Place value blocks

WEBVTT
Kind: captions
Language: en

00:00:01.064 --> 00:00:02.064
- [Voiceover] What number is shown

00:00:02.064 --> 00:00:03.907
by the place value blocks?

00:00:03.907 --> 00:00:06.836
So here we have several
sets of place value blocks,

00:00:06.836 --> 00:00:08.643
some with many many many blocks

00:00:08.643 --> 00:00:10.179
and some with just single blocks

00:00:10.179 --> 00:00:13.337
stacked on top of each
other, and we want to know

00:00:13.337 --> 00:00:17.504
what number is represented bay
all of the blocks combined.

00:00:18.597 --> 00:00:20.663
So let's start over here
with the single blocks

00:00:20.663 --> 00:00:22.378
stacked on top of each other because

00:00:22.378 --> 00:00:24.912
it will be the easiest one to count.

00:00:24.912 --> 00:00:26.661
We can zoom in on that a little bit,

00:00:26.661 --> 00:00:30.006
make it easier for us to count,

00:00:30.006 --> 00:00:31.702
and these are just single blocks, ones,

00:00:31.702 --> 00:00:35.869
stacked on top of each
other, so we can count them,

00:00:36.854 --> 00:00:39.971
and we'll see there's one,
two, three, four, five,

00:00:39.971 --> 00:00:42.554
six, seven, eight, nine blocks.

00:00:44.707 --> 00:00:47.932
Nine blocks right here, then moving over,

00:00:47.932 --> 00:00:51.893
now we have columns of ones,
and each of these columns,

00:00:51.893 --> 00:00:56.770
here's nine because nine is
even with this other nine column

00:00:56.770 --> 00:01:00.067
plus one more is 10, so
each of these columns

00:01:00.067 --> 00:01:02.567
has 10 blocks, these are tens.

00:01:04.441 --> 00:01:07.126
How many tens do we
have, we have one, two,

00:01:07.126 --> 00:01:10.166
three, four, five, five sets of 10,

00:01:10.166 --> 00:01:13.249
or 50, so we have 50 blocks here plus

00:01:15.030 --> 00:01:18.051
nine more in that last column.

00:01:18.051 --> 00:01:22.486
Moving over, now we have
these columns of 10,

00:01:22.486 --> 00:01:24.982
but it's several columns
of 10 stuck together

00:01:24.982 --> 00:01:28.117
to make sort of like a slab.

00:01:28.117 --> 00:01:30.563
How many columns of 10 are in this slab?

00:01:30.563 --> 00:01:33.980
There's one, two, three, four, five, six,

00:01:35.362 --> 00:01:38.362
seven, eight, nine 10 columns of 10.

00:01:41.666 --> 00:01:43.638
10 rows of 10 or 10 columns of 10,

00:01:43.638 --> 00:01:47.805
which is a total of 100, so
each of these slabs is 100,

00:01:48.677 --> 00:01:50.872
and how many slabs do we have?

00:01:50.872 --> 00:01:55.606
We have one, and then two,
a second one back there.

00:01:55.606 --> 00:01:58.273
So we have two hundreds, or 200,

00:02:01.333 --> 00:02:05.984
and then finally, scooching
it over a little bit,

00:02:05.984 --> 00:02:08.332
here we have these slabs of 100,

00:02:08.332 --> 00:02:11.364
these sets of 100, all stacked together,

00:02:11.364 --> 00:02:13.704
so there's one set of 100 here,

00:02:13.704 --> 00:02:17.367
then another set behind
it, and another, and so on.

00:02:17.367 --> 00:02:19.120
So let's count how many hundreds this is.

00:02:19.120 --> 00:02:23.287
We have 100, 200, 300, 400,
500, 600, 700, 800, 900,

00:02:27.514 --> 00:02:30.264
and that last one makes it 1,000,

00:02:31.381 --> 00:02:35.548
so these are thousands, and
how many thousands are there?

00:02:37.382 --> 00:02:39.799
There are one, two, so 2,000.

00:02:45.343 --> 00:02:49.010
Two thousands, zooming
back out, we can look

00:02:52.622 --> 00:02:54.437
at all of the amounts we had.

00:02:54.437 --> 00:02:57.099
We had 2,000 blocks plus 200 more blocks

00:02:57.099 --> 00:03:00.971
plus 50 more blocks plus nine blocks,

00:03:00.971 --> 00:03:03.721
or in total we have 2,259 blocks.

00:03:12.735 --> 00:03:14.461
Moving on to this next one, we know

00:03:14.461 --> 00:03:17.363
what these different sizes represent.

00:03:17.363 --> 00:03:20.363
Here this column at the end is ones.

00:03:21.684 --> 00:03:25.101
Right beside it, these are columns of 10.

00:03:26.144 --> 00:03:28.816
We know those are tens, then we don't have

00:03:28.816 --> 00:03:31.858
any of the hundreds,
any of the where we had

00:03:31.858 --> 00:03:34.804
10 sets of 10 making
sort of like a flat slab,

00:03:34.804 --> 00:03:37.493
we don't have any hundreds in this number,

00:03:37.493 --> 00:03:39.701
but we do have these large cubes

00:03:39.701 --> 00:03:42.595
made up of many many many small cubes,

00:03:42.595 --> 00:03:46.762
and those are thousands, because
they were 10 sets of 100.

00:03:48.375 --> 00:03:51.721
So now let's count, we
have one, two, three, four,

00:03:51.721 --> 00:03:55.888
five, six, seven, eight, ones,
which is the same as eight,

00:03:57.267 --> 00:03:59.767
plus one, two, three tens, 30,

00:04:02.935 --> 00:04:06.018
plus no hundreds again, but one, two,

00:04:09.577 --> 00:04:12.244
three thousands, which is 3,000.

00:04:15.777 --> 00:04:17.215
So when we combine these numbers,

00:04:17.215 --> 00:04:20.836
we need to be careful to
remember there are no hundreds.

00:04:20.836 --> 00:04:25.003
Our number will be three
thousand, zero hundreds, and 38.

00:04:29.000 --> 00:04:33.167
3,038 is the number represented
by these place value blocks.

00:04:36.685 --> 00:04:38.486
For this one, I encourage
you to pause the video

00:04:38.486 --> 00:04:40.329
and see if you can figure out on your own

00:04:40.329 --> 00:04:44.496
what number is represented
by the place value blocks.

00:04:46.183 --> 00:04:47.635
And now we can look at it together.

00:04:47.635 --> 00:04:51.802
Let's remember, this is ones,
tens, hundreds, and thousands.

00:04:57.129 --> 00:05:01.296
So looking at our ones, we have
one, two, three, four ones.

00:05:02.727 --> 00:05:06.227
Four ones plus one, two tens, which is 20,

00:05:08.140 --> 00:05:11.354
10 plus 10 is 20, plus now these hundreds.

00:05:11.354 --> 00:05:13.593
There's several hundreds, let's see,

00:05:13.593 --> 00:05:17.343
100, 200, 300, 400, 500,
600, seven hundreds.

00:05:18.540 --> 00:05:21.976
There's seven of the hundreds plus

00:05:21.976 --> 00:05:25.893
only one of the thousands,
which will be 1,000.

00:05:27.896 --> 00:05:29.860
And now to combine this,
to write this all together,

00:05:29.860 --> 00:05:33.027
this will be 1,724 is the number shown

00:05:37.321 --> 00:05:39.031
with these place value blocks.


Identifying symmetrical figures

WEBVTT
Kind: captions
Language: en

00:00:00.674 --> 00:00:03.335
- [Voiceover] Which
shapes are symmetrical?

00:00:03.335 --> 00:00:05.690
To answer this, we need
to know what it means

00:00:05.690 --> 00:00:08.190
for a shape to be symmetrical.

00:00:09.368 --> 00:00:11.576
A shape is symmetrical if it has

00:00:11.576 --> 00:00:14.076
at least one line of symmetry,

00:00:16.027 --> 00:00:17.610
a line of symmetry.

00:00:19.322 --> 00:00:21.363
And now that answer is only helpful

00:00:21.363 --> 00:00:24.533
if we know what a line of symmetry is.

00:00:24.533 --> 00:00:26.866
So let's talk about it.

00:00:26.866 --> 00:00:31.715
A line of symmetry is a line
where we can fold the image

00:00:31.715 --> 00:00:34.632
and have both halves match exactly.

00:00:35.602 --> 00:00:38.472
Let's look at an example.

00:00:38.472 --> 00:00:40.555
Let's maybe draw a circle

00:00:42.171 --> 00:00:44.386
and then we could put
a line on that circle.

00:00:44.386 --> 00:00:48.053
Let's draw a line maybe
somewhere like this.

00:00:49.443 --> 00:00:52.069
This line is a line of symmetry

00:00:52.069 --> 00:00:55.155
if we can take one side of the line

00:00:55.155 --> 00:00:59.209
and fold it onto the other
and have them match exactly.

00:00:59.209 --> 00:01:01.372
So let's take one side,
doesn't matter which one,

00:01:01.372 --> 00:01:03.289
let's say the top side,

00:01:04.820 --> 00:01:06.366
and if we were gonna fold

00:01:06.366 --> 00:01:08.358
this top side down onto the bottom,

00:01:08.358 --> 00:01:12.406
would it match exactly
what is shown under here?

00:01:12.406 --> 00:01:16.573
Let's see, it would probably
look something like this.

00:01:17.763 --> 00:01:19.267
And does that match exactly?

00:01:19.267 --> 00:01:21.023
No, definitely not.

00:01:21.023 --> 00:01:23.856
So this is not a line of symmetry.

00:01:26.366 --> 00:01:28.283
Let's try another line.

00:01:29.229 --> 00:01:30.545
Maybe if we drew a line

00:01:30.545 --> 00:01:34.927
and we'll try to get as close
down the center as we can here

00:01:34.927 --> 00:01:35.760
like this.

00:01:39.301 --> 00:01:40.990
Try to be as close to
the center as possible

00:01:40.990 --> 00:01:42.648
and here if we took one side,

00:01:42.648 --> 00:01:43.853
again it doesn't matter which side,

00:01:43.853 --> 00:01:46.814
let's say over here,
let's say the left side,

00:01:46.814 --> 00:01:50.897
and we folded this left
side onto the right side,

00:01:52.171 --> 00:01:53.801
would it match exactly

00:01:53.801 --> 00:01:56.587
and if our line truly was
in the center of the circle,

00:01:56.587 --> 00:01:58.087
then yes it would,

00:01:59.492 --> 00:02:03.999
which means that this
line is a line of symmetry

00:02:03.999 --> 00:02:07.607
and because we can draw this
line of symmetry on our circle,

00:02:07.607 --> 00:02:10.933
it means that our circle is symmetrical.

00:02:10.933 --> 00:02:12.863
Shapes are symmetrical if they have

00:02:12.863 --> 00:02:15.781
at least one line of symmetry

00:02:15.781 --> 00:02:18.094
and circles have many, many,
many lines of symmetry.

00:02:18.094 --> 00:02:20.602
There was many places we
could have drawn a line

00:02:20.602 --> 00:02:22.329
and folded it so that it worked

00:02:22.329 --> 00:02:24.719
so the two halves matched exactly.

00:02:24.719 --> 00:02:27.080
But here's one and as soon as we find one,

00:02:27.080 --> 00:02:30.382
we know we have a symmetrical shape.

00:02:30.382 --> 00:02:32.353
So let's go back to the
shapes we were given.

00:02:32.353 --> 00:02:34.613
We can start with the triangle.

00:02:34.613 --> 00:02:36.717
If we draw a line, maybe a vertical line,

00:02:36.717 --> 00:02:39.029
let's try to draw it as close
to the middle as possible,

00:02:39.029 --> 00:02:40.696
something like this,

00:02:41.602 --> 00:02:43.455
and we fold, let's take one side,

00:02:43.455 --> 00:02:45.579
if we fold this side over,

00:02:45.579 --> 00:02:48.226
these two lines might match up nicely,

00:02:48.226 --> 00:02:52.393
but this line here is gonna
create something more like this,

00:02:53.263 --> 00:02:56.084
which does not match
what's shown over here,

00:02:56.084 --> 00:02:58.418
so that's not a line of symmetry,

00:02:58.418 --> 00:03:00.375
and anywhere else vertical, same thing.

00:03:00.375 --> 00:03:02.507
We're not gonna have it lined up.

00:03:02.507 --> 00:03:04.924
So let's try maybe a horizontal line.

00:03:04.924 --> 00:03:07.975
Is there anywhere horizontally
we could draw a line?

00:03:07.975 --> 00:03:09.974
And again, I think we're
gonna see the same thing

00:03:09.974 --> 00:03:11.423
that the top and the bottom of the line

00:03:11.423 --> 00:03:14.725
are not gonna match up exactly.

00:03:14.725 --> 00:03:16.487
So maybe one last thing we could try

00:03:16.487 --> 00:03:19.671
is a diagonal line, something like this.

00:03:19.671 --> 00:03:22.583
Maybe this could be our line of symmetry.

00:03:22.583 --> 00:03:24.951
If we fold this bottom side,

00:03:24.951 --> 00:03:27.905
this might line up pretty nice here

00:03:27.905 --> 00:03:32.072
and then this side is gonna
do something like this.

00:03:33.457 --> 00:03:35.505
So it's close, it's the
closest we've gotten,

00:03:35.505 --> 00:03:37.769
but still does not match exactly.

00:03:37.769 --> 00:03:41.865
For it to be a line of symmetry,
it needs to match exactly.

00:03:41.865 --> 00:03:44.895
So we weren't able to find a
way to draw a vertical line

00:03:44.895 --> 00:03:48.433
or a horizontal line or
even the diagonal line.

00:03:48.433 --> 00:03:51.296
So this shape has no lines of symmetry.

00:03:51.296 --> 00:03:54.296
So we can say it is not symmetrical.

00:03:56.396 --> 00:03:59.140
Moving on to the rectangle.

00:03:59.140 --> 00:04:00.129
Let's try here.

00:04:00.129 --> 00:04:02.776
Again, this time maybe
we'll try a horizontal line.

00:04:02.776 --> 00:04:04.943
We can draw one right here

00:04:06.211 --> 00:04:08.143
and if that line truly is in the middle,

00:04:08.143 --> 00:04:10.438
which is what I've tried for,

00:04:10.438 --> 00:04:14.203
then this side should match
up nicely to this one,

00:04:14.203 --> 00:04:17.352
across the top should
match across the bottom

00:04:17.352 --> 00:04:19.985
and these sides, if I was
right at the halfway point,

00:04:19.985 --> 00:04:22.688
should fold over each other also.

00:04:22.688 --> 00:04:25.990
So it has a line of symmetry
so it is symmetrical.

00:04:25.990 --> 00:04:27.731
It has more than one line of symmetry.

00:04:27.731 --> 00:04:31.340
It has another one in
the middle right here.

00:04:31.340 --> 00:04:35.282
But once we've found one, we
know that it's symmetrical.

00:04:35.282 --> 00:04:38.125
And finally, let's look,
we have a pentagon.

00:04:38.125 --> 00:04:40.897
Here again, trying a line
in the middle in some way

00:04:40.897 --> 00:04:43.356
is usually a good place to start.

00:04:43.356 --> 00:04:44.854
We can try to draw a line right

00:04:44.854 --> 00:04:48.021
if this is right down the center here.

00:04:49.624 --> 00:04:52.173
Then if we folded this side,

00:04:52.173 --> 00:04:55.090
should line up nicely to this side,

00:04:56.054 --> 00:04:58.668
this side and this side would overlap

00:04:58.668 --> 00:05:00.849
and these two would match exactly.

00:05:00.849 --> 00:05:05.265
So again, has one line of
symmetry so it is symmetrical

00:05:05.265 --> 00:05:06.505
and just like the rectangle,

00:05:06.505 --> 00:05:08.275
this one had quite a
few lines of symmetry.

00:05:08.275 --> 00:05:10.600
Here's another line of symmetry,

00:05:10.600 --> 00:05:13.337
here's another line of symmetry,

00:05:13.337 --> 00:05:16.395
here's one more line of symmetry

00:05:16.395 --> 00:05:18.269
and so it has quite a few.

00:05:18.269 --> 00:05:20.686
It has it looks like one, two, three,

00:05:20.686 --> 00:05:22.644
four lines of symmetry,

00:05:22.644 --> 00:05:25.751
but as long as it has
one, it is symmetrical.

00:05:25.751 --> 00:05:27.687
So of the shapes we were given,

00:05:27.687 --> 00:05:31.687
the rectangle and the
pentagon were symmetrical.


Classifying shapes by lines and angles

WEBVTT
Kind: captions
Language: en

00:00:01.150 --> 00:00:04.064
- [Voiceover] Which shape
matches all three clues?

00:00:04.064 --> 00:00:06.119
So here we have three clues

00:00:06.119 --> 00:00:09.296
and we want to see which shape down below

00:00:09.296 --> 00:00:13.037
matches all three of these statements.

00:00:13.037 --> 00:00:14.987
So let's start with the first clue.

00:00:14.987 --> 00:00:18.352
The first clue says the
shape is a quadrilateral,

00:00:18.352 --> 00:00:20.352
quad meaning four-sided.

00:00:23.994 --> 00:00:25.415
So looking down here at our shapes,

00:00:25.415 --> 00:00:27.853
let's see which ones
match that first clue.

00:00:27.853 --> 00:00:31.353
Shape one has one, two, three, four sides.

00:00:32.409 --> 00:00:35.049
So it is a quadrilateral.

00:00:35.049 --> 00:00:38.549
Shape two has one, two, three, four sides.

00:00:40.023 --> 00:00:42.767
So also a quadrilateral.

00:00:42.767 --> 00:00:45.434
Shape three has one, two, three,

00:00:46.397 --> 00:00:48.230
four, five, six sides.

00:00:50.388 --> 00:00:52.613
So it is not a quadrilateral.

00:00:52.613 --> 00:00:55.413
It's a six-sided shape or a hexagon.

00:00:55.413 --> 00:00:56.688
So we can rule that one out.

00:00:56.688 --> 00:00:58.015
It doesn't match clue one

00:00:58.015 --> 00:01:01.557
so there's no way it can
match all three clues.

00:01:01.557 --> 00:01:05.724
And finally shape four has one,
two, three, four sides again

00:01:06.907 --> 00:01:09.407
so it is also a quadrilateral.

00:01:10.334 --> 00:01:14.006
So after clue one, we still
have three possible answers.

00:01:14.006 --> 00:01:16.980
This first shape, the second
shape, and the fourth shape

00:01:16.980 --> 00:01:20.897
all match clue one,
they're all quadrilaterals.

00:01:22.420 --> 00:01:26.587
Looking at clue two, it says
our shape has no right angles.

00:01:29.017 --> 00:01:31.657
Right angles are also 90 degree angles.

00:01:31.657 --> 00:01:33.071
Right angles are 90 degree angles

00:01:33.071 --> 00:01:36.618
and they look something like this

00:01:36.618 --> 00:01:39.845
and we often see them marked
with a square in the middle

00:01:39.845 --> 00:01:41.698
because they are sort
of like square angles.

00:01:41.698 --> 00:01:45.919
We can create a square from
the opening that they form,

00:01:45.919 --> 00:01:47.368
that these angles form.

00:01:47.368 --> 00:01:49.451
So this is a right angle.

00:01:50.596 --> 00:01:52.268
Looking now down at our shapes,

00:01:52.268 --> 00:01:56.329
we can see right away on shape
one has two right angles.

00:01:56.329 --> 00:01:59.429
There's a square corner
and another square corner.

00:01:59.429 --> 00:02:01.422
So this has right angles,

00:02:01.422 --> 00:02:04.967
but the shape we're looking
for has no right angles

00:02:04.967 --> 00:02:07.467
so we can rule this shape out.

00:02:09.335 --> 00:02:12.463
Shape two does not have any right angles.

00:02:12.463 --> 00:02:15.172
These are not squared off corners.

00:02:15.172 --> 00:02:17.415
And same with shape four, no right angles.

00:02:17.415 --> 00:02:21.128
So both of those still match
both clues one and two.

00:02:21.128 --> 00:02:22.354
So we have two shapes left.

00:02:22.354 --> 00:02:26.521
They're both quadrilaterals
and they have no right angles.

00:02:27.467 --> 00:02:30.491
And finally our last clue,
the shape has four sides,

00:02:30.491 --> 00:02:33.291
we knew that 'cause it
was a quadrilateral,

00:02:33.291 --> 00:02:36.272
and those sides are of equal length.

00:02:36.272 --> 00:02:40.758
That means each of the
sides is the same length.

00:02:40.758 --> 00:02:43.350
Looking at this first one
that we have left, shape two,

00:02:43.350 --> 00:02:46.819
it looks like these sides on the ends

00:02:46.819 --> 00:02:50.929
are shorter than the
sides going up and down.

00:02:50.929 --> 00:02:53.799
So it looks like they
are not equal length.

00:02:53.799 --> 00:02:56.954
So we can rule this one out.

00:02:56.954 --> 00:02:59.748
But let's be sure this last one works.

00:02:59.748 --> 00:03:03.252
Here the sides all look like
they're the same length,

00:03:03.252 --> 00:03:05.550
but the way we can know
for sure that they are

00:03:05.550 --> 00:03:07.217
is these tick marks.

00:03:08.532 --> 00:03:10.336
Any time you have these marks,

00:03:10.336 --> 00:03:12.586
it's saying that any side that has

00:03:12.586 --> 00:03:16.250
the same amount of marks
is the same length.

00:03:16.250 --> 00:03:19.893
All four of these sides
have exactly one tick mark

00:03:19.893 --> 00:03:22.560
so they are all equal in length.

00:03:23.418 --> 00:03:26.037
So shape four matches all three clues.

00:03:26.037 --> 00:03:29.632
It is a quadrilateral,
there are no right angles

00:03:29.632 --> 00:03:32.799
and it has four sides of equal length.

00:03:34.041 --> 00:03:36.374
So shape four is our answer.


Angles in circles word problem

WEBVTT
Kind: captions
Language: en

00:00:01.299 --> 00:00:03.169
- [Voiceover] If Arianna
turns the stove dial

00:00:03.169 --> 00:00:05.531
135 degrees to the right,

00:00:05.531 --> 00:00:08.271
what setting will the dial be on?

00:00:08.271 --> 00:00:10.637
So two very important things up here.

00:00:10.637 --> 00:00:14.762
First she's turning the dial 135 degrees.

00:00:14.762 --> 00:00:16.879
And which way is she turning the dial?

00:00:16.879 --> 00:00:19.879
She's turning the dial to the right.

00:00:20.779 --> 00:00:23.534
So here's our dial it's facing up.

00:00:23.534 --> 00:00:25.117
This red dial right here.

00:00:25.117 --> 00:00:27.493
Facing up sort of like on a clock.

00:00:27.493 --> 00:00:32.341
And we're going to be turning
the dial to the right.

00:00:32.341 --> 00:00:34.088
And how far to the right?

00:00:34.088 --> 00:00:35.088
135 degrees.

00:00:36.340 --> 00:00:40.507
So this dial will turn until
it's reached 135 degrees.

00:00:42.072 --> 00:00:43.529
So how can we figure out if we start

00:00:43.529 --> 00:00:45.438
turning this dial when to stop?

00:00:45.438 --> 00:00:48.224
When it's reached 135 degrees.

00:00:48.224 --> 00:00:52.081
Well, one common way would
be to use a protractor.

00:00:52.081 --> 00:00:53.665
We could set up our protractor,

00:00:53.665 --> 00:00:56.204
measure out 135 degrees.

00:00:56.204 --> 00:00:57.911
But in this case we can't do that

00:00:57.911 --> 00:00:59.448
'cause we don't have a protractor.

00:00:59.448 --> 00:01:01.023
So let's use some other information.

00:01:01.023 --> 00:01:03.219
Some other stuff we know about angles

00:01:03.219 --> 00:01:05.792
to see if we can solve this.

00:01:05.792 --> 00:01:09.461
One thing I know, one
angle that we see a lot

00:01:09.461 --> 00:01:11.211
is a 90 degree angle.

00:01:12.783 --> 00:01:14.491
And a 90 degree angle

00:01:14.491 --> 00:01:17.786
if we start up at the top like our dial

00:01:17.786 --> 00:01:19.453
and turn 90 degrees,

00:01:21.118 --> 00:01:23.533
we're gonna end up with
an angle like this.

00:01:23.533 --> 00:01:25.818
An angle where we could put a square

00:01:25.818 --> 00:01:27.814
in the middle and finish the square.

00:01:27.814 --> 00:01:29.645
Well it's like a square angle.

00:01:29.645 --> 00:01:31.843
So this is a 90 degree angle.

00:01:31.843 --> 00:01:33.984
So coming over to our dial,

00:01:33.984 --> 00:01:38.025
if we start at the top
and we go 90 degrees.

00:01:38.025 --> 00:01:41.939
So we start here at the
top and we go 90 degrees,

00:01:41.939 --> 00:01:44.892
we'd end up on the low setting.

00:01:44.892 --> 00:01:45.809
90 degrees.

00:01:47.181 --> 00:01:50.011
But we're not going 90 we're going 135

00:01:50.011 --> 00:01:51.880
which is more than 90 degrees.

00:01:51.880 --> 00:01:53.418
So here's one clue.

00:01:53.418 --> 00:01:56.416
We know we're going farther
than the low setting.

00:01:56.416 --> 00:01:58.204
We don't know how much farther.

00:01:58.204 --> 00:02:02.182
We're definitely gonna
go past the low setting.

00:02:02.182 --> 00:02:04.500
Another angle I could use to help me

00:02:04.500 --> 00:02:05.829
is the straight angle.

00:02:05.829 --> 00:02:06.829
180 degrees.

00:02:08.854 --> 00:02:11.216
If 180 degree angle again starts

00:02:11.216 --> 00:02:13.325
at the top like our knob is currently.

00:02:13.325 --> 00:02:14.696
Like our dial.

00:02:14.696 --> 00:02:16.812
It will go all the way around

00:02:16.812 --> 00:02:20.229
until we have a straight angle like this.

00:02:22.078 --> 00:02:23.653
So again, looking at our knob,

00:02:23.653 --> 00:02:25.857
if we started at the top and we went

00:02:25.857 --> 00:02:27.440
around 180 degrees,

00:02:29.337 --> 00:02:33.366
we would end up facing
straight down at medium.

00:02:33.366 --> 00:02:35.533
This would be 180 degrees.

00:02:38.674 --> 00:02:40.786
So where does 135 fall?

00:02:40.786 --> 00:02:44.703
Well 135 falls somewhere
in between 90 and 180.

00:02:46.060 --> 00:02:48.727
90 was not far enough of a turn.

00:02:49.670 --> 00:02:52.784
And 180 was too far of a turn.

00:02:52.784 --> 00:02:54.821
So we want something in the middle.

00:02:54.821 --> 00:02:57.017
And what setting is in the middle

00:02:57.017 --> 00:02:58.850
of the 90 and the 180?

00:02:59.812 --> 00:03:01.981
Right here in the middle of them

00:03:01.981 --> 00:03:03.148
is medium-low.

00:03:05.813 --> 00:03:09.767
So turning our stove to
135 degrees to the right

00:03:09.767 --> 00:03:12.517
will set our stove to medium-low.


Measuring angles with a circular protractor

WEBVTT
Kind: captions
Language: en

00:00:00.780 --> 00:00:03.232
- [Voiceover] Measure
the angle in degrees.

00:00:03.232 --> 00:00:05.180
So here we have this blue angle

00:00:05.180 --> 00:00:07.557
that we want to measure in degrees,

00:00:07.557 --> 00:00:10.765
and it's sitting on top of this circle.

00:00:10.765 --> 00:00:13.829
That circle is actually a protractor.

00:00:13.829 --> 00:00:16.146
Sometimes we see, and maybe
what you're used to seeing,

00:00:16.146 --> 00:00:18.976
is protractors that are
more semicircle shaped,

00:00:18.976 --> 00:00:21.262
something like this.

00:00:21.262 --> 00:00:23.480
And those semicircle protractors measure

00:00:23.480 --> 00:00:25.563
from zero to 180 degrees.

00:00:27.941 --> 00:00:30.483
Which is good, but a
circle is even better.

00:00:30.483 --> 00:00:31.805
A full circle is better because

00:00:31.805 --> 00:00:35.729
an angle can measure up to 360 degrees.

00:00:35.729 --> 00:00:39.778
So a full circle allows us to
measure and angle of any size,

00:00:39.778 --> 00:00:43.361
instead of only an
angle up to 180 degrees.

00:00:44.641 --> 00:00:47.442
Now the way we're gonna measure this angle

00:00:47.442 --> 00:00:50.888
is the same way we would
on a semicircle protractor.

00:00:50.888 --> 00:00:52.256
The first thing we wanna do is

00:00:52.256 --> 00:00:55.694
make sure one of our
rays lines up to zero.

00:00:55.694 --> 00:00:57.576
So here's one of our rays,

00:00:57.576 --> 00:00:59.893
and it's lining up to
zero on the protractor.

00:00:59.893 --> 00:01:03.258
So that's nice, it's
already lined up for us.

00:01:03.258 --> 00:01:04.881
And then we're gonna measure the opening

00:01:04.881 --> 00:01:09.331
all the way to the other
ray, to right here.

00:01:09.331 --> 00:01:12.243
And so if our angle only
measured opened up this far,

00:01:12.243 --> 00:01:13.899
it would be a 10 degree angle.

00:01:13.899 --> 00:01:15.512
If let's say it opened to here,

00:01:15.512 --> 00:01:17.627
it would be a 50 degree angle.

00:01:17.627 --> 00:01:20.771
But our angle measures
all the way to here,

00:01:20.771 --> 00:01:22.354
to the 160 degrees.

00:01:23.467 --> 00:01:27.050
So 160 degrees is the
measure of our angle.

00:01:29.986 --> 00:01:33.761
And again, when you measure
on a circle protractor,

00:01:33.761 --> 00:01:36.371
or any protractor for that matter,

00:01:36.371 --> 00:01:39.814
you're gonna line one ray up to the zero,

00:01:39.814 --> 00:01:43.986
and then measure the opening
'til you get to the other ray,

00:01:43.986 --> 00:01:47.653
which in this case
opened up to 160 degrees.


Decomposing angles

WEBVTT
Kind: captions
Language: en

00:00:00.273 --> 00:00:04.083
- [Voiceover] What is
the measure of angle EAC?

00:00:04.083 --> 00:00:06.494
So we have this symbol
here, which means angle,

00:00:06.494 --> 00:00:09.600
and then these three letters, EAC.

00:00:09.600 --> 00:00:12.732
Now to measure angle EAC, we need to first

00:00:12.732 --> 00:00:16.065
find angle EAC down here on our picture,

00:00:16.918 --> 00:00:19.241
and the way we can do that
is use these three letters

00:00:19.241 --> 00:00:21.952
and we're gonna go in the
order that they're given to us.

00:00:21.952 --> 00:00:24.169
So the first letter we're told is E,

00:00:24.169 --> 00:00:28.556
so the first letter we'll
find down here is E.

00:00:28.556 --> 00:00:32.306
From there, we'll go to
the second letter, A.

00:00:33.442 --> 00:00:37.275
And then finally, we go
to our last letter, C.

00:00:38.408 --> 00:00:40.817
Again, in the order that
they were told to us.

00:00:40.817 --> 00:00:44.150
So this opening right here is our angle.

00:00:45.132 --> 00:00:49.049
We wanna know how many
degrees is this opening?

00:00:50.531 --> 00:00:52.873
The most common way to measure an angle

00:00:52.873 --> 00:00:54.384
would be to use a protractor,

00:00:54.384 --> 00:00:56.105
but we're not given a protractor,

00:00:56.105 --> 00:00:59.452
so we can't do that, but we
do have enough information

00:00:59.452 --> 00:01:03.432
on this diagram down here to solve this.

00:01:03.432 --> 00:01:07.015
What we can see is that
our large angle EAC

00:01:07.867 --> 00:01:09.948
is made up of two smaller angles.

00:01:09.948 --> 00:01:12.115
This first one, angle EAD.

00:01:17.292 --> 00:01:19.292
Right here, angle EAD...

00:01:21.979 --> 00:01:25.646
plus from there, it
picks up with angle DAC.

00:01:29.036 --> 00:01:29.869
Angle DAC.

00:01:33.712 --> 00:01:38.432
These two angles, this
first one from here to here,

00:01:38.432 --> 00:01:41.217
and then the second from here to here,

00:01:41.217 --> 00:01:45.181
when they're combined,
they make the same size

00:01:45.181 --> 00:01:47.061
opening as our angle.

00:01:47.061 --> 00:01:49.488
So if we can combine these two angles,

00:01:49.488 --> 00:01:52.334
we will know the measure of our angle

00:01:52.334 --> 00:01:54.168
because again, these two combined

00:01:54.168 --> 00:01:56.668
are equal to our entire angle.

00:01:57.579 --> 00:02:00.124
So let's do that, starting with EAD,

00:02:00.124 --> 00:02:02.914
we can see we're told, it's 60 degrees.

00:02:02.914 --> 00:02:05.164
That's a 60 degree opening.

00:02:06.933 --> 00:02:10.183
Plus angle DAC has a 75 degree opening,

00:02:12.396 --> 00:02:16.563
and so if we combine that,
if we go 60 degrees to here

00:02:17.900 --> 00:02:20.115
plus another 75 down to here,

00:02:20.115 --> 00:02:22.647
we've covered our entire angle.

00:02:22.647 --> 00:02:26.064
Our entire opening in 60 plus another 75.

00:02:27.061 --> 00:02:31.730
So we can add these to solve
for the measure of our angle.

00:02:31.730 --> 00:02:35.313
Six tens plus seven
tens is 13 tens or 130.

00:02:37.988 --> 00:02:39.949
13 and then that zero is there

00:02:39.949 --> 00:02:41.402
because we're talking about tens.

00:02:41.402 --> 00:02:44.902
Plus zero ones and five ones is five ones.

00:02:47.646 --> 00:02:50.646
And so 130 plus five is 135 degrees.

00:02:54.046 --> 00:02:58.592
So the measure of our
entire angle, angle EAC

00:02:58.592 --> 00:02:59.842
is 135 degrees.


The Atlantic slave trade

WEBVTT
Kind: captions
Language: en

00:00:00.123 --> 00:00:01.124
- [Voiceover] Hey, Becca.

00:00:01.124 --> 00:00:02.116
- [Voiceover] Hey, Kim.

00:00:02.116 --> 00:00:03.904
So, in this video we're
gonna continue talking

00:00:03.904 --> 00:00:06.383
about how this arbitrary racial hierarchy

00:00:06.383 --> 00:00:08.763
was established in
America, specifically about

00:00:08.763 --> 00:00:11.095
the beginning of the Atlantic slave trade

00:00:11.095 --> 00:00:13.840
and how our society became so stratified

00:00:13.840 --> 00:00:15.607
by race so early on.

00:00:15.607 --> 00:00:16.605
- [Voiceover] Okay, interesting.

00:00:16.605 --> 00:00:19.084
- [Voiceover] The Portuguese
had started to buy slaves

00:00:19.084 --> 00:00:21.863
and bring them to Europe as early as 1526,

00:00:21.863 --> 00:00:25.278
but it wasn't until the 1600s
when slaves were transported

00:00:25.278 --> 00:00:27.611
across the Atlantic and sold

00:00:28.690 --> 00:00:30.683
into servitude in the new colonies.

00:00:30.683 --> 00:00:31.681
- [Voiceover] All right,

00:00:31.681 --> 00:00:33.527
so I'm gonna draw us a
little Atlantic world here

00:00:33.527 --> 00:00:37.360
and please forgive my
terrible maps womanship.

00:00:38.914 --> 00:00:40.580
- [Voiceover] This was directly connected

00:00:40.580 --> 00:00:42.652
to this competition

00:00:42.652 --> 00:00:46.819
between European powers for a
stronghold in the new world,

00:00:47.931 --> 00:00:50.048
so this began with the Spanish

00:00:50.048 --> 00:00:52.564
in 1492 with Christopher Columbus,

00:00:52.564 --> 00:00:57.200
but slowly also the English,
the Dutch, the Portuguese,

00:00:57.200 --> 00:01:00.509
everyone is trying to
establish their own colony

00:01:00.509 --> 00:01:04.485
that they could hopefully gain
a lot of new resources from

00:01:04.485 --> 00:01:07.782
and just establish glory,
really, in this new world

00:01:07.782 --> 00:01:11.232
and having slaves was a really big part

00:01:11.232 --> 00:01:12.885
of being able to do that.

00:01:12.885 --> 00:01:14.365
- [Voiceover] Yeah, I
mean, if you think about,

00:01:14.365 --> 00:01:17.517
just imagine, kind of, living
in, I don't know, England,

00:01:17.517 --> 00:01:20.934
and hearing about how well Spain is doing

00:01:21.865 --> 00:01:26.032
getting all this gold and
silver from the new world,

00:01:27.960 --> 00:01:31.267
so Spain is definitely improving

00:01:31.267 --> 00:01:34.234
it's national standing in Europe

00:01:34.234 --> 00:01:38.949
and the rest of Europe is
thinking, "Mm, sounds to me

00:01:38.949 --> 00:01:41.654
like we need to get in on this game."

00:01:41.654 --> 00:01:43.359
- [Voiceover] And so,
to get in on the game,

00:01:43.359 --> 00:01:45.613
really what the European powers needed

00:01:45.613 --> 00:01:48.437
were laborers to work in
these new plantations.

00:01:48.437 --> 00:01:51.285
As you may know, when
the Europeans came over

00:01:51.285 --> 00:01:53.276
they brought a ton of disease

00:01:53.276 --> 00:01:56.057
which decimated these
Native American populations

00:01:56.057 --> 00:01:59.290
which they had previously used to labor

00:01:59.290 --> 00:02:01.014
through the encomienda system

00:02:01.014 --> 00:02:03.394
so the African slaves
actually had immunities

00:02:03.394 --> 00:02:07.109
to these diseases that the European powers

00:02:07.109 --> 00:02:09.141
really wanted to capitalize upon.

00:02:09.141 --> 00:02:10.685
- [Voiceover] Yeah, I think
what's interesting here

00:02:10.685 --> 00:02:13.024
and the reason that I drew this map

00:02:13.024 --> 00:02:14.708
is because I think it
really helps us understand

00:02:14.708 --> 00:02:18.208
why it was that people who lived over here

00:02:19.097 --> 00:02:22.014
had no immunity to European disease

00:02:23.891 --> 00:02:27.305
and why the people who lived over here did

00:02:27.305 --> 00:02:28.930
because if you think about sailing,

00:02:28.930 --> 00:02:32.082
so here's Europe, and
people had been trading

00:02:32.082 --> 00:02:37.080
with Europe and West Africa
and into the Middle East

00:02:37.080 --> 00:02:40.136
to here for hundreds of years.

00:02:40.136 --> 00:02:41.096
- [Voiceover] Exactly.

00:02:41.096 --> 00:02:43.562
- [Voiceover] So that
gave them plenty of time

00:02:43.562 --> 00:02:46.447
to kind of build up
immunities to each other

00:02:46.447 --> 00:02:49.756
so not only do people in Africa

00:02:49.756 --> 00:02:52.559
have the immunity to disease,

00:02:52.559 --> 00:02:56.948
they're also kind of a
readily available labor source

00:02:56.948 --> 00:03:01.234
because the practice of
taking prisoners of war

00:03:01.234 --> 00:03:04.976
and selling them as slaves
on the west coast of Africa

00:03:04.976 --> 00:03:07.594
was already established so Europeans

00:03:07.594 --> 00:03:09.196
are looking for a labor force that

00:03:09.196 --> 00:03:10.824
isn't gonna die of disease

00:03:10.824 --> 00:03:13.672
and there are people being sold as slaves

00:03:13.672 --> 00:03:15.745
on the west coast of Africa already.

00:03:15.745 --> 00:03:16.801
- [Voiceover] So, at this point,

00:03:16.801 --> 00:03:19.361
there are kind of two
competing labor forces

00:03:19.361 --> 00:03:23.113
between the Native Americans
and the African slaves.

00:03:23.113 --> 00:03:25.659
Colonists start realizing
that the African slaves

00:03:25.659 --> 00:03:29.077
are actually a more economical labor force

00:03:29.077 --> 00:03:33.682
than the Native Americans
since they had this immunity.

00:03:33.682 --> 00:03:35.694
- [Voiceover] Right,
and they're also easier

00:03:35.694 --> 00:03:38.947
to keep as slaves for Europeans

00:03:38.947 --> 00:03:41.646
because they're not on
their home territory.

00:03:41.646 --> 00:03:43.458
You know, if someone
showed up to your town

00:03:43.458 --> 00:03:45.385
and said, "You're my slave now,"

00:03:45.385 --> 00:03:47.498
you're gonna run away to the hills

00:03:47.498 --> 00:03:49.977
and they don't know anything
about where your town is

00:03:49.977 --> 00:03:51.095
so you're fine, right?

00:03:51.095 --> 00:03:54.795
It's hard to enslave people
on their home territory,

00:03:54.795 --> 00:03:57.124
but if you are buying someone

00:03:57.124 --> 00:03:58.897
who has been wrestled away from

00:03:58.897 --> 00:04:01.902
their home in Central Africa,

00:04:01.902 --> 00:04:04.385
brought to the coast, they're with people

00:04:04.385 --> 00:04:06.457
who don't even speak the
same language as them,

00:04:06.457 --> 00:04:09.683
they're put on a ship to the new world

00:04:09.683 --> 00:04:11.494
which is incredibly deadly,

00:04:11.494 --> 00:04:15.536
say probably about 30%
of enslaved Africans

00:04:15.536 --> 00:04:18.607
who were put in what was
called the middle passage

00:04:18.607 --> 00:04:20.524
died during the voyage.

00:04:21.875 --> 00:04:23.053
- [Voiceover] I think
that's a really good point

00:04:23.053 --> 00:04:25.389
and the reason that some colonists

00:04:25.389 --> 00:04:27.564
actually preferred Native American slaves

00:04:27.564 --> 00:04:31.244
is because of their knowledge
of the land and agriculture.

00:04:31.244 --> 00:04:33.944
So, the subordination of
both the Native Americans

00:04:33.944 --> 00:04:36.991
and the African slaves led
to lots of intermarriage

00:04:36.991 --> 00:04:40.364
between the two groups
and so, in the colonies,

00:04:40.364 --> 00:04:42.355
there became a sense of racial mixing

00:04:42.355 --> 00:04:44.427
that we had never seen before.

00:04:44.427 --> 00:04:46.252
- [Voiceover] Interesting,
and I can see how this might

00:04:46.252 --> 00:04:49.245
pose a problem if you're
trying to figure out

00:04:49.245 --> 00:04:52.185
who should be a slave and who should not

00:04:52.185 --> 00:04:55.114
because if you have someone
who belongs to both groups,

00:04:55.114 --> 00:04:56.397
where do you categorize them?

00:04:56.397 --> 00:04:58.795
- [Voiceover] So, a lot of the
Spanish that were coming over

00:04:58.795 --> 00:05:01.761
had trouble distinguishing
who was supposed to be a slave

00:05:01.761 --> 00:05:03.911
and who was a Native American

00:05:03.911 --> 00:05:05.761
as these two groups intermarried?

00:05:05.761 --> 00:05:08.129
So let's check out this painting
to learn a little bit more

00:05:08.129 --> 00:05:10.907
about how the different
groups were mixing at the time

00:05:10.907 --> 00:05:13.525
and how racial hierarchy really solidified

00:05:13.525 --> 00:05:14.903
at this time period.

00:05:14.903 --> 00:05:16.027
- [Voiceover] You can definitely see that

00:05:16.027 --> 00:05:19.156
they've put things in
multiple layers here.

00:05:19.156 --> 00:05:23.870
Here's Virgin Mary, her,
sort of representation of God

00:05:23.870 --> 00:05:25.983
or the higher power and then here you see

00:05:25.983 --> 00:05:30.150
the Spanish, whites, and
below that Native Americans

00:05:31.712 --> 00:05:35.938
who might be the offspring
of white Spanish settlers

00:05:35.938 --> 00:05:37.688
and Native Americans.

00:05:39.102 --> 00:05:41.383
- [Voiceover] A Spanish
and a Native American,

00:05:41.383 --> 00:05:43.311
that was called mestizos, right?

00:05:43.311 --> 00:05:44.309
- [Voiceover] Right.

00:05:44.309 --> 00:05:46.666
Or they might be the offspring

00:05:46.666 --> 00:05:49.583
of a Native American and an African

00:05:50.648 --> 00:05:54.398
and those people were
referred to as creoles.

00:05:55.888 --> 00:05:57.835
So there's a very complex system

00:05:57.835 --> 00:06:02.002
of racial hierarchy in this
Spanish society basically,

00:06:02.978 --> 00:06:07.145
organized around how much
white blood a person had,

00:06:09.191 --> 00:06:12.666
the more privileges and rights
you had in their society.

00:06:12.666 --> 00:06:14.739
- [Voiceover] And you see
the inverse in early America,

00:06:14.739 --> 00:06:17.258
right, in the early 1800s,

00:06:17.258 --> 00:06:20.383
when even one drop of African blood would

00:06:20.383 --> 00:06:22.417
make a person a slave.

00:06:22.417 --> 00:06:24.636
- [Voiceover] Right, and that's one thing

00:06:24.636 --> 00:06:26.587
that is always very confusing even to

00:06:26.587 --> 00:06:27.968
the people of the time period

00:06:27.968 --> 00:06:29.693
because it would be possible for someone

00:06:29.693 --> 00:06:31.096
who looked quite light
skinned to still be enslaved

00:06:31.096 --> 00:06:33.576
by virtue of their parentage.

00:06:33.576 --> 00:06:35.527
- [Voiceover] Exactly and
so this was the system

00:06:35.527 --> 00:06:39.101
by which society, in the
early colonial time period,

00:06:39.101 --> 00:06:41.314
was organized around a completely

00:06:41.314 --> 00:06:43.692
arbitrary factor like race.

00:06:43.692 --> 00:06:46.392
It was simply the easiest
way to identify people

00:06:46.392 --> 00:06:48.385
and create a working class.

00:06:48.385 --> 00:06:50.312
- [Voiceover] And, as we move forward,

00:06:50.312 --> 00:06:53.690
as the English begin
to settle North America

00:06:53.690 --> 00:06:57.628
and shortly after their
settlement import African slaves,

00:06:57.628 --> 00:07:00.250
the United States will become heir

00:07:00.250 --> 00:07:02.204
to a version of this system.


Christopher Columbus part 2

WEBVTT
Kind: captions
Language: en

00:00:00.407 --> 00:00:01.342
- [Voiceover] Hey, Becca.

00:00:01.342 --> 00:00:02.207
- [Voiceover] Hey, Kim.

00:00:02.207 --> 00:00:03.621
- [Voiceover] All right,
so you've brought me here

00:00:03.621 --> 00:00:07.744
to talk about Columbus, and
the origins of Columbus Day.

00:00:07.744 --> 00:00:10.174
So, what's the deal with
Christopher Columbus?

00:00:10.174 --> 00:00:12.137
Was he a good guy?

00:00:12.137 --> 00:00:13.328
- [Voiceover] So that's
a great question, Kim,

00:00:13.328 --> 00:00:14.860
and it's something that historians

00:00:14.860 --> 00:00:16.774
and people across the United States

00:00:16.774 --> 00:00:19.756
have argued about for over a century now,

00:00:19.756 --> 00:00:22.525
since we started celebrating
Columbus Day, especially.

00:00:22.525 --> 00:00:24.441
You always see a lot of op-eds

00:00:24.441 --> 00:00:27.291
and a lot of people
arguing on Columbus Day

00:00:27.291 --> 00:00:29.127
exactly about that question.

00:00:29.127 --> 00:00:30.559
So, in the last video,

00:00:30.559 --> 00:00:32.759
I discussed why Christopher Columbus

00:00:32.759 --> 00:00:34.672
wanted to come to the New World,

00:00:34.672 --> 00:00:37.562
and what happened when he
arrived in the Caribbean.

00:00:37.562 --> 00:00:38.426
So in this video,

00:00:38.426 --> 00:00:40.656
we'll talk a little bit
more about the implications

00:00:40.656 --> 00:00:42.749
of Christopher Columbus's voyage,

00:00:42.749 --> 00:00:45.025
and his legacy and how
it's been remembered

00:00:45.025 --> 00:00:46.474
in the United States.

00:00:46.474 --> 00:00:48.457
- [Voiceover] All right,
so between the good,

00:00:48.457 --> 00:00:51.681
the bad, and the ugly
of Christopher Columbus,

00:00:51.681 --> 00:00:54.155
please tell me that we
can have a Venn diagram.

00:00:54.155 --> 00:00:55.627
Can we have a Venn diagram?

00:00:55.627 --> 00:00:57.452
- [Voiceover] We can
definitely have a Venn diagram.

00:00:57.452 --> 00:01:01.411
So I will make a Venn
diagram of the implications

00:01:01.411 --> 00:01:05.617
or impact of Christopher
Columbus's voyage.

00:01:05.617 --> 00:01:09.691
So this is kind of the
bad, and this is the good.

00:01:09.691 --> 00:01:11.444
- [Voiceover] All right,
and in between we've got,

00:01:11.444 --> 00:01:12.878
I guess, yellow.

00:01:12.878 --> 00:01:15.019
- [Voiceover] We'll talk
about that over here.

00:01:15.019 --> 00:01:16.197
- [Voiceover] I like
how we're talking about

00:01:16.197 --> 00:01:18.206
kind of the impact of
Christopher Columbus,

00:01:18.206 --> 00:01:20.191
because I think that's most important

00:01:20.191 --> 00:01:22.198
from a historical standpoint.

00:01:22.198 --> 00:01:25.703
Not whether or not he,
personally, was a good guy,

00:01:25.703 --> 00:01:28.997
but whether what he did on the aggregate

00:01:28.997 --> 00:01:32.652
has been positive or
negative for world history.

00:01:32.652 --> 00:01:33.485
- [Voiceover] Definitely.

00:01:33.485 --> 00:01:35.152
So, on the good side,

00:01:35.152 --> 00:01:37.933
a lot of historians and
people in the United States

00:01:37.933 --> 00:01:39.839
like to commemorate Christopher Columbus

00:01:39.839 --> 00:01:43.003
for how amazing he was
at navigating the sea.

00:01:43.003 --> 00:01:45.844
He was the first person
to cross the Atlantic,

00:01:45.844 --> 00:01:47.502
and he did it in only five weeks.

00:01:47.502 --> 00:01:49.652
So, he was a really amazing navigator,

00:01:49.652 --> 00:01:52.746
and in that process he
really connected two worlds

00:01:52.746 --> 00:01:55.094
that were otherwise completely distant,

00:01:55.094 --> 00:01:57.970
and really, had no idea
that the other existed.

00:01:57.970 --> 00:02:00.901
- [Voiceover] Okay, so he
didn't discover the New World,

00:02:00.901 --> 00:02:03.703
because the people who
lived in the New World

00:02:03.703 --> 00:02:05.142
had already discovered it,

00:02:05.142 --> 00:02:08.891
but he did connect the
European and African worlds

00:02:08.891 --> 00:02:10.974
with the American worlds.

00:02:12.315 --> 00:02:13.148
- [Voiceover] Exactly, I think that's

00:02:13.148 --> 00:02:14.320
a really good distinction to make.

00:02:14.320 --> 00:02:17.474
He connected, but he did not discover.

00:02:17.474 --> 00:02:19.787
And so a lot of people like to think that

00:02:19.787 --> 00:02:22.041
something we should remember
Christopher Columbus for

00:02:22.041 --> 00:02:24.027
is that he discovered the United States.

00:02:24.027 --> 00:02:26.889
Again, as you can see in my last video,

00:02:26.889 --> 00:02:28.139
he did not discover the United States,

00:02:28.139 --> 00:02:30.709
he actually never went to North America,

00:02:30.709 --> 00:02:32.742
and the person that we
actually have to credit that

00:02:32.742 --> 00:02:33.910
is Leif Ericson.

00:02:33.910 --> 00:02:35.932
And so, can you tell me a
little bit about Leif Ericson?

00:02:35.932 --> 00:02:38.806
- [Voiceover] Leif Ericson was a

00:02:38.806 --> 00:02:41.877
Viking navigator, that
might be all I've got,

00:02:41.877 --> 00:02:43.907
but Vikings were a lot earlier, right?

00:02:43.907 --> 00:02:47.181
- [Voiceover] Yeah, so the
Vikings came to North America

00:02:47.181 --> 00:02:49.904
through what is now Alaska

00:02:49.904 --> 00:02:53.275
400, 500 years before
Christopher Columbus.

00:02:53.275 --> 00:02:57.013
And so they are the people
that actually "discovered"

00:02:57.013 --> 00:02:59.677
North America despite the Native Americans

00:02:59.677 --> 00:03:00.656
that were already there.

00:03:00.656 --> 00:03:04.464
They were the first Europeans
to arrive in North America.

00:03:04.464 --> 00:03:07.294
So we'll talk a little bit
more about the bad implications

00:03:07.294 --> 00:03:09.444
of Christopher Columbus and his contact

00:03:09.444 --> 00:03:10.889
with the New World,

00:03:10.889 --> 00:03:12.528
and that has a lot to
do with his treatment

00:03:12.528 --> 00:03:13.780
of the Native Americans.

00:03:13.780 --> 00:03:17.598
So, you can see that in these
kind of two representations

00:03:17.598 --> 00:03:19.153
of the moment of contact.

00:03:19.153 --> 00:03:22.153
So, here would be the bad, the ugly.

00:03:23.569 --> 00:03:25.819
And this is the kinda good.

00:03:27.014 --> 00:03:28.158
- [Voiceover] Yeah, I can see that

00:03:28.158 --> 00:03:32.536
this painting here on the
right, it's very heroic.

00:03:32.536 --> 00:03:34.145
- [Voiceover] He goes look very heroic.

00:03:34.145 --> 00:03:37.149
- [Voiceover] I know, he's
even looking up into the sky

00:03:37.149 --> 00:03:41.028
as though he's maybe making
eye contact with God.

00:03:41.028 --> 00:03:44.696
- [Voiceover] Definitely God's up here.

00:03:44.696 --> 00:03:46.285
The other interpretation is looking like

00:03:46.285 --> 00:03:48.715
a lot of what historians have read

00:03:48.715 --> 00:03:50.735
in Christopher Columbus's journal

00:03:50.735 --> 00:03:53.715
and in these documents that
he sent back to the Spanish,

00:03:53.715 --> 00:03:56.636
which provide evidence to show that

00:03:56.636 --> 00:03:58.376
Christopher Columbus and his men

00:03:58.376 --> 00:04:00.351
on the Pinta, Nina, and Santa Maria,

00:04:00.351 --> 00:04:03.845
enslaved the native
people, mutilated them,

00:04:03.845 --> 00:04:07.653
and sexually assaulted many native women.

00:04:07.653 --> 00:04:08.986
So the treatment

00:04:11.099 --> 00:04:12.502
of native people.

00:04:12.502 --> 00:04:14.440
- [Voiceover] So he's possibly the father

00:04:14.440 --> 00:04:16.393
of the Atlantic slave trade,

00:04:16.393 --> 00:04:20.155
and I would say, unintentionally the cause

00:04:20.155 --> 00:04:23.893
of a fairly significant human genocide.

00:04:23.893 --> 00:04:25.782
An unintentional human genocide

00:04:25.782 --> 00:04:28.716
in the form of disease
passed to Native Americans.

00:04:28.716 --> 00:04:29.549
- [Voiceover] Definitely.

00:04:29.549 --> 00:04:31.416
Historical records point towards

00:04:31.416 --> 00:04:33.833
Christopher Columbus's violence
towards the native people,

00:04:33.833 --> 00:04:36.964
but disease was really what
decimated the population,

00:04:36.964 --> 00:04:39.815
because when the ships
arrived from Europe,

00:04:39.815 --> 00:04:42.559
they brought weapons, but
they also brought new diseases

00:04:42.559 --> 00:04:44.686
that the native people had
never encountered before,

00:04:44.686 --> 00:04:48.707
and they had no immune system
to fight off these diseases.

00:04:48.707 --> 00:04:52.911
The Taino people were
absolutely decimated.

00:04:52.911 --> 00:04:55.211
- [Voiceover] I think it's
important to note that

00:04:55.211 --> 00:04:57.654
no one coming from
Europe meant to do this.

00:04:57.654 --> 00:04:59.240
This was before germ theory.

00:04:59.240 --> 00:05:01.649
They had an idea that being in contact

00:05:01.649 --> 00:05:03.832
with a sick person might get you sick,

00:05:03.832 --> 00:05:06.813
but they didn't know that
we could carry immunity

00:05:06.813 --> 00:05:08.231
to these diseases.

00:05:08.231 --> 00:05:09.187
- [Voiceover] Exactly.

00:05:09.187 --> 00:05:12.238
That's a good segue into talking about

00:05:12.238 --> 00:05:16.060
what would probably be center
on this little diagram,

00:05:16.060 --> 00:05:17.836
which is the Columbian Exchange.

00:05:17.836 --> 00:05:19.692
So, the Columbian Exchange,

00:05:19.692 --> 00:05:23.146
you can read more about it
in the Khan Academy article

00:05:23.146 --> 00:05:24.682
dedicated to talking about

00:05:24.682 --> 00:05:26.831
exactly what the Columbian Exchange was,

00:05:26.831 --> 00:05:29.119
but I'll give you a
little bit of an overview.

00:05:29.119 --> 00:05:32.766
So, disease was really
what came from Europe

00:05:32.766 --> 00:05:34.318
to the New World.

00:05:34.318 --> 00:05:36.737
- [Voiceover] How about also weapons,

00:05:36.737 --> 00:05:38.820
like firearms and horses.

00:05:40.266 --> 00:05:41.099
- [Voiceover] Horses, definitely.

00:05:41.099 --> 00:05:42.739
- [Voiceover] There were
no horses in the New World,

00:05:42.739 --> 00:05:45.239
so no Native Americans ever rode horses

00:05:45.239 --> 00:05:47.022
until the Spanish brought them over.

00:05:47.022 --> 00:05:48.008
- [Voiceover] And that really changed

00:05:48.008 --> 00:05:49.185
Native American culture,

00:05:49.185 --> 00:05:52.015
because they became so
mobile with these new horses.

00:05:52.015 --> 00:05:54.094
So, coming in from West Africa,

00:05:54.094 --> 00:05:56.207
enslaved people were being sold

00:05:56.207 --> 00:05:59.079
and sent on a brutal
voyage across the Atlantic,

00:05:59.079 --> 00:06:01.065
which many of them didn't survive,

00:06:01.065 --> 00:06:04.222
to work in the fields in the New World.

00:06:04.222 --> 00:06:06.805
- [Voiceover] Yeah,
particularly in what we call

00:06:06.805 --> 00:06:08.720
the Caribbean today, or the West Indies,

00:06:08.720 --> 00:06:11.518
so the islands that were producing sugar,

00:06:11.518 --> 00:06:15.006
like Barbados, the Dominican Republic.

00:06:15.006 --> 00:06:17.012
- [Voiceover] And what was
coming back from the New World

00:06:17.012 --> 00:06:19.956
to Europe was mostly gold,

00:06:19.956 --> 00:06:22.199
as well as Native American slaves.

00:06:22.199 --> 00:06:24.218
- [Voiceover] So, it's kind of a triangle

00:06:24.218 --> 00:06:28.647
between Europe, and
Africa, and the Americas.

00:06:28.647 --> 00:06:30.363
- [Voiceover] Yeah, a lot
of historians have called it

00:06:30.363 --> 00:06:31.812
the Triangular Trade.

00:06:31.812 --> 00:06:33.927
And so I put it in the middle because yes,

00:06:33.927 --> 00:06:36.437
humans were transported as slaves,

00:06:36.437 --> 00:06:39.825
that is obviously on the bad side,

00:06:39.825 --> 00:06:41.778
but there also were new markets,

00:06:41.778 --> 00:06:44.779
and there was this kind
of globalization of trade.

00:06:44.779 --> 00:06:47.980
- [Voiceover] Yes, and things
that existed in the New World

00:06:47.980 --> 00:06:51.381
that were brought back were tomatoes,

00:06:51.381 --> 00:06:55.457
so imagine a world of Italy
where there are no tomatoes.

00:06:55.457 --> 00:06:58.834
It was only after the
connection with the New World.

00:06:58.834 --> 00:07:02.884
Corn, if you think about
staples of the American diet

00:07:02.884 --> 00:07:05.163
and the diets in the world,

00:07:05.163 --> 00:07:08.261
many things came from the Americas.

00:07:08.261 --> 00:07:10.050
- [Voiceover] I had to draw in some corn

00:07:10.050 --> 00:07:11.802
and tomatoes over here.

00:07:11.802 --> 00:07:13.027
And those are definitely on the good side.

00:07:13.027 --> 00:07:16.125
Next I'm gonna talk a little
bit more about Columbus Day,

00:07:16.125 --> 00:07:18.274
and why we celebrate it,

00:07:18.274 --> 00:07:20.878
and why it's become such
a contentious holiday.

00:07:20.878 --> 00:07:24.349
Really, no other holiday
gets as much criticism.

00:07:24.349 --> 00:07:26.686
- [Voiceover] So, when did Columbus Day

00:07:26.686 --> 00:07:30.036
actually start being celebrated?

00:07:30.036 --> 00:07:34.662
I'm gonna assume that
it didn't start in 1493.

00:07:34.662 --> 00:07:37.232
- [Voiceover] That's correct,
Kim, it did not start in 1493.

00:07:37.232 --> 00:07:42.035
It actually began on a
state level in the 1890s.

00:07:42.035 --> 00:07:46.078
So, it had to do with Italian immigration,

00:07:46.078 --> 00:07:48.927
these mostly Catholic Italian immigrants

00:07:48.927 --> 00:07:51.170
coming into the United
States in the 1890s.

00:07:51.170 --> 00:07:55.336
In the 1890s there was a very
anti-immigrant sentiment.

00:07:55.336 --> 00:07:56.881
- [Voiceover] Yeah,
because this is a time when

00:07:56.881 --> 00:07:58.714
you have a lot of Russian Jews

00:07:58.714 --> 00:07:59.917
coming to the United States,

00:07:59.917 --> 00:08:02.791
and also southern, eastern
Europeans in general

00:08:02.791 --> 00:08:04.848
who don't speak English.

00:08:04.848 --> 00:08:08.165
There was much more concern,
and a lot more nativism,

00:08:08.165 --> 00:08:10.059
sort of anti-immigrant sentiment

00:08:10.059 --> 00:08:11.427
directed to these people,

00:08:11.427 --> 00:08:14.599
who many thought were so different

00:08:14.599 --> 00:08:18.736
from white Protestant
Anglo-Saxon Americans

00:08:18.736 --> 00:08:21.715
that they would never
be able to assimilate.

00:08:21.715 --> 00:08:23.937
- [Voiceover] Exactly, so
nativism was running really high,

00:08:23.937 --> 00:08:26.031
that's the anti-immigrant sentiment,

00:08:26.031 --> 00:08:28.002
that was mostly held by Protestants,

00:08:28.002 --> 00:08:30.432
white Protestants in the United States

00:08:30.432 --> 00:08:32.519
during this time of immigration.

00:08:32.519 --> 00:08:34.576
There were a lot of episodes of violence

00:08:34.576 --> 00:08:37.208
against the Italian and
Catholic communities,

00:08:37.208 --> 00:08:40.712
and one actually inspired
the first Columbus Day.

00:08:40.712 --> 00:08:43.797
And so, in 1891 there
was a public lynching

00:08:43.797 --> 00:08:46.307
of 11 Italian immigrants in New Orleans.

00:08:46.307 --> 00:08:47.569
- [Voiceover] Wow, I had no idea.

00:08:47.569 --> 00:08:49.017
- [Voiceover] Yeah, and
it's one of the largest

00:08:49.017 --> 00:08:51.211
public lynchings in American history.

00:08:51.211 --> 00:08:53.060
And so, in response to that,

00:08:53.060 --> 00:08:55.443
the first ever Columbus Day was celebrated

00:08:55.443 --> 00:08:58.971
by Italian immigrants
in New Orleans in 1892.

00:08:58.971 --> 00:09:00.350
This was before it was a federal holiday,

00:09:00.350 --> 00:09:03.387
this was just a celebration
of their heritage

00:09:03.387 --> 00:09:05.093
in a moment where their heritage

00:09:05.093 --> 00:09:08.222
was being violently uprooted.

00:09:08.222 --> 00:09:11.275
The first president to
recommend Columbus Day

00:09:11.275 --> 00:09:14.359
was actually Harrison in '93.

00:09:14.359 --> 00:09:15.192
So, 1893.

00:09:17.396 --> 00:09:19.172
What else was going on at that time, Kim?

00:09:19.172 --> 00:09:21.145
- [Voiceover] Oh, this is
one of my favorite things.

00:09:21.145 --> 00:09:23.562
So in 1893 Chicago celebrated

00:09:24.943 --> 00:09:27.780
the World's Columbian Exposition,

00:09:27.780 --> 00:09:30.009
where the United States

00:09:30.009 --> 00:09:32.743
proclaimed loudly to the world

00:09:32.743 --> 00:09:36.910
that they were a important
cultural and scientific nation,

00:09:38.220 --> 00:09:42.387
so they had exhibitions of all
different types of machinery

00:09:42.387 --> 00:09:43.968
that had been invented,

00:09:43.968 --> 00:09:46.070
and different types of people

00:09:46.070 --> 00:09:48.113
from all over the United States.

00:09:48.113 --> 00:09:52.196
It was really the massive
national event of 1893.

00:09:53.220 --> 00:09:57.099
They did this in 1893
as the 400th anniversary

00:09:57.099 --> 00:09:59.766
of Columbus discovering America,

00:10:01.468 --> 00:10:03.360
but he did that in 1492,

00:10:03.360 --> 00:10:05.520
so they were a year late.

00:10:05.520 --> 00:10:07.169
It took them an extra year

00:10:07.169 --> 00:10:09.388
to get ready for this World's Fair.

00:10:09.388 --> 00:10:12.990
- [Voiceover] It was a very
patriotic sort of event.

00:10:12.990 --> 00:10:14.157
The USA rules,

00:10:16.922 --> 00:10:18.763
and we want everyone to know about that.

00:10:18.763 --> 00:10:20.412
And it really was convenient

00:10:20.412 --> 00:10:23.122
to also celebrate Columbus as that time,

00:10:23.122 --> 00:10:26.205
as to increase this patriotic morale.

00:10:28.318 --> 00:10:30.866
So it wasn't until the New Deal

00:10:30.866 --> 00:10:33.423
when President Franklin Delano Roosevelt

00:10:33.423 --> 00:10:38.226
signed Columbus Day into
law as a federal holiday.

00:10:38.226 --> 00:10:41.137
- [Voiceover] So, why did he
make it a federal holiday?

00:10:41.137 --> 00:10:42.702
- [Voiceover] So, FDR was under

00:10:42.702 --> 00:10:45.726
a lot of pressure from
the Knights of Columbus,

00:10:45.726 --> 00:10:49.465
so this was this Catholic
Italian cultural organization,

00:10:49.465 --> 00:10:51.090
and they lobbied him heavily

00:10:51.090 --> 00:10:54.455
because they really wanted a cultural hero

00:10:54.455 --> 00:10:56.488
for their ethnic identity.

00:10:56.488 --> 00:10:57.699
- [Voiceover] Why are so many people

00:10:57.699 --> 00:10:59.932
upset about Columbus Day today?

00:10:59.932 --> 00:11:03.264
- [Voiceover] So, this sort
of anti-Columbus Day sentiment

00:11:03.264 --> 00:11:06.334
started in the late 80s, early 90s,

00:11:06.334 --> 00:11:08.378
when different states which had

00:11:08.378 --> 00:11:11.207
very high Native American populations

00:11:11.207 --> 00:11:13.367
started to realize that
we were celebrating

00:11:13.367 --> 00:11:17.280
a man who did inflict a
lot of disease and violence

00:11:17.280 --> 00:11:19.756
against the Native peoples
when he arrived here.

00:11:19.756 --> 00:11:23.216
In the 90s, Hawaii,
Alaska, and South Dakota

00:11:23.216 --> 00:11:26.252
all stopped giving people
the day off from work

00:11:26.252 --> 00:11:27.172
for Columbus Day,

00:11:27.172 --> 00:11:29.091
started to kind of disregard

00:11:29.091 --> 00:11:32.184
the federal mandate of a holiday.

00:11:32.184 --> 00:11:33.644
The significance of these three states

00:11:33.644 --> 00:11:37.032
is that they all have very high
Native American populations.

00:11:37.032 --> 00:11:39.944
And actually in 1992, right over here,

00:11:39.944 --> 00:11:42.886
Berkeley, California renamed Columbus Day

00:11:42.886 --> 00:11:44.882
to Indigenous People's Day.

00:11:44.882 --> 00:11:46.577
And a lot of other
states have followed suit

00:11:46.577 --> 00:11:49.041
in this kind of renaming of Columbus Day

00:11:49.041 --> 00:11:51.064
to commemorate the native people

00:11:51.064 --> 00:11:52.476
and the lives that were lost

00:11:52.476 --> 00:11:54.218
during Columbus's voyage

00:11:54.218 --> 00:11:57.546
and the colonization projects that ensued.

00:11:57.546 --> 00:11:58.504
- [Voiceover] So, what do you think?

00:11:58.504 --> 00:12:01.228
At the end of the day,
was Columbus a good guy

00:12:01.228 --> 00:12:02.496
or a bad guy?

00:12:02.496 --> 00:12:03.411
- [Voiceover] You know, Kim,

00:12:03.411 --> 00:12:04.826
I don't think it's actually about him

00:12:04.826 --> 00:12:07.391
as much as it is about
the long-term effects

00:12:07.391 --> 00:12:10.387
of colonization on the
Native American population,

00:12:10.387 --> 00:12:13.059
which were really, really terrible.

00:12:13.059 --> 00:12:14.998
To chalk it up to Christopher Columbus,

00:12:14.998 --> 00:12:17.194
we can definitely not celebrate him,

00:12:17.194 --> 00:12:20.151
but there were so many
other colonization projects,

00:12:20.151 --> 00:12:22.043
and different events that happened

00:12:22.043 --> 00:12:24.110
throughout American history that

00:12:24.110 --> 00:12:25.876
subordinated the Native people,

00:12:25.876 --> 00:12:27.091
and that's really the conversation

00:12:27.091 --> 00:12:28.468
that I wanna keep having.


Common denominators: 3/5 and 7/2

WEBVTT
Kind: captions
Language: en

00:00:01.038 --> 00:00:05.118
- Rewrite each fraction
with a denominator of 10.

00:00:05.118 --> 00:00:06.650
So we have two fractions,

00:00:06.650 --> 00:00:08.905
three fifths and seven halves

00:00:08.905 --> 00:00:13.001
and we wanna take their
denominators of five and two

00:00:13.001 --> 00:00:17.811
and change them to be a
common denominator of 10.

00:00:17.811 --> 00:00:19.868
Lets start with three fifths

00:00:19.868 --> 00:00:21.969
and we can look at this visually.

00:00:21.969 --> 00:00:25.091
Here we can use this rectangle
to represent a whole,

00:00:25.091 --> 00:00:26.549
one whole.

00:00:26.549 --> 00:00:29.605
To show three fifths of
that whole, we're gonna need

00:00:29.605 --> 00:00:33.438
to divide it into fifths
or five equal pieces.

00:00:34.516 --> 00:00:35.599
Lets do that.

00:00:36.536 --> 00:00:37.953
Try to make these

00:00:39.343 --> 00:00:41.093
as equal as possible.

00:00:43.746 --> 00:00:46.996
We have three pieces, and then finally,

00:00:48.280 --> 00:00:49.354
there we go.

00:00:49.354 --> 00:00:53.575
So, these should represent
five equal pieces, or fifths.

00:00:53.575 --> 00:00:57.809
To show three fifths,
we need to shade three

00:00:57.809 --> 00:00:59.614
of those five pieces.

00:00:59.614 --> 00:01:02.947
So, one, two, three of those five pieces

00:01:04.417 --> 00:01:07.834
should be shaded in to show three fifths.

00:01:09.315 --> 00:01:11.940
We've decided we don't
want fifths anymore.

00:01:11.940 --> 00:01:14.179
Now, we want tenths.

00:01:14.179 --> 00:01:16.846
We want a new denominator of 10.

00:01:17.960 --> 00:01:20.640
To change this fraction over here,

00:01:20.640 --> 00:01:22.973
to change this to be tenths,

00:01:23.882 --> 00:01:27.658
we need to split each
of these fifths in half.

00:01:27.658 --> 00:01:30.434
We need to double the amount of pieces.

00:01:30.434 --> 00:01:32.101
We can do that here.

00:01:33.191 --> 00:01:36.996
Now, instead of fifths,
or five equal size pieces,

00:01:36.996 --> 00:01:37.948
we have tenths.

00:01:37.948 --> 00:01:39.823
We have one, two, three, four, five,

00:01:39.823 --> 00:01:42.424
six, seven, eight, nine, ten.

00:01:42.424 --> 00:01:45.733
We found a way to have
tenths without changing

00:01:45.733 --> 00:01:47.312
the amount that's represented.

00:01:47.312 --> 00:01:51.797
The same amount is still
shaded, but now we have tenths.

00:01:51.797 --> 00:01:53.797
Our denominator doubled.

00:01:55.080 --> 00:01:59.247
We multiplied it be two, we
have twice as many pieces.

00:02:00.746 --> 00:02:02.848
But look at what happened
to our numerator,

00:02:02.848 --> 00:02:04.809
instead of three pieces, now we have

00:02:04.809 --> 00:02:08.529
one, two, three, four, five, six pieces.

00:02:08.529 --> 00:02:09.862
It also doubled.

00:02:10.977 --> 00:02:13.477
It also was multiplied by two,

00:02:14.863 --> 00:02:18.065
because if we double all of the pieces,

00:02:18.065 --> 00:02:20.225
well then the shaded
ones will also double.

00:02:20.225 --> 00:02:23.054
Each of those pieces also split in two,

00:02:23.054 --> 00:02:26.897
so now there's twice
as many shaded pieces.

00:02:26.897 --> 00:02:30.897
So, three fifths can be
rewritten as six tenths.

00:02:32.709 --> 00:02:35.417
Three fifths is equal to six tenths,

00:02:35.417 --> 00:02:38.067
and again, we didn't change the fraction.

00:02:38.067 --> 00:02:40.195
We didn't change how much was shaded.

00:02:40.195 --> 00:02:44.114
Three fifths and six tenths
represented the same amount.

00:02:44.114 --> 00:02:46.068
We just changed the denominator

00:02:46.068 --> 00:02:47.432
and wrote it a different way.

00:02:47.432 --> 00:02:51.599
So, three fifths can be rewritten
in tenths as six tenths.

00:02:53.416 --> 00:02:57.583
Now, for seven halves, we
again want a denominator of 10.

00:02:58.954 --> 00:03:02.211
So, we can draw it out, or we
could try to use this pattern

00:03:02.211 --> 00:03:05.628
we just noticed up here to
figure out how to make halves

00:03:05.628 --> 00:03:07.045
turn into tenths.

00:03:07.972 --> 00:03:10.700
To get from fifths to
tenths we had to double,

00:03:10.700 --> 00:03:12.660
or multiply by two.

00:03:12.660 --> 00:03:14.908
To get from halves to tenths,

00:03:14.908 --> 00:03:17.449
we'd have to multiply each of our pieces

00:03:17.449 --> 00:03:18.366
times five.

00:03:21.095 --> 00:03:24.976
Each of our halves would
be split into five pieces.

00:03:24.976 --> 00:03:29.524
So, we multiply two
times five to get tenths.

00:03:29.524 --> 00:03:31.304
Like the pattern showed us up here,

00:03:31.304 --> 00:03:34.418
if the denominator is
multiplied by a number,

00:03:34.418 --> 00:03:37.075
we multiply the numerator
by the same number.

00:03:37.075 --> 00:03:41.833
Those shaded pieces would
also be split five times.

00:03:41.833 --> 00:03:45.000
We multiply our seven times five also.

00:03:45.896 --> 00:03:48.629
You should match the
numerator and denominator

00:03:48.629 --> 00:03:51.302
are multiplied by the same number.

00:03:51.302 --> 00:03:53.219
Seven times five is 35.

00:03:55.564 --> 00:03:58.731
So 35 tenths is equal to seven halves.

00:04:01.928 --> 00:04:05.828
To change these two fractions
to have a common denominator

00:04:05.828 --> 00:04:06.661
of 10,

00:04:07.991 --> 00:04:10.853
three fifths will become six tenths,

00:04:10.853 --> 00:04:14.103
and seven halves will become 35 tenths.


Common denominators: 1/2 and 1/3

WEBVTT
Kind: captions
Language: en

00:00:01.076 --> 00:00:04.076
- [Voiceover] You have two
fractions, 1/4 and 5/6,

00:00:04.076 --> 00:00:06.213
and you want to rewrite
them so they have the same

00:00:06.213 --> 00:00:10.671
denominator, and have
whole number numerators.

00:00:10.671 --> 00:00:13.863
What numbers could you
use for the denominator?

00:00:13.863 --> 00:00:17.116
So here's our fractions, 1/4 and 5/6,

00:00:17.116 --> 00:00:19.559
and we want to rewrite these fractions

00:00:19.559 --> 00:00:21.642
to have new denominators.

00:00:22.509 --> 00:00:26.236
So we currently have a four
and a six as our denominator,

00:00:26.236 --> 00:00:27.796
and can we just put any new thing,

00:00:27.796 --> 00:00:29.330
like maybe five, could we say,

00:00:29.330 --> 00:00:32.201
"Let's change them both to
have five as the denominator."

00:00:32.201 --> 00:00:33.852
The answer is no.

00:00:33.852 --> 00:00:37.950
We have to pick a multiple
of four and six, a multiple,

00:00:37.950 --> 00:00:41.033
some number that we can multiply four

00:00:41.890 --> 00:00:45.230
and get this number as an answer.

00:00:45.230 --> 00:00:47.397
So, for example, for four,

00:00:48.883 --> 00:00:53.708
so multiples of four would
be four times one is four,

00:00:53.708 --> 00:00:58.185
four times two is eight,
four times three is twelve,

00:00:58.185 --> 00:01:01.352
and so on, those are multiples of four

00:01:02.656 --> 00:01:03.782
and let's just pause here

00:01:03.782 --> 00:01:08.152
and look at why we have to pick
a multiple of four and six,

00:01:08.152 --> 00:01:09.825
why we can't just pick any number,

00:01:09.825 --> 00:01:14.744
but we have to pick a
multiple of our denominators.

00:01:14.744 --> 00:01:16.761
So the fraction we were
just talking about was 1/4.

00:01:16.761 --> 00:01:20.442
We could look at either
one, but let's look at 1/4.

00:01:20.442 --> 00:01:24.609
Here we have a picture showing
fourths, and to show 1/4,

00:01:25.890 --> 00:01:29.640
we shade one of these
four equal size pieces.

00:01:31.274 --> 00:01:32.951
Well, maybe I want to change this

00:01:32.951 --> 00:01:36.949
and I want to say I want two,
I want two as my numerator.

00:01:36.949 --> 00:01:39.449
So to have a numerator of two,

00:01:40.605 --> 00:01:45.220
I'm gonna need to split this
fourth up here into two pieces.

00:01:45.220 --> 00:01:47.338
Now I have two shaded pieces.

00:01:47.338 --> 00:01:51.096
So can I say this is two, one, two, out of

00:01:51.096 --> 00:01:54.083
one, two, three, four, five pieces?

00:01:54.083 --> 00:01:58.065
It's not 2/5 because these
are not equal size pieces.

00:01:58.065 --> 00:02:00.858
So if I split this fourth
right here in half,

00:02:00.858 --> 00:02:03.020
I need to split all of them in half,

00:02:03.020 --> 00:02:07.187
and what I'm doing is
doubling the amount of pieces.

00:02:10.038 --> 00:02:14.326
So now this is two pieces,
this is two, and this is two

00:02:14.326 --> 00:02:17.035
because we need equal size pieces.

00:02:17.035 --> 00:02:19.503
So now, this is one, two pieces

00:02:19.503 --> 00:02:23.450
out of one, two, three,
four, five, six, seven, eight

00:02:23.450 --> 00:02:26.943
equal size pieces, so 2/8

00:02:26.943 --> 00:02:30.315
and you can see, eight
is a multiple of four

00:02:30.315 --> 00:02:32.512
because we multiplied by
two and that's what we did,

00:02:32.512 --> 00:02:36.493
we multiplied each of our pieces by two

00:02:36.493 --> 00:02:38.711
and we also multiplied
our numerator by two

00:02:38.711 --> 00:02:40.517
because that was also doubled.

00:02:40.517 --> 00:02:42.627
The amount of shaded pieces doubled

00:02:42.627 --> 00:02:45.605
when the entire amount of pieces doubled

00:02:45.605 --> 00:02:47.323
and we don't have to
do this just with two,

00:02:47.323 --> 00:02:48.958
we could do any multiple of four.

00:02:48.958 --> 00:02:52.041
For example, we can do one more here.

00:02:54.880 --> 00:02:59.094
If we, again, let's shade 1/4,

00:02:59.094 --> 00:03:01.433
one of the four pieces

00:03:01.433 --> 00:03:04.593
and maybe this time we
want to split it into

00:03:04.593 --> 00:03:06.593
three equal size pieces.

00:03:07.969 --> 00:03:10.479
So to have a new numerator of three,

00:03:10.479 --> 00:03:13.330
and these should be equal sized,

00:03:13.330 --> 00:03:15.663
here's a numerator of three,

00:03:17.136 --> 00:03:20.626
but it's, we can't do our denominator yet

00:03:20.626 --> 00:03:23.239
because we don't have equal size pieces,

00:03:23.239 --> 00:03:25.352
so to get equal size pieces,

00:03:25.352 --> 00:03:29.519
we'll need to split each of
these fourths into three.

00:03:30.980 --> 00:03:34.313
So we are tripling the amount of pieces.

00:03:36.874 --> 00:03:39.226
So now we have three shaded pieces

00:03:39.226 --> 00:03:42.752
out of a total of one, two,
three, four, five, six,

00:03:42.752 --> 00:03:46.252
seven, eight, nine, 10, 11, 12, out of 12,

00:03:47.895 --> 00:03:50.030
and I could have figured that
out without even counting

00:03:50.030 --> 00:03:53.447
because I knew that we tripled this time,

00:03:54.466 --> 00:03:58.633
we multiplied our original
denominator times three,

00:03:59.469 --> 00:04:03.636
we tripled, and we also multiplied
our numerator times three

00:04:05.060 --> 00:04:08.638
so these are the multiples,
eight, 12, and so on

00:04:08.638 --> 00:04:10.931
and so those are the
denominators we can pick.

00:04:10.931 --> 00:04:15.522
Something that we can
multiply our denominator by

00:04:15.522 --> 00:04:19.355
so we can multiply the
entire amount of pieces

00:04:20.473 --> 00:04:22.458
and again, so this is super clear,

00:04:22.458 --> 00:04:27.405
1/4 and 2/8 and 3/12, they
all represent the same amount,

00:04:27.405 --> 00:04:31.258
whether we had 1/4, the
original, here's 2/8, 3/12,

00:04:31.258 --> 00:04:34.801
they're all equivalent, they
all represent the same amount,

00:04:34.801 --> 00:04:39.320
they're just different ways
of writing the same number.

00:04:39.320 --> 00:04:40.961
Back to our original question,

00:04:40.961 --> 00:04:45.128
what denominators can we use
for fourths and for sixths?

00:04:46.373 --> 00:04:48.498
Well, we know we need to use multiples,

00:04:48.498 --> 00:04:50.312
so let's look at the multiples.

00:04:50.312 --> 00:04:53.651
For four, we've already
gone through some of these.

00:04:53.651 --> 00:04:57.582
The first multiple of four is
four times one which is four,

00:04:57.582 --> 00:05:00.938
second multiple of four is
eight, four times two is eight,

00:05:00.938 --> 00:05:04.815
so we could split our fourths
into, in half and get eighths

00:05:04.815 --> 00:05:08.716
or we could say four
times three is twelve,

00:05:08.716 --> 00:05:11.003
which we showed again
where we split our fourths,

00:05:11.003 --> 00:05:13.870
each fourth into three equal pieces

00:05:13.870 --> 00:05:17.310
or we could do four
times four which is 16,

00:05:17.310 --> 00:05:21.477
four times five is 20, four
times six is 24, and so on.

00:05:24.007 --> 00:05:25.995
The reason I'm stopping at 24

00:05:25.995 --> 00:05:28.452
is I've looked at my answer choices

00:05:28.452 --> 00:05:31.512
and I can see the largest
possible answer is 24

00:05:31.512 --> 00:05:34.070
so I don't need to write
any larger multiples.

00:05:34.070 --> 00:05:37.457
There are many, many, many
more multiples of four,

00:05:37.457 --> 00:05:38.726
but we don't need to list them all

00:05:38.726 --> 00:05:39.779
because the largest number

00:05:39.779 --> 00:05:43.331
we're gonna have to consider is 24.

00:05:43.331 --> 00:05:45.578
Let's do the same for six.

00:05:45.578 --> 00:05:48.699
We could leave our six
alone, six times one,

00:05:48.699 --> 00:05:51.856
and keep six pieces, or
we could double our six,

00:05:51.856 --> 00:05:53.543
six times two would be 12,

00:05:53.543 --> 00:05:56.610
if we doubled the pieces
we would have 12 pieces.

00:05:56.610 --> 00:05:59.790
We could say six times three, which is 18,

00:05:59.790 --> 00:06:01.277
or six times four, we could divide

00:06:01.277 --> 00:06:03.907
each of our sixths into four pieces

00:06:03.907 --> 00:06:06.931
and we'd have six times four which is 24,

00:06:06.931 --> 00:06:09.869
or twenty-fourths and so on.

00:06:09.869 --> 00:06:12.086
Again, I'll stop at 24 since it's the

00:06:12.086 --> 00:06:15.784
largest number we need to consider.

00:06:15.784 --> 00:06:17.833
So down to our answer choices,

00:06:17.833 --> 00:06:20.054
what numbers could we
use for the denominator?

00:06:20.054 --> 00:06:21.810
Could we use eight?

00:06:21.810 --> 00:06:23.620
Let's look at these lists.

00:06:23.620 --> 00:06:26.314
Eight is a multiple of four,

00:06:26.314 --> 00:06:29.414
so we could definitely
split fourths into eighths,

00:06:29.414 --> 00:06:31.989
but eight is not a multiple of six,

00:06:31.989 --> 00:06:34.789
so we cannot split sixths into eighths,

00:06:34.789 --> 00:06:38.956
so eight will not work as a
denominator for both fractions.

00:06:42.671 --> 00:06:43.754
How about 12?

00:06:44.681 --> 00:06:47.035
12, we can see, is a multiple of four,

00:06:47.035 --> 00:06:49.242
and we showed that, we drew that already,

00:06:49.242 --> 00:06:50.943
and 12 is a multiple of six,

00:06:50.943 --> 00:06:53.416
we could split our sixths
into two equal pieces each

00:06:53.416 --> 00:06:55.391
and we would have twelfths.

00:06:55.391 --> 00:06:59.216
So 12 does work, 12 is a denominator,

00:06:59.216 --> 00:07:03.638
a common denominator
for fourths and sixths.

00:07:03.638 --> 00:07:07.805
18, 18 is here on the sixths,
we could split sixths into 18

00:07:08.705 --> 00:07:10.584
because 18 is a multiple of six,

00:07:10.584 --> 00:07:15.383
but it is not a multiple of
four, so we can rule out 18.

00:07:15.383 --> 00:07:20.172
18 is not a common denominator
and 24, you may remember,

00:07:20.172 --> 00:07:22.703
was the last number we
wrote on both of them

00:07:22.703 --> 00:07:26.870
so yes, 24 could be a denominator
for fourths and sixths.

00:07:28.693 --> 00:07:31.405
So we could use either 12 or 24

00:07:31.405 --> 00:07:33.527
and there's a lot more
numbers we could use, too,

00:07:33.527 --> 00:07:36.217
as common denominators
but from these choices,

00:07:36.217 --> 00:07:38.751
we could use 12 or 24

00:07:38.751 --> 00:07:43.031
as a common denominator
for fourths and sixths

00:07:43.031 --> 00:07:44.685
and just a note, lots of times

00:07:44.685 --> 00:07:46.602
people like to use the smallest one,

00:07:46.602 --> 00:07:50.650
the least common denominator,
which in this case is 12,

00:07:50.650 --> 00:07:51.688
and it makes a lot of sense

00:07:51.688 --> 00:07:54.712
because it's easier to do
computation with smaller numbers

00:07:54.712 --> 00:07:58.300
but you don't absolutely
have to use the smallest one.

00:07:58.300 --> 00:08:00.794
You could use twelfths
or twenty-fourths or,

00:08:00.794 --> 00:08:03.278
or lots of other options, but, again,

00:08:03.278 --> 00:08:06.329
twelfths is probably the
simplest one to work with

00:08:06.329 --> 00:08:07.896
just because generally it's easier

00:08:07.896 --> 00:08:10.014
to work with smaller numbers

00:08:10.014 --> 00:08:13.196
but for this question, the
common denominators we can use

00:08:13.196 --> 00:08:17.363
from these choices for fourths
and sixths are 12 and 24.


Christopher Columbus part 1

WEBVTT
Kind: captions
Language: en

00:00:00.857 --> 00:00:02.784
- [Voiceover] In 1492,
Christopher Columbus

00:00:02.784 --> 00:00:05.462
sailed the ocean blue and
he discovered America,

00:00:05.462 --> 00:00:08.343
discovered the world was, in fact, round,

00:00:08.343 --> 00:00:11.499
and he's a hero and
that's why we get the day

00:00:11.499 --> 00:00:13.088
off from work and school

00:00:13.088 --> 00:00:16.112
and get to celebrate him every October.

00:00:16.112 --> 00:00:19.019
So, you've probably heard
this story maybe once or twice

00:00:19.019 --> 00:00:22.430
but you've probably also
seen competing visions

00:00:22.430 --> 00:00:25.052
of Christopher Columbus and his legacy.

00:00:25.052 --> 00:00:27.432
Some that aren't so favorable.

00:00:27.432 --> 00:00:31.778
In this video series, I will
clear up misconceptions.

00:00:31.778 --> 00:00:35.861
For example, Christopher
Columbus did not discover America

00:00:35.861 --> 00:00:39.344
and he didn't actually discover
that the world was round.

00:00:39.344 --> 00:00:43.767
People already knew that in
about 600 A.D. with Aristotle,

00:00:43.767 --> 00:00:45.731
but hopefully with these
facts and explanations

00:00:45.731 --> 00:00:49.961
of the implications of Christopher
Columbus and his voyage

00:00:49.961 --> 00:00:53.009
that you, as the viewer
and budding historian,

00:00:53.009 --> 00:00:55.023
can decide for yourself if you think

00:00:55.023 --> 00:00:58.070
that Christopher Columbus was a hero,

00:00:58.070 --> 00:01:02.273
so we're gonna change
this into a question.

00:01:02.273 --> 00:01:05.646
Christopher Columbus's voyage
started way before 1492

00:01:05.646 --> 00:01:08.612
when he started petitioning
different European governments

00:01:08.612 --> 00:01:10.992
for funding for his trip.

00:01:10.992 --> 00:01:15.137
So, Christopher Columbus was
actually an Italian navigator

00:01:15.137 --> 00:01:19.607
and he asked the Portuguese
and then he asked the Spanish

00:01:19.607 --> 00:01:23.359
and then, when King Ferdinand
and Queen Isabella of Spain

00:01:23.359 --> 00:01:25.577
wouldn't give him the money originally,

00:01:25.577 --> 00:01:27.204
he even threatened to go to France

00:01:27.204 --> 00:01:29.313
and ask for money from them,

00:01:29.313 --> 00:01:31.972
but eventually he ended
up doing the voyage

00:01:31.972 --> 00:01:33.138
under the Spanish crown

00:01:33.138 --> 00:01:37.305
and he got together a crew of
about 150 men in three ships.

00:01:39.025 --> 00:01:40.348
You probably know the names of those.

00:01:40.348 --> 00:01:44.534
They were the Nina,
Pinta, and Santa Maria.

00:01:44.534 --> 00:01:45.544
There they are.

00:01:45.544 --> 00:01:46.546
They don't look very high tech,

00:01:46.546 --> 00:01:49.348
but they did have a lot of
help from new technology

00:01:49.348 --> 00:01:51.153
in Europe making these brand new ships

00:01:51.153 --> 00:01:53.514
and they were a little bit nicer

00:01:53.514 --> 00:01:55.420
than they look in these
drawings (chuckles).

00:01:55.420 --> 00:01:57.518
Christopher Columbus set out for

00:01:57.518 --> 00:02:00.741
the first voyage ever across the Atlantic.

00:02:00.741 --> 00:02:03.185
So, why was he going across the Atlantic?

00:02:03.185 --> 00:02:05.339
This has to do with a lot of motivations

00:02:05.339 --> 00:02:07.289
that you can read more about in the

00:02:07.289 --> 00:02:10.741
Khan Academy article,
Motivations for Conquest,

00:02:10.741 --> 00:02:13.160
but I'll give you a general overview here.

00:02:13.160 --> 00:02:15.070
The little acronym that
I like to go with is

00:02:15.070 --> 00:02:16.820
God, Gold, and Glory.

00:02:19.665 --> 00:02:21.778
So, these were some of Christopher

00:02:21.778 --> 00:02:23.777
Columbus's main motivations

00:02:23.777 --> 00:02:26.777
and I would say it was
mostly about gold and glory.

00:02:26.777 --> 00:02:29.069
Christopher Columbus
aimed to find a new route

00:02:29.069 --> 00:02:30.695
to the West Indies.

00:02:30.695 --> 00:02:33.479
So, the West Indies were
somewhere, you know, over here,

00:02:33.479 --> 00:02:35.182
really, if you're looking at this map

00:02:35.182 --> 00:02:38.031
and Europeans had to travel by land

00:02:38.031 --> 00:02:40.401
all the way down through the Middle East

00:02:40.401 --> 00:02:41.910
to the West Indies over here.

00:02:41.910 --> 00:02:44.466
Along that route, there
were many middlemen

00:02:44.466 --> 00:02:47.175
that imposed taxes and
it was just a really,

00:02:47.175 --> 00:02:49.019
really hard route to navigate

00:02:49.019 --> 00:02:51.945
so Christopher Columbus
wanted to find a way

00:02:51.945 --> 00:02:55.362
that he could go west to get to the east.

00:02:57.187 --> 00:02:59.221
Christopher Columbus knew
the world was round, right.

00:02:59.221 --> 00:03:01.518
He wanted to go like that,

00:03:01.518 --> 00:03:03.385
but he was the first person
to prove that it was.

00:03:03.385 --> 00:03:06.779
Columbus and his men set out in 1492

00:03:06.779 --> 00:03:10.415
and they have enough food
and water to last them a year

00:03:10.415 --> 00:03:12.448
so this was an unprecedented voyage.

00:03:12.448 --> 00:03:14.780
Everyone was really excited

00:03:14.780 --> 00:03:16.247
and curious about what they would find

00:03:16.247 --> 00:03:19.254
and it ended up taking them five weeks

00:03:19.254 --> 00:03:20.757
so it was a five week voyage

00:03:20.757 --> 00:03:23.176
and it certainly wasn't pretty.

00:03:23.176 --> 00:03:26.916
There were many times where
the ship men lost morale

00:03:26.916 --> 00:03:29.209
and Columbus himself had doubts

00:03:29.209 --> 00:03:32.944
so he even made this promise
to the people on the ship.

00:03:32.944 --> 00:03:34.405
He said, "The first person to see land

00:03:34.405 --> 00:03:36.238
will get a silk coat,"

00:03:37.400 --> 00:03:39.205
and so this was a way
that he increased morale

00:03:39.205 --> 00:03:41.175
when things were looking really rough,

00:03:41.175 --> 00:03:42.723
but he was a very impressive navigator

00:03:42.723 --> 00:03:46.214
and used the stars and
lots of really impressive

00:03:46.214 --> 00:03:50.363
scientific measurement
to arrive in the Bahamas.

00:03:50.363 --> 00:03:52.069
The Bahamas are part of an island group

00:03:52.069 --> 00:03:53.733
called the West Indies and why are

00:03:53.733 --> 00:03:54.792
they called the West Indies?

00:03:54.792 --> 00:03:56.230
Because Christopher Columbus thought

00:03:56.230 --> 00:03:58.222
that he had arrived in the Indies

00:03:58.222 --> 00:04:01.229
which are an island
group in Southeast Asia.

00:04:01.229 --> 00:04:04.155
So, geographers then
named the West Indies west

00:04:04.155 --> 00:04:07.081
as to distinguish them from the island

00:04:07.081 --> 00:04:09.273
that Christopher Columbus
thought that he had,

00:04:09.273 --> 00:04:10.369
in fact, arrived on.

00:04:10.369 --> 00:04:11.876
I know, kind of funny to think about now

00:04:11.876 --> 00:04:14.473
because they are just so far away,

00:04:14.473 --> 00:04:16.044
but Christopher Columbus was determined

00:04:16.044 --> 00:04:19.405
that he had, in fact,
arrived in the East Indies

00:04:19.405 --> 00:04:22.217
so that's where the
name Indians came from.

00:04:22.217 --> 00:04:24.252
The native people were not related to

00:04:24.252 --> 00:04:27.398
or descendents from Indians in any way.

00:04:27.398 --> 00:04:29.313
Christopher Columbus was just determined

00:04:29.313 --> 00:04:31.544
that China was just a
little bit north of them

00:04:31.544 --> 00:04:34.758
and that they had successfully
found this new trade route.

00:04:34.758 --> 00:04:37.962
To give you a sense of where
Christopher Columbus ended up,

00:04:37.962 --> 00:04:39.692
you can check out this map.

00:04:39.692 --> 00:04:43.818
So, he came from Spain and first
landed here in the Bahamas.

00:04:43.818 --> 00:04:46.298
So he named it San Salvador,

00:04:46.298 --> 00:04:48.794
that was the first place that they stopped

00:04:48.794 --> 00:04:52.961
and in San Salvador, they
encountered the Taíno people

00:04:54.605 --> 00:04:58.181
so the Taínos were, historically,
a very friendly people.

00:04:58.181 --> 00:05:01.252
They were very welcoming to
Christopher Columbus and his men

00:05:01.252 --> 00:05:03.626
and Christopher Columbus
actually wrote this all down

00:05:03.626 --> 00:05:06.858
in his journal, so a lot of
the records that historians

00:05:06.858 --> 00:05:09.257
reference and argue a fair amount about

00:05:09.257 --> 00:05:12.078
come from both Columbus's journal

00:05:12.078 --> 00:05:14.598
and his probanzas de merito.

00:05:14.598 --> 00:05:17.848
These were literally
proof of merit in English

00:05:17.848 --> 00:05:20.002
and so Christopher
Columbus had to write back

00:05:20.002 --> 00:05:23.334
to the Spanish crown to make
sure that he was actually

00:05:23.334 --> 00:05:25.772
making progress on his mission,

00:05:25.772 --> 00:05:28.297
that he was, in fact,
finding a new trade route

00:05:28.297 --> 00:05:32.620
and increasing capital
for the Spanish crown

00:05:32.620 --> 00:05:34.027
or else they would stop funding him

00:05:34.027 --> 00:05:35.710
so there's a lot written about his voyage

00:05:35.710 --> 00:05:38.677
between his journal and between
these official documents

00:05:38.677 --> 00:05:40.527
and within those documents,

00:05:40.527 --> 00:05:43.332
you can see that Christopher Columbus

00:05:43.332 --> 00:05:45.080
and his people had intentions

00:05:45.080 --> 00:05:48.859
of conquering and
colonizing the Taíno people.

00:05:48.859 --> 00:05:52.467
Christopher Columbus writes,
"They were very well built

00:05:52.467 --> 00:05:54.646
with very handsome bodies
and very good faces.

00:05:54.646 --> 00:05:57.125
They do not carry arms or know them.

00:05:57.125 --> 00:05:58.750
They should be good servants."

00:05:58.750 --> 00:06:02.024
Later on, he writes about the Taíno people

00:06:02.024 --> 00:06:03.708
who were historically jewelry traders

00:06:03.708 --> 00:06:07.202
and helped them a lot with
finding different resources

00:06:07.202 --> 00:06:09.617
and gold and silver.

00:06:09.617 --> 00:06:14.337
He writes, "I could conquer
the whole of them with 50 men."

00:06:14.337 --> 00:06:16.369
These sorts of quotes
from Columbus's journal

00:06:16.369 --> 00:06:19.859
provide evidence to
historians that Columbus's

00:06:19.859 --> 00:06:22.152
violence against the Taíno people

00:06:22.152 --> 00:06:24.633
was premeditated and planned.

00:06:24.633 --> 00:06:26.951
So, this photo down here
depicts the Taíno people

00:06:26.951 --> 00:06:28.868
welcoming the Spaniards

00:06:33.443 --> 00:06:34.697
and this image depicts

00:06:34.697 --> 00:06:36.276
the traditional Taíno culture.

00:06:36.276 --> 00:06:37.907
You can see the jewelry,

00:06:37.907 --> 00:06:40.229
which Christopher Columbus
writes extensively about,

00:06:40.229 --> 00:06:43.456
lots of gold jewelry, he
found it very beautiful.

00:06:43.456 --> 00:06:45.345
He was met by these friendly people,

00:06:45.345 --> 00:06:48.153
but he did have intentions
of colonizing them

00:06:48.153 --> 00:06:52.320
and turning them into servants
and slaves which he then did.

00:06:53.366 --> 00:06:55.020
So when he returned to Spain,

00:06:55.020 --> 00:06:58.353
25 Taínos got on the ship with him back,

00:06:59.368 --> 00:07:02.416
but only seven survived and
so this began the practice

00:07:02.416 --> 00:07:05.341
of forcing the Taínos into servitude

00:07:05.341 --> 00:07:09.016
which would increase over
the next 10 to 15 years

00:07:09.016 --> 00:07:10.893
during which Christopher
Columbus would come back

00:07:10.893 --> 00:07:13.753
and forth to the Caribbean.

00:07:13.753 --> 00:07:17.243
Ultimately Christopher
Columbus made four voyages,

00:07:17.243 --> 00:07:20.434
so the first one was in 1492, up here,

00:07:20.434 --> 00:07:23.279
but then there were three more voyages

00:07:23.279 --> 00:07:25.392
over the next couple years

00:07:25.392 --> 00:07:27.911
and over the course of
these three voyages,

00:07:27.911 --> 00:07:32.078
the Taíno people were decimated
by violence and disease.

00:07:33.153 --> 00:07:36.197
So, between the forced servitude

00:07:36.197 --> 00:07:40.465
and the mutilation that the
colonizers would practice,

00:07:40.465 --> 00:07:44.815
they would actually cut off
the Taínos limbs or hands

00:07:44.815 --> 00:07:46.690
if they refused to do work for them,

00:07:46.690 --> 00:07:49.244
disease really was what killed

00:07:49.244 --> 00:07:52.230
the most Native Americans at the time.

00:07:52.230 --> 00:07:54.811
On the ships, the colonizers
would bring with them,

00:07:54.811 --> 00:07:57.249
yes, weapons, but most notably microbes

00:07:57.249 --> 00:08:02.230
that the Taíno people were not
accustomed to fighting off.

00:08:02.230 --> 00:08:04.929
When they would come into
contact with these new diseases,

00:08:04.929 --> 00:08:09.297
the Native Americans
were killed in the masses

00:08:09.297 --> 00:08:11.657
so over the course of
Christopher Columbus's

00:08:11.657 --> 00:08:13.828
colonization of the Caribbean,
he ended up going to,

00:08:13.828 --> 00:08:18.298
I'll scroll up and show you
a little bit more on the map,

00:08:18.298 --> 00:08:19.949
he ended up going to San Salvador,

00:08:19.949 --> 00:08:21.774
that was the first stop,

00:08:21.774 --> 00:08:24.353
then to Cuba and then to Española,

00:08:24.353 --> 00:08:26.992
which is the modern day
Dominican Republic and Haiti

00:08:26.992 --> 00:08:29.920
and here, in all these places,
Christopher Columbus's men

00:08:29.920 --> 00:08:33.821
set up different colonies and slowly,

00:08:33.821 --> 00:08:35.690
as Christopher Columbus kind of went back

00:08:35.690 --> 00:08:37.733
and forth to Spain,

00:08:37.733 --> 00:08:40.021
the colonies rebelled against him.

00:08:40.021 --> 00:08:44.369
By his third voyage, Columbus
ultimately gets removed

00:08:44.369 --> 00:08:46.621
completely from this colonization project

00:08:46.621 --> 00:08:48.893
because he proved such an awful leader

00:08:48.893 --> 00:08:53.308
and he really had violent
tendencies toward the Taíno people

00:08:53.308 --> 00:08:55.499
so in the next video I'll
talk a little bit more

00:08:55.499 --> 00:08:59.055
about the implications of the
contact with the new world

00:08:59.055 --> 00:09:01.162
and about how Christopher
Columbus has become

00:09:01.162 --> 00:09:03.972
such a controversial
figure in American memory

00:09:03.972 --> 00:09:05.804
and American celebration.