Language and notation of the circle

WEBVTT
Kind: captions
Language: en

00:00:00.520 --> 00:00:02.500
Let's start again with a point.

00:00:02.500 --> 00:00:05.730
Let's call that point point
A. And what I'm curious about

00:00:05.730 --> 00:00:08.530
is all of the points on
my screen right over here,

00:00:08.530 --> 00:00:11.860
that are exactly 2
centimeters away from A.

00:00:11.860 --> 00:00:16.092
So 2 centimeters on my
screen is about that far.

00:00:16.092 --> 00:00:17.550
So clearly if I
start at A and I go

00:00:17.550 --> 00:00:20.410
2 centimeters in that direction,
this point right over there,

00:00:20.410 --> 00:00:23.840
is 2 centimeters from A. If
I call that point, point B,

00:00:23.840 --> 00:00:27.600
then I could say line
segment AB is 2 centimeters.

00:00:27.600 --> 00:00:28.926
The length is 2 centimeters.

00:00:28.926 --> 00:00:33.280
Remember this would refer
to the actual line segment.

00:00:33.280 --> 00:00:36.332
I could say this looks nice,
but if I talk about its length,

00:00:36.332 --> 00:00:37.790
I would get rid of
that line on top

00:00:37.790 --> 00:00:39.580
and I would just say
AB is equal to 2.

00:00:39.580 --> 00:00:42.540
If I wanted to put units I
could say 2 centimenters.

00:00:42.540 --> 00:00:45.445
But I'm not curious just about
B, I want to think about all

00:00:45.445 --> 00:00:47.800
of the points, the set
of all of the points

00:00:47.800 --> 00:00:51.330
that are exactly 2
centimeters away from A.

00:00:51.330 --> 00:00:53.810
So I could go 2 centimeters
in the other direction,

00:00:53.810 --> 00:00:57.190
maybe get to point
C right over here.

00:00:57.190 --> 00:01:00.170
So AC is also going to be
equal to 2 centimeters,

00:01:00.170 --> 00:01:02.970
but I could go 2 centimeters
in any direction.

00:01:02.970 --> 00:01:04.910
And so if I find the
set of all of the points

00:01:04.910 --> 00:01:07.150
that are exactly 2
centimeters away from A,

00:01:07.150 --> 00:01:11.970
I will get a very familiar
looking shape, like this,

00:01:11.970 --> 00:01:13.930
and I'm trying to
draw it freehand.

00:01:13.930 --> 00:01:16.424
So I would get a shape
that looks like this.

00:01:16.424 --> 00:01:17.590
Actually, let me draw it in.

00:01:17.590 --> 00:01:20.173
I don't want to make you think
that it's only the points where

00:01:20.173 --> 00:01:22.750
there's white, it's all of
these points right over here.

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I don't want to draw a dashed
line over there, which maybe I

00:01:25.250 --> 00:01:28.570
should just, let me
clear out all of these

00:01:28.570 --> 00:01:31.610
and I'll just draw
it as a solid line.

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So this could look
something like that.

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My best attempt.

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And this set of all
of the points that

00:01:40.500 --> 00:01:43.425
are exactly 2
centimeters away from A,

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this is a circle, as I'm sure
you are already familiar with.

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But that is the formal
definition-- the set

00:01:49.030 --> 00:01:51.590
of all points that
are a fixed distance,

00:01:51.590 --> 00:01:53.610
or that have a fixed
distance, from A

00:01:53.610 --> 00:01:55.410
that are a given
distance from A.

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If I said the set of all points
that are 3 centimeters from A,

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it might look
something like this.

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It might look
something like that.

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That would give
us another circle.

00:02:06.120 --> 00:02:07.992
I think you get
the general idea.

00:02:07.992 --> 00:02:09.450
Now what I want to
do in this video

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is introduce ourselves into
some of the concepts and words

00:02:14.180 --> 00:02:16.540
that we use when
dealing with circles.

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So let me get rid of
that 3-centimeter circle.

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So first of all, let's
think about this distance.

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This distance, or one
of these line segments

00:02:26.200 --> 00:02:30.420
that join A, which we would
call the center of the circle.

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So we'll call A the
center of the circle,

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and it makes sense
just from the way

00:02:33.730 --> 00:02:36.250
we use the word center
in everyday life.

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What I want to do is think
about what line segment AB is.

00:02:41.510 --> 00:02:45.740
AB connects the center and it
connects a point on the circle

00:02:45.740 --> 00:02:46.320
itself.

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Remember, the circle itself
is all of the points that

00:02:48.528 --> 00:02:50.140
are equal distance
from the center.

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So AB, any line
segment, I should say,

00:02:53.510 --> 00:02:56.150
that connects the center
to a point on the circle,

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we would call a radius.

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And so the length of the
radius, AB over here,

00:03:03.880 --> 00:03:05.340
is equal to 2 centimeters.

00:03:05.340 --> 00:03:07.830
And you're probably already
familiar with the word radius,

00:03:07.830 --> 00:03:09.663
but I'm just being a
little bit more formal.

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And what's interesting
about geometry,

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at least when you start learning
it at the high school level,

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is it's probably the
first class where you're

00:03:15.220 --> 00:03:18.780
introduced into a slightly more
formal mathematics, where we're

00:03:18.780 --> 00:03:21.720
a little bit more careful
about giving our definitions

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and then building
on those definitions

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to come up with
interesting results

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and proving to ourselves
that we definitely

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know what we think we know.

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And so that's why we're
being a little bit more

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careful with our
language over here.

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So AB is our radius,
line segment AB, and so

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is line segment-- let me
draw another point on here,

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let's say this is X-- so line
segment AX is also a radius.

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Now you can also have other
forms of lines and line

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segments that interact
in interesting ways

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with the circle.

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So you could have a line
that just intersects

00:04:02.680 --> 00:04:05.110
that circle at
exactly one point.

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So let's call that point right
over there, let's call that D.

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And let's say you have a
line, and the only point

00:04:12.570 --> 00:04:16.760
on the circle-- the only point
in the set of all of the points

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that are equal distant from A,
the only point on that circle

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that is also on that
line is point D.

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And we could call that line l.

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So sometimes you'll
see lines specified

00:04:27.390 --> 00:04:29.350
by some of the points on them.

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So for example, if I had another
point right over here called E,

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we could call this line
line DE, or we could just

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put a little script
letter here with an l

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and say this is line l.

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But this line that only
has one point in common

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with our circle, we call
this a tangent line.

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So line l is a tangent.

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It is tangent to the circle.

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So let me write it
this way, line l

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is tangent-- you normally
wouldn't write it

00:05:01.546 --> 00:05:02.920
in caps like this,
I'm just doing

00:05:02.920 --> 00:05:06.840
that for emphasis-- is tangent
to-- instead of writing

00:05:06.840 --> 00:05:09.250
the circle centered
at A, you'll sometimes

00:05:09.250 --> 00:05:13.049
see this notation-- to
the circle centered at A.

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So this tells us that this is
the circle we're talking about.

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Because who knows, maybe we
had another circle over here

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that is centered at
M, another circle.

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So we have to specify it's
not tangent to that one,

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it's tangent to this one.

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So this circle with
a dot in the middle

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tells we're talking
about a circle,

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and this is a circle
centered at point

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A. I want to be very clear,
point A is not on the circle,

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point A is the
center of the circle.

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The points on the circle
are the points equal distant

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from point A. Now, l is
tangent, because it only

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intersects the
circle in one point.

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You could just as
easily imagine a line

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that intersects the
circle at two points.

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So we could call, maybe
this is F and this is G,

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you could call that line FG.

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So we could write it
like this, line FG.

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And this line that
intersects it at two points,

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we call this a
secant of circle A.

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It is a secant line to this
circle right over here,

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because it intersects
it in two points.

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Now, if FG was just
a segment, if it

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didn't keep on going forever,
like lines like to do,

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if we only spoke about
this line segment--

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let me do this in a new
color-- if we only spoke

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about this line segment
between F and G,

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and not thinking about going on
forever, then all of a sudden

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we have a line segment,
which we would specify there.

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And we would call this
a chord of the circle,

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a chord of circle A. It starts
at a point on the circle,

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a point that is exactly in
this case 2 centimeters away,

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and then it finishes at
a point on the circle.

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So it connects two
points on the circle.

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Now, you could have
chords like this,

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and you can also have a
chord, as you can imagine,

00:07:02.630 --> 00:07:04.930
a chord that actually
goes through the center

00:07:04.930 --> 00:07:06.280
of the circle.

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So let's call this
point, point H,

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and you have a straight line
connecting F to H through A.

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So that's about as straight
as I could draw it.

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So if you have a
chord like that,

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that contains the actual
center of the circle,

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of course it goes from
one point of the circle

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to another point of
the circle, and it goes

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through the center
of the circle,

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we call that a diameter of A.

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And you've probably seen
this in tons of problems

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before, when we were not talking
about geometry as formally,

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but the diameter is made
up of exactly two radiuses.

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We already know that a radius
connects a point to the center.

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So you have one
radius right over here

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that connects F and
A, that's one radius,

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and then you have
another radius connecting

00:08:02.400 --> 00:08:05.620
A and H, the center to
a point on the circle.

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So the diameter is made
up of these two radiuses,

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or radii I should
call it, I think

00:08:09.500 --> 00:08:11.570
that's the plural for radius.

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And so the length
of a diameter is

00:08:13.000 --> 00:08:15.700
going to be twice the
length of a radius.

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So we could say the length of
the diameter, so the length

00:08:19.530 --> 00:08:22.580
of FH-- and once again I don't
put the line on top of it

00:08:22.580 --> 00:08:24.300
when I'm just talking
about the length--

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is going to be equal to
FA, the length of segment

00:08:28.410 --> 00:08:34.370
FA, plus the length
of segment AH.

00:08:34.370 --> 00:08:36.309
Now there's one
last thing I want

00:08:36.309 --> 00:08:38.309
to talk about when we're
dealing with circles,

00:08:38.309 --> 00:08:40.360
and that's the idea of an arc.

00:08:40.360 --> 00:08:43.760
So we also have the parts
of the circle itself.

00:08:43.760 --> 00:08:46.600
So let me draw another
circle over here.

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Let's center this circle
right over here at B.

00:08:49.506 --> 00:08:52.080
And I'm going to find
all of the points that

00:08:52.080 --> 00:08:56.470
are a given distance from
B. So it has some radius,

00:08:56.470 --> 00:08:59.150
I'm not going to specify
it right over here,

00:08:59.150 --> 00:09:01.490
and let me pick some random
points on the circle.

00:09:01.490 --> 00:09:10.130
So let's call this J, let's
call that K, let's call this S,

00:09:10.130 --> 00:09:14.297
let's call this T, let's
call this U right over here.

00:09:14.297 --> 00:09:16.880
And I know it doesn't look that
centered, let me try to center

00:09:16.880 --> 00:09:17.830
B a little bit better.

00:09:17.830 --> 00:09:19.520
Let me erase that.

00:09:19.520 --> 00:09:21.110
And if I put B a
little bit closer

00:09:21.110 --> 00:09:25.260
to the center of the circle, so
that's my best shot, so let's

00:09:25.260 --> 00:09:27.220
put B right over there.

00:09:27.220 --> 00:09:29.130
Now, one interesting
thing is, what do you

00:09:29.130 --> 00:09:33.340
call the length of the circle
that goes between two points?

00:09:33.340 --> 00:09:37.140
So what would you call-- let
me get a good color here--

00:09:37.140 --> 00:09:38.607
what would you call this?

00:09:38.607 --> 00:09:40.440
Well, you could imagine
in everyday language

00:09:40.440 --> 00:09:41.990
we would call something
that looks like that an arc,

00:09:41.990 --> 00:09:44.140
and we would also call
that an arc in geometry.

00:09:44.140 --> 00:09:46.350
To specify this
arc we would call

00:09:46.350 --> 00:09:50.456
this JK, the two
endpoints of the arc,

00:09:50.456 --> 00:09:51.830
the two points on
the circle that

00:09:51.830 --> 00:09:53.371
are the endpoints
of the arc, and you

00:09:53.371 --> 00:09:55.130
use a little notation like that.

00:09:55.130 --> 00:09:59.030
So you put a little curve on
top instead of a straight line.

00:09:59.030 --> 00:10:01.620
Now you could also have
another arc that connects JK,

00:10:01.620 --> 00:10:03.010
this is the minor arc.

00:10:03.010 --> 00:10:06.250
It is the shortest way along
the circle to connect J and K,

00:10:06.250 --> 00:10:08.670
but you could also go
the other way around.

00:10:08.670 --> 00:10:10.390
You could also have
this thing that

00:10:10.390 --> 00:10:13.570
goes all the way
around the circle.

00:10:13.570 --> 00:10:15.660
And we would call
that the major arc.

00:10:15.660 --> 00:10:17.870
And normally when you
specify a major arc, just

00:10:17.870 --> 00:10:21.030
to show that you're going
the long way around,

00:10:21.030 --> 00:10:23.420
it's not the shortest way
to get between J and K,

00:10:23.420 --> 00:10:24.840
you'll often specify
another point

00:10:24.840 --> 00:10:25.923
that you're going through.

00:10:25.923 --> 00:10:30.350
So for example, this major arc
we could specify we start at J,

00:10:30.350 --> 00:10:32.530
we went through-- we could
have said U, T, or S,

00:10:32.530 --> 00:10:34.890
but I'll put T right over
there-- we went through T

00:10:34.890 --> 00:10:37.170
and then we went
all the way to K.

00:10:37.170 --> 00:10:40.012
And so this specifies
the major arc

00:10:40.012 --> 00:10:42.470
and this thing could have been
the same thing as if I wrote

00:10:42.470 --> 00:10:48.050
JUK, these are specifying
the same thing, or JSK.

00:10:48.050 --> 00:10:51.150
So there's multiple ways
to specify this major arc

00:10:51.150 --> 00:10:51.990
right over here.

00:10:51.990 --> 00:10:53.790
But the one thing
I make clear is,

00:10:53.790 --> 00:10:56.590
is that the minor arc is
the shortest distance,

00:10:56.590 --> 00:11:01.750
so this is the minor arc, and
the longer distance around

00:11:01.750 --> 00:11:03.000
is the major arc.

00:11:06.470 --> 00:11:09.020
And I'll leave you there and
maybe the next few videos we'll

00:11:09.020 --> 00:11:12.590
start playing with some of this
notation a little bit more.


Inverse property of multiplication

WEBVTT
Kind: captions
Language: en

00:00:00.813 --> 00:00:02.867
Let's say that I have five lemons

00:00:02.867 --> 00:00:07.129
so that's [counting to five] ... five lemons

00:00:07.129 --> 00:00:12.238
and I were to ask you: what do I have to multiply times five to get one?

00:00:12.238 --> 00:00:16.974
or in this case: what do I have to multiply times five lemons to get one lemon?

00:00:16.974 --> 00:00:19.467
and so, another question you might ask

00:00:19.486 --> 00:00:22.812
because really multiplication and division are two sides of the same coin

00:00:22.812 --> 00:00:23.312
is

00:00:23.312 --> 00:00:27.300
what do I have to divide five by to get to one lemon

00:00:27.300 --> 00:00:30.116
or yellow circle, or whatever I have drawn right over here

00:00:30.116 --> 00:00:35.132
Well, if you have five things and you divide by five, you're gonna have five groups of one

00:00:35.132 --> 00:00:39.636
so if you divide by five, you're gonna have [counting to five] ... five groups

00:00:39.636 --> 00:00:44.141
So you could say five divided by five is equal to one

00:00:44.141 --> 00:00:49.400
take five things and divide it into five groups then each group is going to have one in them

00:00:49.400 --> 00:00:54.855
or you could say five times one fifth is equal to one

00:00:54.855 --> 00:00:56.929
(and I use the dot for multiplication)

00:00:56.929 --> 00:01:00.767
I could also say five times one fifth is equal to one

00:01:00.767 --> 00:01:03.631
these are all really saying the same thing

00:01:03.631 --> 00:01:06.467
Maybe what's kind of interesting here

00:01:06.467 --> 00:01:09.128
(although it's not some huge learning)

00:01:09.128 --> 00:01:12.933
it's really just another way of writing what you already probably know,

00:01:12.933 --> 00:01:19.467
is this idea that if I have a number and I multiply times it's multiplicative inverse

00:01:19.467 --> 00:01:22.533
(and most of the time when people talk about inverses in mathematics

00:01:22.533 --> 00:01:24.637
they are talking about the multiplicative inverse)

00:01:24.637 --> 00:01:26.465
then I'm going to get one

00:01:26.465 --> 00:01:28.579
so five time one fifth is equal to one

00:01:28.579 --> 00:01:34.389
but that's just because five times one fifth is the same thing as five divided by five

00:01:34.389 --> 00:01:35.968
if you were to actually multiply this out

00:01:35.968 --> 00:01:38.476
you actually take five times one fifth

00:01:38.476 --> 00:01:44.652
this is equal to five-over-one times one-over-five

00:01:44.652 --> 00:01:47.400
you multiply the numerators: five times one is five

00:01:47.400 --> 00:01:51.133
multiply the denominators: one times five is five

00:01:51.133 --> 00:01:56.634
so you have five fifths, and five fifths is the exact same thing as one

00:01:56.634 --> 00:01:58.445
So if someone where to ask you a question,

00:01:58.445 --> 00:02:01.789
they say "Hey, I have the number 217

00:02:01.789 --> 00:02:07.535
and I want to multiply it by something, and I want to get one after multiplying it by that something"

00:02:07.535 --> 00:02:12.470
Well then you say - Well look, If I took 217 and divided it by 217 that would get me to one

00:02:12.470 --> 00:02:19.761
and dividing by 217 is the exact same thing as multiplying by one-over-217

00:02:19.761 --> 00:02:22.348
multiplying by its multiplicative inverse

00:02:22.348 --> 00:02:25.867
which is, once again, a word that is fancier than the actual concept

00:02:25.867 --> 00:02:28.323
you are just multiplying by the inverse of this number

00:02:28.323 --> 00:02:29.519
Another way to think about it is

00:02:29.519 --> 00:02:35.005
if I have five things and I take one fifth of those things, how many things do I have?

00:02:35.005 --> 00:02:39.777
Well, if I take one fifth of five things I have exactly one thing right over here

00:02:39.777 --> 00:02:42.377
But the general idea is super-duper-duper simple

00:02:42.377 --> 00:02:47.318
if I have some crazy number ... 8,345

00:02:47.318 --> 00:02:50.458
that's actually not so crazy, let's turn it to something in the millions

00:02:50.458 --> 00:02:52.071
... and 271 ...

00:02:52.086 --> 00:02:52.645
so

00:02:52.645 --> 00:02:55.502
8,345,271

00:02:55.502 --> 00:02:57.647
And I say, what do I have to multiply by

00:02:57.647 --> 00:02:59.642
(and now I use this multiplication symbol right now)

00:02:59.642 --> 00:03:03.461
what do I have to multiply that by in order to get one?

00:03:03.461 --> 00:03:05.969
I just have to multiply it by the inverse of this

00:03:05.969 --> 00:03:08.138
the multiplicative inverse of this

00:03:08.138 --> 00:03:16.199
so one-over-8,345,271


Inverse property of addition

WEBVTT
Kind: captions
Language: en

00:00:00.570 --> 00:00:03.110
Let's say that we have the
number 5, and we're asked,

00:00:03.110 --> 00:00:07.870
what number do we add to
the number 5 to get to 0?

00:00:07.870 --> 00:00:10.620
And you might already know
this, but I'll just draw it out.

00:00:10.620 --> 00:00:13.900
So let's say we have a
number line right over here.

00:00:13.900 --> 00:00:16.300
And 0 is sitting
right over there.

00:00:16.300 --> 00:00:19.740
And we are already
sitting here at 5.

00:00:19.740 --> 00:00:23.995
So to go from 5 to 0, we have
to go five spaces to the left.

00:00:27.710 --> 00:00:29.550
And if we're going five
spaces to the left,

00:00:29.550 --> 00:00:32.400
that means that we
are adding negative 5.

00:00:32.400 --> 00:00:34.780
So if we add negative
5 right here,

00:00:34.780 --> 00:00:38.250
then that is going
to get us back to 0.

00:00:38.250 --> 00:00:40.750
That is going to get us
back right over here to 0.

00:00:40.750 --> 00:00:42.680
And you probably
already knew this.

00:00:42.680 --> 00:00:45.900
And this is a pretty maybe
common sense thing right here.

00:00:45.900 --> 00:00:49.170
But there's a fancy word for
it called the additive inverse

00:00:49.170 --> 00:00:50.070
property.

00:00:50.070 --> 00:00:52.060
And all the additive--
I'll just write it down.

00:00:52.060 --> 00:00:53.768
I think it's kind of
ridiculous that it's

00:00:53.768 --> 00:00:55.940
given such a fancy word
for such a simple idea--

00:00:55.940 --> 00:00:58.600
additive inverse property.

00:00:58.600 --> 00:01:00.650
And it's just the idea
that if you have a number

00:01:00.650 --> 00:01:03.920
and you add the additive
inverse of the number, which

00:01:03.920 --> 00:01:06.320
is what most people call
the negative of the number--

00:01:06.320 --> 00:01:08.530
if you add the negative of
the number to your number,

00:01:08.530 --> 00:01:10.920
you're going to get back
to 0 because they have

00:01:10.920 --> 00:01:13.860
the same size, you
could view it that way.

00:01:13.860 --> 00:01:16.190
They both have a magnitude
of 5, but this is going five

00:01:16.190 --> 00:01:20.060
to the right and then you're
going five back to the left.

00:01:20.060 --> 00:01:24.860
Similarly, if you started at--
let me draw another number line

00:01:24.860 --> 00:01:29.310
right over here-- if you
started at negative 3.

00:01:29.310 --> 00:01:31.570
If you're starting right
over here at negative 3,

00:01:31.570 --> 00:01:34.040
so you've already moved
three spaces to the left,

00:01:34.040 --> 00:01:39.030
and someone says, well what
do I have to add to negative 3

00:01:39.030 --> 00:01:39.920
to get back to 0?

00:01:39.920 --> 00:01:42.660
Well, I have to move three
spaces to the right now.

00:01:42.660 --> 00:01:45.160
And three spaces to the right
is in the positive direction.

00:01:45.160 --> 00:01:47.540
So I have to add positive 3.

00:01:47.540 --> 00:01:51.270
So if I add positive 3 to
negative 3, I will get 0.

00:01:51.270 --> 00:02:00.030
So in general, if I have any
number-- if I have 1,725,314

00:02:00.030 --> 00:02:03.170
and I say, what do I need to
add to this to get back to 0?

00:02:03.170 --> 00:02:07.010
Well, I have to essentially
go in the opposite direction.

00:02:07.010 --> 00:02:09.180
I have to go in the
leftwards direction.

00:02:09.180 --> 00:02:11.000
So I'm going to subtract
the same amount.

00:02:11.000 --> 00:02:13.880
Or I could say, I'm going
to add the additive inverse,

00:02:13.880 --> 00:02:16.270
or I'm going to add the
negative version of it.

00:02:16.270 --> 00:02:18.690
So this is going to be
the same thing as adding

00:02:18.690 --> 00:02:26.230
negative 1,725,314 and
that'll just get me back to 0.

00:02:26.230 --> 00:02:29.850
Similarly, if I say, what number
do I have to add to negative 7

00:02:29.850 --> 00:02:30.410
to get to 0?

00:02:30.410 --> 00:02:33.430
Well, if I'm already at negative
7, I have to go 7 to the right

00:02:33.430 --> 00:02:35.510
so I have to add positive 7.

00:02:35.510 --> 00:02:39.080
And this is going
to be equal to 0.

00:02:39.080 --> 00:02:41.460
And this all comes
from the general idea

00:02:41.460 --> 00:02:44.970
5 plus negative 5, 5
plus the negative of 5,

00:02:44.970 --> 00:02:47.410
or 5 plus the
additive inverse of 5,

00:02:47.410 --> 00:02:51.314
you can just view this as
another way of 5 minus 5.

00:02:51.314 --> 00:02:52.730
And if you have
five of something,

00:02:52.730 --> 00:02:55.540
and you take away five, you've
learned many, many years ago

00:02:55.540 --> 00:02:58.524
that that is just
going to get you to 0.


Partial quotient method of division 2

WEBVTT
Kind: captions
Language: en

00:00:00.260 --> 00:00:02.920
I thought I would do another
example of the partial quotient

00:00:02.920 --> 00:00:05.370
method for long division,
so that it actually

00:00:05.370 --> 00:00:08.619
has some positives to it, it
actually is kind of fun to do.

00:00:08.619 --> 00:00:10.660
So let's say I want to do
something really hairy,

00:00:10.660 --> 00:00:16.160
like 291 divided into--
let me just throw

00:00:16.160 --> 00:00:19.861
some digits over
here-- 390-- actually,

00:00:19.861 --> 00:00:21.610
let's throw another
digit right over here.

00:00:21.610 --> 00:00:24.050
So this is, how
many times does 291

00:00:24.050 --> 00:00:29.440
go into-- what is
this-- 9,873,952?

00:00:29.440 --> 00:00:31.770
And to just kind of
get our bearings,

00:00:31.770 --> 00:00:34.029
we know what 291 times 1 is.

00:00:34.029 --> 00:00:34.820
That's pretty easy.

00:00:34.820 --> 00:00:38.590
291 times 1 is clearly just 291.

00:00:38.590 --> 00:00:41.270
We know what 291 times 10 is.

00:00:41.270 --> 00:00:44.252
That's clearly 2,910.

00:00:44.252 --> 00:00:47.550
Now let's get some stuff in
between here that will help us

00:00:47.550 --> 00:00:50.840
as we try to approximate
how many times 291 goes

00:00:50.840 --> 00:00:53.380
into this crazy thing over here.

00:00:53.380 --> 00:00:54.270
So let's just pick.

00:00:54.270 --> 00:00:56.730
And in the last example,
I picked 2 and 5.

00:00:56.730 --> 00:00:58.602
You could just pick
3 and 6 if you want.

00:00:58.602 --> 00:00:59.560
You could pick 2 and 7.

00:00:59.560 --> 00:01:00.560
You could pick
whatever you want.

00:01:00.560 --> 00:01:03.250
You could even just do 1, one
of them, one of the above.

00:01:03.250 --> 00:01:10.700
But let's just say 291 times--
let's try 3 out-- 291 times 3.

00:01:10.700 --> 00:01:12.260
So I could do this in my head.

00:01:12.260 --> 00:01:14.110
Or just make sure I
don't make a mistake,

00:01:14.110 --> 00:01:15.520
let me do it right over here.

00:01:15.520 --> 00:01:20.480
So 291 times 3 is--
1 times 3 is 3.

00:01:20.480 --> 00:01:22.950
9 times 3 is 27.

00:01:22.950 --> 00:01:24.700
2 times 3 is 6.

00:01:24.700 --> 00:01:27.390
6 plus 2 is 8.

00:01:27.390 --> 00:01:31.220
So this is equal to 873.

00:01:31.220 --> 00:01:34.010
It's actually strange that
873 showed up over there.

00:01:34.010 --> 00:01:36.410
Maybe my brain is doing strange
things in the background.

00:01:36.410 --> 00:01:38.159
But anyway, that has
actually no relevance

00:01:38.159 --> 00:01:40.580
to the actual solution
of this problem.

00:01:40.580 --> 00:01:44.146
And let's also try 291 times 6.

00:01:46.920 --> 00:01:49.270
Let's figure out what that is.

00:01:49.270 --> 00:01:52.110
So 291 times 6, it's
actually just going

00:01:52.110 --> 00:01:53.330
to be this thing times 2.

00:01:53.330 --> 00:01:54.660
But I'll just calculate it.

00:01:54.660 --> 00:01:58.120
291 times 6-- 1 times 6 is 6.

00:01:58.120 --> 00:02:00.330
9 times 6 is 54.

00:02:00.330 --> 00:02:03.720
2 times 6 is 12, plus 5 is 17.

00:02:03.720 --> 00:02:08.889
So it's 1,746.

00:02:08.889 --> 00:02:10.850
And you might say,
Sal, why did you

00:02:10.850 --> 00:02:13.210
go through the trouble of
figuring out this and this?

00:02:13.210 --> 00:02:16.280
And I'm just using these
as some approximation tools

00:02:16.280 --> 00:02:18.380
when we try to figure out
how many times 291 goes

00:02:18.380 --> 00:02:20.895
into this whole crazy mess.

00:02:20.895 --> 00:02:23.340
So first of all, let's just
look at this whole thing.

00:02:23.340 --> 00:02:25.785
This is 9,873,000.

00:02:25.785 --> 00:02:28.720
So let's just say, how
many times does 291

00:02:28.720 --> 00:02:32.180
go into 9 million?

00:02:32.180 --> 00:02:36.720
So 291 times 3 would be 873.

00:02:36.720 --> 00:02:40.700
We want to have a bunch
of zeros after the 873.

00:02:40.700 --> 00:02:43.550
So think of it this way--
and I'm picking 873,

00:02:43.550 --> 00:02:46.910
because its leading digit is
as close to the 9 as possible.

00:02:46.910 --> 00:02:49.420
But it's definitely
lower than the 9.

00:02:49.420 --> 00:02:52.070
So you say, OK,
873-- and I'm going

00:02:52.070 --> 00:02:56.060
to have one, two, three,
four zeros behind it.

00:02:56.060 --> 00:03:01.086
So 291 times 3 will give me 873.

00:03:01.086 --> 00:03:02.460
But I have to
multiply it times 3

00:03:02.460 --> 00:03:05.830
with one, two, three,
four zeros to get

00:03:05.830 --> 00:03:09.940
this number, 8.73 million.

00:03:09.940 --> 00:03:11.640
So I have to multiply
it by 30,000.

00:03:11.640 --> 00:03:14.500
But I got that straight from
this idea, that 291 times 3

00:03:14.500 --> 00:03:16.320
is 873.

00:03:16.320 --> 00:03:18.930
So let's subtract
this right over here.

00:03:18.930 --> 00:03:21.880
Let's subtract this,
2 minus 0 is 2.

00:03:21.880 --> 00:03:26.170
5, 9, 3, 7 minus 3 is 4.

00:03:26.170 --> 00:03:27.750
8 minus 7 is 1.

00:03:27.750 --> 00:03:30.260
9 minus 8 is 1.

00:03:30.260 --> 00:03:35.870
So now we're left
with 1,143,952.

00:03:35.870 --> 00:03:40.190
So which of these just
gets us right under that?

00:03:40.190 --> 00:03:43.105
So let's see.

00:03:43.105 --> 00:03:43.830
Let's see.

00:03:43.830 --> 00:03:47.750
If we want to go to-- we
can't go straight to 1,746,

00:03:47.750 --> 00:03:49.410
that will be too big over here.

00:03:49.410 --> 00:03:51.300
We might want to do 873 again.

00:03:51.300 --> 00:03:57.590
But this time, we're
going to do it 873,000.

00:03:57.590 --> 00:04:01.460
That is equal to 3-- and then
you have one, two, three zeros,

00:04:01.460 --> 00:04:03.110
so one, two, three.

00:04:03.110 --> 00:04:06.330
3 times 291 is 873.

00:04:06.330 --> 00:04:08.240
3,000 is 873,000.

00:04:08.240 --> 00:04:09.910
Let me write this a
little bit neater.

00:04:09.910 --> 00:04:19.620
My handwriting is-- so this is
going to be 3,000 times 291.

00:04:19.620 --> 00:04:20.750
And just let me make sure.

00:04:20.750 --> 00:04:21.959
This is a 2 right over here.

00:04:21.959 --> 00:04:23.310
2 minus 0 is 2.

00:04:23.310 --> 00:04:27.110
And then you subtract again.

00:04:27.110 --> 00:04:28.630
2 minus 0 is 2.

00:04:28.630 --> 00:04:30.370
5 minus 0 is 5.

00:04:30.370 --> 00:04:31.850
9 minus 0 is 9.

00:04:31.850 --> 00:04:34.390
3 minus 3 is 0.

00:04:34.390 --> 00:04:37.460
And then you have 4 minus 7.

00:04:37.460 --> 00:04:39.040
So the way I like
to do it when I

00:04:39.040 --> 00:04:40.730
have to start
regrouping and borrowing

00:04:40.730 --> 00:04:42.810
is making sure I
go from the left.

00:04:42.810 --> 00:04:45.030
So this 1, I could
borrow from there,

00:04:45.030 --> 00:04:47.310
so that this becomes an 11.

00:04:47.310 --> 00:04:50.280
And then the 4, I can
borrow 1 from here,

00:04:50.280 --> 00:04:51.400
so that becomes a 10.

00:04:51.400 --> 00:04:53.160
And then this becomes a 14.

00:04:53.160 --> 00:04:56.090
So 14 minus 7 is 7.

00:04:56.090 --> 00:04:58.480
10 minus 8 is 2.

00:04:58.480 --> 00:05:01.435
So I'm down to 270,952.

00:05:01.435 --> 00:05:04.464
So what's right below that?

00:05:04.464 --> 00:05:06.130
So it seems that we
can get pretty close

00:05:06.130 --> 00:05:12.310
if we do 291 times 6,
so if you do a 1,746

00:05:12.310 --> 00:05:14.240
and then add two zeros to it.

00:05:14.240 --> 00:05:17.590
This is going to be
times 6 with two zeros,

00:05:17.590 --> 00:05:20.290
so this is times 600.

00:05:20.290 --> 00:05:22.561
Once again, you subtract.

00:05:22.561 --> 00:05:24.810
And let's say I'm only using
the sixes and the threes,

00:05:24.810 --> 00:05:26.180
because I figured those
out ahead of time,

00:05:26.180 --> 00:05:27.763
so I didn't have to
do any extra math.

00:05:27.763 --> 00:05:29.690
So 2 minus 0 is 2.

00:05:29.690 --> 00:05:31.400
5 minus 0 is 5.

00:05:31.400 --> 00:05:33.240
9 minus 6 is 3.

00:05:33.240 --> 00:05:36.360
0 minus 4-- well,
there's a couple

00:05:36.360 --> 00:05:38.320
of ways you could
think about doing this.

00:05:38.320 --> 00:05:39.840
You could borrow from here.

00:05:39.840 --> 00:05:41.030
That will become a 6.

00:05:41.030 --> 00:05:42.450
This becomes a 10.

00:05:42.450 --> 00:05:44.640
10 minus 4 is 6.

00:05:44.640 --> 00:05:47.160
Now this one's lower, so
it has to borrow as well.

00:05:47.160 --> 00:05:48.950
Make this into a 16.

00:05:48.950 --> 00:05:53.107
16 minus 7-- and I have multiple
videos on how to borrow,

00:05:53.107 --> 00:05:54.440
if I'm doing that part too fast.

00:05:54.440 --> 00:05:56.440
But the idea here is to
show you a different way

00:05:56.440 --> 00:05:57.170
of long division.

00:05:57.170 --> 00:05:59.690
So 16 minus 7 is 9.

00:05:59.690 --> 00:06:02.710
So now we're at 96,352.

00:06:02.710 --> 00:06:05.530
And once again, it
looks like the 873

00:06:05.530 --> 00:06:07.070
is about as close as we can get.

00:06:07.070 --> 00:06:11.090
So let me put a 873 over
here with two zeros.

00:06:11.090 --> 00:06:13.990
So that would literally
be 291 times 3

00:06:13.990 --> 00:06:16.960
with two zeros times 300.

00:06:16.960 --> 00:06:19.870
And so once again, we
want to subtract here.

00:06:19.870 --> 00:06:23.860
2 minus 0-- you
get a 2, a 5, a 0.

00:06:23.860 --> 00:06:25.180
Make this a 16.

00:06:25.180 --> 00:06:26.020
Make this an 8.

00:06:26.020 --> 00:06:28.400
16 minus 7 is 9.

00:06:28.400 --> 00:06:31.760
And then we have to
get close to 9,052.

00:06:31.760 --> 00:06:38.020
Once again, that 873, those
digits look pretty good, 873.

00:06:38.020 --> 00:06:40.780
We have to multiply
3 and then 10,

00:06:40.780 --> 00:06:43.950
so this is going to be
times 30 right over here.

00:06:43.950 --> 00:06:45.720
We subtract again.

00:06:45.720 --> 00:06:48.130
2 minus 0 is 2.

00:06:48.130 --> 00:06:50.460
5 minus 3 is 2.

00:06:50.460 --> 00:06:52.337
And then you have
90 minus 87 is 3.

00:06:52.337 --> 00:06:54.670
I'm doing the subtraction a
little fast, just so that we

00:06:54.670 --> 00:06:56.690
can get the general idea.

00:06:56.690 --> 00:06:58.820
Then we have to go into 322.

00:06:58.820 --> 00:07:00.853
And how can we
get close to that?

00:07:00.853 --> 00:07:03.311
Well, actually, 291 is
pretty darn close to that.

00:07:03.311 --> 00:07:06.260
So you go into it one time.

00:07:06.260 --> 00:07:09.710
1 times 291 is 291.

00:07:09.710 --> 00:07:11.990
2 minus 1 is 1.

00:07:11.990 --> 00:07:14.070
32 minus 29 is 3.

00:07:14.070 --> 00:07:16.730
So you have a remainder of 31.

00:07:16.730 --> 00:07:19.714
291 cannot go into 31 any
more, so that's our remainder.

00:07:19.714 --> 00:07:21.130
But how many times
did it actually

00:07:21.130 --> 00:07:23.080
go into this big,
beastly number?

00:07:23.080 --> 00:07:26.114
This 9,873,952?

00:07:26.114 --> 00:07:27.530
Well there, we
just have to add up

00:07:27.530 --> 00:07:28.960
all of these right over here.

00:07:28.960 --> 00:07:32.890
30 plus 3,000-- we can even do
it in our head-- 30 plus 3,000

00:07:32.890 --> 00:07:34.636
is 33,000.

00:07:34.636 --> 00:07:46.330
33,600, 33,900,
33,931, and we are

00:07:46.330 --> 00:07:49.380
done, assuming I haven't
made some silly mistake.

00:07:49.380 --> 00:07:55.275
291 goes into this thing 33,931
times with a remainder of 31.


Partial quotient method of division

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:02.770
Let's say we need to figure
out how many times 16 goes

00:00:02.770 --> 00:00:05.221
into 1,388.

00:00:05.221 --> 00:00:06.720
And what I want to
do is first think

00:00:06.720 --> 00:00:08.970
about how we traditionally
solve a problem like this

00:00:08.970 --> 00:00:10.630
and then introduce
another method that

00:00:10.630 --> 00:00:13.450
allows for a little
bit more approximation.

00:00:13.450 --> 00:00:16.990
So traditionally you would say,
well, 16 does not go into 1

00:00:16.990 --> 00:00:17.700
any times.

00:00:17.700 --> 00:00:19.210
So then you move over one spot.

00:00:19.210 --> 00:00:20.970
Well, how many times
does it go into 13?

00:00:20.970 --> 00:00:22.700
Well, it still does
not go into 13.

00:00:22.700 --> 00:00:24.830
And then you go
all the way to 138.

00:00:24.830 --> 00:00:27.990
And you say, well,
16 does go into 138.

00:00:27.990 --> 00:00:30.830
And you say, how many
times will it go into 138?

00:00:30.830 --> 00:00:32.619
And you might try 9 first.

00:00:32.619 --> 00:00:35.340
And I'll do all my arithmetic
here on the right side.

00:00:35.340 --> 00:00:44.550
So you'll say, 16 times
9-- 6 times 9 is 54.

00:00:47.270 --> 00:00:51.830
1 times 9 is 9, plus 5 is 14.

00:00:51.830 --> 00:00:54.050
So it goes 144 times.

00:00:54.050 --> 00:00:55.170
So that's still too big.

00:00:55.170 --> 00:00:57.060
That's larger than 138.

00:00:57.060 --> 00:00:59.230
So it's going to go
into it eight times.

00:00:59.230 --> 00:01:01.370
Eight times will
be less than 138.

00:01:01.370 --> 00:01:02.630
So you would stick an 8 here.

00:01:02.630 --> 00:01:04.660
And notice, I had to do this
little trial and error here.

00:01:04.660 --> 00:01:06.650
I had to make sure I got
the right exact number.

00:01:06.650 --> 00:01:08.566
I had to make sure I put
an 8 right over here.

00:01:08.566 --> 00:01:12.410
Then you say, 8 times 6 is 48.

00:01:12.410 --> 00:01:17.880
And then 8 times 1
is 8, plus 4 is 12.

00:01:17.880 --> 00:01:20.750
So 8 times 16 is 128.

00:01:20.750 --> 00:01:24.680
So when I subtract, I get
the remainder from 138.

00:01:24.680 --> 00:01:27.300
So I get a remainder
of 8 minus 8 is 0.

00:01:27.300 --> 00:01:28.790
3 minus 2 is 1.

00:01:28.790 --> 00:01:30.024
And then these cancel out.

00:01:30.024 --> 00:01:31.190
So I have a remainder of 10.

00:01:31.190 --> 00:01:32.960
But I still have this
8 right over here,

00:01:32.960 --> 00:01:34.010
so I bring that down.

00:01:34.010 --> 00:01:35.590
So I have 108.

00:01:35.590 --> 00:01:37.090
And then I do the
same thing again.

00:01:37.090 --> 00:01:39.173
Let me get rid of this so
we don't get distracted.

00:01:39.173 --> 00:01:42.640
We say, how many times
does 16 go into 108?

00:01:42.640 --> 00:01:43.952
And you can approximate.

00:01:43.952 --> 00:01:45.910
You say, well, it's
definitely not eight times.

00:01:45.910 --> 00:01:47.280
Eight times is 128.

00:01:47.280 --> 00:01:48.911
Is it, maybe, seven times?

00:01:48.911 --> 00:01:50.910
And then you might do a
little math on the side.

00:01:50.910 --> 00:01:53.220
See-- 16 times 7.

00:01:53.220 --> 00:01:55.442
6 times 7 is 42.

00:01:55.442 --> 00:02:03.180
1 times 7 is 7, plus 4 is 11.

00:02:03.180 --> 00:02:04.060
So you get 112.

00:02:04.060 --> 00:02:06.280
So that's still too large,
so it's going to be 6.

00:02:06.280 --> 00:02:08.430
But notice, we had to
do this little side work

00:02:08.430 --> 00:02:11.490
on the side right over here
to realize it wasn't seven.

00:02:11.490 --> 00:02:13.910
Now six is the
largest how many times

00:02:13.910 --> 00:02:16.700
you go into 108
without going over it.

00:02:16.700 --> 00:02:19.691
So 6 times 6 is 36.

00:02:19.691 --> 00:02:22.150
Carry the 3, or regroup
the 3, depending

00:02:22.150 --> 00:02:23.240
on how you think about it.

00:02:23.240 --> 00:02:25.830
6 times 1 is 6, plus 3 is 9.

00:02:29.140 --> 00:02:30.340
Then you subtract again.

00:02:30.340 --> 00:02:32.720
8 minus 6 is 2.

00:02:32.720 --> 00:02:35.079
And then you can just
say 10 minus 9 is 1,

00:02:35.079 --> 00:02:36.120
or you could even borrow.

00:02:36.120 --> 00:02:37.161
You could make this a 10.

00:02:37.161 --> 00:02:38.610
And then that goes away.

00:02:38.610 --> 00:02:40.050
10 minus 9 is 1.

00:02:40.050 --> 00:02:41.187
So then you have 12.

00:02:41.187 --> 00:02:43.270
And if we're not going
into decimals, you're done.

00:02:43.270 --> 00:02:45.340
Because 16 does not go into 12.

00:02:45.340 --> 00:02:51.392
So 16 goes into 1,388 86
times with a remainder of 12.

00:02:51.392 --> 00:02:55.370
That right over there
is your remainder.

00:02:55.370 --> 00:02:57.500
And that's all a
decent way of doing it.

00:02:57.500 --> 00:02:59.000
And that's the way
you traditionally

00:02:59.000 --> 00:02:59.770
know how to do it.

00:02:59.770 --> 00:03:00.670
But what I want
to do is introduce

00:03:00.670 --> 00:03:02.580
another maybe a little
more interesting way

00:03:02.580 --> 00:03:04.380
to solve a
long-division problem.

00:03:04.380 --> 00:03:11.679
So once again, let's do
our 16 goes into 1,388.

00:03:11.679 --> 00:03:13.220
And what we're going
to do is give us

00:03:13.220 --> 00:03:15.510
much more leeway
for approximation,

00:03:15.510 --> 00:03:16.940
or for essentially guessing.

00:03:16.940 --> 00:03:18.610
And what we want to
do is just guess.

00:03:18.610 --> 00:03:20.780
We're going to make
guesses for how many times

00:03:20.780 --> 00:03:24.750
16 goes into the numbers
without overestimating,

00:03:24.750 --> 00:03:26.470
without jumping too high.

00:03:26.470 --> 00:03:28.280
And now we're not
just going to think

00:03:28.280 --> 00:03:30.430
about the 1 or
the 13 or the 138.

00:03:30.430 --> 00:03:34.040
We're going to think about
the whole number as a whole.

00:03:34.040 --> 00:03:36.290
And before we do that, I'm
going to get two things out

00:03:36.290 --> 00:03:37.990
of the way, just
because it will help us.

00:03:37.990 --> 00:03:39.406
I'm just going to
remind ourselves

00:03:39.406 --> 00:03:41.767
what 16 times 2
and 16 times 5 are.

00:03:41.767 --> 00:03:43.600
And I'm just picking
these as random numbers

00:03:43.600 --> 00:03:45.260
that we can use to approximate.

00:03:45.260 --> 00:03:46.530
You don't have to use 2 and 5.

00:03:46.530 --> 00:03:47.530
You can use any numbers.

00:03:47.530 --> 00:03:49.210
Maybe I'll show
other examples there.

00:03:49.210 --> 00:03:53.740
So 16 times 2, we know, is 32.

00:03:53.740 --> 00:03:58.180
And 16 times 5 is
50 plus 30, is 80.

00:03:58.180 --> 00:04:01.430
So let's just keep these
two results in mind

00:04:01.430 --> 00:04:03.476
while we try to tackle
this right over here.

00:04:03.476 --> 00:04:04.850
So the first thing
to think about

00:04:04.850 --> 00:04:11.072
is our best guess for how many
times does 16 go into 1,388.

00:04:11.072 --> 00:04:13.280
Or another way to think
about, how many times does 16

00:04:13.280 --> 00:04:14.390
go into 1,000?

00:04:14.390 --> 00:04:18.769
Let's just do something at
a very rough approximation.

00:04:18.769 --> 00:04:25.570
Well, we know it's not going
to be 100, because 100 times 16

00:04:25.570 --> 00:04:26.810
would be 1,600.

00:04:26.810 --> 00:04:28.990
You would just throw those
two 0's at the end of it.

00:04:28.990 --> 00:04:31.480
And [? you'd ?] say, how many
times does it go into 1,000?

00:04:31.480 --> 00:04:37.436
Well, we know if 16 times 5 is
80, we know that 16 times 50

00:04:37.436 --> 00:04:41.455
would be 800.

00:04:41.455 --> 00:04:43.650
So let's use that.

00:04:43.650 --> 00:04:46.490
And I'm using the 5-- I'm
multiplying it by another 10

00:04:46.490 --> 00:04:49.730
to get to 50-- instead of the
2 because 800 is a lot closer

00:04:49.730 --> 00:04:53.090
than 320 to our 1,000
that we care about.

00:04:53.090 --> 00:05:01.041
So what we could say is, well,
16 times 50 will get us to 800.

00:05:01.041 --> 00:05:02.540
And once again, how
did I know that?

00:05:02.540 --> 00:05:05.330
Well, 16 times 5, I know
ahead of time, is 80.

00:05:05.330 --> 00:05:09.200
So 16 times 50, I
multiplied by 10-- 5 times

00:05:09.200 --> 00:05:10.520
10-- it'll get us to 800.

00:05:10.520 --> 00:05:12.385
And then I just subtract.

00:05:12.385 --> 00:05:13.690
So I subtract here.

00:05:13.690 --> 00:05:17.160
8 minus 0 is 8.

00:05:17.160 --> 00:05:20.990
And then you could
say 13 minus 5 is 588.

00:05:20.990 --> 00:05:25.600
And now we ask ourselves, how
many times does 16 go into 588?

00:05:25.600 --> 00:05:26.844
How close can we get to that?

00:05:26.844 --> 00:05:28.260
And let's just
assume that we only

00:05:28.260 --> 00:05:29.843
know this stuff right
over here, or we

00:05:29.843 --> 00:05:32.480
can multiply 16 times
a multiple of 10.

00:05:32.480 --> 00:05:35.646
So 800 would once
again be too big.

00:05:35.646 --> 00:05:36.995
That gets us above 588.

00:05:36.995 --> 00:05:41.680
Let's just go with
320 right over here.

00:05:41.680 --> 00:05:44.122
We know that 16 times 2 is 32.

00:05:44.122 --> 00:05:50.140
So 16 times 20 is
going to be 320.

00:05:50.140 --> 00:05:52.200
I just multiplied
the 2 times 10,

00:05:52.200 --> 00:05:54.470
which would give us
our product times 10.

00:05:54.470 --> 00:05:57.060
And so we can subtract
this right over here.

00:05:57.060 --> 00:06:00.092
8 minus 0 is 8.

00:06:00.092 --> 00:06:01.710
8 minus 2 is 6.

00:06:01.710 --> 00:06:04.840
And then 5 minus 3 is 2.

00:06:04.840 --> 00:06:07.570
So now I'm left with 268.

00:06:07.570 --> 00:06:11.262
And we say, how many
times does 16 go into 268?

00:06:14.154 --> 00:06:15.210
Well, let's see.

00:06:15.210 --> 00:06:16.270
800 is too big.

00:06:16.270 --> 00:06:18.740
Even 320 is now too big.

00:06:18.740 --> 00:06:22.100
Well, we could say-- 10
times 16 will get us to 160.

00:06:22.100 --> 00:06:23.100
Let's just try that out.

00:06:23.100 --> 00:06:24.760
We don't even have to get
the right exact answer.

00:06:24.760 --> 00:06:27.590
We don't have to get the highest
multiple that's less than 260.

00:06:27.590 --> 00:06:31.070
We just have to make sure
that we're still within 268.

00:06:31.070 --> 00:06:33.060
Let me do a new color over here.

00:06:33.060 --> 00:06:38.370
If we multiply 16
times 10, we get 160.

00:06:38.370 --> 00:06:40.270
160, we subtract again.

00:06:40.270 --> 00:06:42.896
So 8 minus 0 is 8.

00:06:42.896 --> 00:06:44.620
6 minus 6 is 0.

00:06:44.620 --> 00:06:47.560
2 minus 1 is 1.

00:06:47.560 --> 00:06:49.560
And then we're left with,
well, how many times

00:06:49.560 --> 00:06:52.010
does 16 go into 108?

00:06:52.010 --> 00:06:55.710
And we know 16 times 5 is 80.

00:06:55.710 --> 00:06:57.860
So let's just try out 5.

00:06:57.860 --> 00:07:00.810
16 times 5 is 80.

00:07:00.810 --> 00:07:02.750
We subtract right over here.

00:07:02.750 --> 00:07:04.992
8 minus 0 is 8.

00:07:04.992 --> 00:07:06.480
10 minus 8 is 2.

00:07:06.480 --> 00:07:07.806
So we're left with 28.

00:07:07.806 --> 00:07:08.930
And now it's pretty simple.

00:07:08.930 --> 00:07:10.680
How many times
does 16 go into 28?

00:07:10.680 --> 00:07:15.185
Well, it only goes
into it one time.

00:07:15.185 --> 00:07:20.050
And then when you subtract
16 from 28, 8 minus 6 is 2.

00:07:20.050 --> 00:07:21.520
2 minus 1 is 1.

00:07:21.520 --> 00:07:23.604
You're left with
a remainder of 12.

00:07:23.604 --> 00:07:25.020
But you might say,
well, how do we

00:07:25.020 --> 00:07:29.520
know how many times
does 16 go into 1,388?

00:07:29.520 --> 00:07:32.410
Well, it goes 50 times
plus 20 times plus 10 times

00:07:32.410 --> 00:07:35.520
plus 5 times plus 1 time.

00:07:35.520 --> 00:07:37.810
So that's going to
be-- we can just add up

00:07:37.810 --> 00:07:39.840
all of these things on
the right-hand side.

00:07:39.840 --> 00:07:44.860
This is going to be 50 plus
20 is 70, plus 10 is 80,

00:07:44.860 --> 00:07:49.000
plus 5 is 85, plus 1 is 86.

00:07:49.000 --> 00:07:50.100
So there we have it.

00:07:50.100 --> 00:07:54.130
It went into it 86 times
with a remainder of 12.

00:07:54.130 --> 00:07:56.610
And what's cool about this
method is that at every step,

00:07:56.610 --> 00:07:58.230
I could have put a
60 over here and I

00:07:58.230 --> 00:07:59.730
could have done
the math correctly.

00:07:59.730 --> 00:08:02.390
Or I could have picked my
two multiples to be 16 times

00:08:02.390 --> 00:08:03.382
6 and 16 times 3.

00:08:03.382 --> 00:08:05.340
And I would have gotten
different results here.

00:08:05.340 --> 00:08:07.300
But at the end, I would still
have gotten the right answer.

00:08:07.300 --> 00:08:09.640
So what it does is it gives us
a method so that we're always

00:08:09.640 --> 00:08:11.780
thinking about-- we're
always kind of biting away

00:08:11.780 --> 00:08:13.940
chunks of what
we're dividing into.

00:08:13.940 --> 00:08:16.610
So first we bit off
an 800-piece chunk.

00:08:16.610 --> 00:08:19.300
Then we bit off a
320-piece chunk.

00:08:19.300 --> 00:08:21.660
And we keep going
until we essentially

00:08:21.660 --> 00:08:23.650
can't divide by 16 any more.

00:08:23.650 --> 00:08:26.890
So hopefully you found
that kind of interesting.


Interest rate swap 2

WEBVTT
Kind: captions
Language: en

00:00:00.754 --> 00:00:07.125
In the last video company A took out a $1mn loan from lender 1 at a variable interest rate

00:00:07.125 --> 00:00:12.521
and company B took out a fixed rate $1mn loan from lender 2.

00:00:12.521 --> 00:00:19.618
and then they entered into this swap agreement where company A pays a fixed 7% every period.

00:00:19.618 --> 00:00:26.146
7% on a notional 1mn. Notional meaning that the 1mn doesn't exchange hands, only the interest does.

00:00:26.146 --> 00:00:29.938
A pays the 7% on the notional 1mn every period to B.

00:00:29.954 --> 00:00:34.515
B pays LIBOR + 1% on that notional 1mn every period to A.

00:00:34.592 --> 00:00:37.825
So pays a variable rate on that notional amount.

00:00:38.254 --> 00:00:43.310
What I am going to do in this video is go through the numerical mechanics to show that in effect,

00:00:43.310 --> 00:00:48.633
Company A now has a fixed rate loan when you think of it from the point of view the interest it is paying

00:00:48.633 --> 00:00:50.695
and company B now has a variable rate loan.

00:00:51.002 --> 00:00:54.692
They have kind of swapped the fixed and variable natures of their loans.

00:00:54.952 --> 00:00:58.059
So lets think about what happens with company A in period 1.

00:00:58.059 --> 00:01:04.925
In period 1: So in the old period 1 it had to pay $70,000 of interest to the lender.

00:01:05.695 --> 00:01:21.804
So it had to pay in period 1, comapny A had to pay $70,000 to lender 1 but now thats not all it has to do.

00:01:22.096 --> 00:01:24.833
Definitely it still has to do that. This loan is still in effect.

00:01:24.833 --> 00:01:31.054
But now it also has to pay 7, has to pay 7% fixed to B on that notional 1mn

00:01:31.115 --> 00:01:41.833
so it also has to pay $70,000(7% on a mn) to company B,

00:01:41.833 --> 00:01:46.300
But in exchange for that, it's going to get LIBOR +1% from B.

00:01:46.331 --> 00:01:53.033
So its going to get LIBOR (we are assuming it is 5% in period1).

00:01:53.033 --> 00:01:58.029
5% + 1% = 6%, 6% on a notional $1mn is $60,000.

00:01:58.090 --> 00:02:09.571
$60k from B. So net net it pays 70, it pays 70 twice but then it gets back 60.

00:02:09.571 --> 00:02:17.054
So its paying $80,000. So the net is paying $80,000.

00:02:17.054 --> 00:02:20.485
Now think about what happens in period 2 when LIBOR changes.

00:02:20.485 --> 00:02:26.085
So in period 2, now LIBOR changes to 4%

00:02:26.085 --> 00:02:33.552
and so A will have to pay 4% + the 2% on its loan which is 6% or $60,000.

00:02:33.552 --> 00:02:37.254
A will have to pay $60,000 to its lender.

00:02:37.254 --> 00:02:48.685
It would have to pay B the 70,000 still, it would pay to B 70,000

00:02:48.685 --> 00:02:58.823
but in exchange it would get LIBOR + 1% from B. LIBOR is 4%.

00:02:58.823 --> 00:03:01.254
4% + 1% is 5%.

00:03:01.254 --> 00:03:07.018
It would get $50,000. So it would get 50,000 in that period from B.

00:03:07.018 --> 00:03:13.536
So whats the total amount that it pays. It pays 60 +70 = 130,000.

00:03:13.536 --> 00:03:16.285
But then it gets back 50,000 from the swap agreement.

00:03:16.285 --> 00:03:24.321
So it pays $80,000. Notice that it doesn't change from any period..

00:03:24.321 --> 00:03:31.018
I encourage you to try out changing the actual LIBOR rate and you see it doesn't change the amount that A pays.

00:03:31.018 --> 00:03:33.618
A is now in effect paying a fixed rate.

00:03:33.618 --> 00:03:36.018
Now the opposite is going to happen with B.

00:03:36.018 --> 00:03:39.048
In the old one, every period it pays $80,000.

00:03:39.048 --> 00:03:41.285
But now its going to be a little bit different.

00:03:41.285 --> 00:03:47.705
In period 1, it still pays $80,000 so that we can write that in every period

00:03:47.721 --> 00:03:55.941
In period 2, it still pays $80,000 and then its going to get 7% every period from company A

00:03:55.941 --> 00:04:06.562
So it would get $70,000 but its going to be paying LIBOR + 1%

00:04:06.777 --> 00:04:15.695
So in Period 1, its going to pay $60,000.

00:04:15.818 --> 00:04:21.090
And then in period 2, its going to pay $50,000.

00:04:21.152 --> 00:04:27.571
So net you pay 50, you get 70 so thats a part of, you are still paying 10 and you pay another 60

00:04:27.633 --> 00:04:31.896
So net is your going to pay 70k in period 1

00:04:31.896 --> 00:04:37.455
and then in period 2, you're going to pay 60k

00:04:37.455 --> 00:04:41.367
So now Comapny A is paying a fixed 8% every period.

00:04:41.367 --> 99:59:59.999
and company B is going to pay essentially a variable rate.


Interest rate swap 1

WEBVTT
Kind: captions
Language: en

00:00:00.720 --> 00:00:02.820
Let's say that we've
got company A over here,

00:00:02.820 --> 00:00:04.910
and it takes out
a $1 million loan,

00:00:04.910 --> 00:00:08.920
and it pays a variable
interest rate on that loan.

00:00:08.920 --> 00:00:13.430
It pays LIBOR plus 2%.

00:00:13.430 --> 00:00:16.830
And LIBOR stands for London
Interbank Offer Rate.

00:00:16.830 --> 00:00:20.720
It's one of the major benchmarks
for variable interest rates.

00:00:20.720 --> 00:00:22.840
And so it pays that
to some lender.

00:00:22.840 --> 00:00:26.620
This is the person who
lent company A the money.

00:00:26.620 --> 00:00:30.440
It pays them a variable
interest rate every period.

00:00:30.440 --> 00:00:36.570
So for example, in period
one if LIBOR is at 5%,

00:00:36.570 --> 00:00:42.520
then in that period, company
A will pay 7%, or $70,000

00:00:42.520 --> 00:00:44.370
to the lender in that period.

00:00:44.370 --> 00:00:48.120
In period two, if
LIBOR goes, let's say

00:00:48.120 --> 00:00:50.610
LIBOR goes down a
little bit to 4%,

00:00:50.610 --> 00:00:56.680
then company A is going to
pay 4 plus 2, which is 6%,

00:00:56.680 --> 00:01:00.740
which is $60,000 in interest.

00:01:00.740 --> 00:01:03.100
Let's say that we have
another company, company B,

00:01:03.100 --> 00:01:04.390
right over here.

00:01:04.390 --> 00:01:08.980
It also borrows $1 million, but
it borrows it at a fixed rate.

00:01:08.980 --> 00:01:11.870
Let's say it borrows it
at a fixed rate of 8%.

00:01:14.840 --> 00:01:17.020
So in each period,
regardless of what

00:01:17.020 --> 00:01:20.280
happens to LIBOR or any
other benchmark-- so

00:01:20.280 --> 00:01:23.484
this is to probably another
lender, or different lender,

00:01:23.484 --> 00:01:25.150
than the person that
A borrowed it from.

00:01:25.150 --> 00:01:26.608
And it could be a
bank, or it might

00:01:26.608 --> 00:01:28.660
be another company, or
an investor of some kind.

00:01:28.660 --> 00:01:31.710
We will call this
Lender 1 and Lender 2.

00:01:31.710 --> 00:01:33.990
So regardless of the
period, right now

00:01:33.990 --> 00:01:36.620
company B will pay
8% of $1 million

00:01:36.620 --> 00:01:39.760
in each period, which
is about $80,000,

00:01:39.760 --> 00:01:43.150
or exactly $80,000, each period.

00:01:43.150 --> 00:01:45.189
Now let's say that
neither of these parties

00:01:45.189 --> 00:01:46.730
are really happy
with that situation.

00:01:46.730 --> 00:01:48.630
Company A doesn't
like the variability,

00:01:48.630 --> 00:01:51.000
the unpredictability in
what happens to LIBOR,

00:01:51.000 --> 00:01:53.970
so they can't plan for
how much they have to pay.

00:01:53.970 --> 00:01:56.306
Company B feels like they're
overpaying for interest.

00:01:56.306 --> 00:01:58.930
They feel like, wow, the people
who are doing variable interest

00:01:58.930 --> 00:02:01.510
rates, they're paying a
less amount of interest

00:02:01.510 --> 00:02:02.920
every period.

00:02:02.920 --> 00:02:04.540
And maybe they also,
company B also,

00:02:04.540 --> 00:02:07.280
thinks that interest rates
are going to go down,

00:02:07.280 --> 00:02:09.462
or that short term,
or that variable rate

00:02:09.462 --> 00:02:11.420
is going to go down,
LIBOR is going to go down.

00:02:11.420 --> 00:02:12.880
So that's an even
bigger reason why

00:02:12.880 --> 00:02:15.810
they want to become a
variable rate borrower.

00:02:15.810 --> 00:02:17.520
So what they can do,
and neither of them

00:02:17.520 --> 00:02:19.186
can get out of these
lending agreements,

00:02:19.186 --> 00:02:21.910
but what they can do is
agree to essentially swap

00:02:21.910 --> 00:02:24.730
some or all of their
interest rate payments.

00:02:24.730 --> 00:02:27.710
So for example, they can
enter into an agreement,

00:02:27.710 --> 00:02:30.650
and this would be called an
interest rate swap, where

00:02:30.650 --> 00:02:36.200
company A agrees
to pay B-- maybe,

00:02:36.200 --> 00:02:43.770
let's make up a number here-- 7%
on a notional $1 million loan.

00:02:43.770 --> 00:02:46.480
So, the $1 million will
never change hands,

00:02:46.480 --> 00:02:50.800
but company A agrees to pay B
7% of that notional $1 million,

00:02:50.800 --> 00:02:52.950
or $70,000 per period.

00:02:52.950 --> 00:03:01.210
And in return, company B agrees
to pay A a variable rate.

00:03:01.210 --> 00:03:07.690
Let's say it's LIBOR
plus 1%, right over here.

00:03:07.690 --> 00:03:09.200
And this little
agreement-- and they

00:03:09.200 --> 00:03:11.325
agreed they would agree to
do this for some amount.

00:03:11.325 --> 00:03:13.180
And once again, this
is LIBOR plus 1%

00:03:13.180 --> 00:03:16.629
on a notional $1 million.

00:03:16.629 --> 00:03:18.670
And that word notional
just means that $1 million

00:03:18.670 --> 00:03:20.378
will never change
hands, and they're just

00:03:20.378 --> 00:03:24.080
going to exchange the interest
payments on $1 million.

00:03:24.080 --> 00:03:27.970
And this agreement
right over here

00:03:27.970 --> 00:03:31.149
is called an interest rate swap.

00:03:31.149 --> 00:03:32.190
And I'll leave you there.

00:03:32.190 --> 00:03:33.565
In the next video,
we'll actually

00:03:33.565 --> 00:03:38.920
go through the mechanics to
see that A is truly now paying

00:03:38.920 --> 00:03:41.500
a fixed rate when you put in
all of their different payments

00:03:41.500 --> 00:03:43.450
into both the swap
and the lender,

00:03:43.450 --> 00:03:46.500
and Company B, after entering
into this swap agreement,

00:03:46.500 --> 00:03:50.660
is now really paying a
variable interest rate.


Interpreting futures fair value in the premarket

WEBVTT
Kind: captions
Language: en

00:00:00.580 --> 00:00:02.640
In the first video
on futures fair value

00:00:02.640 --> 00:00:06.210
we learned that it was the
price at which an investor would

00:00:06.210 --> 00:00:09.710
be neutral between buying
the stock on the actual stock

00:00:09.710 --> 00:00:13.154
market or buying the front
month futures contract.

00:00:13.154 --> 00:00:14.570
What I want to do
in this video is

00:00:14.570 --> 00:00:16.570
talk about how
does one interpret

00:00:16.570 --> 00:00:19.519
the fair value, especially
relative to the futures price.

00:00:19.519 --> 00:00:21.060
So let's say you
wake up one morning.

00:00:21.060 --> 00:00:24.100
The market hasn't opened yet,
the stock market hasn't opened,

00:00:24.100 --> 00:00:27.370
and you see a quote like
this for stock ABCD.

00:00:27.370 --> 00:00:31.650
The fair value, according to the
closing of yesterday's trading,

00:00:31.650 --> 00:00:35.050
the fair value is $102,
but the futures market,

00:00:35.050 --> 00:00:39.660
which usually has trading
hours beyond the regular market

00:00:39.660 --> 00:00:42.890
and often times 24 hours,
so the futures market

00:00:42.890 --> 00:00:45.030
trading price for the
front month future,

00:00:45.030 --> 00:00:48.450
even though the fair value based
on yesterday's closing is 102,

00:00:48.450 --> 00:00:52.000
the futures market is
trading it at $101.

00:00:52.000 --> 00:00:53.600
So how would you
use that information

00:00:53.600 --> 00:00:56.210
or how would one interpret
that information?

00:00:56.210 --> 00:00:59.440
So in the futures market,
people are trading the futures

00:00:59.440 --> 00:01:02.270
contract, they're buying
and selling at a price

00:01:02.270 --> 00:01:06.500
below the fair value based
on yesterday's close price.

00:01:06.500 --> 00:01:09.320
So what that means is is
that the market thinks

00:01:09.320 --> 00:01:12.920
that this is actually no longer
the correct price of the stock.

00:01:12.920 --> 00:01:15.200
They think that the
correct price of the stock

00:01:15.200 --> 00:01:16.750
is the stock at
which they would be

00:01:16.750 --> 00:01:20.025
neutral between that price
and this futures contract.

00:01:20.025 --> 00:01:21.150
So I don't know what it is.

00:01:21.150 --> 00:01:23.525
You would have to discount it
back by the risk-free rate,

00:01:23.525 --> 00:01:25.840
but maybe it's something
like-- so this is implicitly

00:01:25.840 --> 00:01:29.370
saying that the correct price
of the stock isn't $100.

00:01:29.370 --> 00:01:31.540
if the futures
price was $102, it

00:01:31.540 --> 00:01:33.200
would say that the
stock should be 100.

00:01:33.200 --> 00:01:35.419
If the futures
prices is $101, it

00:01:35.419 --> 00:01:37.710
means that maybe the stock
is something less than that.

00:01:37.710 --> 00:01:43.435
Maybe if we do our math maybe
it implies a stock price of $99.

00:01:48.780 --> 00:01:52.230
So the way you would potentially
act on it, although it's easier

00:01:52.230 --> 00:01:53.695
said than done is
say, well, look.

00:01:53.695 --> 00:01:55.790
That means that, at least
in the very early stages

00:01:55.790 --> 00:01:59.410
once the market opens, the
stock is going to go down.

00:01:59.410 --> 00:02:01.452
Now, your initial reaction
might be saying, wow,

00:02:01.452 --> 00:02:02.410
this is really amazing.

00:02:02.410 --> 00:02:04.035
This is some type of
a future indicator

00:02:04.035 --> 00:02:05.900
and it is a pretty
strong future indicator.

00:02:05.900 --> 00:02:08.990
When you see this, when you see
the actual price of the future

00:02:08.990 --> 00:02:11.980
being below the fair
value, it is very likely

00:02:11.980 --> 00:02:13.790
that the stock will open down.

00:02:13.790 --> 00:02:17.980
Unfortunately, you have many,
many very sophisticated,

00:02:17.980 --> 00:02:19.720
high-frequency
traders who already

00:02:19.720 --> 00:02:21.930
have their computers
set up to look

00:02:21.930 --> 00:02:23.990
at this type of a
discrepancy and they're

00:02:23.990 --> 00:02:25.540
going to be ultra
fast and they're

00:02:25.540 --> 00:02:27.810
optimizing how fast their
bandwidth is so that they

00:02:27.810 --> 00:02:29.970
can do these in a
matter of split seconds.

00:02:29.970 --> 00:02:32.410
So it's very,
very, very unlikely

00:02:32.410 --> 00:02:36.740
that an average investor or
even a reasonably sophisticated

00:02:36.740 --> 00:02:38.920
investor will be able
to take advantage

00:02:38.920 --> 00:02:41.380
of this type of an arbitrage
or this type of an expected

00:02:41.380 --> 00:02:45.590
arbitrage to know that this
price is likely to go down.

00:02:45.590 --> 00:02:48.220
Now, if the opposite
happened and let's

00:02:48.220 --> 00:02:51.190
say that the fair
value is $102, which

00:02:51.190 --> 00:02:54.660
implies the fair value of the
front month futures contract

00:02:54.660 --> 00:02:58.100
is $102, which implies
$100 stock price.

00:02:58.100 --> 00:03:01.210
Let's say that the
futures is actually

00:03:01.210 --> 00:03:04.250
trading even though
the fair value is $102,

00:03:04.250 --> 00:03:09.540
let's say that it
is trading at $105.

00:03:09.540 --> 00:03:12.510
So this is a situation that
since the market closed,

00:03:12.510 --> 00:03:14.021
the futures market
for some reason

00:03:14.021 --> 00:03:16.020
thinks that the stock is
going to be worth more.

00:03:16.020 --> 00:03:18.140
This would imply a
stock price of maybe,

00:03:18.140 --> 00:03:19.390
I don't know what it might be.

00:03:19.390 --> 00:03:20.931
I'm not going to do
the math exactly,

00:03:20.931 --> 00:03:24.500
but maybe a price
of $103 or $104.

00:03:24.500 --> 00:03:26.710
And so if you saw this
where the futures price is

00:03:26.710 --> 00:03:29.350
above the fair value
in the pre-market,

00:03:29.350 --> 00:03:31.940
that means that the
stock is likely to go up.

00:03:31.940 --> 00:03:34.290
But once again, it's very
hard to take advantage

00:03:34.290 --> 00:03:36.623
of because you're going to
see that movement very, very,

00:03:36.623 --> 00:03:37.980
very quickly.


Center for Future of Museums

WEBVTT
Kind: captions
Language: en

00:00:00.821 --> 00:00:02.534
These are questions that I got from the

00:00:02.534 --> 00:00:04.570
Center For The Future Museums.

00:00:04.570 --> 00:00:07.080
They say for readers who
may be unfamiliar with

00:00:07.080 --> 00:00:09.673
Khan Academy, can you
give a capsule description

00:00:09.673 --> 00:00:12.242
of your work? I'll make
it even clear. It's just

00:00:12.242 --> 00:00:15.161
not my work anymore, we're
a team of 15 and growing

00:00:15.161 --> 00:00:17.005
people, actually, I think we're now at 16.

00:00:17.005 --> 00:00:21.413
It started off as, essentially,
it got most know for

00:00:21.413 --> 00:00:24.162
video library that I
originally made for my cousins,

00:00:24.162 --> 00:00:26.673
put them on YouTube, got
really popular. I was

00:00:26.673 --> 00:00:29.669
doing it as a hobby
really, I had a day job as

00:00:29.669 --> 00:00:33.866
an analysis at an investment
fund. I was also working

00:00:33.866 --> 00:00:36.003
on a primitive version
of software to quiz them

00:00:36.003 --> 00:00:38.490
and things like that.
Then in 2009 I quit my job

00:00:38.490 --> 00:00:42.411
to work on it full time.
2010 we got funding to

00:00:42.411 --> 00:00:44.943
work on it. Most of the
funding is actually to work

00:00:44.943 --> 00:00:48.488
on the software platform.
The software lets students

00:00:48.488 --> 00:00:50.673
start at any place 1
plus 1 equals 2. It will

00:00:50.673 --> 00:00:54.271
generate problems for them.
It'll allow them to move ahead

00:00:54.271 --> 00:00:57.007
as they gain proficiency
as they gain mastery

00:00:57.007 --> 00:00:59.487
of subjects. They learn at
their own pace. They make

00:00:59.487 --> 00:01:02.003
sure that all of the gaps
are filled. The videos

00:01:02.003 --> 00:01:04.760
are there to compliment
the exercise platform.

00:01:04.760 --> 00:01:06.487
Right now there's over
2,700 videos covering

00:01:06.487 --> 00:01:08.931
everything from basic
mathematics to calculus

00:01:08.931 --> 00:01:12.082
to college level differential
equations in your algebra,

00:01:12.082 --> 00:01:15.831
and sciences, biology,
chemistry, and a little bit

00:01:15.831 --> 00:01:18.000
of history, economics, and finance.

00:01:18.000 --> 00:01:21.003
The exercises are deeper
K through 12 math.

00:01:21.003 --> 00:01:24.075
Over the next year,
hopefully, we'll all see it

00:01:24.075 --> 00:01:28.408
get to fairly deep K through,
I would say, 14 math,

00:01:28.408 --> 00:01:31.161
so cover all the advanced
mathematics. Then beyond

00:01:31.161 --> 00:01:33.339
that we're going to see
the exercise platform move

00:01:33.339 --> 00:01:35.826
into physics, chemistry,
and even parts of biology,

00:01:35.826 --> 00:01:37.495
and maybe grammar, and things like that.

00:01:37.495 --> 00:01:40.937
The whole idea for us as
not for profit, is to be ...

00:01:40.937 --> 00:01:47.003
1. For anyone. Anyone to get an education.

00:01:47.003 --> 00:01:49.086
Our mission to going to be
a world class education.

00:01:49.086 --> 00:01:56.151
Anyone, anywhere for free. Free education.

00:01:56.151 --> 00:02:00.606
2. Is to be a tool that
can be levered inside

00:02:00.606 --> 00:02:03.533
the classroom to make the
classroom more interactive.

00:02:03.533 --> 00:02:06.590
Tool to make the classroom
more interactive.

00:02:06.590 --> 00:02:10.044
Classroom interactive. When
I say his, it's a little

00:02:10.044 --> 00:02:12.460
intuitive, because we
are a technology tool,

00:02:12.460 --> 00:02:15.462
and we involve on demand
video. We involve exercises

00:02:15.462 --> 00:02:17.190
that are done on the
computer. How are we making

00:02:17.190 --> 00:02:19.129
it more interactive? When
I say more interactive,

00:02:19.129 --> 00:02:20.795
I literally mean interactive with humans.

00:02:20.795 --> 00:02:23.249
In the model we're experimenting with now,

00:02:23.249 --> 00:02:25.316
and the initial results
seem very very promising

00:02:25.316 --> 00:02:28.313
in the real classrooms
that we've been dealing

00:02:28.313 --> 00:02:31.122
with. So much of the
scaffolding of knowledge,

00:02:31.122 --> 00:02:34.920
the conceptional
development, so much of the

00:02:34.920 --> 00:02:38.584
exercises can be done
on the online platform.

00:02:38.584 --> 00:02:40.586
What we're saying is take
that part out side of

00:02:40.586 --> 00:02:42.928
the classroom experience.
This can be done at

00:02:42.928 --> 00:02:45.885
a students pace at their
time. Give that data

00:02:45.885 --> 00:02:47.719
to the teacher, and so
when the student goes into

00:02:47.719 --> 00:02:51.986
the classroom you have
all this freed up time

00:02:51.986 --> 00:02:54.385
so the students can teach
each other. Their all

00:02:54.385 --> 00:02:56.807
learning at different
paces, and the teacher can

00:02:56.807 --> 00:02:59.888
do more focus more deep
interventions with the students.

00:02:59.888 --> 00:03:04.184
The teachers now have all of this data.

00:03:04.184 --> 00:03:06.722
It frees up time, and powers
the teacher with data.

00:03:06.722 --> 00:03:09.680
All of class time no
longer one pace fits all,

00:03:09.680 --> 00:03:12.222
one size fits all lectures,
its all about everyone

00:03:12.222 --> 00:03:16.141
working at their own pace.
Every minute of a teachers

00:03:16.141 --> 00:03:19.224
time and every minute of
a students time is either,

00:03:19.224 --> 00:03:21.558
working at their own pace or
interacting with each other.

00:03:21.558 --> 00:03:23.998
That's what we talk about
it as a tool. Right now

00:03:23.998 --> 00:03:27.664
most of the users are right
over here. Most of the

00:03:27.664 --> 00:03:29.465
users are right over here.
We have about 2 1/2 million

00:03:29.465 --> 00:03:32.977
unique students a month, and that
numbers growing exponentially really.

00:03:32.977 --> 00:03:35.928
They've already watched
over 70 million videos,

00:03:35.928 --> 00:03:37.742
and they've done over
100 million exercises.

00:03:37.742 --> 00:03:40.794
We have about a million
exercises done per day now.

00:03:40.794 --> 00:03:45.660
That number is also
growing rapidly. That's

00:03:45.660 --> 00:03:47.597
kind of the general overview
of what we're doing.

00:03:47.597 --> 00:03:50.076
One thing I want to be
clear here is for both of

00:03:50.076 --> 00:03:55.413
these, we've only had
funding for about 12 months.

00:03:55.413 --> 00:03:58.741
I've been doing this
one form or another for

00:03:58.741 --> 00:04:00.824
5 or 6 years now, or
actually closer to 7 years.

00:04:00.824 --> 00:04:03.489
As an organization we've only
been around for less that a year.

00:04:03.489 --> 00:04:10.930
These are works in progress.
We are all ready seeing

00:04:10.930 --> 00:04:12.748
good results and good traction
with what we all ready

00:04:12.748 --> 00:04:15.930
have. We hope to learn
more and more from the

00:04:15.930 --> 00:04:18.466
schools and the teachers and the parents

00:04:18.466 --> 00:04:20.659
and the students that we're
working with. To just improve

00:04:20.659 --> 00:04:23.192
them better and better and
make this part, make the

00:04:23.192 --> 00:04:27.334
education, the classroom, more
and more rich experiences.

00:04:27.334 --> 00:04:29.505
Either through things we
do directly, or through

00:04:29.505 --> 00:04:31.597
the things that we enable
because we're taking

00:04:31.597 --> 00:04:33.412
other things off the table.

00:04:33.412 --> 00:04:36.392
Question number 2. What
do you see as the greatest

00:04:36.392 --> 00:04:38.669
barrier technological,
cultural, or political to

00:04:38.669 --> 00:04:41.594
mainstreaming the Khan Academy
system into public education?

00:04:41.594 --> 00:04:46.003
I think the first is
something that I'll put firmly

00:04:46.003 --> 00:04:48.997
on Khan Academy shoulders,
on our shoulders, is that,

00:04:48.997 --> 00:04:50.376
we have to make a very compelling case.

00:04:50.376 --> 00:04:52.786
A compelling case isn't just
a cool piece of software

00:04:52.786 --> 00:04:54.990
that a lot of people are
using, or a bunch of videos

00:04:54.990 --> 00:04:57.058
a lot of people are
using, that's part of it.

00:04:57.058 --> 00:04:59.525
We do have traction. That
traction happened organically,

00:04:59.525 --> 00:05:02.689
which I think does speak
to it. No one forces

00:05:02.689 --> 00:05:04.655
these 2 million or 2 1/2
million students every

00:05:04.655 --> 00:05:07.183
month to use our sight.
They, themselves, find it

00:05:07.183 --> 00:05:10.717
compelling. That by itself
isn't enough. We need

00:05:10.717 --> 00:05:13.599
to go into classrooms,
and I think it's very

00:05:13.599 --> 00:05:15.358
important that people
understand that we don't

00:05:15.358 --> 00:05:17.453
think we have a perfective
solution. We think we

00:05:17.453 --> 00:05:20.357
have the start of a
compelling solution. What we

00:05:20.357 --> 00:05:22.524
want to do is work with,
and this is what we are

00:05:22.524 --> 00:05:24.520
doing with our pilot
classrooms. We want to work

00:05:24.520 --> 00:05:27.449
with these teachers, students,
parents to make a better

00:05:27.449 --> 00:05:29.719
product and see how this
product can be used,

00:05:29.719 --> 00:05:34.783
to see how we can make
the classroom as human

00:05:34.783 --> 00:05:36.859
of an experience as possible.

00:05:36.859 --> 00:05:39.237
Then, of course, we have
to prove that it works.

00:05:39.237 --> 00:05:41.736
Proving that it works,
you know, there is one

00:05:41.736 --> 00:05:44.404
metric that people, the
education, or maybe the

00:05:44.404 --> 00:05:46.796
policy world like, which
is performance on test

00:05:46.796 --> 00:05:48.662
scores. We definitely
want to make sure that we

00:05:48.662 --> 00:05:51.593
have improvements or at
minimum know negatives.

00:05:51.593 --> 00:05:54.265
So far, it does like we are
seeing dramatic improvement

00:05:54.265 --> 00:05:59.328
in certain classes using
the model [advocate] and

00:05:59.328 --> 00:06:01.797
using these tools.
Improvement also happens in

00:06:01.797 --> 00:06:06.666
intangible ways. If now
kids are able to as good

00:06:06.666 --> 00:06:08.736
on the test as they were
before or even better

00:06:08.736 --> 00:06:11.911
on the test, but now they
have a better attitude

00:06:11.911 --> 00:06:14.499
towards mathematics. Their
more attentive in class.

00:06:14.499 --> 00:06:19.263
Their able to be exposed.
You have all this

00:06:19.263 --> 00:06:21.910
freed up class time to
projects and experiences

00:06:21.910 --> 00:06:23.907
that they wouldn't
otherwise been exposed to

00:06:23.907 --> 00:06:26.536
that can't necessarily be
captured on an assessment exam.

00:06:26.536 --> 00:06:28.792
If those things are
happening, we also view that

00:06:28.792 --> 00:06:31.397
as signs of success. These
are things that we have

00:06:31.397 --> 00:06:34.746
to prove. Once we do and
hopefully we are able

00:06:34.746 --> 00:06:36.419
to prove all of those
things, and it seems like

00:06:36.419 --> 00:06:38.414
we are on track, hopefully, knock on wood

00:06:38.414 --> 00:06:43.127
to do those things. The next
thing is to really just ...

00:06:43.127 --> 00:06:48.862
we are a free solution.
We are not for profit.

00:06:48.862 --> 00:06:50.993
People know that we
aren't doing this to make

00:06:50.993 --> 00:06:53.205
money off of it, we're doing
this because we generaly

00:06:53.205 --> 00:06:58.599
care about education. I think
people want to understand

00:06:58.599 --> 00:07:00.828
what we are talking about.
Right now there's some

00:07:00.828 --> 00:07:03.262
[knee jerk] reactions
that thinks were all about

00:07:03.262 --> 00:07:05.600
kids spending all of
their time on a computer,

00:07:05.600 --> 00:07:07.992
spending all of their time watching videos

00:07:07.992 --> 00:07:10.499
that somehow replace
teachers. We're about the

00:07:10.499 --> 00:07:12.762
opposite of that. We
think class time should be

00:07:12.762 --> 00:07:14.830
about interaction. We
think we are the catalysis

00:07:14.830 --> 00:07:16.868
to take lectures out of
the classroom, to make the

00:07:16.868 --> 00:07:20.494
classroom more interactive.
People have to get over

00:07:20.494 --> 00:07:24.869
those [knee jerk] reactions,
which I think aren't

00:07:24.869 --> 00:07:27.262
correct perceptions of
what we're trying to do.

00:07:27.262 --> 00:07:30.421
Then beyond that is just
a willingness to change.

00:07:30.421 --> 00:07:32.669
I think the willingness
to change, there are

00:07:32.669 --> 00:07:35.496
many opened minded teachers
that are all ready doing it.

00:07:35.496 --> 00:07:37.335
Those are the ones we are working with

00:07:37.335 --> 00:07:39.149
to really help define what
we are and help define

00:07:39.149 --> 00:07:42.563
what our future should
be. Those are going well,

00:07:42.563 --> 00:07:44.470
and I don't know what
percentage of teachers will

00:07:44.470 --> 00:07:47.331
fall into that cap, where
they will see a good tool

00:07:47.331 --> 00:07:49.286
and like and it seems it has good results.

00:07:49.286 --> 00:07:51.133
It gels with their was of
teaching, they'll adopt it.

00:07:51.133 --> 00:07:56.465
The last thing I'd want
to see is people being

00:07:56.465 --> 00:07:58.874
forced to use Khan Academy.
I really want it to

00:07:58.874 --> 00:08:04.923
be something that's opted
into. If you force them

00:08:04.923 --> 00:08:06.522
to use even something
that's the best tool on

00:08:06.522 --> 00:08:08.852
the planet, and they don't want to use it,

00:08:08.852 --> 00:08:10.918
they can make it a not-so-great tool,

00:08:10.918 --> 00:08:14.116
and a not-so-great
experience. Our main concern

00:08:14.116 --> 00:08:16.785
is really to show that
it's a viable model,

00:08:16.785 --> 00:08:19.924
it's a good model. It has
all of the effects that

00:08:19.924 --> 00:08:21.924
we want it to have, but
it really is improving

00:08:21.924 --> 00:08:24.826
education, both from
assessment point of view

00:08:24.826 --> 00:08:29.748
and from a intangible point
of view. We offer it free.

00:08:29.748 --> 00:08:32.403
We give as much information
to teachers, policy

00:08:32.403 --> 00:08:36.323
makers, and parents so
that their own schools can

00:08:36.323 --> 00:08:38.407
adopt it if they want
to. All of our tools are

00:08:38.407 --> 00:08:40.415
all ready available for
free, all the tools our

00:08:40.415 --> 00:08:43.412
pilots are using. Any
classroom can use today, and

00:08:43.412 --> 00:08:46.590
then just see what happens,
I guess is the simple answer.

00:08:46.590 --> 00:08:49.855
Next question. Currently,
Khan Academy content

00:08:49.855 --> 00:08:53.459
is heavy on subjects that
focus on facts and absolutes,

00:08:53.459 --> 00:08:56.916
math, chemistry, physics.
Is that mostly a function

00:08:56.916 --> 00:08:59.496
of your background and expertise,
or inheriting the format?

00:08:59.496 --> 00:09:02.387
What are the limitations
with your current model

00:09:02.387 --> 00:09:05.121
for covering squishy topics
like art, literature,

00:09:05.121 --> 00:09:07.382
that are about aesthetics
and interpretation?

00:09:07.382 --> 00:09:11.462
I would say it is true we
are covering math, chemistry,

00:09:11.462 --> 00:09:14.461
physics, and sometimes their
not as fact or absolute

00:09:14.461 --> 00:09:16.952
basis, sometimes people
perceive them to be.

00:09:16.952 --> 00:09:18.124
With that said,

00:09:18.124 --> 00:09:20.884
I've also started making
videos on history and

00:09:20.884 --> 00:09:23.786
economics. Although
economics is often considered

00:09:23.786 --> 00:09:28.702
a science, it can be a squishy
subject where aesthetics

00:09:28.702 --> 00:09:31.288
and interpenetration do begin to matter.

00:09:31.288 --> 00:09:33.708
One thing you will see, and I
think this is very interesting

00:09:33.708 --> 00:09:37.255
for the audience for the
future of the museums is,

00:09:37.255 --> 00:09:40.381
you will start to see we
are bringing some people

00:09:40.381 --> 00:09:42.719
on board in the very near
future on art history.

00:09:42.719 --> 00:09:45.648
They've all ready made
some really tremendous

00:09:45.648 --> 00:09:47.796
videos, and I will make
the formal announcement

00:09:47.796 --> 00:09:50.878
once we have everything
integrated. They've done

00:09:50.878 --> 00:09:53.206
a really good job with
art history. They've had

00:09:53.206 --> 00:09:55.048
these interesting conversations about it.

00:09:55.048 --> 00:09:58.880
I think that's actually
a good model not for just

00:09:58.880 --> 00:10:02.318
art history, but it's a good
model for a lot of the humanities.

00:10:02.318 --> 00:10:06.795
In something like history
or whatever humanities

00:10:06.795 --> 00:10:08.463
you want to pick, it's
nice to have scalpel,

00:10:08.463 --> 00:10:10.132
even in art history you
want to have a scalpel.

00:10:10.132 --> 00:10:16.457
You want to know what it
means to be a serial painter.

00:10:16.457 --> 00:10:20.916
When did the broke period take place?

00:10:20.916 --> 00:10:23.918
Or, whatever it might be.
That's where, kind of,

00:10:23.918 --> 00:10:25.804
more traditional Khan
Academy style videos are

00:10:25.804 --> 00:10:28.121
useful to get you the
scalpel of information.

00:10:28.121 --> 00:10:32.711
The conversation type style
which these professors have

00:10:32.711 --> 00:10:35.446
kind of pioneered, is
really interesting to get

00:10:35.446 --> 00:10:37.380
multiple view points.
Even if they don't cover

00:10:37.380 --> 00:10:40.010
all of the multiple view
points, it kind of gives

00:10:40.010 --> 00:10:42.261
us the freedom to realize
you can have multiple

00:10:42.261 --> 00:10:45.594
view points. They, themselves,
can form their own.

00:10:45.594 --> 00:10:48.009
You're going to see a lot more
of that in the near future.

00:10:48.009 --> 00:10:50.185
That's on the video side.
On the exercise side,

00:10:50.185 --> 00:10:52.843
once again, we can start
to develop exercises that

00:10:52.843 --> 00:10:55.094
help. At least make sure
you have the scalpel

00:10:55.094 --> 00:10:57.710
of information. You know
where the Civil War fit into

00:10:57.710 --> 00:11:01.758
the scope of US History. You
know what the Magna Carta

00:11:01.758 --> 00:11:05.095
even was and how it
relates to other documents.

00:11:05.095 --> 00:11:08.447
Once you have that
scalpel, you're prepared to

00:11:08.447 --> 00:11:10.266
participate in a deeper
discussion in class,

00:11:10.266 --> 00:11:14.254
a deeper project, or a deeper
type of simulation in class.

00:11:14.254 --> 00:11:17.543
Next question. Can the Khan
Academy model as it currently works

00:11:17.543 --> 00:11:20.738
help kids go from learning
facts and operations

00:11:20.738 --> 00:11:23.808
to critical reasoning,
or does that require a

00:11:23.808 --> 00:11:28.407
different model? I'd actually
say this what we're about.

00:11:28.407 --> 00:11:32.464
Right now the problem I
think with a lot of text

00:11:32.464 --> 00:11:34.467
books and some classes
is that they are focused

00:11:34.467 --> 00:11:39.080
too much on facts and
operations. If you look

00:11:39.080 --> 00:11:41.904
at any of the Khan Academy
math videos, sometimes

00:11:41.904 --> 00:11:44.268
the facts and operations
are shown, but their

00:11:44.268 --> 00:11:46.869
never shown devoid of
the motivation for doing

00:11:46.869 --> 00:11:49.664
that fact and operation.
Their never devoid of

00:11:49.664 --> 00:11:51.471
the conceptional
understanding. Why it makes

00:11:51.471 --> 00:11:53.995
intuitive sense? Why you
can critically deduce

00:11:53.995 --> 00:11:56.164
that. You can reason
those facts and operations

00:11:56.164 --> 00:11:58.832
just by thinking about the
problem in the right way.

00:11:58.832 --> 00:12:01.417
How multiple problems in
different fields actually

00:12:01.417 --> 00:12:04.412
reduce to the same core distilled problem.

00:12:04.412 --> 00:12:06.832
I actually think that
right now Khan Academy

00:12:06.832 --> 00:12:09.914
is all about critical
reasoning. Especially on the

00:12:09.914 --> 00:12:12.604
video side. I think on
the exercise there's a lot

00:12:12.604 --> 00:12:14.835
more work we have to do,
but we do want to get

00:12:14.835 --> 00:12:17.736
there. So, we do expose
students some more simulations,

00:12:17.736 --> 00:12:22.339
more projects, more things
that require more than

00:12:22.339 --> 00:12:24.336
just knowing the steps
of how to do a problem.

00:12:24.336 --> 00:12:26.832
This is, I think, in the
videos we're all ready

00:12:26.832 --> 00:12:28.739
doing this to a large
degree. I thinks that's why

00:12:28.739 --> 00:12:31.010
Khan Academy videos have
gotten popular. On the

00:12:31.010 --> 00:12:33.673
exercises we're starting
with the base scalpel

00:12:33.673 --> 00:12:35.735
right now, and right now
the exercise are more

00:12:35.735 --> 00:12:37.868
in this direction. I think
over time we're going

00:12:37.868 --> 00:12:40.014
to see more and more
exercises that point to

00:12:40.014 --> 00:12:42.177
critical reasoning,
simulations, things where

00:12:42.177 --> 00:12:43.916
you're going have to
manipulate, kind of virtual

00:12:43.916 --> 00:12:46.791
manipulative's to get
to some type of goal.

00:12:47.022 --> 00:12:50.397
Next question. 25 years
from now, what do you

00:12:50.397 --> 00:12:52.726
think a school day will
be like for an 8-year-old

00:12:52.726 --> 00:12:55.205
kid in America? Will she
be commuting to a physical

00:12:55.205 --> 00:12:57.656
classroom or accessing
content from home? How will

00:12:57.656 --> 00:13:00.259
she study? Who will her
teachers be and what

00:13:00.259 --> 00:13:02.208
will be their role? I'll
answer the first question.

00:13:02.208 --> 00:13:06.459
Ideally, they will be going
to a physical classroom.

00:13:06.459 --> 00:13:09.129
If their in a very rural
place, or they don't

00:13:09.129 --> 00:13:12.551
have access, they might
be able to learn accessing

00:13:12.551 --> 00:13:15.725
content from home. I think,
we the organization think,

00:13:15.725 --> 00:13:18.468
physical interaction with
other people is a huge

00:13:18.468 --> 00:13:23.715
part of maturing, and we
hope there's a physical

00:13:23.715 --> 00:13:26.393
classroom. We think it
might be a very different

00:13:26.393 --> 00:13:29.396
type of physical classroom.
I kind of imagine

00:13:29.396 --> 00:13:32.260
every student can work at their own pace.

00:13:32.260 --> 00:13:35.393
You don't have to separate
kids by age group anymore.

00:13:35.393 --> 00:13:38.393
The benefits of kids
helping each other. I would

00:13:38.393 --> 00:13:42.331
imagine one really large
room, or maybe several

00:13:42.331 --> 00:13:44.858
really large rooms.
Instead of having 30 kids

00:13:44.858 --> 00:13:47.996
in that room, maybe you
have 200 kids in that room.

00:13:47.996 --> 00:13:50.470
Obviously, instead of
having 1 teacher, you have

00:13:50.470 --> 00:13:54.393
maybe ... 200 kids and
you obviously want to

00:13:54.393 --> 00:13:56.142
have as many teachers
as possible. The lower

00:13:56.142 --> 00:13:57.729
the student to teacher ratio the better.

00:13:57.729 --> 00:14:05.058
Maybe you have ... N
teachers ... if you have

00:14:05.058 --> 00:14:07.260
25 to 1 ratio, you would
have 8 teachers here.

00:14:07.260 --> 00:14:09.661
You would have 8 teachers
here. I think that's

00:14:09.661 --> 00:14:12.060
about consistent with many public schools.

00:14:12.060 --> 00:14:13.859
Every student would be
working at their own pace

00:14:13.859 --> 00:14:15.969
for some part of the day in every subject.

00:14:15.969 --> 00:14:19.526
All the way from grammar
to history to mathematics.

00:14:19.526 --> 00:14:21.725
The teachers are there
to mentor them, to guide

00:14:21.725 --> 00:14:25.725
them, to help them get
past hurdles. So much of

00:14:25.725 --> 00:14:28.067
the learning can hopefully
be done in very efficiently,

00:14:28.067 --> 00:14:32.393
most of the day is spent doing projects.

00:14:32.393 --> 00:14:35.813
If this is the school day
we want this part course

00:14:35.813 --> 00:14:41.726
skills, and the rest
of the day is projects.

00:14:41.726 --> 00:14:44.802
The rest of the day is projects.

00:14:44.802 --> 00:14:47.323
Kids writing software.
Kids conducting scientific

00:14:47.323 --> 00:14:49.793
experiments, real scientific experiments.

00:14:49.793 --> 00:14:53.313
Kids producing video content or web pages,

00:14:53.313 --> 00:14:57.056
blogs, newspapers, composing music, or

00:14:57.056 --> 00:14:59.993
writing short stories.
Whatever it is, their

00:14:59.993 --> 00:15:02.390
doing projects, and the
main role of the teachers

00:15:02.390 --> 00:15:04.993
will not only be to
help kids get past their

00:15:04.993 --> 00:15:06.895
hurdles with the course
skills, so that the kids

00:15:06.895 --> 00:15:09.478
can still perform on
these other external exams

00:15:09.478 --> 00:15:11.663
and all the rest. Also,
be the mentor for the

00:15:11.663 --> 00:15:14.993
projects. We see not just
the teachers being the

00:15:14.993 --> 00:15:18.066
mentors for both of
these parts, we see the

00:15:18.066 --> 00:15:20.402
students mentoring each
other. If you have kids

00:15:20.402 --> 00:15:23.229
of all different age groups
together, then you can

00:15:23.229 --> 00:15:25.327
have students who are
more advanced or have an

00:15:25.327 --> 00:15:27.596
act for it, to mentor students
who are less advanced,

00:15:27.596 --> 00:15:30.899
or who need help in a specific domain.

00:15:30.899 --> 00:15:34.820
We like to see the eventual
real powerful transcript.

00:15:34.820 --> 00:15:36.490
This is something we
all ready take to heart

00:15:36.490 --> 00:15:38.592
when we're hiring people.
It's nice if you went

00:15:38.592 --> 00:15:40.823
to a fancy school, with
a fancy GPA, with a fancy

00:15:40.823 --> 00:15:42.823
standardized test scores,
but what we really care about

00:15:42.823 --> 00:15:44.993
is what have you built
before? What have you

00:15:44.993 --> 00:15:47.739
started with a blank
slate? Have you ever put

00:15:47.739 --> 00:15:49.991
your ideas into action? Have
you ever built anything?

00:15:49.991 --> 00:15:52.736
We think that the resume
of the future will really

00:15:52.736 --> 00:15:56.926
be the projects you
work on over the course

00:15:56.926 --> 00:15:59.733
of your school years, both
in K through 12 and college.

00:15:59.733 --> 00:16:02.529
Frankly, I think that
division between K through 12

00:16:02.529 --> 00:16:04.860
and college will also
start to get blurred.

00:16:04.860 --> 00:16:08.990
Last question. You've said
your goal is to create

00:16:08.990 --> 00:16:10.796
tens of thousands of
videos in pretty much every

00:16:10.796 --> 00:16:13.459
subject, and the worlds
first free, world-class

00:16:13.459 --> 00:16:15.408
virtual school where
anyone can learn anything.

00:16:15.408 --> 00:16:17.660
Can you suggest ways
that museums or museum

00:16:17.660 --> 00:16:19.827
practitioners could
contribute to Khan Academy?

00:16:19.827 --> 00:16:25.993
I encourage museums or
museum practitioners to both

00:16:25.993 --> 00:16:29.074
make content, and I think
some of the art history

00:16:29.074 --> 00:16:30.656
content you'll see from us
in the near future, will

00:16:30.656 --> 00:16:32.798
give a very good idea
of how to make that type

00:16:32.798 --> 00:16:35.745
of content. So, one to
make content and maybe

00:16:35.745 --> 00:16:37.997
share it with Khan Academy,
maybe make it part of

00:16:37.997 --> 00:16:39.728
the Khan Academy library.
We're hoping to build

00:16:39.728 --> 00:16:41.530
tools so that other people
can contribute to the

00:16:41.530 --> 00:16:46.125
library in some way. I
think the other possibility

00:16:46.125 --> 00:16:50.164
to leverage Khan Academy
material or Khan Academy

00:16:50.164 --> 00:16:52.863
like material. If you
have an instillation or

00:16:52.863 --> 00:16:56.595
you have a painting on
something, instead of having

00:16:56.595 --> 00:16:59.490
a little plaque or next
to the thing that has a

00:16:59.490 --> 00:17:01.727
hundred word description
of it, why not have

00:17:01.727 --> 00:17:03.797
an explanation of it? Why
not have someone, maybe,

00:17:03.797 --> 00:17:05.665
Khan Academy style
explaining what that painting

00:17:05.665 --> 00:17:08.199
is all about. Maybe,
using some of our videos

00:17:08.199 --> 00:17:10.245
that you're about to see
in the next months on

00:17:10.245 --> 00:17:15.261
our history. Why not have
people contribute their own

00:17:15.261 --> 00:17:17.670
interpretations of the
art done Khan Academy

00:17:17.670 --> 00:17:21.504
style or just an audio
track. I think it lands

00:17:21.504 --> 00:17:23.927
itself to a very interesting
question which is

00:17:23.927 --> 00:17:27.085
where are museums going?
I think their similar

00:17:27.085 --> 00:17:29.166
to schools in that. Before
you had to have a physical

00:17:29.166 --> 00:17:31.088
location to have a
school. Similarly you have

00:17:31.088 --> 00:17:33.126
to have a physical
location to have a museum.

00:17:33.126 --> 00:17:34.912
I think where museums
are going to go is that

00:17:34.912 --> 00:17:36.749
their going to turn into these amazing ...

00:17:36.749 --> 00:17:38.131
I mean most museums I know of are amazing.

00:17:38.131 --> 00:17:40.186
Physical spaces, architectural
spaces, community

00:17:40.186 --> 00:17:42.754
spaces, and I think
they'll always be there.

00:17:42.754 --> 00:17:44.924
I think they'll always be a
role for those physical spaces.

00:17:44.924 --> 00:17:48.127
I think what will happen
is that the content

00:17:48.127 --> 00:17:50.689
in those physical spaces
will be much more dynamic.

00:17:50.689 --> 00:17:52.862
They won't just be this
insulation that sits

00:17:52.862 --> 00:17:55.088
there for 3 months or 6 months or a year.

00:17:55.088 --> 00:17:57.796
They'll be information
and installations that

00:17:57.796 --> 00:18:01.059
almost change based on
the interactions with

00:18:01.059 --> 00:18:03.500
the people who visit the installations.

00:18:03.500 --> 00:18:05.529
A lot of that static
content, the paintings,

00:18:05.529 --> 00:18:08.525
or the installations, those
can also be virtualized.

00:18:08.525 --> 00:18:11.174
If someone goes to the
physical museum that's

00:18:11.174 --> 00:18:13.926
obviously the best
experience. If you virtualize

00:18:13.926 --> 00:18:17.198
them in the right way, you
can also then bring the

00:18:17.198 --> 00:18:18.863
museum experience to
people who don't have the

00:18:18.863 --> 00:18:20.794
privilege of going to
museum. I think the Google

00:18:20.794 --> 00:18:23.014
art projects starts to
hint at some of this.

00:18:23.014 --> 00:18:25.924
If you have the Google
art project, which gives

00:18:25.924 --> 00:18:28.758
us very high resolution
pictures of art, that

00:18:28.758 --> 00:18:31.462
one can zoom into. You
couple it with kind of

00:18:31.462 --> 00:18:34.467
a conversational commentary
on art history or

00:18:34.467 --> 00:18:38.087
on the art itself. I think
you start to get close

00:18:38.087 --> 00:18:41.596
to that type of experience.