Measuring width in inches

WEBVTT
Kind: captions
Language: en

00:00:00.640 --> 00:00:02.960
- [Instructor] So right
over here, I have a flower

00:00:02.960 --> 00:00:05.090
and I have a ruler

00:00:05.090 --> 00:00:09.860
and what I wanna do is figure
out how wide this flower is.

00:00:09.860 --> 00:00:11.110
So you can pause the video

00:00:11.110 --> 00:00:13.193
and think about how I would do that.

00:00:14.280 --> 00:00:16.760
All right, now let's do this together.

00:00:16.760 --> 00:00:19.410
So if I wanna figure out
how wide the flower is,

00:00:19.410 --> 00:00:20.365
first I could say, all right,

00:00:20.365 --> 00:00:23.480
the left side of the
flower goes about this far.

00:00:23.480 --> 00:00:26.220
So let me draw a line here just
so we can really keep track

00:00:26.220 --> 00:00:27.670
of how far we go to the left

00:00:27.670 --> 00:00:32.240
and then the right side of the
flower goes about that far.

00:00:32.240 --> 00:00:33.830
So let's keep track of that

00:00:33.830 --> 00:00:37.820
and then we can use our
ruler to measure the distance

00:00:37.820 --> 00:00:39.513
between those two lines.

00:00:40.641 --> 00:00:42.110
We can rotate it a little bit

00:00:43.630 --> 00:00:45.940
then I'm going to move it a little bit

00:00:47.030 --> 00:00:49.670
and I want the left edge of the ruler

00:00:49.670 --> 00:00:51.610
to start at that left line.

00:00:51.610 --> 00:00:55.460
So starting right over
here and then we could see

00:00:55.460 --> 00:00:58.570
that it's one, two, three inches roughly

00:00:58.570 --> 00:01:00.580
to get us to the right side.

00:01:00.580 --> 00:01:03.910
So it looks like this
flower right over here

00:01:03.910 --> 00:01:07.960
is three inches wide.


Length word problem example

WEBVTT
Kind: captions
Language: en

00:00:00.710 --> 00:00:02.130
- [Instructor] We're told that Pilar

00:00:02.130 --> 00:00:05.350
has 85 inches of ribbon.

00:00:05.350 --> 00:00:09.420
She gives her friend,
Nico, 19 inches of ribbon.

00:00:09.420 --> 00:00:12.910
How much ribbon does Pilar have left?

00:00:12.910 --> 00:00:15.510
Pause this video and see
if you can figure that out.

00:00:16.530 --> 00:00:18.000
All right, now let's do it together.

00:00:18.000 --> 00:00:21.760
So Pilar is starting
with 85 inches of ribbon.

00:00:21.760 --> 00:00:24.610
And I could represent that
with what's sometimes known

00:00:24.610 --> 00:00:26.120
as a tape diagram.

00:00:26.120 --> 00:00:27.840
I guess you could call it a ribbon diagram

00:00:27.840 --> 00:00:29.180
in this case.

00:00:29.180 --> 00:00:33.490
So let's say the width of
this rectangle or this tape

00:00:33.490 --> 00:00:38.190
or this ribbon represents
the length of Pilar's ribbon.

00:00:38.190 --> 00:00:43.190
So this is 85 inches of
ribbon right over here.

00:00:44.010 --> 00:00:48.120
She gives her friend, Nico,
19 inches of the ribbon.

00:00:48.120 --> 00:00:49.150
I'll do that in red.

00:00:49.150 --> 00:00:51.410
So gives away 19 inches.

00:00:51.410 --> 00:00:54.910
So I could think about
giving away 19 inches.

00:00:54.910 --> 00:00:57.430
And this is just, I'm
not doing it exactly,

00:00:57.430 --> 00:00:59.240
but you get a sense of things.

00:00:59.240 --> 00:01:03.810
So 19 inches might be about that much.

00:01:03.810 --> 00:01:06.850
So that's 19 inches

00:01:06.850 --> 00:01:09.140
that Pilar gives away.

00:01:09.140 --> 00:01:11.900
So how much ribbon does Pilar have left?

00:01:11.900 --> 00:01:16.540
Well, it would be this
section right over here.

00:01:16.540 --> 00:01:19.740
Now how do we figure out
how much she has left,

00:01:19.740 --> 00:01:21.810
this question mark right over here?

00:01:21.810 --> 00:01:23.470
Well, there's a couple of
ways to think about it.

00:01:23.470 --> 00:01:26.220
You could say 19 plus the question mark

00:01:26.220 --> 00:01:27.480
is equal to 85.

00:01:27.480 --> 00:01:29.010
Let me write that down.

00:01:29.010 --> 00:01:33.810
19 plus question mark,

00:01:33.810 --> 00:01:36.593
plus what we're trying to
figure out, is equal to 85.

00:01:38.540 --> 00:01:41.030
So the amount she gave away
plus the amount she has left

00:01:41.030 --> 00:01:42.550
is equal to 85.

00:01:42.550 --> 00:01:45.090
Or you could say if I start with 85

00:01:45.090 --> 00:01:47.150
and if I were to take away 19,

00:01:47.150 --> 00:01:48.850
well, that's what I have left.

00:01:48.850 --> 00:01:52.500
So you could also say that question mark,

00:01:52.500 --> 00:01:54.210
the amount that she has left,

00:01:54.210 --> 00:01:58.967
is equal to 85 minus, minus 19.

00:02:01.290 --> 00:02:04.670
So what is 85 minus 19?

00:02:04.670 --> 00:02:07.010
Well, there is a bunch of
ways that we can compute it.

00:02:07.010 --> 00:02:09.750
One way to do it is I could rewrite 85

00:02:09.750 --> 00:02:13.330
as 80 plus 5,

00:02:13.330 --> 00:02:16.470
separate essentially the tens
place from the ones place.

00:02:16.470 --> 00:02:18.540
We have 8 tens, which
is the same thing as 80

00:02:18.540 --> 00:02:19.660
and then 5 ones.

00:02:19.660 --> 00:02:23.480
And then rewrite 19 as 10 and 9.

00:02:23.480 --> 00:02:25.260
So if I'm subtracting 19,

00:02:25.260 --> 00:02:30.260
I'm really subtracting
10 and subtracting 9.

00:02:31.540 --> 00:02:33.200
Now why is that useful?

00:02:33.200 --> 00:02:36.010
Well, it's pretty
straightforward to say that

00:02:36.010 --> 00:02:40.720
all right, 80 minus 10 is
going to be equal to 70.

00:02:40.720 --> 00:02:44.370
Eight 10s minus one ten is
going to be equal to seven 10s.

00:02:44.370 --> 00:02:47.570
And so I could rewrite this as 70

00:02:48.570 --> 00:02:51.663
plus five minus nine.

00:02:52.930 --> 00:02:55.810
Now, if I just try to figure
out what five minus nine is,

00:02:55.810 --> 00:02:57.950
we get into a little bit of
trouble, because nine is bigger

00:02:57.950 --> 00:03:02.220
than five, but what if we were
to rewrite nine in two parts?

00:03:02.220 --> 00:03:04.010
If we were to say look,
nine is the same thing

00:03:04.010 --> 00:03:06.740
as four plus five, so
if I'm subtracting nine,

00:03:06.740 --> 00:03:09.283
that's the same thing as subtracting five

00:03:09.283 --> 00:03:12.420
and then subtracting four.

00:03:12.420 --> 00:03:14.760
And this makes it a little bit easier,

00:03:14.760 --> 00:03:18.360
because we know that
five minus five is zero,

00:03:18.360 --> 00:03:23.360
and so we can rewrite this as 70 minus 4.

00:03:24.250 --> 00:03:25.940
Now what's going to be?

00:03:25.940 --> 00:03:29.730
Well we know that 10 minus
four is equal to six,

00:03:29.730 --> 00:03:33.793
so 70 minus four is
going to be equal to 66.

00:03:35.920 --> 00:03:37.320
And we're all done.

00:03:37.320 --> 00:03:41.533
That's how much ribbon, she
has 66 inches of ribbon left.


Partitioning rectangles

WEBVTT
Kind: captions
Language: en

00:00:00.380 --> 00:00:03.120
- [Instructor] So I have a
rectangle drawn right over here.

00:00:03.120 --> 00:00:06.660
And my goal is to split this rectangle up

00:00:06.660 --> 00:00:09.970
into smaller, equal squares.

00:00:09.970 --> 00:00:11.920
And the way that I'm going to do that

00:00:11.920 --> 00:00:16.920
is by first dividing this
rectangle into two rows,

00:00:17.270 --> 00:00:19.630
and I should say two equal rows.

00:00:19.630 --> 00:00:22.500
And then I'm going to
divide this rectangle

00:00:22.500 --> 00:00:27.030
into five equal columns.

00:00:27.030 --> 00:00:28.237
Now, I know some of you are saying,

00:00:28.237 --> 00:00:30.890
"What is a row and what is a column?"

00:00:30.890 --> 00:00:33.440
So a row, at least my
brain thinks about it

00:00:34.308 --> 00:00:39.308
as a part of the rectangle that
is going from left to right.

00:00:39.430 --> 00:00:40.976
One way to think about it,

00:00:40.976 --> 00:00:43.876
if I had a bunch of, let's say
that these are apples here.

00:00:44.850 --> 00:00:48.160
And if I wanted to think about dividing

00:00:48.160 --> 00:00:50.010
these apples into rows,

00:00:50.010 --> 00:00:53.000
I would say that this is the first row.

00:00:53.000 --> 00:00:54.860
This is a second row.

00:00:54.860 --> 00:00:57.280
And that this is a third row.

00:00:57.280 --> 00:00:59.220
If I were to think in terms of columns,

00:00:59.220 --> 00:01:02.610
I tend to think of
columns as going up down.

00:01:02.610 --> 00:01:06.310
And so the columns, this
would be one column.

00:01:06.310 --> 00:01:08.220
This would be another column.

00:01:08.220 --> 00:01:09.840
This would be a third column,

00:01:09.840 --> 00:01:12.230
and this would be a fourth column.

00:01:12.230 --> 00:01:15.070
So now that we understand
what rows and columns are,

00:01:15.070 --> 00:01:16.330
let's first think about,

00:01:16.330 --> 00:01:18.810
maybe pause this video and
think about how would you divide

00:01:18.810 --> 00:01:20.713
this rectangle into two rows.

00:01:22.210 --> 00:01:24.780
Well, the way that I would tackle it is,

00:01:24.780 --> 00:01:29.010
I would draw a line that
goes from left to right,

00:01:29.010 --> 00:01:30.260
and there you have it.

00:01:30.260 --> 00:01:33.260
I now have the rectangle
split into one row

00:01:33.260 --> 00:01:35.360
and now a second row.

00:01:35.360 --> 00:01:37.210
Now pause the video
and you could draw this

00:01:37.210 --> 00:01:38.790
if you have a pencil and paper with you,

00:01:38.790 --> 00:01:41.080
or you could just think
about what I should do.

00:01:41.080 --> 00:01:44.433
How would I now divide this
rectangle into five columns?

00:01:46.070 --> 00:01:50.767
Well, what I could do
is make a bunch of lines

00:01:50.767 --> 00:01:53.000
that go from top to bottom.

00:01:53.000 --> 00:01:55.200
So that's one column there.

00:01:55.200 --> 00:01:58.043
This is a second column.

00:01:59.748 --> 00:02:01.840
This is a third column.

00:02:01.840 --> 00:02:06.840
This is a fourth column
and a fifth column.

00:02:07.420 --> 00:02:08.253
So there you have it.

00:02:08.253 --> 00:02:11.100
I have two rows, one row, two rows,

00:02:11.100 --> 00:02:12.260
and I have five columns.

00:02:12.260 --> 00:02:16.000
One, two, three, four, five.

00:02:16.000 --> 00:02:19.210
Now what's interesting is
when I split the rectangle

00:02:19.210 --> 00:02:21.930
in this way into two
rows and five columns,

00:02:21.930 --> 00:02:25.873
how many equal size squares did I create?

00:02:26.890 --> 00:02:30.140
Well, I've created one,
two, three, four, five,

00:02:30.140 --> 00:02:34.300
six, seven, eight, nine, 10 equal squares.

00:02:34.300 --> 00:02:38.060
And that makes sense
because each row has five.

00:02:38.060 --> 00:02:41.550
I have one, two, three, four, five.

00:02:41.550 --> 00:02:44.800
One, two, three, four, five.

00:02:44.800 --> 00:02:48.230
And five plus five is equal to 10.

00:02:48.230 --> 00:02:52.350
Another way to think about
it is each column has two,

00:02:52.350 --> 00:02:57.350
one, two, one, two, one,
two, one two, one, two.

00:02:58.250 --> 00:03:00.100
And two plus two is four,

00:03:00.100 --> 00:03:05.100
plus two is six, plus two
is eight, plus two is 10.

00:03:05.200 --> 00:03:08.200
So that's what splitting
the rectangle into two rows

00:03:08.200 --> 00:03:09.760
and five columns gets me,

00:03:09.760 --> 00:03:12.263
it splits it into 10 sections.


Shapes and angles

WEBVTT
Kind: captions
Language: en

00:00:00.740 --> 00:00:02.080
- [Narrator] In this
video, we're gonna talk

00:00:02.080 --> 00:00:05.820
about shapes and something called angles,

00:00:05.820 --> 00:00:08.470
which you've might have
heard the word before.

00:00:08.470 --> 00:00:11.190
So the first question is what is an angle?

00:00:11.190 --> 00:00:14.270
Well let me draw a shape
and that might help explain

00:00:14.270 --> 00:00:15.550
what an angle is.

00:00:15.550 --> 00:00:18.380
So I'm gonna draw a triangle,

00:00:18.380 --> 00:00:22.410
and you might already know that
a triangle has three sides.

00:00:22.410 --> 00:00:25.920
You can see one side,
two sides, three sides,

00:00:25.920 --> 00:00:28.470
but it also has three angles.

00:00:28.470 --> 00:00:29.700
Now, what are the angles?

00:00:29.700 --> 00:00:31.400
Well for a shape like this, you can think

00:00:31.400 --> 00:00:34.610
of an angle as where two
of the sides come together.

00:00:34.610 --> 00:00:38.190
So for example, this right
over here is an angle

00:00:38.190 --> 00:00:40.410
because two of the sides
have come together there,

00:00:40.410 --> 00:00:43.510
this side and this side
come together at that point.

00:00:43.510 --> 00:00:44.900
So that's an angle.

00:00:44.900 --> 00:00:46.640
This is another angle.

00:00:46.640 --> 00:00:48.180
And that's another angle.

00:00:48.180 --> 00:00:50.960
So not only does a
triangle have three sides,

00:00:50.960 --> 00:00:54.610
it also has three angles.

00:00:54.610 --> 00:00:56.040
Now let me ask you a question.

00:00:56.040 --> 00:01:00.810
If I had a rectangle like this,

00:01:00.810 --> 00:01:04.120
how many angles does it have?

00:01:04.120 --> 00:01:05.920
Pause this video and think about it.

00:01:07.240 --> 00:01:08.770
Well, we can see the angles.

00:01:08.770 --> 00:01:11.780
We have one angle here,
another angle here,

00:01:11.780 --> 00:01:15.410
so two, three and four.

00:01:15.410 --> 00:01:18.650
So not only does a
rectangle have four sides,

00:01:18.650 --> 00:01:21.010
it also has four angles.

00:01:21.010 --> 00:01:23.530
Now what if I were to give
you another four-sided figure

00:01:23.530 --> 00:01:26.830
another quadrilateral,
quadrilateral's a very fancy word,

00:01:26.830 --> 00:01:29.140
but it really just
means four-sided figure,

00:01:29.140 --> 00:01:30.860
but one that's not a rectangle.

00:01:30.860 --> 00:01:33.810
What if I were to give
you something like this?

00:01:33.810 --> 00:01:36.710
So this type of a quadrilateral,

00:01:36.710 --> 00:01:40.000
it still has four sides,

00:01:40.000 --> 00:01:41.740
but you can see that it looks

00:01:41.740 --> 00:01:44.300
a little bit different than a rectangle,

00:01:44.300 --> 00:01:46.820
I can do it so it's pretty straight.

00:01:46.820 --> 00:01:49.500
It still has one, two, three, four sides.

00:01:49.500 --> 00:01:50.850
How many angles do we have?

00:01:50.850 --> 00:01:52.920
And this figure is called a trapezoid.

00:01:52.920 --> 00:01:55.333
How many angles does a trapezoid have?

00:01:56.280 --> 00:01:57.950
Well, let me count them again.

00:01:57.950 --> 00:02:00.690
So we have one angle right over here,

00:02:00.690 --> 00:02:05.470
two, three, and four.

00:02:05.470 --> 00:02:08.700
So this quadrilateral, this trapezoid,

00:02:08.700 --> 00:02:13.700
like a rectangle, has both
four sides and four angles.

00:02:13.740 --> 00:02:15.735
Now, if I were to go the other way around,

00:02:15.735 --> 00:02:17.740
if I were to ask you to draw a figure,

00:02:17.740 --> 00:02:20.160
and if you have pencil and
paper I encourage you to do it,

00:02:20.160 --> 00:02:24.300
try to draw a shape that has five angles

00:02:24.300 --> 00:02:26.723
and see if you know the
name for that shape.

00:02:27.860 --> 00:02:30.010
All right, now let's
try to do this together

00:02:30.010 --> 00:02:32.280
and let me do this in a fun color,

00:02:32.280 --> 00:02:34.010
watch I'll do it in purple.

00:02:34.010 --> 00:02:38.170
So that is one angle right over there,

00:02:38.170 --> 00:02:40.060
then I have two angles,

00:02:40.060 --> 00:02:44.150
then I have three angles,
and now I have four angles.

00:02:44.150 --> 00:02:46.010
And if I meet there, I get five angles.

00:02:46.010 --> 00:02:47.980
So we could see the angles here.

00:02:47.980 --> 00:02:52.980
I have one, two, three,
four, five angles here.

00:02:55.682 --> 00:03:00.560
You also might see that I have one, two,

00:03:00.560 --> 00:03:04.190
three, four, five sides.

00:03:04.190 --> 00:03:06.430
And what do we call a five sided figure?

00:03:06.430 --> 00:03:09.270
We call that a pentagon.

00:03:09.270 --> 00:03:11.410
This is a pentagon right over here.

00:03:11.410 --> 00:03:14.280
So five angles and we had five sides.

00:03:14.280 --> 00:03:16.430
And so you could imagine
if I had six angles,

00:03:16.430 --> 00:03:18.130
what type of a figure would it be?

00:03:19.000 --> 00:03:20.400
Well, I might not even draw it,

00:03:20.400 --> 00:03:21.880
you could draw it on paper if you like,

00:03:21.880 --> 00:03:25.210
but if you had six angles,
you're going to have a hexagon,

00:03:25.210 --> 00:03:27.493
which is a six sided figure.


Adding two digit numbers on a number line

WEBVTT
Kind: captions
Language: en

00:00:00.590 --> 00:00:02.160
- [Instructor] We're told
that Cara had a tower

00:00:02.160 --> 00:00:04.650
with 42 blocks.

00:00:04.650 --> 00:00:08.380
She added 12 red blocks,

00:00:08.380 --> 00:00:12.360
14 more blue blocks,

00:00:12.360 --> 00:00:16.140
and 16 purple blocks.

00:00:16.140 --> 00:00:17.530
So what we want to do in this video

00:00:17.530 --> 00:00:21.650
is think about how many
total blocks Cara now has.

00:00:21.650 --> 00:00:23.380
And to help us with that,

00:00:23.380 --> 00:00:26.480
we are going to set up a little
bit of a number line here.

00:00:26.480 --> 00:00:29.800
And this number line, it keeps
going in both directions,

00:00:29.800 --> 00:00:31.100
and I'm going to set it up so

00:00:31.100 --> 00:00:35.860
this big, thick hash mark here is 40.

00:00:35.860 --> 00:00:38.450
I wanna make sure that
I can include 42 here.

00:00:38.450 --> 00:00:42.174
And you can see, we go 41, 42, 43, 44, 45,

00:00:42.174 --> 00:00:44.690
46, 47, 48, 49, 50.

00:00:44.690 --> 00:00:46.600
So each of the thick ones are 10 more.

00:00:46.600 --> 00:00:51.600
So that's 50, 60, 70, and 80.

00:00:52.140 --> 00:00:54.270
What I'd like you to
do is pause this video,

00:00:54.270 --> 00:00:57.300
think about where 42
is on this number line,

00:00:57.300 --> 00:01:00.570
and then think about how
do we add these blocks

00:01:00.570 --> 00:01:01.980
on this number line to think about

00:01:01.980 --> 00:01:04.653
how many total blocks Cara now has.

00:01:05.790 --> 00:01:07.940
All right, now let's do this together.

00:01:07.940 --> 00:01:09.810
So let's start with her starting point,

00:01:09.810 --> 00:01:13.140
the 42 blocks right over here.

00:01:13.140 --> 00:01:14.730
So we see this is 40.

00:01:14.730 --> 00:01:16.450
So we go 41, 42.

00:01:16.450 --> 00:01:19.980
So this right over here
is Cara's starting point.

00:01:19.980 --> 00:01:23.700
That is 42 blocks.

00:01:23.700 --> 00:01:26.450
Now first she adds 12 red blocks.

00:01:26.450 --> 00:01:28.470
So you could just count
on the number line.

00:01:28.470 --> 00:01:32.940
So if you add one, two,
three, four, five, six,

00:01:32.940 --> 00:01:37.480
seven, eight, nine, 10, 11, 12,

00:01:37.480 --> 00:01:39.200
you get right over there.

00:01:39.200 --> 00:01:44.200
So this right over here is
all of us adding 12 blocks.

00:01:45.060 --> 00:01:46.860
Now where does that get us to?

00:01:46.860 --> 00:01:48.500
Well we can see that we are now

00:01:48.500 --> 00:01:52.410
one, two, three, four past 50.

00:01:52.410 --> 00:01:54.363
So we are now at 54.

00:01:55.670 --> 00:01:56.750
Right over there.

00:01:56.750 --> 00:01:57.910
And you could have done it another way.

00:01:57.910 --> 00:01:59.530
You could have just added
right from the get-go.

00:01:59.530 --> 00:02:02.517
You could have said, "All
right, I'm going to add 12,

00:02:02.517 --> 00:02:04.957
"so it takes me eight to get to 50

00:02:04.957 --> 00:02:08.880
"and then I have four
more left, gets me to 54."

00:02:08.880 --> 00:02:12.940
And then we need to add
those 14 more blue blocks.

00:02:12.940 --> 00:02:14.700
So let's add 14 from here.

00:02:14.700 --> 00:02:19.700
One, two, three, four,
five, six, seven, eight,

00:02:19.840 --> 00:02:24.130
nine, 10, 11, 12, 13, 14,

00:02:24.130 --> 00:02:25.690
gets us right over there.

00:02:25.690 --> 00:02:29.900
So we add another 14, we get over there.

00:02:29.900 --> 00:02:32.550
And now what number are we at?

00:02:32.550 --> 00:02:34.070
Well, there's two ways to think about it.

00:02:34.070 --> 00:02:37.330
You can see that we are
one, two, three, four,

00:02:37.330 --> 00:02:40.270
five, six, seven, eight above 60,

00:02:40.270 --> 00:02:41.930
which would tell us we're at 68,

00:02:41.930 --> 00:02:44.070
or you could see that we are two below 70,

00:02:44.070 --> 00:02:45.780
which would also be 68.

00:02:45.780 --> 00:02:48.280
So we're now at 68 total blocks.

00:02:48.280 --> 00:02:51.130
And then we add the 16 purple blocks.

00:02:51.130 --> 00:02:52.050
So let's do that.

00:02:52.050 --> 00:02:57.010
Let's add one, two, three,
four, five, six, seven, eight,

00:02:57.010 --> 00:03:00.900
nine, 10, 11, 12, 13,

00:03:00.900 --> 00:03:04.000
14, 15, 16

00:03:04.000 --> 00:03:05.250
and we get right over there.

00:03:05.250 --> 00:03:06.790
We're very lucky that our number line

00:03:06.790 --> 00:03:09.490
just happened to have
the right number of marks

00:03:09.490 --> 00:03:10.530
right over here.

00:03:10.530 --> 00:03:15.380
So then we add 16 and
we can see that we are

00:03:15.380 --> 00:03:17.490
one, two, three, four past 80.

00:03:17.490 --> 00:03:20.140
So we're at 84 total blocks.

00:03:20.140 --> 00:03:21.950
Another way you could
have thought about it is

00:03:21.950 --> 00:03:24.750
it would have taken us
two blocks to go to 70,

00:03:24.750 --> 00:03:26.640
then we would have 14 left.

00:03:26.640 --> 00:03:29.850
Another 10 to get to 80 and
then we would have four left

00:03:29.850 --> 00:03:31.790
and then you get to 84.

00:03:31.790 --> 00:03:35.343
But now Cara has a total of 84 blocks.


Multi step addition word problem

WEBVTT
Kind: captions
Language: en

00:00:00.160 --> 00:00:01.600
- [Sal] We're told that Joe started

00:00:01.600 --> 00:00:02.910
his math homework.

00:00:02.910 --> 00:00:07.400
He finished 23 problems by himself.

00:00:07.400 --> 00:00:12.000
He finished 13 more
problems with help from Sal.

00:00:12.000 --> 00:00:14.290
I don't know if they're
talking about me or not.

00:00:14.290 --> 00:00:19.170
And then they say there are
nine math problems left.

00:00:19.170 --> 00:00:20.180
And then they ask us,

00:00:20.180 --> 00:00:25.180
how many math problems did
Joe have when he started?

00:00:25.360 --> 00:00:27.960
So, pause this video and see
if you can work through that

00:00:27.960 --> 00:00:29.673
before we do it together.

00:00:30.610 --> 00:00:33.470
All right, so the way
my brain thinks about it

00:00:33.470 --> 00:00:36.950
is there's some amount
that he started with.

00:00:36.950 --> 00:00:40.510
So, let's put a big bar over here.

00:00:40.510 --> 00:00:44.500
This is some amount that Joe started with.

00:00:44.500 --> 00:00:48.793
So, let me write that, starting amount.

00:00:50.110 --> 00:00:52.690
And then he was able to do many of them,

00:00:52.690 --> 00:00:56.210
so he's finished 23 problems by himself.

00:00:56.210 --> 00:00:58.800
So, let me draw 23 here.

00:00:58.800 --> 00:01:03.063
So, he was able to finish 23 by himself.

00:01:04.400 --> 00:01:06.790
Then he finished 13 more with help

00:01:06.790 --> 00:01:09.460
from someone with my name, maybe it's me.

00:01:09.460 --> 00:01:13.720
So, then he did 13 more
with help from Sal.

00:01:13.720 --> 00:01:16.620
So, that's 13 right over there.

00:01:16.620 --> 00:01:20.640
And then the total amount left was nine.

00:01:20.640 --> 00:01:23.480
So, the total amount left
has to be able to finish up,

00:01:23.480 --> 00:01:26.150
be just as long as our starting amount.

00:01:26.150 --> 00:01:28.390
So, this is nine right over here.

00:01:28.390 --> 00:01:32.840
So, this is left, thus, 23 was
the ones he did by himself.

00:01:32.840 --> 00:01:37.480
The 13 was with help from me
and then he had nine left.

00:01:37.480 --> 00:01:39.480
So, if you wanna know the starting amount,

00:01:39.480 --> 00:01:42.160
how many math problems did
Joe have when he started,

00:01:42.160 --> 00:01:47.130
you have to add together
23 plus 13 plus nine.

00:01:47.130 --> 00:01:48.540
So, how do we do that?

00:01:48.540 --> 00:01:50.210
Well, let's do it one at a time.

00:01:50.210 --> 00:01:51.950
So, let's just think about
how many he finished,

00:01:51.950 --> 00:01:53.860
and then we can add to
that how many is left,

00:01:53.860 --> 00:01:55.590
and that's the starting amount.

00:01:55.590 --> 00:01:57.240
So, the amount that he finished.

00:01:57.240 --> 00:01:59.940
So, that's this amount right over here,

00:01:59.940 --> 00:02:03.320
the ones he did by himself,
plus the ones he did with Sal.

00:02:03.320 --> 00:02:08.320
That's going to be 23 plus 13.

00:02:08.520 --> 00:02:11.380
Now, 23 plus 13 is the same thing,

00:02:11.380 --> 00:02:13.440
if I just think about
it, I have two tens here,

00:02:13.440 --> 00:02:16.063
so that's 20 plus three,

00:02:16.900 --> 00:02:19.000
plus 10 plus three.

00:02:19.000 --> 00:02:20.640
That one is in the tens place.

00:02:20.640 --> 00:02:22.920
Plus 10 plus three.

00:02:22.920 --> 00:02:27.120
Well, that's the same thing
as if I just look at the,

00:02:27.120 --> 00:02:29.890
if I just look at the
tens right over there.

00:02:29.890 --> 00:02:32.530
20 plus 10,

00:02:32.530 --> 00:02:35.410
plus three plus three.

00:02:35.410 --> 00:02:37.530
20 plus 10 is 30.

00:02:37.530 --> 00:02:39.810
So, this is going to be equal to 30,

00:02:39.810 --> 00:02:42.130
plus three plus three is six.

00:02:42.130 --> 00:02:44.820
So, this is going to be equal to 36.

00:02:44.820 --> 00:02:46.560
So, this whole amount right over here,

00:02:46.560 --> 00:02:50.200
the amount of problems that
Joe either did by himself,

00:02:50.200 --> 00:02:54.960
or with the help of Sal,
that is 36 problems.

00:02:54.960 --> 00:02:56.730
And so, to figure out the starting amount,

00:02:56.730 --> 00:02:58.930
we just have to figure
out the total that he did,

00:02:58.930 --> 00:03:02.040
plus how many are left to
get the starting amount.

00:03:02.040 --> 00:03:05.350
So, what is 36 plus nine?

00:03:05.350 --> 00:03:07.450
Well, the way my brain thinks about it,

00:03:07.450 --> 00:03:08.530
let me just do it right over here.

00:03:08.530 --> 00:03:12.380
36 plus nine is equal to what?

00:03:12.380 --> 00:03:17.350
Well, this is the same thing
as 30 plus six plus nine,

00:03:17.350 --> 00:03:22.280
and six plus nine, you
may already know is 15.

00:03:22.280 --> 00:03:23.580
Another way you could think about it

00:03:23.580 --> 00:03:27.930
is if you start at nine, you
have to add one to get to 10,

00:03:27.930 --> 00:03:32.390
and then you have five left
over from the six to get to 15.

00:03:32.390 --> 00:03:34.490
So, another way to rewrite this,

00:03:34.490 --> 00:03:37.340
30 plus 15 is the same thing

00:03:37.340 --> 00:03:42.340
as 30 plus 10 plus five.

00:03:43.730 --> 00:03:47.720
30 plus 10, this right
over here, that's 40.

00:03:47.720 --> 00:03:52.720
So, it's going to be 40 plus
five which is equal to 45.

00:03:52.900 --> 00:03:56.530
So, Joe had 45 problems when he started.

00:03:56.530 --> 00:03:59.710
He did 23 by himself, then he did 13,

00:03:59.710 --> 00:04:00.840
and he would have nine left.

00:04:00.840 --> 00:04:02.890
And you would see if you start with 45,

00:04:02.890 --> 00:04:06.720
and if you were to subtract
23 and then subtract 13,

00:04:06.720 --> 00:04:09.483
you actually would indeed have nine left.


Multi step subtraction word problem

WEBVTT
Kind: captions
Language: en

00:00:00.320 --> 00:00:01.640
- [Instructor] We're told that a train

00:00:01.640 --> 00:00:05.390
traveling through Japan has 90 passengers.

00:00:05.390 --> 00:00:09.800
52 passengers get off in Tokyo.

00:00:09.800 --> 00:00:14.800
In Kobe, another 29
passengers get off the train.

00:00:15.150 --> 00:00:18.570
No new passengers get on the train.

00:00:18.570 --> 00:00:20.820
And then they ask us how many passengers

00:00:20.820 --> 00:00:23.200
are still on the train?

00:00:23.200 --> 00:00:25.240
Pause this video and see if
you can work through that

00:00:25.240 --> 00:00:28.020
before we work on this together.

00:00:28.020 --> 00:00:29.780
All right, now let's do this together.

00:00:29.780 --> 00:00:31.310
So first, what we can think about

00:00:31.310 --> 00:00:33.540
is how many total passengers there are,

00:00:33.540 --> 00:00:36.430
and then to figure out how many are left,

00:00:36.430 --> 00:00:38.080
well, you have to start with your total,

00:00:38.080 --> 00:00:40.380
take away 52 that get off in Tokyo,

00:00:40.380 --> 00:00:43.200
then take away another
29 that get off in Kobe,

00:00:43.200 --> 00:00:45.260
and then however many you have left,

00:00:45.260 --> 00:00:47.030
that's how many are still on the train.

00:00:47.030 --> 00:00:49.670
And we can imagine that
with a tape diagram.

00:00:49.670 --> 00:00:52.180
So let's say that the length of this tape

00:00:52.180 --> 00:00:54.210
or the length of this rectangle

00:00:54.210 --> 00:00:58.050
represents the initial,
the starting 90 passengers.

00:00:58.050 --> 00:01:00.883
So that's 90 passengers.

00:01:03.040 --> 00:01:05.750
And then how many get off in Tokyo, 52,

00:01:05.750 --> 00:01:08.810
and I'm doing this so
that we can visualize it,

00:01:08.810 --> 00:01:10.540
so we can think about what it looks like.

00:01:10.540 --> 00:01:14.603
So we'll take away 52, which
might be something like this.

00:01:15.550 --> 00:01:20.323
So 52 off in Tokyo,

00:01:21.590 --> 00:01:22.423
Tokyo,

00:01:22.423 --> 00:01:24.530
and then we have another 29 passengers

00:01:24.530 --> 00:01:27.400
that get off the train in Kobe.

00:01:27.400 --> 00:01:31.810
So then another 29, maybe
that's something like this,

00:01:31.810 --> 00:01:36.810
get off in Kobe, so 29 off in Kobe.

00:01:39.840 --> 00:01:42.100
And so how many passengers are still left?

00:01:42.100 --> 00:01:43.610
Well, if you start with 90,

00:01:43.610 --> 00:01:47.450
52 get off in Tokyo, 29 get off in Kobe,

00:01:47.450 --> 00:01:51.420
then this last part of
the length of the tape,

00:01:51.420 --> 00:01:54.010
that would be how many are left.

00:01:54.010 --> 00:01:57.880
So right over there,
this is the, how many,

00:01:57.880 --> 00:02:02.880
how many, how many left,

00:02:03.060 --> 00:02:06.080
would be the length of
this red part of the tape.

00:02:06.080 --> 00:02:10.270
'Cause we've taken off the
52 and the 29 off of the 90.

00:02:10.270 --> 00:02:12.640
So to figure that out, we
could first try to figure out

00:02:12.640 --> 00:02:15.930
what is 90 minus 52?

00:02:15.930 --> 00:02:17.100
If you haven't figured that out,

00:02:17.100 --> 00:02:20.180
you could pause the video
and try to figure that out.

00:02:20.180 --> 00:02:21.590
All right, well, one
way to think about it,

00:02:21.590 --> 00:02:26.590
90 minus 52 is the same thing
as 90 minus 50 minus two.

00:02:28.390 --> 00:02:32.400
So I could write it this
way, minus 50 minus two.

00:02:32.400 --> 00:02:35.780
And you might recognize that 90 minus 50,

00:02:35.780 --> 00:02:38.870
that's 9 tens minus 5 tens,
that's going to be 4 tens.

00:02:38.870 --> 00:02:40.370
This is going to be 40.

00:02:40.370 --> 00:02:43.780
So this is going to be 40 minus 2,

00:02:43.780 --> 00:02:47.970
and then 2 less than 40,
well, that's going to be 38.

00:02:47.970 --> 00:02:50.793
So this is going to be equal to 38.

00:02:51.800 --> 00:02:54.300
So if you only had that one
stop after that first stop,

00:02:54.300 --> 00:02:56.600
you have 38 passengers left on the train.

00:02:56.600 --> 00:03:00.660
And so that 38 is this
amount right over here.

00:03:00.660 --> 00:03:03.790
But then we know another
29 get off in Kobe.

00:03:03.790 --> 00:03:05.750
So we need to start with that 38,

00:03:05.750 --> 00:03:09.980
and 29 are going to get off, so minus 29.

00:03:09.980 --> 00:03:13.540
And we can view this as,
maybe we could rewrite this,

00:03:13.540 --> 00:03:18.420
this is equal to 30 plus 8, that's 38,

00:03:18.420 --> 00:03:21.430
and we're going to subtract 20 and 9.

00:03:21.430 --> 00:03:24.860
So subtract 20 and subtract 9.

00:03:24.860 --> 00:03:26.640
This wouldn't be subtract
20 and then add 9.

00:03:26.640 --> 00:03:27.510
That wouldn't be 29.

00:03:27.510 --> 00:03:30.770
We're subtracting 2 tens and 9 ones.

00:03:30.770 --> 00:03:32.630
So we're subtracting 20 and 9.

00:03:33.600 --> 00:03:37.800
So first, we could view
this as 30 minus 20,

00:03:37.800 --> 00:03:39.400
which is going to be 10.

00:03:39.400 --> 00:03:43.993
And then we're going to
add 8 and then subtract 9,

00:03:45.230 --> 00:03:46.630
subtract 9.

00:03:46.630 --> 00:03:48.620
Now, what is 10 plus 8?

00:03:48.620 --> 00:03:51.950
10 plus 8 we know is 18.

00:03:51.950 --> 00:03:55.340
Now, if we subtract 9 from 18,

00:03:55.340 --> 00:03:57.270
you might already know
that that's going to be 9.

00:03:57.270 --> 00:03:58.180
Another way to think about it

00:03:58.180 --> 00:03:59.690
is if you subtract 8 from 18,

00:03:59.690 --> 00:04:01.150
you're going to be just left with 10,

00:04:01.150 --> 00:04:02.440
and then you have one more to take away.

00:04:02.440 --> 00:04:04.610
So you're going to be left with 9.

00:04:04.610 --> 00:04:08.880
So we are going to have 9
passengers left on the train.

00:04:08.880 --> 00:04:12.420
Start with 90, 52 get
off, there's 38 left.

00:04:12.420 --> 00:04:14.170
Then another 29 get off.

00:04:14.170 --> 00:04:16.623
Now we have 9 left.


Adding four two digit numbers

WEBVTT
Kind: captions
Language: en

00:00:00.480 --> 00:00:01.580
- [Instructor] What I
wanna do in this video

00:00:01.580 --> 00:00:06.410
is try to figure out what
35 plus 22 plus 10 plus 16

00:00:06.410 --> 00:00:08.330
is equal to.

00:00:08.330 --> 00:00:11.893
So pause this video and see
if you can figure that out.

00:00:13.020 --> 00:00:15.490
All right, now let's work
through this together.

00:00:15.490 --> 00:00:19.700
Now, as you will learn, there's
many ways to approach this,

00:00:19.700 --> 00:00:21.060
but the way I'll think about it

00:00:21.060 --> 00:00:23.760
is by thinking about place value.

00:00:23.760 --> 00:00:27.210
For example, when we look at 35,

00:00:27.210 --> 00:00:30.110
we have 3 tens and 5 ones.

00:00:30.110 --> 00:00:33.530
3 tens, right over here,
that's the same thing as 30.

00:00:33.530 --> 00:00:38.250
So you could view 35 as 30 plus 5.

00:00:39.180 --> 00:00:41.610
And we can do the same thing for 22.

00:00:41.610 --> 00:00:46.430
22 is 2 tens, which is 20,
that's what that 2 tells us,

00:00:46.430 --> 00:00:47.930
plus 2 ones.

00:00:47.930 --> 00:00:49.930
So 20 plus 2.

00:00:49.930 --> 00:00:54.080
And then we have 10, which
is just 1 ten and no ones.

00:00:54.080 --> 00:00:55.690
So plus 10.

00:00:55.690 --> 00:00:58.260
And then 16, we could rewrite that

00:00:58.260 --> 00:01:00.670
as being the same thing as 1 ten.

00:01:00.670 --> 00:01:02.980
So 10 plus 6 ones,

00:01:02.980 --> 00:01:05.010
plus 6 ones.

00:01:05.010 --> 00:01:06.680
Now, why was this useful?

00:01:06.680 --> 00:01:09.340
Now I could take all of the things

00:01:09.340 --> 00:01:10.730
that are a certain number of tens,

00:01:10.730 --> 00:01:15.730
so 30, 20, 10, and 10, and
try to add those together.

00:01:16.000 --> 00:01:19.310
And then separately, I will try to add

00:01:19.310 --> 00:01:22.850
the 5, the 2, and the 6.

00:01:22.850 --> 00:01:24.120
And when you see when I do it,

00:01:24.120 --> 00:01:27.220
I think it'll make a little
more sense why it's useful.

00:01:27.220 --> 00:01:32.220
So, we have a 30 plus 20 plus 10 plus 10,

00:01:35.360 --> 00:01:37.070
plus that purple 10,

00:01:37.070 --> 00:01:38.730
plus that purple 10.

00:01:38.730 --> 00:01:41.920
So I've already accounted
for the 30, the 20,

00:01:41.920 --> 00:01:43.320
that 10 and that 10.

00:01:43.320 --> 00:01:44.980
And then I'll have all of the things

00:01:44.980 --> 00:01:47.100
that were written in
the ones place before.

00:01:47.100 --> 00:01:50.920
So plus 5 ones, so I
got that taken care of,

00:01:50.920 --> 00:01:54.920
plus 2 ones, that's taken care of,

00:01:54.920 --> 00:01:56.850
plus 6 ones,

00:01:56.850 --> 00:01:58.840
plus 6 ones.

00:01:58.840 --> 00:02:01.940
And now all of these we can think about.

00:02:01.940 --> 00:02:03.950
What is 30 plus 20?

00:02:03.950 --> 00:02:07.040
Well, 30 plus 20 is going to be 50,

00:02:07.040 --> 00:02:09.410
and then 50 plus 10 is 60,

00:02:09.410 --> 00:02:12.520
and then 60 plus 10 is 70.

00:02:12.520 --> 00:02:14.190
So that's all going to be 70.

00:02:14.190 --> 00:02:15.220
Another way to think about it

00:02:15.220 --> 00:02:19.590
is we have 3 tens plus 2
tens plus 1 ten plus 1 ten.

00:02:19.590 --> 00:02:24.250
3 plus 2 plus 1 plus 1
is 7, so we have 7 tens.

00:02:25.190 --> 00:02:27.360
And you actually saw that up here as well,

00:02:27.360 --> 00:02:32.360
3 tens plus 2 tens plus 1 ten plus 1 ten,

00:02:32.820 --> 00:02:35.490
that's going to give us 7 tens.

00:02:35.490 --> 00:02:38.440
And then we can add this other part

00:02:38.440 --> 00:02:43.440
where we see 5 plus 2 is 7 plus 6 is 13.

00:02:45.530 --> 00:02:48.470
So it's 70 plus 13.

00:02:48.470 --> 00:02:50.700
Now, what is 70 plus 13?

00:02:50.700 --> 00:02:52.410
Well, I could rewrite 13.

00:02:52.410 --> 00:02:56.110
I could do something similar as 10 plus 3,

00:02:56.110 --> 00:02:58.310
And that makes it a
little bit more obvious.

00:02:58.310 --> 00:03:01.490
We can see that that's the
same thing as 70 plus 10,

00:03:01.490 --> 00:03:04.970
which is 80 plus 3,

00:03:04.970 --> 00:03:07.840
which is the same thing
as 8 tens and 3 ones,

00:03:07.840 --> 00:03:10.973
which is equal to 83.

00:03:12.840 --> 00:03:13.673
And we're done.


Adding multiple two digit numbers word problem

WEBVTT
Kind: captions
Language: en

00:00:00.180 --> 00:00:02.620
- [Instructor] We're told
that Tomer has a bookshelf.

00:00:02.620 --> 00:00:06.600
The table below shows how
many books are on each shelf.

00:00:06.600 --> 00:00:08.820
So the first shelf has 19 books,

00:00:08.820 --> 00:00:11.210
the second shelf has 24 books,

00:00:11.210 --> 00:00:13.440
the third shelf has 32 books,

00:00:13.440 --> 00:00:16.670
and the fourth shelf has 7 books.

00:00:16.670 --> 00:00:20.950
How many books are on the
bookshelves all together?

00:00:20.950 --> 00:00:23.430
So pause this video and see
if you can work that out

00:00:23.430 --> 00:00:25.180
before we work through it together.

00:00:26.220 --> 00:00:27.960
All right, now let's
work through it together.

00:00:27.960 --> 00:00:30.850
So if we wanna figure out how many books

00:00:30.850 --> 00:00:34.070
are on the bookshelves all together

00:00:34.070 --> 00:00:37.380
or on the bookshelf altogether,
we essentially have to add

00:00:37.380 --> 00:00:41.690
19 books to 24 books
to 32 books to 7 books.

00:00:41.690 --> 00:00:46.690
So really, this is going to
be 19 plus 24 plus 32 plus 7.

00:00:49.240 --> 00:00:51.410
That's what we really have to figure out.

00:00:51.410 --> 00:00:52.810
Now, how can we do that?

00:00:52.810 --> 00:00:55.540
Well, I like to do that by separating out

00:00:55.540 --> 00:00:58.270
the tens place from the ones place.

00:00:58.270 --> 00:01:03.270
For example, I could
rewrite 19 as 10 plus 9.

00:01:04.780 --> 00:01:09.130
I have one 10 and 9 ones, one 10, 9 ones.

00:01:09.130 --> 00:01:13.740
I could rewrite 24 as 20 plus 4.

00:01:13.740 --> 00:01:16.910
So plus 20 plus 4,

00:01:16.910 --> 00:01:21.593
I could rewrite 32 as 30 plus 2.

00:01:22.660 --> 00:01:26.000
And last but not least, I could rewrite,

00:01:26.000 --> 00:01:28.960
let me find a nice color
here, maybe I'll use blue,

00:01:28.960 --> 00:01:30.160
I could rewrite 7.

00:01:30.160 --> 00:01:31.410
Well, actually, I want won't rewrite 7.

00:01:31.410 --> 00:01:35.140
7 only has 7 ones, so I'll
just write 7 right there.

00:01:35.140 --> 00:01:38.580
And now what I can do is
I can take each of these

00:01:38.580 --> 00:01:43.580
that came from our tens
places right over here.

00:01:44.320 --> 00:01:48.173
So I would have 10 plus 20,

00:01:49.440 --> 00:01:52.090
I'm just crossing it out so
I can keep track of things,

00:01:52.090 --> 00:01:55.250
plus 30, plus 30.

00:01:55.250 --> 00:01:59.890
So I did these three, and then
I would have all of the ones

00:01:59.890 --> 00:02:01.680
or the things that I
got from the ones place,

00:02:01.680 --> 00:02:03.140
and let me do that in orange.

00:02:03.140 --> 00:02:06.800
So it's the 9, the 4, the 2, and the 7.

00:02:06.800 --> 00:02:11.800
So plus 9 plus 4 plus 2 plus 7.

00:02:11.890 --> 00:02:15.590
Now, what's 10 plus 20 plus 30?

00:02:15.590 --> 00:02:20.590
10 plus 20 is 30, and then
that plus 30 is going to be 60.

00:02:20.980 --> 00:02:22.130
Another way to think about it,

00:02:22.130 --> 00:02:24.560
I have one 10 plus another two tens,

00:02:24.560 --> 00:02:27.500
which would give me three
tens, plus another three tens,

00:02:27.500 --> 00:02:30.760
which would give me
six tens, so that's 60.

00:02:30.760 --> 00:02:33.230
And then how do I think about this?

00:02:33.230 --> 00:02:34.730
Well, I can do this in any order.

00:02:34.730 --> 00:02:38.900
I can see that 2 plus 7,
that's going to be equal to 9,

00:02:38.900 --> 00:02:42.820
and I can see that 9
plus 9 is equal to 18.

00:02:42.820 --> 00:02:47.480
So this is going to be the
same thing as 18 plus 4.

00:02:47.480 --> 00:02:50.180
And then let's see it
takes two to get to 20,

00:02:50.180 --> 00:02:52.370
and then I have another two.

00:02:52.370 --> 00:02:54.300
Actually, let me write it that way.

00:02:54.300 --> 00:02:56.870
So I could also write this as 60 plus,

00:02:56.870 --> 00:03:00.550
and if I just take 2 from
the 4 and put it onto the 18,

00:03:00.550 --> 00:03:04.240
this would be 20 plus 2,

00:03:04.240 --> 00:03:06.730
this and this are equivalent.

00:03:06.730 --> 00:03:07.950
And the reason why I did that

00:03:07.950 --> 00:03:11.000
is it's easy now to add 20 to 60.

00:03:11.000 --> 00:03:14.210
20 to 60, that's two tens plus six tens,

00:03:14.210 --> 00:03:17.180
that's going to give us eight
tens, that's going to be 80.

00:03:17.180 --> 00:03:21.460
And then 80 plus 2 is, of
course, going to give us,

00:03:21.460 --> 00:03:23.590
and we can have something of a drum roll,

00:03:23.590 --> 00:03:25.960
almost have the answer, 82.

00:03:25.960 --> 00:03:29.363
That's how many books
Tomer has all together.


Getting a sense of meters and centimeters

WEBVTT
Kind: captions
Language: en

00:00:01.000 --> 00:00:01.833
- [Instructor] In this video,

00:00:01.833 --> 00:00:05.310
I'm going to talk about a unit
of length known as the meter,

00:00:05.310 --> 00:00:06.760
which you might have heard of before.

00:00:06.760 --> 00:00:11.210
It's really probably the
most used unit of length

00:00:11.210 --> 00:00:12.410
in the world.

00:00:12.410 --> 00:00:16.930
And so the natural question
is how long is a meter?

00:00:16.930 --> 00:00:19.290
Well, one way to get a
rough sense of a meter

00:00:19.290 --> 00:00:22.160
is imagine a reasonably
tall basketball player.

00:00:22.160 --> 00:00:25.510
So a good bit taller
than your average man.

00:00:25.510 --> 00:00:28.290
So a good bit taller than
me, I'm about average height.

00:00:28.290 --> 00:00:30.780
So that's your basketball player there.

00:00:30.780 --> 00:00:32.113
He's got his basketball.

00:00:33.050 --> 00:00:36.530
He might be roughly two meters tall.

00:00:36.530 --> 00:00:39.960
So this would be two meters,

00:00:39.960 --> 00:00:44.170
one meter, and this lowercase
m is short for meter.

00:00:44.170 --> 00:00:46.400
And then two meters.

00:00:46.400 --> 00:00:48.520
Another way to think about a meter

00:00:48.520 --> 00:00:51.330
is if you took a long step,

00:00:51.330 --> 00:00:54.060
if you're, let's say,
seven or eight years old,

00:00:54.060 --> 00:00:56.640
and if you were to take a long step,

00:00:56.640 --> 00:01:00.180
you might travel about a meter.

00:01:00.180 --> 00:01:02.680
So that's your long step,

00:01:02.680 --> 00:01:05.320
right over there.

00:01:05.320 --> 00:01:08.050
It might be close to a meter, roughly,

00:01:08.050 --> 00:01:10.170
it's not necessarily going
to be exactly a meter,

00:01:10.170 --> 00:01:12.480
but it might be close.

00:01:12.480 --> 00:01:17.480
Now a related unit of length
is known as the centimeter,

00:01:18.520 --> 00:01:20.850
and you might already recognize

00:01:20.850 --> 00:01:24.180
that it has the word meter in it,

00:01:24.180 --> 00:01:26.630
and it also has the word centi.

00:01:26.630 --> 00:01:30.592
Now you might already
know that the word cent,

00:01:30.592 --> 00:01:32.660
100 cents make $1.

00:01:32.660 --> 00:01:36.000
You might know the word
century, that's 100 years.

00:01:36.000 --> 00:01:38.390
So you might say, is this 100 meters?

00:01:38.390 --> 00:01:40.560
You'd be kind of close,
but kind of far off.

00:01:40.560 --> 00:01:43.670
It's not 100 meters, it's
not bigger than a meter.

00:01:43.670 --> 00:01:46.370
It's actually a lot smaller than a meter.

00:01:46.370 --> 00:01:50.950
A centimeter, 100 of them
will equal one meter.

00:01:50.950 --> 00:01:53.990
So one way to think about it
is if I write it in shorthand

00:01:53.990 --> 00:01:57.410
100 and you normally write
it as lowercase c and m.

00:01:57.410 --> 00:02:02.310
So 100 centimeters are equal to one meter.

00:02:02.310 --> 00:02:04.910
So on these pictures right over here,

00:02:04.910 --> 00:02:09.910
a centimeter would be much
smaller than a meter right over,

00:02:10.310 --> 00:02:11.550
even what I just drew there

00:02:11.550 --> 00:02:13.760
would be a lot less than a centimeter.

00:02:13.760 --> 00:02:15.970
And one way to think about a centimeter,

00:02:15.970 --> 00:02:18.610
it might be if you stick your finger out,

00:02:18.610 --> 00:02:22.860
your finger, depending on
how large your finger is,

00:02:22.860 --> 00:02:26.470
might be about a centimeter wide.

00:02:26.470 --> 00:02:28.680
As a grown average-sized man,

00:02:28.680 --> 00:02:32.510
my finger is actually
about two centimeters wide.

00:02:32.510 --> 00:02:35.360
If I take my index finger
and if I were to measure it,

00:02:35.360 --> 00:02:39.740
I would approximate it
as about two centimeters.

00:02:39.740 --> 00:02:42.380
So 100 centimeters make up a meter,

00:02:42.380 --> 00:02:44.850
which hopefully makes a
little bit of sense to you.

00:02:44.850 --> 00:02:46.480
Now given what we've just learned

00:02:46.480 --> 00:02:48.870
about meters and centimeters,

00:02:48.870 --> 00:02:52.110
let's think about what is
better to measure with,

00:02:52.110 --> 00:02:54.290
depending on the size of the thing.

00:02:54.290 --> 00:02:59.290
So if I was looking at a let's
say fairly tall of some kind,

00:03:00.480 --> 00:03:02.260
what would I wanna measure that with?

00:03:02.260 --> 00:03:04.870
Would I be more likely
to measure that in meters

00:03:04.870 --> 00:03:07.660
or would I be more likely to measure that

00:03:07.660 --> 00:03:09.830
in the centimeters?

00:03:09.830 --> 00:03:11.730
Pause this video and think about that.

00:03:12.920 --> 00:03:15.200
Well, a fairly tall tree
is going to be a lot taller

00:03:15.200 --> 00:03:17.160
than even this basketball player,

00:03:17.160 --> 00:03:21.520
so normally, people are likely
to measure this in meters.

00:03:21.520 --> 00:03:24.700
A reasonably tall tree could
be 10 meters or 20 meters,

00:03:24.700 --> 00:03:28.560
or even in certain cases
30 meters or taller.

00:03:28.560 --> 00:03:33.560
Now what if I were instead
measuring the length of a mouse,

00:03:35.230 --> 00:03:39.210
so my best drawing of a mouse
here, draw its little paws,

00:03:39.210 --> 00:03:40.910
kind of looks like a fish with a tail.

00:03:40.910 --> 00:03:42.620
But let's say that this is a mouse,

00:03:42.620 --> 00:03:45.610
would I measure this in
meters or centimeters?

00:03:45.610 --> 00:03:50.610
Well, a mouse is much smaller
in length than a tree is tall,

00:03:50.760 --> 00:03:54.743
so you would likely measure
this in centimeters.

00:03:56.308 --> 00:04:01.308
A small mouse might be
maybe five or 10 centimeters

00:04:02.860 --> 00:04:05.600
in length, right over here.

00:04:05.600 --> 00:04:07.710
Now let's compare another way

00:04:07.710 --> 00:04:09.600
or decide another way to think about

00:04:09.600 --> 00:04:12.560
whether we're measuring
in centimeters or meters.

00:04:12.560 --> 00:04:16.297
Let's say that I went
to the local gymnasium,

00:04:17.462 --> 00:04:19.490
and there's a pool there.

00:04:19.490 --> 00:04:22.150
There's a pool, that's
the water in the pool.

00:04:22.150 --> 00:04:24.520
And I were to measure the length.

00:04:24.520 --> 00:04:27.380
And I know it is 25-something,

00:04:27.380 --> 00:04:31.320
it's either 25 meters or 25 centimeters.

00:04:31.320 --> 00:04:33.500
Remember, this is the pool at the gym.

00:04:33.500 --> 00:04:34.333
Pause this video,

00:04:34.333 --> 00:04:37.963
do you think this would be
25 centimeters or 25 meters?

00:04:39.680 --> 00:04:42.950
Well, as you can imagine,
the length of a pool,

00:04:42.950 --> 00:04:44.380
this tall basketball player,

00:04:44.380 --> 00:04:46.760
many of them could lie down and to end

00:04:46.760 --> 00:04:48.530
to get to this length of this pool.

00:04:48.530 --> 00:04:51.600
So this would be a 25 meter pool.

00:04:51.600 --> 00:04:53.903
A 25 centimeter pool,

00:04:56.320 --> 00:04:57.370
that would actually probably be

00:04:57.370 --> 00:04:59.218
about the size of a cell phone

00:04:59.218 --> 00:05:01.330
or maybe smaller or a little bit larger,

00:05:01.330 --> 00:05:03.600
depending on the cell phone
that you're talking about.

00:05:03.600 --> 00:05:08.420
So for a pool, you'd be
talking in terms of meters.

00:05:08.420 --> 00:05:12.050
What if we had a building of some kind,

00:05:12.050 --> 00:05:14.823
so this is a building right over here,

00:05:15.970 --> 00:05:19.770
and let's say it is a
four storey building.

00:05:22.290 --> 00:05:26.380
And someone were to say that
it is 15 something tall,

00:05:26.380 --> 00:05:30.093
would this be 15 meters
tall or 15 centimeters tall?

00:05:31.500 --> 00:05:33.960
Well, 15 centimeters, that
might be a Lego building.

00:05:33.960 --> 00:05:37.243
A real building would be
15 meters in this scenario.

00:05:38.170 --> 00:05:43.170
Now what if I were to say
the length of my thumb,

00:05:45.700 --> 00:05:48.870
the length of my thumb, right over here.

00:05:48.870 --> 00:05:51.690
And I know it is five-something,

00:05:51.690 --> 00:05:55.810
this length right over
here, it is five-something,

00:05:55.810 --> 00:05:57.670
it's either five meters
or five centimeters,

00:05:57.670 --> 00:05:59.750
which one do you think it is?

00:05:59.750 --> 00:06:01.220
Well, if it was five meters,

00:06:01.220 --> 00:06:03.860
I would be a very, very, very large giant.

00:06:03.860 --> 00:06:08.610
My thumb would be twice as
tall or more than twice as tall

00:06:08.610 --> 00:06:10.620
as a fairly tall basketball player.

00:06:10.620 --> 00:06:15.080
So this would be five
centimeters right over here.

00:06:15.080 --> 00:06:16.590
So hopefully that gives you a sense

00:06:16.590 --> 00:06:18.320
of meters and centimeters.

00:06:18.320 --> 00:06:20.410
And on Khan Academy,
there's a lot more practice.

00:06:20.410 --> 00:06:21.740
So you can get a little bit more sense

00:06:21.740 --> 00:06:23.690
of estimating with
these, or thinking about

00:06:23.690 --> 00:06:27.353
when one unit or the
other is more appropriate.


Time on a number line example

WEBVTT
Kind: captions
Language: en

00:00:00.400 --> 00:00:01.233
- [Instructor] We're told to look

00:00:01.233 --> 00:00:03.120
at the following number line.

00:00:03.120 --> 00:00:06.080
In this number line, we
actually have times on it,

00:00:06.080 --> 00:00:07.890
so you could even call it a timeline.

00:00:07.890 --> 00:00:09.910
We're starting at one o'clock here.

00:00:09.910 --> 00:00:14.910
Then we go to 1:15, 1:30,
1:45, then two o'clock.

00:00:15.120 --> 00:00:18.820
And it says, what time is
shown on the number line?

00:00:18.820 --> 00:00:22.400
So, pause this video and see
if you can figure that out.

00:00:22.400 --> 00:00:26.070
All right, so the hour I think
is pretty straightforward.

00:00:26.070 --> 00:00:29.570
We are past one o'clock but
we are before two o'clock.

00:00:29.570 --> 00:00:33.480
So, we know that the hour is
going to be one something.

00:00:33.480 --> 00:00:34.750
It's not going to be two something

00:00:34.750 --> 00:00:37.040
'cause we haven't gotten
to two o'clock yet.

00:00:37.040 --> 00:00:40.960
Now, what is the number of
minutes after one o'clock?

00:00:40.960 --> 00:00:42.210
Well, we have a hint here.

00:00:42.210 --> 00:00:46.090
It's going to be between 15 and 30.

00:00:46.090 --> 00:00:47.710
And where would it be?

00:00:47.710 --> 00:00:49.580
Well, one way to tell is if you look

00:00:49.580 --> 00:00:50.950
at each of these tick marks,

00:00:50.950 --> 00:00:53.300
it looks like they represent a minute.

00:00:53.300 --> 00:00:54.220
Let's just count.

00:00:54.220 --> 00:00:57.000
If we start at one, we go to 1:01,

00:00:57.000 --> 00:01:00.140
two, three, four, five,

00:01:00.140 --> 00:01:03.028
six, seven, eight, nine,

00:01:03.028 --> 00:01:07.090
10, 11, 12, 13, 14, 15.

00:01:07.090 --> 00:01:10.340
Yep, it looks like each of
these tick marks is a minute.

00:01:10.340 --> 00:01:11.180
So, we just have to figure out

00:01:11.180 --> 00:01:14.060
how many tick marks we are past 1:15.

00:01:14.060 --> 00:01:18.800
So, we can see that we
can go from 15 to 16,

00:01:18.800 --> 00:01:21.465
17, 18, 19, 20,

00:01:21.465 --> 00:01:23.048
21, 22, 23, 24, 25.

00:01:25.187 --> 00:01:28.710
So, we're 25 minutes past one o'clock.

00:01:28.710 --> 00:01:30.530
Another way you could
have thought about it

00:01:30.530 --> 00:01:35.530
is each of these medium tick
marks represent five minutes.

00:01:36.330 --> 00:01:39.540
And you can count, one,
two, three, four, five.

00:01:39.540 --> 00:01:41.910
So, that's five, that's another five.

00:01:41.910 --> 00:01:43.380
So, this time right over here

00:01:43.380 --> 00:01:45.530
is going to be five plus five is 10,

00:01:45.530 --> 00:01:48.520
it's going to be 10 minutes past 1:15.

00:01:48.520 --> 00:01:52.300
Well, 15 plus 10 is 25 again.

00:01:52.300 --> 00:01:54.450
So, the time shown on
the number line 1:25.


Reasoning with systems of equations

WEBVTT
Kind: captions
Language: en

00:00:00.840 --> 00:00:01.870
- [Sal] In a previous video,

00:00:01.870 --> 00:00:06.610
we talk about the notion of
equivalence with equations.

00:00:06.610 --> 00:00:08.300
And equivalence is just this notion

00:00:08.300 --> 00:00:10.930
that there's different ways of writing

00:00:10.930 --> 00:00:13.420
what our equivalent statements in algebra.

00:00:13.420 --> 00:00:15.740
And I can give some simple examples.

00:00:15.740 --> 00:00:19.880
I could say two x equals 10,
or I could say x equals five.

00:00:19.880 --> 00:00:21.910
These are equivalent equations.

00:00:21.910 --> 00:00:22.910
Why are they?

00:00:22.910 --> 00:00:25.010
Because an x satisfies one of them

00:00:25.010 --> 00:00:27.160
if and only if it satisfies the other.

00:00:27.160 --> 00:00:29.205
And you can verify that in both cases,

00:00:29.205 --> 00:00:33.140
x equals five is the only
x that satisfies both.

00:00:33.140 --> 00:00:36.732
Another set of equivalent
equations, you could have two x

00:00:36.732 --> 00:00:40.350
is equal to eight and x equals four.

00:00:40.350 --> 00:00:42.260
These two are equivalent equations.

00:00:42.260 --> 00:00:46.820
An x satisfies one if and only
if it satisfies the other.

00:00:46.820 --> 00:00:49.050
In this video, we're going
to extend our knowledge

00:00:49.050 --> 00:00:52.520
of equivalence to thinking
about equivalent systems.

00:00:52.520 --> 00:00:54.463
And really, in your past
when you were solving

00:00:54.463 --> 00:00:57.415
systems of equations,
you were doing operations

00:00:57.415 --> 00:00:59.560
assuming equivalence, but you might not

00:00:59.560 --> 00:01:01.990
have just been thinking about it that way.

00:01:01.990 --> 00:01:05.170
So let's give ourselves a system.

00:01:05.170 --> 00:01:07.680
So let's say this system tells us

00:01:07.680 --> 00:01:10.860
that there's some x y pair
where two times that x

00:01:10.860 --> 00:01:14.130
plus that y is equal to eight,

00:01:14.130 --> 00:01:19.130
and that x plus that y is equal to five.

00:01:20.300 --> 00:01:23.400
Now we can have an equivalent system

00:01:23.400 --> 00:01:26.060
if we replace either of these equations

00:01:26.060 --> 00:01:27.760
with an equivalent version.

00:01:27.760 --> 00:01:29.830
So for example, many of you when you look

00:01:29.830 --> 00:01:32.050
to try to solve this, you might say well,

00:01:32.050 --> 00:01:34.080
if this was a negative two x here,

00:01:34.080 --> 00:01:36.310
maybe I could eventually
add the left side.

00:01:36.310 --> 00:01:37.960
And we'll talk about why that is

00:01:37.960 --> 00:01:39.870
an equivalence preserving operation.

00:01:39.870 --> 00:01:42.180
But in order to get a
negative two out here,

00:01:42.180 --> 00:01:44.570
you'd have to multiply
this entire equation

00:01:44.570 --> 00:01:45.950
times negative two.

00:01:45.950 --> 00:01:48.837
And so if you did that, if you
multiplied both sides of this

00:01:48.837 --> 00:01:52.820
times negative two, times negative two,

00:01:52.820 --> 00:01:57.040
what you're going to get is negative two x

00:01:57.040 --> 00:02:00.220
minus two y is equal to negative 10.

00:02:00.220 --> 00:02:03.940
This equation and this
equation are equivalent.

00:02:03.940 --> 00:02:04.773
Why?

00:02:04.773 --> 00:02:07.230
Because any x y pair that
satisfies one of them

00:02:07.230 --> 00:02:10.110
will satisfy the other, or
an x y pair satisfies one

00:02:10.110 --> 00:02:13.050
if and only if it satisfies the other.

00:02:13.050 --> 00:02:15.470
And so if I now think about the system,

00:02:15.470 --> 00:02:18.140
the system where I've
rewritten this second equation

00:02:18.140 --> 00:02:20.864
and my first equation is the same,

00:02:20.864 --> 00:02:25.864
this is an equivalent
system to our first system.

00:02:27.290 --> 00:02:30.210
So these, any x y pair, if an x y pair

00:02:30.210 --> 00:02:31.930
satisfies one of these systems,

00:02:31.930 --> 00:02:35.193
it's going to satisfy
the other and vice versa.

00:02:36.080 --> 00:02:39.110
Now the next interesting
thing that you might realize,

00:02:39.110 --> 00:02:40.840
and if you were just trying to solve this,

00:02:40.840 --> 00:02:43.140
and this isn't an introductory
video in solving systems,

00:02:43.140 --> 00:02:45.280
so I'm assuming some familiarity with it,

00:02:45.280 --> 00:02:47.870
you've probably seen
solving by elimination

00:02:47.870 --> 00:02:49.865
where you say okay, look,
if I can somehow add these,

00:02:49.865 --> 00:02:52.030
the left side to the left
side and the right side

00:02:52.030 --> 00:02:55.090
to the right side, these
x's will quote cancel out

00:02:55.090 --> 00:02:56.670
and then I'll just be left with y's.

00:02:56.670 --> 00:02:58.010
And we've done this before.

00:02:58.010 --> 00:03:00.440
You can kind of think you're
trying to solve for y.

00:03:00.440 --> 00:03:02.110
But in this video, I
want to think about why

00:03:02.110 --> 00:03:04.268
you end up with an equivalent system

00:03:04.268 --> 00:03:06.140
if you were to do that.

00:03:06.140 --> 00:03:08.350
And one way to think about it is

00:03:08.350 --> 00:03:11.300
what I'm going to do to create
an equivalent system here

00:03:11.300 --> 00:03:15.800
is I am going to keep my first equation,

00:03:15.800 --> 00:03:19.078
two x plus y is equal to eight.

00:03:19.078 --> 00:03:22.040
But then I'm gonna take my second equation

00:03:22.040 --> 00:03:25.780
and add the same thing to both sides.

00:03:25.780 --> 00:03:27.640
We know if you add or
subtract the same thing

00:03:27.640 --> 00:03:29.050
to both sides of an equation,

00:03:29.050 --> 00:03:31.290
you get an equivalent equation.

00:03:31.290 --> 00:03:32.740
So I'm gonna do that over here.

00:03:32.740 --> 00:03:34.350
But it's gonna be a
little bit interesting.

00:03:34.350 --> 00:03:38.130
So if you had negative two x minus two y

00:03:38.130 --> 00:03:40.740
is equal to negative 10,
and what I want to do

00:03:40.740 --> 00:03:42.890
is I want to add eight to both sides.

00:03:42.890 --> 00:03:44.456
So I could do it like this.

00:03:44.456 --> 00:03:46.640
I could add eight to both sides.

00:03:46.640 --> 00:03:48.970
But remember, our system
is saying that both

00:03:48.970 --> 00:03:50.296
of these statements are true,

00:03:50.296 --> 00:03:53.410
that two x plus y is equal to eight

00:03:53.410 --> 00:03:56.960
and negative two x minus two
y is equal to negative 10.

00:03:56.960 --> 00:04:00.460
So instead of adding
explicitly eight to both sides,

00:04:00.460 --> 00:04:01.802
I could add something that's equivalent

00:04:01.802 --> 00:04:04.060
to eight to both sides.

00:04:04.060 --> 00:04:06.313
And I know something that
is equivalent to eight

00:04:06.313 --> 00:04:08.830
based on this first equation.

00:04:08.830 --> 00:04:11.200
I could add eight, and I could do eight

00:04:11.200 --> 00:04:14.840
on the left hand side, or I
could just add two x plus y.

00:04:14.840 --> 00:04:16.945
So two x plus y.

00:04:16.945 --> 00:04:19.440
Now I really want you, you
might want to pause your video

00:04:19.440 --> 00:04:21.308
and say okay, how can I do this?

00:04:21.308 --> 00:04:23.360
Why is Sal saying that I'm adding

00:04:23.360 --> 00:04:25.300
the same thing to both sides?

00:04:25.300 --> 00:04:27.500
Because remember, when
we're taking a system,

00:04:27.500 --> 00:04:30.150
we're assuming that both
of these need to be true.

00:04:30.150 --> 00:04:33.071
An x y pair satisfies one
equation if and only if,

00:04:33.071 --> 00:04:36.310
only if, if and only if
it satisfies the other.

00:04:36.310 --> 00:04:39.700
So here, we know that x, two x plus y

00:04:39.700 --> 00:04:41.520
needs to be equal to eight.

00:04:41.520 --> 00:04:43.198
So if I'm adding two x plus y to the left

00:04:43.198 --> 00:04:44.890
and I'm adding eight to the right,

00:04:44.890 --> 00:04:48.150
I'm really just adding
eight to both sides,

00:04:48.150 --> 00:04:49.960
which is equivalence preserving.

00:04:49.960 --> 00:04:53.680
And when you do that, you
get, these negative two x

00:04:53.680 --> 00:04:56.290
and two x cancels out, you get negative y

00:04:56.290 --> 00:04:59.280
is equal to negative two.

00:04:59.280 --> 00:05:01.810
And so I can rewrite that second equation

00:05:01.810 --> 00:05:06.707
as negative y is equal to negative two.

00:05:08.170 --> 00:05:09.070
And I know what you're thinking.

00:05:09.070 --> 00:05:10.410
You're like wait, but I'm used

00:05:10.410 --> 00:05:12.300
to solving systems of equations.

00:05:12.300 --> 00:05:14.080
I'm used to just adding these two together

00:05:14.080 --> 00:05:15.670
and then I just have this one equation.

00:05:15.670 --> 00:05:19.400
And really, that's not super
mathematically rigorous

00:05:19.400 --> 00:05:21.780
because the other equation is still there.

00:05:21.780 --> 00:05:22.910
It's still a constraint.

00:05:22.910 --> 00:05:24.260
Oftentimes, you solve for one

00:05:24.260 --> 00:05:26.600
and then you quote substitute back in.

00:05:26.600 --> 00:05:29.377
But really, the both equations
are there the whole time.

00:05:29.377 --> 00:05:32.850
You're just rewriting
them in equivalent ways.

00:05:32.850 --> 00:05:34.930
So once again, this system, this system,

00:05:34.930 --> 00:05:36.540
and this system are all equivalent.

00:05:36.540 --> 00:05:38.965
Any x y pair that
satisfies one will satisfy

00:05:38.965 --> 00:05:41.540
all of them, and vice versa.

00:05:41.540 --> 00:05:43.100
And once again, we can continue

00:05:43.100 --> 00:05:45.610
to rewrite this in equivalent ways.

00:05:45.610 --> 00:05:47.580
That second equation, I can multiply

00:05:47.580 --> 00:05:48.960
both sides by negative one.

00:05:48.960 --> 00:05:50.550
That's equivalence preserving.

00:05:50.550 --> 00:05:54.660
And if I did that, then
I get, I haven't changed

00:05:54.660 --> 00:05:58.380
my top equation, two x
plus y is equal to eight.

00:05:58.380 --> 00:06:00.620
And on the second one,
if I multiply both sides

00:06:00.620 --> 00:06:05.380
by negative one, I get y is equal to two.

00:06:05.380 --> 00:06:08.020
Once again, these are
all equivalent systems.

00:06:08.020 --> 00:06:10.900
I know I'm, I sound
very repetitive in this.

00:06:10.900 --> 00:06:13.300
But now, I can do another
thing to make this,

00:06:13.300 --> 00:06:16.100
to keep the equivalence
but get a clearer idea

00:06:16.100 --> 00:06:18.270
of what that x y pair is.

00:06:18.270 --> 00:06:21.510
If we know that y is equal to two

00:06:21.510 --> 00:06:24.310
and we know that that's
true in both equations,

00:06:24.310 --> 00:06:25.790
remember, it is an and here.

00:06:25.790 --> 00:06:27.890
We're assuming there's x y, some x y pair

00:06:27.890 --> 00:06:29.600
that satisfies both.

00:06:29.600 --> 00:06:31.580
Two x plus y needs to be equal to eight

00:06:31.580 --> 00:06:34.040
and y is equal to two.

00:06:34.040 --> 00:06:36.550
Well that means up here where we see a y,

00:06:36.550 --> 00:06:38.470
we can write an equivalent system

00:06:38.470 --> 00:06:39.610
where instead of writing a y there,

00:06:39.610 --> 00:06:42.370
we could write a two because
we know that y is equal to two.

00:06:42.370 --> 00:06:46.420
And so we can rewrite that top equation

00:06:46.420 --> 00:06:48.330
by substituting a two for y.

00:06:48.330 --> 00:06:53.330
So we could rewrite that as two
x plus two is equal to eight

00:06:54.020 --> 00:06:57.200
and y is equal to two.

00:06:57.200 --> 00:06:59.320
So this is an and right over there.

00:06:59.320 --> 00:07:01.330
It's implicitly there.

00:07:01.330 --> 00:07:04.600
And of course, we can
keep going from there.

00:07:04.600 --> 00:07:06.400
I'll scroll down a little bit.

00:07:06.400 --> 00:07:08.340
I could write another
equivalent system to this

00:07:08.340 --> 00:07:10.730
by doing equivalence preserving operations

00:07:10.730 --> 00:07:11.740
on that top equation.

00:07:11.740 --> 00:07:14.040
What if I subtracted two from both sides

00:07:14.040 --> 00:07:14.930
of that top equation?

00:07:14.930 --> 00:07:17.200
It's still going to be
an equivalent equation.

00:07:17.200 --> 00:07:21.300
And so I could rewrite
it as, if I subtract two

00:07:21.300 --> 00:07:24.690
from both sides, I'm gonna
get two x is equal to six.

00:07:24.690 --> 00:07:26.970
And then that second
equation hasn't changed.

00:07:26.970 --> 00:07:29.090
Y is equal to two.

00:07:29.090 --> 00:07:31.860
So there's some x y pair
that if it satisfies one,

00:07:31.860 --> 00:07:34.240
it satisfies the other, and vice versa.

00:07:34.240 --> 00:07:36.570
This system is equivalent to every system

00:07:36.570 --> 00:07:40.020
that I've written so far in
this chain of operations,

00:07:40.020 --> 00:07:42.750
so to speak, and then of
course, this top equation,

00:07:42.750 --> 00:07:44.270
an equivalence preserving operation

00:07:44.270 --> 00:07:46.640
is to divide both sides by a non,

00:07:46.640 --> 00:07:48.090
the same nonzero value.

00:07:48.090 --> 00:07:50.540
And in this case, I could
divide both sides by two.

00:07:50.540 --> 00:07:53.280
And then I would get, if
I divide the top by two,

00:07:53.280 --> 00:07:58.280
I would get x equals three,
and y is equal to two.

00:07:58.650 --> 00:08:00.260
And once again, this is a different way

00:08:00.260 --> 00:08:01.093
of thinking about it.

00:08:01.093 --> 00:08:04.680
All I'm doing is rewriting the same system

00:08:04.680 --> 00:08:08.190
in an equivalent way that just
gets us a little bit clearer

00:08:08.190 --> 00:08:12.580
as to what that x y pair actually is.

00:08:12.580 --> 00:08:14.740
In the past, you might've just, you know,

00:08:14.740 --> 00:08:17.200
just assumed that you can
add both sides of an equation

00:08:17.200 --> 00:08:18.630
or do this type of elimination

00:08:18.630 --> 00:08:20.080
or do some type of substitution

00:08:20.080 --> 00:08:22.047
to just quote figure out the x and y.

00:08:22.047 --> 00:08:24.850
But really, you're rewriting the system.

00:08:24.850 --> 00:08:26.600
You're rewriting the
constraints of the system

00:08:26.600 --> 00:08:29.570
in equivalent ways to
make it more explicit

00:08:29.570 --> 00:08:33.000
what that x y pair is that satisfies

00:08:33.000 --> 00:08:34.883
both equations in the system.


Interpret quadratic models: Factored form

WEBVTT
Kind: captions
Language: en

00:00:00.450 --> 00:00:01.850
- [Instructor] We're
told that Rodrigo watches

00:00:01.850 --> 00:00:04.690
a helicopter take off from a platform.

00:00:04.690 --> 00:00:08.760
The height of the helicopter,
in meters above the ground,

00:00:08.760 --> 00:00:13.400
t minutes after takeoff is modeled by,

00:00:13.400 --> 00:00:16.480
and we see this function right over here.

00:00:16.480 --> 00:00:19.260
Rodrigo wants to know when the helicopter

00:00:19.260 --> 00:00:22.040
will land on the ground.

00:00:22.040 --> 00:00:24.923
So pause this video and see
if you can figure that out.

00:00:26.420 --> 00:00:28.470
All right, now let's
think about this together.

00:00:28.470 --> 00:00:30.390
So let's just imagine
actually what the graph

00:00:30.390 --> 00:00:32.170
of this function looks like.

00:00:32.170 --> 00:00:34.230
And it'll also help us
imagine what's going on

00:00:34.230 --> 00:00:35.550
with the helicopter.

00:00:35.550 --> 00:00:40.550
So our horizontal axis,
this is t, time in minutes,

00:00:42.550 --> 00:00:46.570
and then our vertical axis is height.

00:00:46.570 --> 00:00:48.720
So height as a function of time.

00:00:48.720 --> 00:00:50.180
And maybe I just write it like this.

00:00:50.180 --> 00:00:51.443
I'll just write height,

00:00:52.480 --> 00:00:56.850
and this is given in
meters above the ground.

00:00:56.850 --> 00:00:59.150
Now I don't know exactly
what the graph looks like,

00:00:59.150 --> 00:01:01.380
but given that I have
a negative coefficient

00:01:01.380 --> 00:01:03.000
on my quadratic term,

00:01:03.000 --> 00:01:06.500
I know that it is a downward
opening parabola like that.

00:01:06.500 --> 00:01:09.290
And it says that the helicopter
takes off of a platform.

00:01:09.290 --> 00:01:11.460
So however high the platform is,

00:01:11.460 --> 00:01:14.730
then it takes off and it's
going to do something like this.

00:01:14.730 --> 00:01:17.320
I don't know exactly what
the graph looks like,

00:01:17.320 --> 00:01:19.440
but probably something like this.

00:01:19.440 --> 00:01:23.280
Now, if they asked us
what is the highest point

00:01:23.280 --> 00:01:27.370
of the helicopter, and at
what time does it happen,

00:01:27.370 --> 00:01:29.720
then we'd wanna figure
out what the vertex is

00:01:29.720 --> 00:01:31.160
of this parabola.

00:01:31.160 --> 00:01:32.550
But that's not what they're asking.

00:01:32.550 --> 00:01:36.250
They're asking when does the
helicopter land on the ground?

00:01:36.250 --> 00:01:38.430
That's this time right over here.

00:01:38.430 --> 00:01:39.730
So if we wanted to find the vertex,

00:01:39.730 --> 00:01:41.760
we would wanna put this into vertex form,

00:01:41.760 --> 00:01:43.390
but here we wanna figure out when does

00:01:43.390 --> 00:01:45.110
that function equal zero.

00:01:45.110 --> 00:01:49.840
We want to find a zero of this
quadratic right over here.

00:01:49.840 --> 00:01:52.160
So the best way that I
can think about doing it

00:01:52.160 --> 00:01:53.630
is try to factor it,

00:01:53.630 --> 00:01:55.830
try to set them this thing equal to zero,

00:01:55.830 --> 00:01:58.450
and then factor it and
then see what t values

00:01:58.450 --> 00:01:59.610
make that equal to zero.

00:01:59.610 --> 00:02:00.740
So let me do that.

00:02:00.740 --> 00:02:05.740
So I say negative three t
squared plus 24t plus 60,

00:02:06.050 --> 00:02:07.740
remember we care when our height

00:02:07.740 --> 00:02:10.540
is equal to zero, equal zero.

00:02:10.540 --> 00:02:13.020
So let's see maybe the
first thing I would do

00:02:13.020 --> 00:02:16.010
just to simplify the second
degree term a little bit.

00:02:16.010 --> 00:02:18.920
Let's just divide both
sides by negative three.

00:02:18.920 --> 00:02:19.870
If we did that,

00:02:19.870 --> 00:02:23.290
this would become t squared
24 divided by negative three

00:02:23.290 --> 00:02:25.630
is negative eight, negative eight t.

00:02:25.630 --> 00:02:29.290
60 divided by negative
three is negative 20,

00:02:29.290 --> 00:02:30.800
and then zero divided by negative three

00:02:30.800 --> 00:02:33.090
is of course still zero.

00:02:33.090 --> 00:02:35.830
And now can I think of
two numbers whose product

00:02:35.830 --> 00:02:37.450
is negative 20?

00:02:37.450 --> 00:02:38.990
So they would have different signs

00:02:38.990 --> 00:02:40.290
in order to get a negative product,

00:02:40.290 --> 00:02:42.163
and who sum is negative eight.

00:02:43.090 --> 00:02:48.090
So let's see what about
negative 10 and two,

00:02:48.147 --> 00:02:50.250
and that scene seems to work.

00:02:50.250 --> 00:02:55.250
So I could write this as t
minus 10, times t plus two

00:02:55.750 --> 00:02:57.210
is equal to zero.

00:02:57.210 --> 00:02:59.855
And so in order to make
this expression equals zero,

00:02:59.855 --> 00:03:02.290
either one of these
could be equal to zero.

00:03:02.290 --> 00:03:05.180
So either t minus 10 is equal to zero,

00:03:05.180 --> 00:03:08.160
or t plus two is equal to zero.

00:03:08.160 --> 00:03:09.630
And of course on the left here,

00:03:09.630 --> 00:03:11.100
I can add 10 to both sides.

00:03:11.100 --> 00:03:12.950
So either t equals 10,

00:03:12.950 --> 00:03:15.670
or I could subtract two
from both sides here,

00:03:15.670 --> 00:03:17.600
t is equal to negative two.

00:03:17.600 --> 00:03:20.050
So there's two places where the function

00:03:20.050 --> 00:03:21.400
is equal to zero.

00:03:21.400 --> 00:03:24.110
One at time t equals negative two,

00:03:24.110 --> 00:03:27.240
and one at time t is equal to 10.

00:03:27.240 --> 00:03:29.850
Now we're assuming we're
dealing with positive time here.

00:03:29.850 --> 00:03:31.950
We don't know what the
helicopter was doing

00:03:31.950 --> 00:03:33.450
before the takeoff.

00:03:33.450 --> 00:03:35.160
So we wouldn't really think about this.

00:03:35.160 --> 00:03:37.010
So what we really care about is that t

00:03:37.010 --> 00:03:39.290
is equal to 10 minutes.

00:03:39.290 --> 00:03:43.120
That's when the helicopter
is right over there.

00:03:43.120 --> 00:03:45.230
And actually we know at t equals zero,

00:03:45.230 --> 00:03:46.510
these two terms become zero.

00:03:46.510 --> 00:03:49.150
We know it takes off at 60 meters.

00:03:49.150 --> 00:03:50.274
It goes up.

00:03:50.274 --> 00:03:51.750
If we figured out the vertex,

00:03:51.750 --> 00:03:53.250
we would know how high it went,

00:03:53.250 --> 00:03:55.080
but then it starts going back down,

00:03:55.080 --> 00:03:56.870
and in 10 minutes after takeoff,

00:03:56.870 --> 00:03:59.443
it is back at zero, back on the ground.


Using text features to locate information

WEBVTT
Kind: captions
Language: en

00:00:00.220 --> 00:00:01.290
- [David] Hello, readers.

00:00:01.290 --> 00:00:03.790
Today we're going to talk
about how to use text features

00:00:03.790 --> 00:00:07.070
to find information in a
piece of nonfiction writing

00:00:07.070 --> 00:00:10.730
like a textbook, an encyclopedia
entry or a news article.

00:00:10.730 --> 00:00:12.200
Information in these texts

00:00:12.200 --> 00:00:14.900
is organized with a
specific purpose in mind.

00:00:14.900 --> 00:00:17.330
The author wants you to be
able to read the text features

00:00:17.330 --> 00:00:20.610
like a map so you can find
the information that you need.

00:00:20.610 --> 00:00:22.860
So the first text feature
I wanna talk about today

00:00:22.860 --> 00:00:25.645
is the title and that's just the name

00:00:25.645 --> 00:00:28.080
at the top of a piece of writing.

00:00:28.080 --> 00:00:29.500
And its purpose is to tell you

00:00:29.500 --> 00:00:32.083
really what you're about to read.

00:00:32.920 --> 00:00:34.130
Let me give you an example.

00:00:34.130 --> 00:00:36.670
We can see this article
here, this text in yellow,

00:00:36.670 --> 00:00:39.410
this is the title and it
says, "All about Pets."

00:00:39.410 --> 00:00:42.300
What does that tell us about
the content of this writing?

00:00:42.300 --> 00:00:44.060
It's gonna be all about pets.

00:00:44.060 --> 00:00:47.920
Now below it, in green,
you can see three examples

00:00:47.920 --> 00:00:51.060
of the next kind of text
feature that I wanna talk about,

00:00:51.060 --> 00:00:53.700
which are called headings.

00:00:53.700 --> 00:00:55.260
And we'll go back to that
other screen in a second,

00:00:55.260 --> 00:00:56.093
don't worry.

00:00:56.093 --> 00:00:59.270
And headings organize
information into sections.

00:00:59.270 --> 00:01:01.850
So we can see that there
are three big headings here.

00:01:01.850 --> 00:01:04.450
We've got popular pets, unusual pets,

00:01:04.450 --> 00:01:05.930
and taking care of your pets.

00:01:05.930 --> 00:01:07.300
These are the three headings

00:01:07.300 --> 00:01:12.300
that all fall under the main
topic of all about pets.

00:01:12.360 --> 00:01:14.910
Smaller than a heading is a subheading,

00:01:14.910 --> 00:01:17.840
which organizes text into
even smaller sections.

00:01:17.840 --> 00:01:19.470
So if we go back to the text again,

00:01:19.470 --> 00:01:22.870
we can see that under the
main heading of popular pets,

00:01:22.870 --> 00:01:25.950
there are three subsections,
cats, dogs and fish,

00:01:25.950 --> 00:01:28.630
the three most popular
pets in the United States.

00:01:28.630 --> 00:01:30.880
Another important text
feature you might see

00:01:30.880 --> 00:01:34.430
in a piece of writing is
bold text, bold words.

00:01:34.430 --> 00:01:35.930
And that's when a word or phrase

00:01:35.930 --> 00:01:39.760
is printed in a thicker darker letter,

00:01:39.760 --> 00:01:41.810
and I'll show you exactly
what that looks like.

00:01:41.810 --> 00:01:44.000
But the purpose of it,
the reason that an author

00:01:44.000 --> 00:01:47.700
might choose to include bold
text in a piece of writing

00:01:47.700 --> 00:01:50.990
is to point out important
terms to the reader,

00:01:50.990 --> 00:01:53.390
specific words that they want you to know.

00:01:53.390 --> 00:01:55.440
And usually that's in the interest

00:01:55.440 --> 00:01:58.130
of teaching you, the reader, a new word.

00:01:58.130 --> 00:02:02.800
If we scan this page for bold
text, I see three examples.

00:02:02.800 --> 00:02:04.570
Do you see how the words are darker

00:02:04.570 --> 00:02:06.670
and the letters themselves are thicker?

00:02:06.670 --> 00:02:08.520
That's what it means to be bold.

00:02:08.520 --> 00:02:11.220
That's what it means
for a word to be bold.

00:02:11.220 --> 00:02:13.830
So we've got rare, companions.

00:02:13.830 --> 00:02:15.260
Over here in this little sidebar,

00:02:15.260 --> 00:02:17.840
we've got the word endangered.

00:02:17.840 --> 00:02:19.690
And many times in pieces of writing

00:02:19.690 --> 00:02:23.120
that use bold words like
this, there will be a section

00:02:23.120 --> 00:02:25.430
at the end of the chapter
called a glossary,

00:02:25.430 --> 00:02:28.930
which is really kind of a
holding pen for vocabulary words.

00:02:28.930 --> 00:02:30.610
You flip to end, you look at the glossary,

00:02:30.610 --> 00:02:34.460
and it lists all the bolded
words and their definitions.

00:02:34.460 --> 00:02:37.400
Now I just referred to a sidebar,

00:02:37.400 --> 00:02:40.980
which is this little section
here in this orange-yellow box.

00:02:40.980 --> 00:02:42.880
Now a sidebar is where an editor

00:02:42.880 --> 00:02:44.440
or an author puts information

00:02:44.440 --> 00:02:47.630
that doesn't really fit
in the rest of the text.

00:02:47.630 --> 00:02:51.260
So this is next to the
unusual pets heading.

00:02:51.260 --> 00:02:52.397
And we can see that it begins,

00:02:52.397 --> 00:02:55.110
"While having an unusual
pet can be perfectly fine."

00:02:55.110 --> 00:02:56.700
It's connected to this section,

00:02:56.700 --> 00:03:00.050
but it's not essential to
the point of this paragraph.

00:03:00.050 --> 00:03:02.100
Sidebars are where you
put important information

00:03:02.100 --> 00:03:05.050
that otherwise wouldn't
fit into the piece.

00:03:05.050 --> 00:03:09.430
This teal box here that says
take a peek at what's inside,

00:03:09.430 --> 00:03:13.780
grooming tips 3, healthy
treats 5, training your pet 8,

00:03:13.780 --> 00:03:15.470
this is a table of contents.

00:03:15.470 --> 00:03:17.060
So if this page, all about pets,

00:03:17.060 --> 00:03:19.740
is the first page of a magazine,
we've opened the cover,

00:03:19.740 --> 00:03:21.460
and now we're looking at the first page,

00:03:21.460 --> 00:03:23.690
then this little box here is telling us

00:03:23.690 --> 00:03:25.810
what to expect in the
rest of the magazine,

00:03:25.810 --> 00:03:27.880
what page numbers we can find

00:03:27.880 --> 00:03:29.920
all of these other articles on.

00:03:29.920 --> 00:03:32.530
There's also a similar
thing called an index,

00:03:32.530 --> 00:03:35.130
which is located in the back of a book.

00:03:35.130 --> 00:03:38.323
And that's just a list of
all the topics in the piece

00:03:38.323 --> 00:03:40.590
in alphabetical order.

00:03:40.590 --> 00:03:43.050
So if I wanna flip to the
back of this piece of writing,

00:03:43.050 --> 00:03:47.680
and see if I can find a
place where it mentions pugs,

00:03:47.680 --> 00:03:50.580
I would go and start with the
section that begins with P,

00:03:50.580 --> 00:03:52.410
look for a mention of pug dogs,

00:03:52.410 --> 00:03:55.890
and then I would go to the
page where pugs are listed.

00:03:55.890 --> 00:03:57.430
And then this final heading on this page

00:03:57.430 --> 00:03:59.060
is called taking care of your pet,

00:03:59.060 --> 00:04:00.230
and what's interesting about it

00:04:00.230 --> 00:04:03.330
is that it contains a bulleted list.

00:04:03.330 --> 00:04:06.840
These little round dots, we call bullets.

00:04:06.840 --> 00:04:08.850
Sometimes putting things
in a list like this

00:04:08.850 --> 00:04:12.070
is the quickest most efficient
way to share information.

00:04:12.070 --> 00:04:13.770
So this is a three point list

00:04:13.770 --> 00:04:15.850
that all pets need some
sort of food and water,

00:04:15.850 --> 00:04:18.170
a place to sleep and rest,
way to exercise or play,

00:04:18.170 --> 00:04:21.130
ba-ba-ba, three different little points.

00:04:21.130 --> 00:04:23.060
And lists will either use bullets

00:04:23.060 --> 00:04:25.680
like these little round
things, numbered lists,

00:04:25.680 --> 00:04:27.790
or sometimes lists that just use

00:04:27.790 --> 00:04:29.960
letters of the alphabet for each point.

00:04:29.960 --> 00:04:31.390
So A, food and water.

00:04:31.390 --> 00:04:32.702
B, a place to rest or sleep.

00:04:32.702 --> 00:04:34.840
And C, a way to exercise or play.

00:04:34.840 --> 00:04:36.590
Now down here at the
very bottom of the page

00:04:36.590 --> 00:04:38.160
it says want to learn more?

00:04:38.160 --> 00:04:43.160
Www.avma.org/resourcestools/pet-owners/petcare.

00:04:44.730 --> 00:04:47.110
And when I move my cursor over it,

00:04:47.110 --> 00:04:48.990
you can see there's a little flag,

00:04:48.990 --> 00:04:50.700
the cursor changes to a pointy finger,

00:04:50.700 --> 00:04:52.300
and that means it's a hyperlink.

00:04:52.300 --> 00:04:54.340
And that's gonna take us to a website.

00:04:54.340 --> 00:04:55.830
And here we are on the website

00:04:55.830 --> 00:04:58.120
of the American Veterinary
Medical Association.

00:04:58.120 --> 00:05:01.260
So this is a website
operated by animal doctors.

00:05:01.260 --> 00:05:03.050
And you can see that this
page too is organized

00:05:03.050 --> 00:05:05.080
under the title of "Pet Care."

00:05:05.080 --> 00:05:07.150
It's got a bunch of different subheadings

00:05:07.150 --> 00:05:10.040
like responsible pet
ownership, preventive care,

00:05:10.040 --> 00:05:11.790
and keep them healthy.

00:05:11.790 --> 00:05:13.840
So to review, the title tells us

00:05:13.840 --> 00:05:15.440
what the article is going to be about.

00:05:15.440 --> 00:05:18.860
The heading divides up
that article into chunks.

00:05:18.860 --> 00:05:21.910
The subheading divides it
up into even smaller chunks.

00:05:21.910 --> 00:05:23.580
Sidebars contain text

00:05:23.580 --> 00:05:26.380
that wouldn't fit elsewhere in the piece.

00:05:26.380 --> 00:05:28.450
Bold type tells us what words

00:05:28.450 --> 00:05:30.970
the author thinks are
important for us to learn.

00:05:30.970 --> 00:05:34.610
Tables of contents tell us
what content we can expect.

00:05:34.610 --> 00:05:37.760
And finally, hyperlinks
connect us to other places

00:05:37.760 --> 00:05:40.820
on the internet where we
can learn more things.

00:05:40.820 --> 00:05:42.973
You can learn anything, David out.


Different mediums and the tone of the text

WEBVTT
Kind: captions
Language: en

00:00:02.210 --> 00:00:03.660
- [David] Hello readers.

00:00:03.660 --> 00:00:05.959
I would like to show you
one of my favorite things

00:00:05.959 --> 00:00:07.273
I ever wrote.

00:00:08.460 --> 00:00:09.720
It's this splash page

00:00:09.720 --> 00:00:11.510
from this comic I wrote some years ago,

00:00:11.510 --> 00:00:14.010
illustrated by my friend Cour Billadeau.

00:00:14.010 --> 00:00:16.200
You'll notice it has
almost no words in it,

00:00:16.200 --> 00:00:18.050
at least in this form.

00:00:18.050 --> 00:00:20.300
Now, let me show you the script.

00:00:20.300 --> 00:00:22.990
Pages three and four, panel one.

00:00:22.990 --> 00:00:24.800
A double-page spread,

00:00:24.800 --> 00:00:27.530
the whole greenhouse
revealed, in widescreen.

00:00:27.530 --> 00:00:28.740
It's glorious.

00:00:28.740 --> 00:00:32.410
Wisps of steam curl up from
bubbling patches of pool,

00:00:32.410 --> 00:00:36.090
green kelpy tendrils twine
up the sides of the building.

00:00:36.090 --> 00:00:39.100
Everything is suffused with
a delicate, green glow.

00:00:39.100 --> 00:00:41.830
Absent the gro-lights,
some of the algae fluoresce

00:00:41.830 --> 00:00:43.970
in a range of cool-spectrum colors.

00:00:43.970 --> 00:00:45.980
But primarily greens.

00:00:45.980 --> 00:00:50.050
Eugene is dwarfed by its
almost cosmic magnificence.

00:00:50.050 --> 00:00:53.150
Caption, I can't describe it.

00:00:53.150 --> 00:00:55.230
None of that language,
except for the caption,

00:00:55.230 --> 00:00:57.350
shows up in the final layout.

00:00:57.350 --> 00:01:00.100
All of that was me, the
writer, giving art direction

00:01:00.100 --> 00:01:01.550
to Cour, the illustrator.

00:01:01.550 --> 00:01:05.321
Then they translated that
language into their own version.

00:01:05.321 --> 00:01:07.930
I think it's a pretty
faithful translation.

00:01:07.930 --> 00:01:11.450
My words are translated through
Cour's design sensibilities

00:01:11.450 --> 00:01:13.370
and turned into artwork.

00:01:13.370 --> 00:01:16.650
When you translate a written
work into a different medium,

00:01:16.650 --> 00:01:19.240
whether it's illustrated,
animated, recorded,

00:01:19.240 --> 00:01:21.900
or performed live it changes.

00:01:21.900 --> 00:01:24.373
It becomes a fundamentally
different object.

00:01:25.470 --> 00:01:28.720
As readers, it's a
valuable skill to explore

00:01:28.720 --> 00:01:32.710
how a text changes as it shifts
from one medium to another.

00:01:32.710 --> 00:01:35.640
And when I say, medium,
I mean a style of work,

00:01:35.640 --> 00:01:38.600
like a stage play, a
film, a graphic novel,

00:01:38.600 --> 00:01:40.840
and audio drama, any of that.

00:01:40.840 --> 00:01:43.490
Good readers analyze those changes

00:01:43.490 --> 00:01:47.190
and use them to understand
decisions that creators make.

00:01:47.190 --> 00:01:48.940
If you're watching Romeo and Juliet

00:01:48.940 --> 00:01:50.630
and the director has made the decision

00:01:50.630 --> 00:01:53.160
to dress everyone in towering robot suits,

00:01:53.160 --> 00:01:55.660
a detail that is definitely
not in the play as written,

00:01:55.660 --> 00:01:57.670
what does that decision tell you?

00:01:57.670 --> 00:01:58.910
What does it mean to you?

00:01:58.910 --> 00:02:01.690
Maybe you have had the experience
of reading a book series

00:02:01.690 --> 00:02:02.830
that was important to you

00:02:02.830 --> 00:02:04.710
and then they made it into a movie

00:02:04.710 --> 00:02:06.520
and you were so excited to see the movie,

00:02:06.520 --> 00:02:09.700
and you sat down to see
it and it was awful.

00:02:09.700 --> 00:02:11.420
Like, they cast the wrong actors

00:02:11.420 --> 00:02:13.890
and they simplified the
plot until it made no sense,

00:02:13.890 --> 00:02:17.320
and it just didn't feel right.

00:02:17.320 --> 00:02:20.010
That feeling is an
example of this tension,

00:02:20.010 --> 00:02:22.440
this change, between a written material

00:02:22.440 --> 00:02:24.690
and its visual adaptation.

00:02:24.690 --> 00:02:27.820
Sometimes it can be bad,
sometimes it can be good.

00:02:27.820 --> 00:02:30.492
Some readers can imagine
what characters in books

00:02:30.492 --> 00:02:32.260
look or sound like,

00:02:32.260 --> 00:02:34.260
hearing them in their mind's ear,

00:02:34.260 --> 00:02:36.670
seeing them in their mind's eye.

00:02:36.670 --> 00:02:39.260
The way your imagination
renders a character

00:02:39.260 --> 00:02:40.410
is going to be different from

00:02:40.410 --> 00:02:43.170
how someone else's imagination does it.

00:02:43.170 --> 00:02:45.690
So let's compare the
script for this audio drama

00:02:45.690 --> 00:02:48.350
we've got on Khan Academy,
Hands Off My Phone,

00:02:48.350 --> 00:02:50.860
and let's compare that
against the recorded version.

00:02:50.860 --> 00:02:52.950
So first, I'm going to put up the script

00:02:52.950 --> 00:02:54.440
and I'd like you to pause the video

00:02:54.440 --> 00:02:56.713
and just read it to yourself very quickly.

00:03:02.820 --> 00:03:05.840
And now let's take a listen
to the recorded version.

00:03:05.840 --> 00:03:10.670
(upbeat music)
(bell ringing)

00:03:10.670 --> 00:03:12.040
- [Sebastian] Oh no he didn't.

00:03:12.040 --> 00:03:13.880
That is so harsh.
- [Valentina] Right?

00:03:13.880 --> 00:03:15.130
- [Sebastian] Your dad
took your phone away,

00:03:15.130 --> 00:03:16.940
just for getting a D on the history test?

00:03:16.940 --> 00:03:17.773
- [Valentina] Yep.

00:03:17.773 --> 00:03:19.200
- [Sebastian] My mind is blown.

00:03:19.200 --> 00:03:20.260
- [Valentina] Mine too.

00:03:20.260 --> 00:03:21.930
- [Sebastian] I mean,
that was an easy test.

00:03:21.930 --> 00:03:22.763
- [Valentina] What?

00:03:22.763 --> 00:03:23.770
- [Sebastian] I can't believe you got a D.

00:03:23.770 --> 00:03:24.603
- [Valentina] Hey!

00:03:24.603 --> 00:03:25.436
That's not really--

00:03:25.436 --> 00:03:26.650
- [Sebastian] And your dad
is the school principal,

00:03:26.650 --> 00:03:28.460
and he took your phone away.

00:03:28.460 --> 00:03:29.293
Whoa.
(chuckling)

00:03:29.293 --> 00:03:32.060
- [Valentina] You know,
this isn't really helping.

00:03:32.060 --> 00:03:34.360
- [Sebastian] Your life
is so bleak right now.

00:03:35.370 --> 00:03:36.980
- [David] So you can read that script

00:03:36.980 --> 00:03:40.650
and think, oh hey, Sebastian
is being earnestly sympathetic.

00:03:40.650 --> 00:03:43.800
Like, he really recognizes
that his friend is hurting,

00:03:43.800 --> 00:03:44.900
but when you hear that performance

00:03:44.900 --> 00:03:47.110
the way I interpreted this line

00:03:47.110 --> 00:03:50.210
is that Sebastian is
low-key roasting Valentina.

00:03:50.210 --> 00:03:53.570
He's not saying your life
is so bleak in a kind way.

00:03:53.570 --> 00:03:55.330
He's rubbing salt into the wounds

00:03:55.330 --> 00:03:57.380
and being a dingus about it.

00:03:57.380 --> 00:04:00.010
There's also other stuff that's
not explicitly in the script

00:04:00.010 --> 00:04:02.372
like, that opening musical sting.

00:04:02.372 --> 00:04:04.171
(upbeat music)

00:04:04.171 --> 00:04:07.120
And the ringing of the bell.
(bell ringing)

00:04:07.120 --> 00:04:09.730
Or those background school noises.

00:04:09.730 --> 00:04:11.520
All of that is meant to represent the fact

00:04:11.520 --> 00:04:13.860
that you're listening to a fictional show

00:04:13.860 --> 00:04:15.773
that takes place in a school setting.

00:04:16.670 --> 00:04:17.910
Does it work?

00:04:17.910 --> 00:04:19.383
That's for you to decide.

00:04:19.383 --> 00:04:22.250
When you watch or listen to a performance

00:04:22.250 --> 00:04:24.910
or a recording, or when
you look at illustrations,

00:04:24.910 --> 00:04:27.010
ask yourself some questions.

00:04:27.010 --> 00:04:29.440
For an audio piece, how
do the sound effects,

00:04:29.440 --> 00:04:32.364
the acting decisions, and
the music impact the story

00:04:32.364 --> 00:04:36.530
or affect the meaning of the
words the characters say?

00:04:36.530 --> 00:04:38.920
How does the way an actor delivers a line

00:04:38.920 --> 00:04:40.530
change its emphasis?

00:04:40.530 --> 00:04:43.090
Was someone being sarcastic or sincere

00:04:43.090 --> 00:04:45.143
in a way you didn't expect, for example?

00:04:46.000 --> 00:04:47.500
For an illustrated story,

00:04:47.500 --> 00:04:49.830
how do those illustrations
help you understand

00:04:49.830 --> 00:04:53.540
the author's tone and do you
agree with those choices?

00:04:53.540 --> 00:04:55.244
Is the author's
interpretation of the story

00:04:55.244 --> 00:04:56.893
the same as yours?

00:04:57.800 --> 00:05:01.100
For a TV show, or a movie, or a play,

00:05:01.100 --> 00:05:03.790
in addition to all the
decisions made by actors

00:05:03.790 --> 00:05:06.240
about how to use their
voices, shape their faces,

00:05:06.240 --> 00:05:07.500
or hold their bodies,

00:05:07.500 --> 00:05:09.880
how does the set tell the story?

00:05:09.880 --> 00:05:12.340
How do costumes tell the story?

00:05:12.340 --> 00:05:16.120
How does lighting or special
effects impact the tone?

00:05:16.120 --> 00:05:17.640
For TV and film,

00:05:17.640 --> 00:05:21.180
how does the camera impact
the way the story is told?

00:05:21.180 --> 00:05:23.380
The way a piece of film text is edited,

00:05:23.380 --> 00:05:25.520
its cuts, its angles, its rhythms,

00:05:25.520 --> 00:05:27.930
can help shape the way you, as a viewer,

00:05:27.930 --> 00:05:32.381
as a reader of visual text, understand it.

00:05:32.381 --> 00:05:36.220
And if you can learn that,
then you can learn anything.

00:05:36.220 --> 00:05:37.053
David out.