All right, this is
[Fourth-Grade] module 1 Lesson 2 we're going to be continuing talking about place value
And we're going to continue that concept of recognizing that the columns are
related by a factor of 10 for example if you have
Five thousands, and you have five hundreds we want students to recognize that five
Thousands is ten times bigger
Than five hundreds and that five hundred is ten times bigger
than five tens and
that five tens is
ten times bigger than five ones, so really if we were going to multiply this by
10
It would give us five in the ten thousands column
similarly if we were to take this five and multiply by ten
It would give us
Five in the thousands Column Etc
So let's put this into practice
So it says as you did during [the] lesson ostensibly this is going to happen teachers in the classroom and parents
Maybe hopefully this happened in the classroom today
[a] label and represent the product or quotient by drawing disks on the place value chart, so the idea is
We know that. There's this beautiful shortcut that parents and teachers often know Joe's to auto zero or oh just chopped off a zero
But the purpose of this lesson is [to] explain
try and Demonstrate why that thing happens and
So that students we're going to try and give students a chance to develop some number sense
So the first thing we're going to do is we're going to fill in
then labels ones tens hundreds
thousands
and then oh my goodness ten
Thousands and in this case that's going to be enough
And it says the first thing we're going to do we're [going] to do [10] times for thousands. So we're going to take that
For thousands and we're going to model that in our place value chart
So it's going to look like [1] [2] [3] [4] all right and then
Because [it] says we're going to have 10 times that
We need to have 10 rows of this, so let's get going so that's one row
two Rows
three Rows
4 Rows
5 Rows
6 Rows 7
8
9 and 10 so we now have 10 rows. So what does that mean that means we now have?
40
Thousands, how do I know that well because we have 10 by 4 so 10 times 4 is [40], so we now have 40
thousands
But we know [that] for every 10
So we have 10 right here means we can cash those in for a dot in the next column over
We can cash these 10 in for a dot over here
We can cash these 10 for a dot over here and lastly we can cash these 10 for a dot over here
and that gives us for
thousands Hopes Note for
10
thousands
That gives us for ten thousands another way
You can write for 10 thousands is to say we have 40 oops [ah] we have yeah
40,000
All right, because we have for 10,000 so that means we have 40,000 now. Here's the cool thing
I want us our students to start noticing here now. I want our students to start noticing that we had
four in
the thousands Column and
then when we multiplied by ten what happened well when we multiplied by ten
That eventually meant
We had we ended up with
four in
the ten thousands Column
All right, so this kind of went away
And it's as if the four moved to the column to the left it moved one space to the [left]
That's kind of the shortcut teachers that we eventually want our students to start seeing
Now this is the exact reverse, so we're going to write ones tens hundreds
thousands and then ten thousands
All right, and we're going to divide by ten this time, so we're going to begin by modeling our
Four thousand, so one two three [four] so we have four
thousands, but now we need to divide [that] by ten
so the way, we're going to do that is we for each one of these dots in the
thousands Column, we're going to cash it in for
Ten in the hundreds Column so we can see that
this guy right [here] is going to get cashed in for
Ten
ten in the hundreds Column, and then we can see that this guy is going to get cashed in for
Ten one two three four five six seven eight nine
ten in the tens Column, and then each one of these guys in the
thousands Column is going to be cashed in for
Ten in the hundreds Column one two three four five six seven eight nine
Ten and then one two three four five six seven eight nine ten so now
What do we end up with well we end up with?
40 whoa, I want to [erase] that we're going to end up with
40
hundreds
right here 40 hundreds
Now we're going to divide. What is 40?
divided by 10 40 hundredths divided by 10 so 40 divided by 10 gives us 4
But for what well let's see
So right here. We're going to take our 40 and we're going to divide it [in] two by oops by 10 groups one group
two groups three groups four groups five six seven eight nine ten another way
You could have set in then so each group is four. So the answer is four and then it's hundreds of
[course] another way, we could have done it is we could have looked at groups of ten one group of ten
another group of ten another group of ten and lastly a group of ten
equaling four groups and so the answer is [four] hundreds we could think of it either way and
[of] course [for] [hundreds] is
Equal to [four] [hundred] so what we want students to see is
that the shortcut and I'm going to erase this and
The shortcut that we want students to see is that we started?
with four in the thousands column, but then when we divided by ten
We ended up with
four in the hundreds column
Just going to do one or two from this table
It says solve each expression
By writing the solution in unit form parents and teachers you guys probably don't exactly know what unit form is
So let's take a look at this ten times three tens
That's going to equal 30
Tens and what I want you to do is I want you to think of this word
Maybe is replace it with apples so 10 times
[3] apples gives you 30 apples, so that's 30 10, and then of course
you could
Teachers at this point you could have your students visualize or maybe explicitly?
Write out once ones tens
hundreds oh, I'm moving real fast ETC, and then they may need to
Model things or imagine this in our table
So oh 30 tens and every group of 10 equals a hundred. [oh] ok, so in
Standard form this would be three hundred
Because 30 tens is equal to three hundreds
one Last one might be nine ten
Thousands divided by Ten Well nine ten thousands divided by [Ten] is
[ninety] thousand s so that's going to be nine
thousands and
Then that's going to look like nine
Thousand like this alright, so unit form is a phrase that you might not be familiar with and [that's] what it looks like
All right, just a [little] bit more of an example only now
It's getting a little bit more elaborate because now we're mixing our unit, so we have ones
Tens and
Teachers I make my students draw these charts
I am [not] nice, and I don't provide it for them, and why is that well?
It's because I want them to continually practice
Writing the Columns ones tens hundreds thousands and then oftentimes next they go millions. Okay? No, it's going to be ten
Thousands, and we want them to just continually practice that so I don't give them a chart. I make them write it out. Oh
so let's take a look let's take a look at this one right here, so
five Hundred and Five tens
And we're going to multiply [that] by ten so the idea would be we're going to model this and it would look like
five hundred s one two three four five and it would like five tens one two three four five all right and
Then we're going to multiply
By ten, so what we want our students to learn is that when we multiply by ten?
these
five dots are going to move into the thousands Column and
these five dots and the tens are going to move into the
hundreds column because when you multiply by ten it moves it into the column to your
Left because that's the way it is and then of course
What ends up over here nothing?
Nothing ends up there, so we're going to put a big old fat zero so the idea would [be] well
What is our answer in unit Form well the answer would be?
50
hundreds
and
50 Tens
or students might want to write it as five thousands and
five hundreds I
Don't know what the answer is in [the] answer key
[but] personally as a teacher. I would accept either of those because they're both correct and unit form is nice
But it's not going to have this [long-lasting]
implication if students
Choose one or the other [I] mean it's not going to impact how they behave or how they're going to perform
mathematically in fifth or sixth or seventh [grade]
And then of course the standard form is you look at your chart down here and you go?
Oh look at that
five thousand five hundred
And that's our answer so standard form would look like five thousand five hundred and I like to put commas
But you absolutely do not have to put commas
similarly
here if we were to divide
so for ten thousand s
Divided by 10 gives us four thousands
And eight hundreds divided by 10 gives us eight
Tens and so the standard form
would end up looking like this now of course I kind of went fast on that and students might need to model it with
chips in a place value chart
and
anyway, but I kind of skipped through that real quick and
last one
What's what's a video without a word problem to practice says Emily collected nine hundred fifty Dollars selling?
Girl-scout cookies, I wish I had some of them emily's troop collected ten times as much as she did so
How much money did the troop raise so the idea would be?
Well if we're going to put in Emily's money nine hundred fifty dollars. So here's our ones
Here's our tens, and here's our
hundreds
and
Then if we're going to multiply by ten well that means this nine is going to move into the thousands column
this five is going to move into
the hundreds Column
This zero is going to move into the tens column so to speak and then we have nothing left over here
So what do we put right there? We put a big old fat zero because there's nothing there. There's nothing left over and
so the answer is
nine thousand five hundred Dollars nine thousand
[Rosen's]
Here so we end up with nine thousand five hundred and nothing else. [so] nine thousand five hundred and nothing else and
that wraps up
Fourth-Grade module [1] lesson two where we're starting to learn
place value, and how each Column is
Related to the Columns next door