it once, and
let me do it one more time. So one thing that we could do is
we could regroup from one place to the next. So, for example,
we could take if we wanted to-- we could take
1 from the hundreds place. Taking 1 from the hundreds
place will make this a 5. That's essentially
taking 100 away. So this is really
making this a 500. And we could give
that 100 to-- well, we could actually give
it to either place, but let's give it
to the tens place. So we're going to give
100 to the tens place. Now, if you give 100
to the tens place and you already had 70 there,
what's it going to be equal to? Well, it's going
to be equal to 170. Well, how would we
represent that is tens? Well, 170 is 17 tens. So we could just say
that 7 becomes 17. Now, we could keep doing that. We could regroup some of
this value in the tens place to the ones place. So, for example, we could
give 10 from the tens place and give it to the ones place. Let's do that. So let's take 10 away from here. So that becomes 160. This becomes 16. And let's give that
10 to the ones place. Well, what does the
ones place now become? Well, 10 plus 5 is 15. So this 5 is now a 15. Let's do another scenario. Let's do something nutty. Let's take 200 from
the hundreds place. So this is going to now 4, and
this is going to become 400. That's what this
4 now represents. And let's give 100
to the tens place. And let's give another
100 to the ones place. So in other words, I'm
just regrouping that 200. Those 200's, I've taken
from the hundreds place, and I'm going to give it
to these other places. So now the tens place
is going to be 170. We're going to have 170
here, which is 17 tens. So you could say that
the tens place is now 17. And now the ones
place, well, I had 5, and now I'm going
to add 100 to it. So it's going to be 105. And 105 ones is literally 105. And notice, this is 400 plus
17 tens, which is 170 plus 105. You add these together,
you're still going to get 675. Let's do that again. So let's take, I don't know. Let's take all of
the hundreds away. Let's take all of
the hundreds away. So that goes zero. That goes zero. And let's give 400
to the tens place. So let's give 400
to the tens place. Well, that'll make that 470. Let me do that in
that green color. That will make that 470, which
is the same thing as 47 tens. And then I still have 200
to give to the ones place. So let me do that. So I still have 200 to
give to the ones place. And so that's going
to go from 5 to 205. Once again, all
I've done is I've regrouped the value
in the number 675. Any of these still
represent 675. You can add these
numbers on the right. They all add up to 675.