Vi and Sal talk about the mysteries of Benford's law

WEBVTT
Kind: captions
Language: en

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SAL KHAN: I am very
excited to have

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Vi Hart visiting the
office over here.

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And we were just having a
very mathematical conversation

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earlier today.

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And she mentioned something
that is fascinating.

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VI HART: Yeah, I
was just telling

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Sal about a cool thing
called Benford's Law.

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SAL KHAN: Benford's Law.

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And what is Benford's law?

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VI HART: It's this
weird phenomenon

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that you get when you're looking
at numbers in the real world.

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So for example, we've
got some graphs here.

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If you take the populations
of all the countries and you,

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say all right, what
is the first digit

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of the population
of the country?

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Whether it's 1 million
or 1,000 or 100,000,

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we'll say, OK,
that starts with 1.

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So we'll count up all of the
countries that start with 1.

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And I guess here
we've got 27 of them.

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SAL KHAN: Yes, about 27.

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So literally anything
that starts with a 1 here.

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So it could be a country
that has a population of 1,

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a population of 17, or a
population of 1 billion,

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300 million, blah, blah, blah.

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They would all fall into
this bucket right over here.

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VI HART: Right.

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And then if you
start with 2, you

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fall in the second bucket,
and so on and so forth.

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SAL KHAN: Better color.

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Oh yeah, go ahead.

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VI HART: Yeah,
definitely better color.

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SAL KHAN: Better color.

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VI HART: Oh, that's great.

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SAL KHAN: Yeah, that's
the blue, better contrast.

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VI HART: So the
question is, all right,

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you'd think you'd have kind
of random numbers here.

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SAL KHAN: Yes.

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For that first digit,
it's kind of random.

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VI HART: Yeah.

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I mean, there's huge differences
in populations of countries.

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Some have billions
and some have--

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I don't know what the
smallest population is.

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SAL KHAN: Yes.

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It's, like, Montenegro
or something like that.

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VI HART: Yeah.

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So--

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SAL KHAN: Montenegro
is not a country.

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What am I thinking?

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I'm thinking of-- what's the one
that's on the French Riviera?

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Anyway, we can edit that out.

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[LAUGHTER]

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VI HART: I don't know.

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I would be interested
to see for populations

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of states and everything.

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SAL KHAN: The Vatican is the
smallest country, I believe.

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VI HART: Yeah, it is.

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Does that still count?

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I guess--

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SAL KHAN: I think
the Vatican counts.

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They have their own-- yes.

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VI HART: I don't know exactly
what the requirements were

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to be. [INAUDIBLE].

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SAL KHAN: But it would
include the Vatican, which

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I think would be in,
like, the thousands.

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VI HART: Yeah.

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And so why would this happen?

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Why would you see
more 1's than 2's?

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Like, what is going on?

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SAL KHAN: Yeah.

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And it's not some small chance.

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I mean, we were talking
also about the idea

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that it is more likely to
have odd-numbered addresses

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than even-numbered.

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We were talking
about that earlier.

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VI HART: Yeah, I just
learned about that recently.

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And that makes sense.

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SAL KHAN: That makes sense,
because every house will

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have a number 1 on it, or a 10.

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VI HART: Right, every street,
if your street starts,

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you know, with house
number 1, house number 2,

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house number 3, if you have
an odd number of houses,

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then your street has more odd
numbers than even numbers.

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SAL KHAN: Exactly.

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And if you have an even number,
you have the same amount.

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VI HART: Right.

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SAL KHAN: Right.

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VI HART: But that's starting
with 1, which is odd.

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Whereas here, populations
don't start with 1.

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SAL KHAN: Exactly.

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And that phenomenon that
we're talking about the street

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numbers, it's not an
extreme phenomenon.

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It's like, 50 point
some 0-- you have

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a slightly higher probability
of having an odd-numbered house,

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or I guess a 1 house,
than everything else.

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VI HART: Yeah, it's kind of
exactly what you would expect.

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SAL KHAN: It's exactly
what you'd expect.

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But here, it's a significantly
higher probability,

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of a random
country's population,

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that its first digit is a 1
versus its first digit as an 8

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or a 9.

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I mean, it seems a
little bit strange.

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VI HART: Yeah.

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And this isn't
just in countries.

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You see this if you're looking
at a lot of financial stuff.

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Like, how much money
does a company make.

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SAL KHAN: Yes.

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The 1's just show up as a first
digit much more frequently.

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VI HART: Much more
frequently, yeah.

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And here, we have
another fancy graph,

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which is completely crazy.

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It's the first digit
of physical constants.

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So what would be examples
of some physical constants?

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SAL KHAN: I'm
assuming that-- and we

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weren't able to figure out
exactly what they applied

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here-- but I'm assuming it's
things like the Gravitational

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constant, Planck's constant.

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And this seems kind
of crazy to me,

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because it depends on the
units that you're using,

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it depends on a
whole bunch of things

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that you have to
assume about it.

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But even when you use these
kind of arbitrary physical

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constants, which I'm
assuming they're doing here,

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the most significant digit
in these physical constants

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is still much more
likely to be 1.

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It almost exactly
follows Benford's Law.

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And it kind of gives
you goose pimples.

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VI HART: Yeah.

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So the challenge here
is to-- oh, by the way,

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Benford is the guy
with the glasses.

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SAL KHAN: Oh, yes.

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Yes, you might be wondering.

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These aren't-- yes.

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These are--

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VI HART: They're
not both Benford.

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SAL KHAN: These are not Benford
pre-shave and post-shave.

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No.

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This right there is Benford.

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And obviously it was named
after him, Benford's Law.

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But we put this gentleman,
who didn't shave--

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VI HART: Yeah, the cool guy
with the beard is Simon Newcomb.

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SAL KHAN: Simon Newcomb.

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VI HART: Not Duke Nukem.

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SAL KHAN: Not Duke Nukem.

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And we put him here
because he's actually

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the first person who
stated Benford's Law.

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He obviously did not
call it Benford's Law.

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VI HART: And he had
the better beard.

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SAL KHAN: And he
had, yes, the most--

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he was overall a more
imposing character.

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At least to me.

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This guy looks a little
bit like Harry Truman.

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Maybe this is Harry.

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I don't know.

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Yeah, maybe I've got
the wrong picture.

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Anyway, let's just--

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VI HART: So the question, what
is kind of a pure case of this?

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I mean, when you've
this random data,

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you see some fluctuations.

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Like, in a country,
right, there are more--

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SAL KHAN: It's
pretty close, though.

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It's pretty close to that curve.

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VI HART: Yeah, and our
sample size is pretty low.

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I mean--

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SAL KHAN: Right.

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VI HART: --when
you've only got--

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SAL KHAN: There's,
like, 200 countries

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or something like that.

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VI HART: Yeah.

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SAL KHAN: It went
up by, like, 50--

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VI HART: It doesn't
perfectly follow it.

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SAL KHAN: --after the Soviet
Union fell and all that.

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But yeah, it's not a
huge number of countries.

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And even physical
constants, I don't

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know how many physical constants
they randomly sampled over

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here, but it is shockingly
close to Benford's law curve.

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But there's kind of a more
pure way of studying it.

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VI HART: Right.

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So when we look at
this other graph,

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this is kind of like
the pure Benford's Law.

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SAL KHAN: Pure Benford's Law.

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So that's this curve
that we're kind of

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fitting to that other,
more rough data.

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And what's amazing
here is that if we

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take kind of pure
mathematical constructs,

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like the powers of 2, or--

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VI HART: Or the
Fibonacci series.

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You'd think that in
the Fibonacci series,

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you're adding all this
stuff up, and why--

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SAL KHAN: And then you
just take the first digit--

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VI HART: Just the first digit.

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SAL KHAN: --and put
them in these piles,

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it would actually exactly
match Benford's Law.

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Like, no deviation.

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It is exactly--

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VI HART: Right,
mathematically [INAUDIBLE].

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SAL KHAN: Mathematically.

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So let's just be clear,
because this is fascinating.

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So if you were to take
the powers of 2's, you

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get 1, 2, 4, 8, 16, 32, 64.

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I'm gonna go pretty
high so you can

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start to see how
we're doing this.

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128, 256, 512.

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And you just keep
going on and on forever

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with every power of 2.

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And you say, OK, how many
of these start with a 1?

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And you would go
and you would say,

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well, this starts with
a 1, this starts with--

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or the most
significant digit is 1.

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That starts with a 1,
that starts with a 1.

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And you would just find the
percentage that start with a 1.

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And you would plot
it on-- you would

00:06:42.725 --> 00:06:44.600
give the 1's that credit
for that percentage.

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And then you'd say, OK, the
ones that start with a 2.

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And you'd say, OK,
that starts with a 2,

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and that starts with 2.

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But we want to
keep going on this.

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And we could probably do
this with a computer program

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or something, where we'd
go really high powers of 2.

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And then you would
say, what percentage

00:06:57.800 --> 00:07:00.200
of all of these powers
of 2 start with a 2?

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You would, say, get this
percentage right over here.

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The numbers that start with
a 9, you would get this.

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And you would perfectly
match Benford's Law.

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This seems magical.

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VI HART: It does
seem pretty magical.

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SAL KHAN: And this isn't
just for powers of 2.

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This is powers of any number.

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VI HART: Almost any number.

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There's special cases.

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SAL KHAN: I believe it
might be every number.

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Oh, yes.

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No.
VI HART: Well, powers of 1.

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SAL KHAN: 1 would
not work, right.

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VI HART: And then there's,
like, powers of 10.

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SAL KHAN: Powers of 10
would not work as well, yes.

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But every other-- numbers that
kind of mix it up a little bit.

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VI HART: Powers of 0.

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SAL KHAN: Yes.

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You are correct.

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Every number that would
mix it up a little bit.

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VI HART: Yeah.

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It'd have to have a
certain amount of mixing it

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up a little bit.

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SAL KHAN: Right, right.

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But every other, yes, they would
exhibit Benford's distribution.

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And so we want to challenge
you to think about why that is.

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And maybe you could even
put your own explanations

00:07:43.700 --> 00:07:46.700
in our little message board,
on either YouTube or our page,

00:07:46.700 --> 00:07:47.600
if you're curious.

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But we'll challenge you
to think why that is.

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And then we'll offer at least a
decent shot at an explanation.

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Maybe we'll have
other explanations.

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VI HART: Yeah.

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SAL KHAN: So actually, we'll
leave you there in this video.

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And the next video
will explain why

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we think-- an intuitive
reason why it works.


Intro to lines, line segments, and rays

WEBVTT
Kind: captions
Language: en

00:00:00.534 --> 00:00:01.950
What I want to do
in this video is

00:00:01.950 --> 00:00:10.800
think about the difference
between a line segment, a line,

00:00:10.800 --> 00:00:13.210
and a ray.

00:00:13.210 --> 00:00:18.780
And this is the pure geometrical
versions of these things.

00:00:18.780 --> 00:00:20.640
And so, a line segment
is actually probably

00:00:20.640 --> 00:00:23.950
what most of us associate with
a line in our everyday lives.

00:00:23.950 --> 00:00:27.210
A line segment is
something just like that.

00:00:27.210 --> 00:00:29.560
For lack of a better
word, a straight line.

00:00:29.560 --> 00:00:32.330
But why we call it a
segment is that it actually

00:00:32.330 --> 00:00:34.300
has a starting and
a stopping point.

00:00:34.300 --> 00:00:36.210
So, most of the lines
that we experience

00:00:36.210 --> 00:00:38.590
in our everyday
reality are actually

00:00:38.590 --> 00:00:40.240
line segments when
we think of it

00:00:40.240 --> 00:00:42.242
from a pure geometrical
point of view.

00:00:42.242 --> 00:00:44.200
and I know I drew a little
bit of a curve here,

00:00:44.200 --> 00:00:46.570
but this is supposed to
be completely straight,

00:00:46.570 --> 00:00:47.950
but this is a line segment.

00:00:47.950 --> 00:00:50.870
The segment is based
on the fact that it

00:00:50.870 --> 00:00:52.770
has an ending point
and a starting point,

00:00:52.770 --> 00:00:54.630
or a starting point
and an ending point.

00:00:54.630 --> 00:00:56.380
A line, if you're
thinking about it

00:00:56.380 --> 00:01:01.370
in the pure geometric sense
of a line, is essentially,

00:01:01.370 --> 00:01:02.412
it does not stop.

00:01:02.412 --> 00:01:04.620
It doesn't have a starting
point and an ending point.

00:01:04.620 --> 00:01:08.230
It keeps going on forever
in both directions.

00:01:08.230 --> 00:01:09.735
So a line would look like this.

00:01:13.060 --> 00:01:15.110
And to show that it
keeps on going on

00:01:15.110 --> 00:01:18.610
forever in that direction right
over there, we draw this arrow,

00:01:18.610 --> 00:01:20.980
and to keep showing
that it goes on forever

00:01:20.980 --> 00:01:22.620
in kind of the down
left direction,

00:01:22.620 --> 00:01:25.040
we draw this arrow
right over here.

00:01:25.040 --> 00:01:28.090
So obviously, I've never
encountered something

00:01:28.090 --> 00:01:31.530
that just keeps on
going straight forever.

00:01:31.530 --> 00:01:33.530
But in math-- that's the
neat thing about math--

00:01:33.530 --> 00:01:35.620
we can think about
these abstract notions.

00:01:35.620 --> 00:01:39.660
And so the mathematical purest
geometric sense of a line

00:01:39.660 --> 00:01:43.100
is this straight thing
that goes on forever.

00:01:43.100 --> 00:01:45.000
Now, a ray is
something in between.

00:01:45.000 --> 00:01:48.070
A ray has a well
defined starting point.

00:01:48.070 --> 00:01:50.140
So that's its starting
point, but then

00:01:50.140 --> 00:01:52.580
it just keeps on
going on forever.

00:01:52.580 --> 00:01:55.650
So the ray might
start over here,

00:01:55.650 --> 00:01:59.760
but then it just keeps on going.

00:01:59.760 --> 00:02:02.195
So that right over
there is a ray.

00:02:02.195 --> 00:02:04.070
Now, with that out of
the way, let's actually

00:02:04.070 --> 00:02:06.550
try to do the Khan
Academy module

00:02:06.550 --> 00:02:09.570
on recognizing the difference
between line segments, lines,

00:02:09.570 --> 00:02:10.160
and rays.

00:02:10.160 --> 00:02:12.451
And I think you'll find it
pretty straightforward based

00:02:12.451 --> 00:02:14.630
on our little classification
right over here.

00:02:14.630 --> 00:02:19.625
So, let me get the module going.

00:02:19.625 --> 00:02:22.780
Where did I put it?

00:02:22.780 --> 00:02:23.780
There you go.

00:02:23.780 --> 00:02:24.700
All right.

00:02:24.700 --> 00:02:26.860
So what is this thing
right over here?

00:02:26.860 --> 00:02:28.680
Well, it has two
arrows on both ends,

00:02:28.680 --> 00:02:31.320
so it's implying that
it goes on forever.

00:02:31.320 --> 00:02:33.122
So this is going to be a line.

00:02:33.122 --> 00:02:34.080
Let's check our answer.

00:02:34.080 --> 00:02:35.720
Yeah, it's a line.

00:02:35.720 --> 00:02:38.509
Now it's taking some time,
oh, correct, next question.

00:02:38.509 --> 00:02:40.050
All right, now what
about this thing?

00:02:40.050 --> 00:02:41.826
Well, once again,
arrows on both sides.

00:02:41.826 --> 00:02:43.200
It means that this
thing is going

00:02:43.200 --> 00:02:45.430
to go on forever
in both directions.

00:02:45.430 --> 00:02:47.850
So once again, it is a line.

00:02:47.850 --> 00:02:49.040
Fair enough.

00:02:49.040 --> 00:02:50.510
Let's do another one.

00:02:50.510 --> 00:02:53.030
Here we have one arrow,
so it goes on forever

00:02:53.030 --> 00:02:56.120
in this direction, but it has
a well-defined starting point.

00:02:56.120 --> 00:02:58.630
So it starts there, and
then goes on forever.

00:02:58.630 --> 00:03:00.530
And if you remember,
that's what a ray is.

00:03:00.530 --> 00:03:04.026
One starting point,
but goes on forever.

00:03:04.026 --> 00:03:05.900
Or one way to think
about it, goes on forever

00:03:05.900 --> 00:03:07.480
in only one direction.

00:03:07.480 --> 00:03:09.750
So that is a ray.

00:03:09.750 --> 00:03:11.609
So let's do another question.

00:03:11.609 --> 00:03:14.150
This right over here, you have
a starting point and an ending

00:03:14.150 --> 00:03:16.649
point, or you could call this
the start point and the ending

00:03:16.649 --> 00:03:19.260
point, but it doesn't go on
forever in either direction.

00:03:19.260 --> 00:03:23.690
So this right over
here is a line segment.

00:03:23.690 --> 00:03:24.690
There you go.

00:03:24.690 --> 00:03:27.832
So hopefully that gives
you enough to work

00:03:27.832 --> 00:03:29.040
your way through this module.

00:03:29.040 --> 00:03:32.370
And you might notice, when I
did this module right here,

00:03:32.370 --> 00:03:33.330
there is no video.

00:03:33.330 --> 00:03:34.970
And that's exactly
what this video is.

00:03:34.970 --> 00:03:37.139
It's the video for this module.


Comparing absolute values

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:04.530
Let's do some examples
comparing absolute values.

00:00:04.530 --> 00:00:06.470
So let's say we were
to ask ourselves

00:00:06.470 --> 00:00:12.260
how the absolute value of
negative 9, I should say,

00:00:12.260 --> 00:00:19.429
how that compares to the
absolute value of-- let

00:00:19.429 --> 00:00:20.970
me think of a good
number-- let's say

00:00:20.970 --> 00:00:23.476
the absolute value
of negative 7.

00:00:23.476 --> 00:00:25.100
So let's think about
this a little bit,

00:00:25.100 --> 00:00:27.650
and let's think about what
negative 9 looks like,

00:00:27.650 --> 00:00:29.784
or where it is on the number
line, where negative 7

00:00:29.784 --> 00:00:30.700
is on the number line.

00:00:30.700 --> 00:00:33.410
Let's look at what the
absolute values mean,

00:00:33.410 --> 00:00:36.124
and then we should probably
be able to do this comparison.

00:00:36.124 --> 00:00:38.040
So there's a couple of
ways to think about it.

00:00:38.040 --> 00:00:40.690
One is you could draw
them on the number line.

00:00:40.690 --> 00:00:46.570
So if this is 0, if this
is negative 7, and then

00:00:46.570 --> 00:00:49.710
this is negative
9 right over here.

00:00:49.710 --> 00:00:52.310
Now, when you take the
absolute value of a number,

00:00:52.310 --> 00:00:55.780
you're really saying how
far is that number from 0,

00:00:55.780 --> 00:00:58.200
whether it's to the left
or to the right of 0.

00:00:58.200 --> 00:01:03.010
So, for example, negative
9 is 9 to the left of 0.

00:01:03.010 --> 00:01:07.280
So the absolute value of
negative 9 is exactly 9.

00:01:07.280 --> 00:01:09.250
This evaluates to 9,

00:01:09.250 --> 00:01:13.260
Negative 7 is exactly
7 to the left of 0.

00:01:16.020 --> 00:01:20.140
So the absolute value of
negative 7 is positive 7.

00:01:20.140 --> 00:01:22.010
And so if you were
to compare 9 and 7,

00:01:22.010 --> 00:01:23.760
this is a little bit
more straightforward.

00:01:23.760 --> 00:01:29.124
9 is clearly greater than 7.

00:01:29.124 --> 00:01:31.540
And if you ever get confused
with the greater than or less

00:01:31.540 --> 00:01:33.520
than symbols, just
remember that the symbol

00:01:33.520 --> 00:01:35.690
is larger on the left-hand side.

00:01:35.690 --> 00:01:37.600
So that's the greater than side.

00:01:37.600 --> 00:01:39.530
If I were to write
this-- and this

00:01:39.530 --> 00:01:41.806
is actually also
a true statement.

00:01:41.806 --> 00:01:43.930
If you took these without
the absolute value signs,

00:01:43.930 --> 00:01:49.300
it is also true that negative
9 is less than negative 7.

00:01:49.300 --> 00:01:52.851
Notice the smaller side
is on the smaller number.

00:01:52.851 --> 00:01:54.350
And so that's the
interesting thing.

00:01:54.350 --> 00:01:56.980
Negative 9 is less
than negative 7,

00:01:56.980 --> 00:01:58.990
but their absolute
value, since negative 9

00:01:58.990 --> 00:02:03.040
is further to the left of 0,
it is-- the absolute value

00:02:03.040 --> 00:02:05.230
of negative 9, which
is 9, is greater

00:02:05.230 --> 00:02:08.080
than the absolute
value of negative 7.

00:02:08.080 --> 00:02:11.160
Another way to think about it is
if you take the absolute value

00:02:11.160 --> 00:02:12.660
of a number, it's
really just going

00:02:12.660 --> 00:02:14.550
to be the positive
version of that number.

00:02:14.550 --> 00:02:19.300
So if you took the absolute
value of 9, that equals 9.

00:02:19.300 --> 00:02:21.040
Or the absolute
value of negative 9,

00:02:21.040 --> 00:02:22.310
that is also equal to 9.

00:02:22.310 --> 00:02:23.810
Well, when you think
of it visually,

00:02:23.810 --> 00:02:25.440
that's because both
of these numbers

00:02:25.440 --> 00:02:27.310
are exactly 9 away from 0.

00:02:27.310 --> 00:02:31.820
This is 9 to the right of 0,
and this is 9 to the left of 0.

00:02:31.820 --> 00:02:33.950
Let's do a few more of these.

00:02:33.950 --> 00:02:39.770
So let's say that we wanted to
compare the absolute value of 2

00:02:39.770 --> 00:02:43.760
to the absolute value of 3.

00:02:43.760 --> 00:02:46.080
Well, the absolute value
of a positive number

00:02:46.080 --> 00:02:47.600
is just going to
be that same value.

00:02:47.600 --> 00:02:50.090
2 is two to the right
of 0, so this is just

00:02:50.090 --> 00:02:51.800
going to evaluate to 2.

00:02:51.800 --> 00:02:53.682
And then the
absolute value of 3,

00:02:53.682 --> 00:02:55.140
that's just going
to evaluate to 3.

00:02:55.140 --> 00:02:57.220
It's actually pretty
straightforward.

00:02:57.220 --> 00:03:00.620
So 2 is clearly the
smaller number here.

00:03:00.620 --> 00:03:02.980
And so we clearly
get 2 is less than 3,

00:03:02.980 --> 00:03:05.370
or the absolute value
of 2 is less than 3.

00:03:05.370 --> 00:03:07.870
So we have a less
than right over here.

00:03:07.870 --> 00:03:10.570
Let's say you
wanted to compare--

00:03:10.570 --> 00:03:13.610
I'm trying to find a suitable
color-- the absolute value

00:03:13.610 --> 00:03:18.917
of negative 8 to the
absolute value of 8.

00:03:18.917 --> 00:03:20.750
Well, one way to think
about is that they're

00:03:20.750 --> 00:03:22.910
both 8 away from 0.

00:03:22.910 --> 00:03:24.410
This 8 to the left of 0.

00:03:24.410 --> 00:03:25.940
This is 8 to the right of 0.

00:03:25.940 --> 00:03:28.460
So both of these
things evaluate to 8.

00:03:28.460 --> 00:03:31.710
Absolute value of
negative 8 is 8.

00:03:31.710 --> 00:03:33.930
Absolute value of 8 is 8.

00:03:33.930 --> 00:03:37.830
And so, clearly,
8 is equal to 8.

00:03:37.830 --> 00:03:39.610
Let me do a couple
more examples.

00:03:39.610 --> 00:03:43.620
Let's say I wanted to
compare the absolute value

00:03:43.620 --> 00:03:48.790
of negative 1, and I want to
compare that to positive 2.

00:03:48.790 --> 00:03:50.680
So the absolute
value of negative 1

00:03:50.680 --> 00:03:53.260
is just the positive
version of 1,

00:03:53.260 --> 00:03:56.120
or it's just the positive
version of negative 1,

00:03:56.120 --> 00:03:57.750
which is just 1.

00:03:57.750 --> 00:03:59.770
So 1 is clearly less than 2.

00:03:59.770 --> 00:04:02.020
Or the other way to think
about it, the absolute value

00:04:02.020 --> 00:04:06.072
of negative 1 is
clearly less than 2.


Ordering negative numbers

WEBVTT
Kind: captions
Language: en

00:00:00.610 --> 00:00:03.220
I've got five numbers
here, and the goal

00:00:03.220 --> 00:00:08.400
is to order them from
least to greatest.

00:00:08.400 --> 00:00:11.550
And it might be obvious to you
that all five of these numbers

00:00:11.550 --> 00:00:13.080
are negative numbers.

00:00:13.080 --> 00:00:16.050
So let's just think about
which of these is the greatest

00:00:16.050 --> 00:00:17.150
number.

00:00:17.150 --> 00:00:19.642
And you might be tempted
to say oh, well, you know,

00:00:19.642 --> 00:00:21.850
if these were all positive,
40 would be the greatest.

00:00:21.850 --> 00:00:25.160
So you might be tempted to say
negative 40 is the greatest.

00:00:25.160 --> 00:00:28.000
But you have to realize what
the negative is telling you,

00:00:28.000 --> 00:00:29.210
and to think about that.

00:00:29.210 --> 00:00:32.159
Think about if these
were your dollar amounts

00:00:32.159 --> 00:00:33.390
in your bank account.

00:00:33.390 --> 00:00:36.200
Would you rather have negative
$40 in your bank account

00:00:36.200 --> 00:00:39.200
or negative $7 in
your bank account?

00:00:39.200 --> 00:00:42.480
Negative 40 means that
you owe the bank $40.

00:00:42.480 --> 00:00:44.940
So it's 40 less
than having nothing.

00:00:44.940 --> 00:00:48.720
Negative 7 would mean that
you owe the bank only $7.

00:00:48.720 --> 00:00:50.750
So it's actually the
case that negative 40

00:00:50.750 --> 00:00:52.730
is less than negative 7.

00:00:52.730 --> 00:00:56.380
And out of all of these numbers,
it is the least of all of them.

00:00:56.380 --> 00:00:59.417
So negative 40 is the very
least that you could do.

00:00:59.417 --> 00:01:01.750
That's the least amount of
money that you would want out

00:01:01.750 --> 00:01:04.030
of these comparisons
in your bank account,

00:01:04.030 --> 00:01:05.570
or the smallest amount of money.

00:01:05.570 --> 00:01:07.000
You owe the bank $40.

00:01:07.000 --> 00:01:09.710
Not only do you have nothing,
you owe the bank $40.

00:01:09.710 --> 00:01:15.860
Then the next smallest
number would be negative 30.

00:01:15.860 --> 00:01:19.690
And then the next smallest
after that would be negative 25.

00:01:22.490 --> 00:01:25.765
And then the next smallest
after that would be negative 10.

00:01:28.280 --> 00:01:32.600
And then finally, the greatest
of all of these numbers-- and I

00:01:32.600 --> 00:01:35.070
will do it in pink--
the greatest of all

00:01:35.070 --> 00:01:37.580
of these numbers is negative 7.

00:01:37.580 --> 00:01:39.170
And if it's still
not obvious to you,

00:01:39.170 --> 00:01:41.950
you could also think of
them in temperature terms.

00:01:41.950 --> 00:01:43.790
Which of these is the
coldest temperature,

00:01:43.790 --> 00:01:46.460
whether you're talking
about Celsius or Fahrenheit?

00:01:46.460 --> 00:01:48.470
Negative 40 would be
the coldest temperature.

00:01:48.470 --> 00:01:51.050
Negative 7 would be the
warmest temperature.

00:01:51.050 --> 00:01:54.060
There would be the most heat
in the air at negative 7.

00:01:54.060 --> 00:01:57.240
Another way to think about it
is we could draw a number line.

00:01:57.240 --> 00:02:00.300
So let's draw a number
line right over here.

00:02:00.300 --> 00:02:04.440
If this is a zero, and we could
put maybe positive 7 up here.

00:02:04.440 --> 00:02:06.380
Positive 7 isn't one
of these numbers,

00:02:06.380 --> 00:02:08.280
but then we could plot
all the other numbers.

00:02:08.280 --> 00:02:11.160
So this right here
might be negative 7.

00:02:11.160 --> 00:02:14.410
If that's negative 7, then
maybe this right over here

00:02:14.410 --> 00:02:15.340
would be negative 10.

00:02:15.340 --> 00:02:19.140
Notice we go further and
further to the left of zero.

00:02:19.140 --> 00:02:22.350
And then we go a little
bit further to the left.

00:02:22.350 --> 00:02:24.570
We get negative 25.

00:02:24.570 --> 00:02:29.430
A little bit further to the
left than that is negative 30.

00:02:29.430 --> 00:02:33.930
And then you go even
further to the left

00:02:33.930 --> 00:02:35.820
and you get to negative 40.

00:02:35.820 --> 00:02:38.990
So if you think of it this
way, the least of these numbers

00:02:38.990 --> 00:02:41.830
is the one that's furthest to
the left on the number line,

00:02:41.830 --> 00:02:46.195
and the greatest is the one
that's furthest to the right.


Comparing and ordering fractions

WEBVTT
Kind: captions
Language: en

00:00:00.510 --> 00:00:03.250
What I want to do in this
video is order these fractions

00:00:03.250 --> 00:00:05.030
from least to greatest.

00:00:05.030 --> 00:00:07.510
And the easiest way
and the way that I

00:00:07.510 --> 00:00:10.485
think we can be sure we'll
get the right answer here

00:00:10.485 --> 00:00:12.860
is to find a common denominator,
because if we don't find

00:00:12.860 --> 00:00:15.220
a common denominator,
these fractions are really

00:00:15.220 --> 00:00:15.960
hard to compare.

00:00:15.960 --> 00:00:20.750
4/9 versus 3/4 versus
4/5, 11/12, 13/15.

00:00:20.750 --> 00:00:24.320
You can try to estimate
them, but you'll

00:00:24.320 --> 00:00:26.830
be able to directly
compare them if they all

00:00:26.830 --> 00:00:28.020
had the same denominator.

00:00:28.020 --> 00:00:30.400
So the trick here, or at
least the first trick here,

00:00:30.400 --> 00:00:32.860
is to try to find that
common denominator.

00:00:32.860 --> 00:00:34.650
And there's many ways to do it.

00:00:34.650 --> 00:00:36.390
You could just pick
one of these numbers

00:00:36.390 --> 00:00:40.105
and keep taking its multiples
and find that multiple that

00:00:40.105 --> 00:00:41.810
is divisible by all the rest.

00:00:41.810 --> 00:00:44.410
Another way to do it is look
at the prime factorization

00:00:44.410 --> 00:00:46.790
of each of these numbers.

00:00:46.790 --> 00:00:48.890
And then the least
common multiple of them

00:00:48.890 --> 00:00:51.970
will have to have at least all
of those prime numbers in it.

00:00:51.970 --> 00:00:53.990
It has to be composed
of all of these numbers.

00:00:53.990 --> 00:00:55.350
So let's do it that second way.

00:00:55.350 --> 00:00:58.610
And then let's verify that
it definitely is divisible.

00:00:58.610 --> 00:01:01.700
So 9 is the same
thing as 3 times 3.

00:01:01.700 --> 00:01:05.640
So our least common
multiple is going

00:01:05.640 --> 00:01:08.790
to have at least
one 3 times 3 in it.

00:01:08.790 --> 00:01:11.910
And then 4 is the same
thing as 2 times 2.

00:01:11.910 --> 00:01:14.590
So we're going to also
have to have a 2 times 2

00:01:14.590 --> 00:01:18.050
in our prime factorization
of our least common multiple.

00:01:18.050 --> 00:01:19.910
5 is a prime number.

00:01:19.910 --> 00:01:22.420
So we're going to need
to have a 5 in there.

00:01:22.420 --> 00:01:25.660
And then 12-- I'm going
to do that in yellow.

00:01:25.660 --> 00:01:28.710
12 is the same thing
as 2 times 6, which

00:01:28.710 --> 00:01:31.540
is the same thing as 2 times 3.

00:01:31.540 --> 00:01:33.930
And so in our least
common multiple,

00:01:33.930 --> 00:01:35.220
we have to have two 2's.

00:01:35.220 --> 00:01:38.730
But we already have two 2's
right over here from our 4.

00:01:38.730 --> 00:01:42.710
And we already have
one 3 right over here.

00:01:42.710 --> 00:01:45.430
Another way to think about it
is something that is divisible

00:01:45.430 --> 00:01:49.742
by both 9 and 4 is going
to be divisible by 12,

00:01:49.742 --> 00:01:51.450
because you're going
to have the two 2's.

00:01:51.450 --> 00:01:54.690
And you're going to have
that one 3 right over there.

00:01:54.690 --> 00:01:57.720
And then, finally, we need
to be divisible by 15's

00:01:57.720 --> 00:01:58.790
prime factors.

00:01:58.790 --> 00:02:00.580
So let's look at
15's prime factors.

00:02:00.580 --> 00:02:03.980
15 is the same
thing as 3 times 5.

00:02:03.980 --> 00:02:06.640
So once again, this number
right over here already has a 3

00:02:06.640 --> 00:02:07.200
in it.

00:02:07.200 --> 00:02:09.470
And it already has a 5 in it.

00:02:09.470 --> 00:02:12.310
So we're cool for 15,
for 12, and, obviously,

00:02:12.310 --> 00:02:13.469
for the rest of them.

00:02:13.469 --> 00:02:15.010
So this is our least
common multiple.

00:02:15.010 --> 00:02:17.180
And we can just
take this product.

00:02:17.180 --> 00:02:22.080
And so this is going to be
equal to 3 times 3 is 9.

00:02:22.080 --> 00:02:23.800
9 times 2 is 18.

00:02:23.800 --> 00:02:26.370
18 times 2 is 36.

00:02:26.370 --> 00:02:31.190
36 times 5, you could do that
in your head if you're like.

00:02:31.190 --> 00:02:32.860
But I'll do it on the
side just in case.

00:02:32.860 --> 00:02:35.790
36 times 5, just so
that we don't mess up.

00:02:35.790 --> 00:02:40.476
6 times 5 is 30.

00:02:40.476 --> 00:02:44.970
3 times 5 is 15 plus 3 is 180.

00:02:44.970 --> 00:02:47.480
So our least common
multiple is 180.

00:02:47.480 --> 00:02:49.630
So we want to rewrite
all of these fractions

00:02:49.630 --> 00:02:52.990
with 180 in the denominator.

00:02:52.990 --> 00:02:58.160
So this first fraction,
4/9, is what over 180?

00:02:58.160 --> 00:03:03.600
To go from 9 to 180, we have to
multiply the denominator by 20.

00:03:03.600 --> 00:03:06.160
So let me do it this way.

00:03:06.160 --> 00:03:12.340
So if we do 4/9, to get the
denominator of 9 to be 180,

00:03:12.340 --> 00:03:14.346
you have to multiply it by 20.

00:03:14.346 --> 00:03:15.720
And since we don't
want to change

00:03:15.720 --> 00:03:17.428
the value of the
fraction, we should also

00:03:17.428 --> 00:03:19.540
multiply the 4 by 20.

00:03:19.540 --> 00:03:21.840
So we're just really
multiplying by 20/20.

00:03:21.840 --> 00:03:28.380
And so 4/9 is going to be
the same thing as 80/180.

00:03:28.380 --> 00:03:32.330
Now, let's do the
same thing for 3/4.

00:03:32.330 --> 00:03:34.830
Well, what do we have to
multiply the denominator by

00:03:34.830 --> 00:03:38.150
to get us to 180?

00:03:38.150 --> 00:03:39.600
So it looks like 45.

00:03:39.600 --> 00:03:42.720
You could divide 4 into
180 to figure that out.

00:03:42.720 --> 00:03:49.022
But if you take 4 times
45, 4 times 40 is 160.

00:03:49.022 --> 00:03:50.124
4 times 5 is 20.

00:03:50.124 --> 00:03:50.790
You add them up.

00:03:50.790 --> 00:03:52.090
You get 180.

00:03:52.090 --> 00:03:54.070
So if you multiply
the denominator by 45,

00:03:54.070 --> 00:03:58.300
you also have to multiply
the numerator by 45.

00:03:58.300 --> 00:04:02.650
3 times 45 is 120 plus 15.

00:04:02.650 --> 00:04:06.050
So it's 135.

00:04:06.050 --> 00:04:10.510
And the denominator here is 180.

00:04:10.510 --> 00:04:11.595
Now, let's do 4/5.

00:04:15.130 --> 00:04:17.730
To get our
denominator to be 180,

00:04:17.730 --> 00:04:20.850
what do you have
to multiply 5 by?

00:04:20.850 --> 00:04:21.350
Let's see.

00:04:21.350 --> 00:04:25.190
If you multiply 5 by
30, you'll get to 150.

00:04:25.190 --> 00:04:26.759
But then you have another 30.

00:04:26.759 --> 00:04:28.300
Actually, we know
it right over here.

00:04:28.300 --> 00:04:31.690
You have to multiply it by 36.

00:04:31.690 --> 00:04:34.630
Well, then you have to multiply
the numerator by 36 as well.

00:04:34.630 --> 00:04:36.880
And so our denominator
is going to be 180.

00:04:36.880 --> 00:04:39.782
Our numerator, 4
times 30 is 120.

00:04:39.782 --> 00:04:42.650
4 times 6 is 24.

00:04:42.650 --> 00:04:46.970
So it's 144/180.

00:04:46.970 --> 00:04:49.690
And then we have
only two more to do.

00:04:49.690 --> 00:04:50.640
So we have our 11/12.

00:04:54.830 --> 00:04:57.480
So to get the
denominator to be 180,

00:04:57.480 --> 00:05:03.084
we have to multiply 12
by-- so 12 times 10 is 120.

00:05:03.084 --> 00:05:04.000
Then you have 60 left.

00:05:04.000 --> 00:05:07.690
So you have to multiply it
by 15, 15 In the denominator,

00:05:07.690 --> 00:05:10.540
and 15 in the numerator.

00:05:10.540 --> 00:05:13.990
And so the denominator
gives us 180.

00:05:13.990 --> 00:05:15.480
And 11 times 15.

00:05:15.480 --> 00:05:18.190
So 10 times 15 is 150.

00:05:18.190 --> 00:05:20.020
And then you have one more 15.

00:05:20.020 --> 00:05:24.520
So it's going to be 165.

00:05:24.520 --> 00:05:26.473
And then, finally,
we have 13/15.

00:05:32.020 --> 00:05:36.040
To get our denominator to be
180, have to multiply it by 12.

00:05:36.040 --> 00:05:38.585
We already figured out
that 12 times 15 is 180.

00:05:38.585 --> 00:05:40.460
So you have to
multiply it by 12.

00:05:40.460 --> 00:05:42.872
That will give us 180
in the denominator.

00:05:42.872 --> 00:05:45.080
And so you have to also
multiply the numerator by 12,

00:05:45.080 --> 00:05:47.310
so that we don't change
the value of the fraction.

00:05:47.310 --> 00:05:50.730
We know 12 times 12 is 144.

00:05:50.730 --> 00:05:53.430
You could put one
more 12 in there.

00:05:53.430 --> 00:05:55.827
You get 156.

00:05:55.827 --> 00:05:56.660
Did I do that right?

00:05:56.660 --> 00:06:00.730
12 plus 144 is going to be 156.

00:06:00.730 --> 00:06:04.800
So we've rewritten
each of these fractions

00:06:04.800 --> 00:06:07.870
with that new common
denominator of 180.

00:06:07.870 --> 00:06:09.840
And now, it's very
easy to compare them.

00:06:09.840 --> 00:06:12.270
You really just have to
look at the numerators.

00:06:12.270 --> 00:06:14.360
So the smallest
of the numerators

00:06:14.360 --> 00:06:16.860
is this 80 right over here.

00:06:16.860 --> 00:06:19.500
So 4/9 is the smallest.

00:06:19.500 --> 00:06:21.084
4/9 is the least
of these numbers.

00:06:21.084 --> 00:06:22.500
So let me just
write it over here.

00:06:22.500 --> 00:06:23.520
So this is our ordering.

00:06:23.520 --> 00:06:27.370
We have 4/9 comes first, which
is the same thing as 80/180.

00:06:27.370 --> 00:06:30.620
Let me write it
both ways-- 80/180.

00:06:30.620 --> 00:06:32.550
Then the next the
smallest number

00:06:32.550 --> 00:06:35.210
looks like it's this
135 right over here.

00:06:38.740 --> 00:06:40.850
I want to do it in
that same color.

00:06:40.850 --> 00:06:46.930
The next one is going to
be that 135/180, which

00:06:46.930 --> 00:06:48.660
is the same thing as 3/4.

00:06:51.740 --> 00:06:54.430
And then the next one is
going to be-- let's see,

00:06:54.430 --> 00:06:57.160
we have the 144/180.

00:06:57.160 --> 00:07:01.520
So this is going to
be the 144/180, which

00:07:01.520 --> 00:07:04.160
is the same thing as 4/5.

00:07:04.160 --> 00:07:07.150
And then we have two more.

00:07:07.150 --> 00:07:10.560
The next is this 156/180.

00:07:10.560 --> 00:07:15.020
So then we have
our 156/180, which

00:07:15.020 --> 00:07:16.540
is the same thing as 13/15.

00:07:19.960 --> 00:07:23.390
And then we have one
left over, the 165/180,

00:07:23.390 --> 00:07:27.000
which is the same thing-- I
want to do that in yellow.

00:07:27.000 --> 00:07:32.106
We have our 165/180, which
is the same thing as 11/12.

00:07:35.290 --> 00:07:37.220
And we're done.

00:07:37.220 --> 00:07:39.890
We have finished our ordering.

00:07:39.890 --> 00:07:43.980
So if you're doing the Khan
Academy module on this,

00:07:43.980 --> 00:07:47.475
this is what you would input
into that little box there.


More angle measurements using a protractor

WEBVTT
Kind: captions
Language: en

00:00:00.610 --> 00:00:02.830
This is the video for
the measuring angles

00:00:02.830 --> 00:00:05.630
module because, clearly, at the
time that I'm doing this video,

00:00:05.630 --> 00:00:08.950
there is no video for the
measuring angles module.

00:00:08.950 --> 00:00:10.330
And this is a
pretty neat module.

00:00:10.330 --> 00:00:14.799
This was made by Omar Rizwan,
one of our amazing high school

00:00:14.799 --> 00:00:16.340
interns that we had
this past summer.

00:00:16.340 --> 00:00:17.970
This is the summer of 2011.

00:00:17.970 --> 00:00:20.540
And what it really is, is
it makes you measure angles.

00:00:20.540 --> 00:00:23.310
And he made this really
cool protractor tool here

00:00:23.310 --> 00:00:25.020
so that you actually
use this protractor

00:00:25.020 --> 00:00:26.680
to measure the angles there.

00:00:26.680 --> 00:00:28.965
And so the trick here is you
would actually measure it

00:00:28.965 --> 00:00:31.080
the way you would
measure any angle using

00:00:31.080 --> 00:00:32.840
an actual physical protractor.

00:00:32.840 --> 00:00:35.250
You'd want to put the center
of the protractor right

00:00:35.250 --> 00:00:38.710
at the vertex of where
the two lines intersect.

00:00:38.710 --> 00:00:41.460
You can view it as the
vertex of the angle.

00:00:41.460 --> 00:00:43.060
And then you'd want
to rotate it so

00:00:43.060 --> 00:00:46.160
that, preferably, this edge,
this edge at 0 degrees,

00:00:46.160 --> 00:00:50.480
is at one of these sides.

00:00:50.480 --> 00:00:53.010
So let's do it so that
this edge right over here

00:00:53.010 --> 00:00:55.890
is right along this line.

00:00:55.890 --> 00:00:58.070
So let me rotate it.

00:00:58.070 --> 00:01:02.260
So then-- I've got to rotate
it a little bit further, maybe

00:01:02.260 --> 00:01:02.810
one more.

00:01:02.810 --> 00:01:04.519
No, that's too far.

00:01:04.519 --> 00:01:07.370
So that looks about right.

00:01:07.370 --> 00:01:09.110
And then if you
look at it this way,

00:01:09.110 --> 00:01:11.734
you can see that the angle-- and
I don't have my Pen tool here.

00:01:11.734 --> 00:01:14.220
I'm just using my
regular web browser--

00:01:14.220 --> 00:01:15.680
if you look at the
angle here, you

00:01:15.680 --> 00:01:18.390
see that the other line
goes to 130 degrees.

00:01:18.390 --> 00:01:21.050
So this angle that we
need to measure here

00:01:21.050 --> 00:01:25.340
is 130 degrees, assuming
you can read sideways.

00:01:25.340 --> 00:01:27.800
So that is 130 degrees.

00:01:27.800 --> 00:01:29.407
Let me check my answer.

00:01:29.407 --> 00:01:30.490
Very good, I got it right.

00:01:30.490 --> 00:01:31.930
It would have been
embarrassing if I didn't.

00:01:31.930 --> 00:01:33.060
Let's do the next question.

00:01:33.060 --> 00:01:35.500
I'll do a couple of
examples like this.

00:01:35.500 --> 00:01:40.510
So once again, let us put the
center of the protractor right

00:01:40.510 --> 00:01:42.330
at the vertex right over there.

00:01:42.330 --> 00:01:44.460
And let's get this
0 degrees side

00:01:44.460 --> 00:01:48.050
to be on one of these sides
so that this angle will

00:01:48.050 --> 00:01:49.820
be within the protractor.

00:01:49.820 --> 00:01:52.400
So let me rotate it this way.

00:01:52.400 --> 00:01:56.120
And this really is pretty cool
what Omar did with this module.

00:01:56.120 --> 00:01:57.450
So let's see.

00:01:57.450 --> 00:02:00.490
Let's do it one more time.

00:02:00.490 --> 00:02:01.650
That's too far.

00:02:01.650 --> 00:02:03.350
And so that looks about right.

00:02:03.350 --> 00:02:07.500
And then you can see that
the angle right over here,

00:02:07.500 --> 00:02:10.240
if we look at where the
other line points to,

00:02:10.240 --> 00:02:11.860
it is 40 degrees.

00:02:14.390 --> 00:02:15.910
Check answer-- very good.

00:02:15.910 --> 00:02:17.320
Let's do another one.

00:02:17.320 --> 00:02:18.995
This is fun.

00:02:18.995 --> 00:02:20.870
So let's get our protractor
right over there.

00:02:20.870 --> 00:02:23.120
And you don't always have
to do it in that same order.

00:02:23.120 --> 00:02:25.615
You could rotate it first
so that the 0 degrees is--

00:02:25.615 --> 00:02:27.740
and what you want to do is
you want to rotate the 0

00:02:27.740 --> 00:02:30.240
degrees to one of the sides
so that the angle is still

00:02:30.240 --> 00:02:31.200
within the protractor.

00:02:31.200 --> 00:02:33.120
So let's rotate it around.

00:02:33.120 --> 00:02:35.746
So if you did it like
that-- so you don't always

00:02:35.746 --> 00:02:37.120
have to do it in
that same order.

00:02:37.120 --> 00:02:38.891
Although I think it's
easier to rotate it

00:02:38.891 --> 00:02:40.640
when you have the
center of the protractor

00:02:40.640 --> 00:02:43.260
at the vertex of the angle.

00:02:43.260 --> 00:02:46.130
So we have to rotate
it a little bit more.

00:02:46.130 --> 00:02:48.400
So 0 degrees is this line.

00:02:48.400 --> 00:02:51.250
And then as we go
further and further up,

00:02:51.250 --> 00:02:53.660
I guess, since this
is on its side,

00:02:53.660 --> 00:02:56.654
it looks like this other
line gets us to 150 degrees.

00:02:56.654 --> 00:02:59.070
And hopefully you're noticing
that the higher the degrees,

00:02:59.070 --> 00:03:01.560
the more open this angle is.

00:03:01.560 --> 00:03:05.250
And so this one right
over here is 150 degrees.

00:03:05.250 --> 00:03:08.790
And so let's do that-- 150.

00:03:08.790 --> 00:03:09.940
Let's do one more.

00:03:09.940 --> 00:03:11.970
Now let me show
you what not to do.

00:03:11.970 --> 00:03:14.600
So what not to do
is-- so you could

00:03:14.600 --> 00:03:17.460
put the center right over there.

00:03:17.460 --> 00:03:19.150
And you might say,
OK, let me make

00:03:19.150 --> 00:03:22.720
the 0 go right over on
this side, right over here.

00:03:22.720 --> 00:03:28.590
So if you did that, notice
your angle would not

00:03:28.590 --> 00:03:29.660
be within the protractor.

00:03:29.660 --> 00:03:30.800
So you won't be
able to measure it.

00:03:30.800 --> 00:03:33.300
And what you're attempting to
do is measure this outer angle

00:03:33.300 --> 00:03:35.150
over here, which is
an angle, but that's

00:03:35.150 --> 00:03:37.740
not the angle that this question
is asking us to measure.

00:03:37.740 --> 00:03:40.020
This little arc over
here is telling us

00:03:40.020 --> 00:03:42.220
that that's the angle
that we need to measure.

00:03:42.220 --> 00:03:44.810
So that arc has to be
within the protractor.

00:03:44.810 --> 00:03:47.620
So let's rotate this
protractor a little bit more.

00:03:47.620 --> 00:03:49.810
I overdid it.

00:03:49.810 --> 00:03:52.850
And so this looks like
this is 0 degrees,

00:03:52.850 --> 00:03:56.770
and then this right
over here is 60 degrees.

00:03:56.770 --> 00:03:59.180
60 degrees-- we got
that one right, too.

00:03:59.180 --> 00:04:01.980
So hopefully that helps
you with this module.

00:04:01.980 --> 00:04:04.290
It's kind of fun.


Setting up proportions to solve word problems

WEBVTT
Kind: captions
Language: en

00:00:00.630 --> 00:00:02.240
I have three word problems here.

00:00:02.240 --> 00:00:03.890
And what I want to
do in this video

00:00:03.890 --> 00:00:07.310
is not solve the word problems
but just set up the equation

00:00:07.310 --> 00:00:09.990
that we could solve to get the
answer to the word problems.

00:00:09.990 --> 00:00:11.865
And essentially, we're
going to be setting up

00:00:11.865 --> 00:00:13.670
proportions in either case.

00:00:13.670 --> 00:00:18.350
So in this first problem, we
have 9 markers cost $11.50.

00:00:18.350 --> 00:00:22.140
And then they ask us, how
much would 7 markers cost?

00:00:22.140 --> 00:00:24.820
And let's just set x to
be equal to our answer.

00:00:24.820 --> 00:00:28.310
So x is equal to the
cost of 7 markers.

00:00:31.476 --> 00:00:33.100
So the way to solve
a problem like this

00:00:33.100 --> 00:00:36.050
is to set up two ratios and then
set them equal to each other.

00:00:36.050 --> 00:00:39.910
So you could say that the ratio
of 9 markers to the cost of 9

00:00:39.910 --> 00:00:44.720
markers, so the ratio of
the number of markers, so 9,

00:00:44.720 --> 00:00:50.740
to the cost of the
9 markers, to 11.50,

00:00:50.740 --> 00:00:54.580
this should be equal to
the ratio of our new number

00:00:54.580 --> 00:01:04.849
of markers, 7, to whatever
the cost of the 7 markers are,

00:01:04.849 --> 00:01:06.850
to x.

00:01:06.850 --> 00:01:07.970
Let me do x in green.

00:01:10.560 --> 00:01:12.500
So this is a completely
valid proportion here.

00:01:12.500 --> 00:01:16.870
The ratio of 9 markers
to the cost of 9 markers

00:01:16.870 --> 00:01:20.309
is equal to 7 markers to
the cost of 7 markers.

00:01:20.309 --> 00:01:22.100
And then you could
solve this to figure out

00:01:22.100 --> 00:01:24.967
how much those 7
markers would cost.

00:01:24.967 --> 00:01:26.550
And you could flip
both sides of this,

00:01:26.550 --> 00:01:28.780
and it would still be a
completely valid ratio.

00:01:28.780 --> 00:01:35.595
You could have 11.50 to 9.

00:01:35.595 --> 00:01:38.570
The ratio between the cost
of the markers to the number

00:01:38.570 --> 00:01:47.830
of markers you're
buying, 11.50 to 9,

00:01:47.830 --> 00:01:51.300
is equal to the ratio of the
cost of 7 markers to the number

00:01:51.300 --> 00:01:53.100
of markers, which
is obviously 7.

00:01:53.100 --> 00:01:56.470
So all I would do is flip
both sides of this equation

00:01:56.470 --> 00:01:58.220
right here to get
this one over here.

00:01:58.220 --> 00:02:01.820
You could also think about
the ratios in other ways.

00:02:01.820 --> 00:02:11.380
You could say that the ratio
of 9 markers to 7 markers

00:02:11.380 --> 00:02:15.360
is going to be the same as
the ratio of their costs,

00:02:15.360 --> 00:02:19.080
is going to be equal to the
ratio of the cost of 9 markers

00:02:19.080 --> 00:02:22.120
to the cost of 7 markers.

00:02:22.120 --> 00:02:25.000
And then, obviously, you could
flip both of these sides.

00:02:27.895 --> 00:02:30.580
Let me do that in the
same magenta color.

00:02:30.580 --> 00:02:33.880
The ratio of 7
markers to 9 markers

00:02:33.880 --> 00:02:36.790
is the same thing as
the ratio of the cost

00:02:36.790 --> 00:02:41.060
of 7 markers to the
cost of 9 markers.

00:02:41.060 --> 00:02:42.340
So that is 11.50.

00:02:42.340 --> 00:02:46.140
So all of these would be valid
proportions, valid equations

00:02:46.140 --> 00:02:47.840
that describe what's
going on here.

00:02:47.840 --> 00:02:50.729
And then you would just have
to essentially solve for x.

00:02:50.729 --> 00:02:52.270
So let's do this
one right over here.

00:02:52.270 --> 00:02:54.740
7 apples cost $5.

00:02:54.740 --> 00:02:57.620
How many apples can
I buy it with $8?

00:02:57.620 --> 00:03:01.720
So one again, we're going to
assume that what they're asking

00:03:01.720 --> 00:03:06.620
is how many apples--
let's call that x.

00:03:06.620 --> 00:03:08.950
x is what we want to solve for.

00:03:08.950 --> 00:03:10.980
So 7 apples costs $5.

00:03:10.980 --> 00:03:14.790
So we have the ratio between
the number of apples, 7,

00:03:14.790 --> 00:03:18.470
and the cost of
the apples, 5, is

00:03:18.470 --> 00:03:23.520
going to be equal to the
ratio between another number

00:03:23.520 --> 00:03:29.380
of apples, which is now x, and
the cost of that other number

00:03:29.380 --> 00:03:30.490
of apples.

00:03:30.490 --> 00:03:33.200
And it's going to be $8.

00:03:33.200 --> 00:03:36.310
And so notice here in this first
situation, what was unknown

00:03:36.310 --> 00:03:37.300
was the cost.

00:03:37.300 --> 00:03:39.000
So we kind of had
the number of apples

00:03:39.000 --> 00:03:41.220
to cost, the number
of apples to cost.

00:03:41.220 --> 00:03:44.825
Now in this example, the
unknown is the number of apples,

00:03:44.825 --> 00:03:47.975
so number of apples to cost,
number of apples to cost.

00:03:47.975 --> 00:03:50.350
And we could do all of the
different scenarios like this.

00:03:50.350 --> 00:03:55.610
You could also say the
ratio between 7 apples

00:03:55.610 --> 00:03:58.320
and x apples is
going to be the same

00:03:58.320 --> 00:04:03.110
as the ratio between
the cost of 7 apples

00:04:03.110 --> 00:04:06.870
and the cost of 8 apples.

00:04:06.870 --> 00:04:08.390
Obviously, you can
flip both sides

00:04:08.390 --> 00:04:10.430
of these in either
of these equations

00:04:10.430 --> 00:04:11.530
to get two more equations.

00:04:11.530 --> 00:04:15.056
And any of these would
be valid equations.

00:04:15.056 --> 00:04:16.180
Now let's do this last one.

00:04:19.775 --> 00:04:21.320
I'll use new colors here.

00:04:21.320 --> 00:04:25.140
A cake recipe for 5
people requires 2 eggs.

00:04:30.180 --> 00:04:32.935
So we want to know how many
eggs-- so this we'll call x.

00:04:32.935 --> 00:04:34.560
And you don't always
have to call it x.

00:04:34.560 --> 00:04:35.650
You could call it e for eggs.

00:04:35.650 --> 00:04:37.608
Well, e isn't a good
idea, because e represents

00:04:37.608 --> 00:04:40.360
another number once you
get to higher mathematics.

00:04:40.360 --> 00:04:43.680
But you could call them y
or z or any variable-- a,

00:04:43.680 --> 00:04:44.900
b, or c, anything.

00:04:44.900 --> 00:04:47.650
How many eggs do we need
for a 15-person cake?

00:04:51.580 --> 00:04:56.620
So you could say the ratio of
people to eggs is constant.

00:04:56.620 --> 00:05:06.740
So if we have 5 people for
2 eggs, then for 15 people,

00:05:06.740 --> 00:05:08.530
we are going to need x eggs.

00:05:08.530 --> 00:05:10.730
This ratio is going
to be constant.

00:05:10.730 --> 00:05:12.880
5/2 is equal to 15/x.

00:05:12.880 --> 00:05:14.670
Or you could flip
both sides of this.

00:05:14.670 --> 00:05:21.320
Or you could say the
ratio between 5 and 15

00:05:21.320 --> 00:05:24.580
is going to be equal to the
ratio between the number

00:05:24.580 --> 00:05:33.420
of eggs for 5 people-- let me
do that in that blue color--

00:05:33.420 --> 00:05:36.330
and the number of
eggs for 15 people.

00:05:36.330 --> 00:05:39.320
And obviously, you could flip
both sides of this equation.

00:05:39.320 --> 00:05:40.820
So all of these,
we've essentially

00:05:40.820 --> 00:05:43.650
set up the proportions
that describe

00:05:43.650 --> 00:05:46.460
each of these problems.

00:05:46.460 --> 00:05:48.170
And then you can
go later and solve

00:05:48.170 --> 00:05:50.980
for x to actually
get the answer.


21st Century Challenges (Royal Geographic Society)

WEBVTT
Kind: captions
Language: en

00:00:00.686 --> 00:00:03.201
Voiceover: This video is to
answer some questions part

00:00:03.201 --> 00:00:05.104
for the Royal Geographic Society.

00:00:05.104 --> 00:00:08.493
This is part of their 21st
Century Challenges Series.

00:00:08.493 --> 00:00:14.976
First the general questions, so
the first question right up here is

00:00:14.976 --> 00:00:18.108
will changes in education
in the coming decades

00:00:18.108 --> 00:00:21.442
be evolutionary or revolutionary?

00:00:21.442 --> 00:00:27.151
Evolutionary would kind of imply small
changes, maybe not so noticeable changes

00:00:27.166 --> 00:00:30.472
but then maybe over a long period
of time they add up to a lot

00:00:30.472 --> 00:00:32.554
or revolutionary, everything all at once.

00:00:32.554 --> 00:00:36.350
I hope you don't think that
I'm not answering the question

00:00:36.350 --> 00:00:37.656
but I think it's going to be both.

00:00:37.656 --> 00:00:40.925
It's already been stated independent
of education that we are in

00:00:40.925 --> 00:00:44.741
and information revolution right now
and I think that's pretty obvious.

00:00:44.741 --> 00:00:47.663
First you have the computers and
then obviously you have the internet.

00:00:47.663 --> 00:00:51.519
Everything now becomes accessible and
it's becoming all of that more accessible

00:00:51.519 --> 00:00:53.664
every almost moment that passes by.

00:00:53.664 --> 00:00:56.996
The funny thing is the
information revolution

00:00:56.996 --> 00:01:01.662
and there's no industry that revolves
around information more than education.

00:01:01.662 --> 00:01:04.522
I guess there's other industries that
are close like finance and whatever else.

00:01:04.522 --> 00:01:09.222
But education really is about, I
would say information or knowledge

00:01:09.222 --> 00:01:11.122
or conveying information

00:01:11.122 --> 00:01:14.458
or transferring understanding
from one person to another.

00:01:14.458 --> 00:01:17.411
It is really about a
transferring information

00:01:17.411 --> 00:01:19.988
or a communication
between different people.

00:01:19.988 --> 00:01:23.239
The information revolution
should I guess naturally,

00:01:23.239 --> 00:01:26.331
the education revolution
should be part of it,

00:01:26.331 --> 00:01:29.524
and it really just maybe
hasn't for a bunch of reasons.

00:01:29.524 --> 00:01:35.122
There are different [nurses] in
place to keep it from changing.

00:01:36.537 --> 00:01:39.788
My sense is and this
is true of many things,

00:01:39.788 --> 00:01:43.078
is that when people are most
pessimistic about something

00:01:43.078 --> 00:01:47.825
that's when it's about to change in
a really, really, really big way.

00:01:47.825 --> 00:01:50.405
That's when it's about to give

00:01:50.405 --> 00:01:53.655
and I think we are at that
moment in education where,

00:01:53.655 --> 00:01:56.589
sure people have been talking about
technology education for a long time.

00:01:56.589 --> 00:01:59.786
People have been trying to
improve education for a long time

00:01:59.786 --> 00:02:04.185
but the unfortunate narrative is every
year we just hear things of get ...

00:02:04.185 --> 00:02:06.989
They see more at least based on the
narrative we're hearing in the media.

00:02:06.989 --> 00:02:09.986
It seems like it's getting worse,
getting more expensive too.

00:02:09.986 --> 00:02:12.076
So depending on how you do it,

00:02:12.076 --> 00:02:15.744
either worse performance at
kind of the grade school levels

00:02:15.744 --> 00:02:19.258
or at the higher education levels just
getting more and more and more expensive

00:02:19.258 --> 00:02:20.578
and less affordable.

00:02:20.578 --> 00:02:24.022
Even if you can afford and you take
on the loans it's becoming less clear

00:02:24.022 --> 00:02:27.326
that you're able to even get the
return when you go into the job market,

00:02:27.326 --> 00:02:29.723
whether you've been
[necessarily] not employable.

00:02:29.723 --> 00:02:32.528
So yes, I think the revolution is coming.

00:02:32.528 --> 00:02:35.007
I think it's going to come
in a bunch of different ways.

00:02:35.007 --> 00:02:38.842
I think you're going to start
seeing a decoupling of learning

00:02:38.842 --> 00:02:41.195
from credentialing.

00:02:41.195 --> 00:02:44.335
Right now, the word education
is even kind of modeled

00:02:44.335 --> 00:02:46.493
because it's actually a
whole bunch of things.

00:02:46.493 --> 00:02:49.902
Inside of education you
have the idea of learning

00:02:49.902 --> 00:02:52.325
and this is what most people
associate with education.

00:02:52.325 --> 00:02:55.237
You also have the idea of
credentialing which is,

00:02:55.237 --> 00:02:57.467
"I got a degree from here or there."

00:02:57.467 --> 00:02:59.532
Then you also have an
element of socialization

00:02:59.532 --> 00:03:02.386
which is a very important
element, socialization.

00:03:03.093 --> 00:03:06.366
When people talk about education it's
not clear what they're talking about,

00:03:06.366 --> 00:03:09.014
most people are talking about ...
Think they're talking about this

00:03:09.014 --> 00:03:12.258
but when you ask them why they're
willing to go $200,000 in debt,

00:03:12.258 --> 00:03:15.592
they'll be talking about this right here.

00:03:15.592 --> 00:03:18.592
What I hope to see is that
this actually becomes decoupled

00:03:18.592 --> 00:03:21.299
and when it becomes decoupled, it
becomes actually more interesting.

00:03:21.299 --> 00:03:25.404
Because if someone can earn a
credential by proving what they know

00:03:25.404 --> 00:03:27.466
and they don't have to sit
some place for four years

00:03:27.466 --> 00:03:29.995
and they don't have to pay $200,000,

00:03:29.995 --> 00:03:33.725
then all of a sudden the learning
will happen in whatever way

00:03:33.725 --> 00:03:35.478
is easiest for that person.

00:03:35.478 --> 00:03:37.753
It could be through something
like the Khan academy,

00:03:37.753 --> 00:03:42.121
it could be attending a
traditional university, it
could be learning on the job.

00:03:42.121 --> 00:03:46.519
What's powerful that is if the credential
is done independently from that,

00:03:46.519 --> 00:03:48.991
then the credential can also
become much more powerful.

00:03:48.991 --> 00:03:52.588
Right now you have a reality where
you have thousands of universities,

00:03:52.588 --> 00:03:54.191
and I'll talk about universities,

00:03:54.191 --> 00:03:57.086
the high school diploma has
become almost meaningless now.

00:03:57.086 --> 00:04:00.164
No one even says, "I'll give you a job
because you have a high school diploma."

00:04:00.164 --> 00:04:01.664
They don't know what that even means.

00:04:01.664 --> 00:04:04.126
On the other side of it you have
people getting into universities

00:04:04.126 --> 00:04:06.053
that don't have a high school diploma.

00:04:06.053 --> 00:04:08.074
That just have really good
standardized test scores

00:04:08.074 --> 00:04:10.670
and they've done amazing things
when they were before college,

00:04:10.670 --> 00:04:12.253
and they were home schooled or whatever.

00:04:12.253 --> 00:04:16.505
What you have right now is the
credentialing is kind of been done

00:04:16.505 --> 00:04:19.106
by the same people who
are doing the learning.

00:04:19.106 --> 00:04:20.292
It makes everyone say,

00:04:20.292 --> 00:04:23.497
"Well look, how do we know what the
standards are in that university?"

00:04:23.497 --> 00:04:25.098
"How do we know what the standards
are at that high school?"

00:04:25.098 --> 00:04:29.452
That's what's making standardized
tests and all of that so valuable,

00:04:29.452 --> 00:04:32.375
regardless of whether you
actually view them as valuable

00:04:32.375 --> 00:04:34.851
but that's why people are
putting so much emphasis on them.

00:04:34.851 --> 00:04:40.114
What would be valuable is if the
credentials is more recognized.

00:04:40.114 --> 00:04:43.048
If there's a nationally or
internationally recognized credentials

00:04:43.048 --> 00:04:45.516
because right know you could
go to a regional university.

00:04:45.516 --> 00:04:49.181
Maybe your regional university
or your local community college,

00:04:49.181 --> 00:04:52.248
maybe it's amazing at this, maybe
it's better than Harvard at this,

00:04:52.248 --> 00:04:55.099
maybe it's better than any
university at the teaching part,

00:04:55.099 --> 00:05:01.052
and maybe it's graduates actually
do know the material really, deeply,

00:05:01.052 --> 00:05:03.302
and amazing, and they know it
better than the kids graduating

00:05:03.302 --> 00:05:04.226
from the Ivy League.

00:05:04.226 --> 00:05:06.741
But the sad reality right
now is even if they do,

00:05:06.741 --> 00:05:11.185
their credential will not carry as much
weight in the eyes of most employers

00:05:11.185 --> 00:05:15.328
as that Harvard degree will or that
Stanford degree, or that MIT degree.

00:05:15.328 --> 00:05:18.720
So they have a credentialing problem,
but if you decouple this things

00:05:18.720 --> 00:05:21.144
the students will learn from
the regional university,

00:05:21.144 --> 00:05:25.257
could go and prove that they know
it just as good as anyone else.

00:05:25.257 --> 00:05:29.311
I think you're going to see
some very interesting things

00:05:29.311 --> 00:05:32.324
or I think once you open this up
and people can get the credential

00:05:32.324 --> 00:05:37.398
and obviously the cost of getting tested,
even if it's a very rigorous test,

00:05:37.398 --> 00:05:40.393
even if it's a more rigorous test
than what's going on right now

00:05:40.393 --> 00:05:43.991
in the best universities, that's
not going to cost 50,000 a year.

00:05:43.991 --> 00:05:46.809
You ask a university right now why
they're charging 50,000 a year,

00:05:46.809 --> 00:05:51.324
they'll say, "Look at our
facilities. Look at our campus."

00:05:51.324 --> 00:05:53.591
"Look at our professor's salaries."

00:05:53.591 --> 00:05:57.257
They don't say, "We're
charging you $50,000 a year"

00:05:57.257 --> 00:05:59.483
"because we're giving you
really rigorous exams."

00:05:59.483 --> 00:06:01.594
"We're giving you oral
exams and all the rest."

00:06:01.594 --> 00:06:06.124
If you ask students why they're
paying $50,000 they'll tell you,

00:06:06.124 --> 00:06:07.927
that for the most part they're
paying for the credentials,

00:06:07.927 --> 00:06:10.814
and then some students
hopefully for the learning,

00:06:10.814 --> 00:06:15.641
and then some for the socialization and
that socialization can take many forms.

00:06:15.641 --> 00:06:18.732
I suspect the credentialing
itself can be done in a better way

00:06:18.732 --> 00:06:19.991
than it's being done now.

00:06:19.991 --> 00:06:23.827
That can be much cheaper, I'm
talking in orders hundreds of dollars

00:06:23.827 --> 00:06:25.476
as opposed to thousands of dollars.

00:06:25.476 --> 00:06:29.657
Then it opens up the learning
part to whatever works best,

00:06:29.657 --> 00:06:31.329
and I suspect once you do that

00:06:31.329 --> 00:06:34.404
then now higher education
institutions won't have

00:06:34.404 --> 00:06:39.565
this kind of control over the market

00:06:39.565 --> 00:06:44.479
and it will be very hard
for them to justify raising
their tuition 6% every year

00:06:44.479 --> 00:06:45.998
and it would be very hard for them to ...

00:06:45.998 --> 00:06:50.244
They would have to prove the case
that it really is worth $50,000

00:06:50.244 --> 00:06:54.079
that their graduates really are
performing better on these credentials

00:06:54.079 --> 00:06:58.263
than say people who use the Khan Academy
or go to their local community college

00:06:58.263 --> 00:06:59.820
or learn on the job.

00:06:59.820 --> 00:07:01.903
I think you're definitely
going to see that coming.

00:07:01.903 --> 00:07:05.005
I think in 10 years or so
you're going to see that shift

00:07:05.005 --> 00:07:10.662
and you're actually going to see that
tuition cost you're going to give.

00:07:10.662 --> 00:07:14.565
Because they're already becoming
so unaffordable for so many people

00:07:14.565 --> 00:07:16.933
that I think everyone's going
to wake up at some point

00:07:16.933 --> 00:07:19.604
and realize that there
has to be another way.

00:07:19.604 --> 00:07:23.405
How important is knowledge
in a modern education?

00:07:23.405 --> 00:07:26.936
Knowledge is one of these words that
depends how you think about knowledge.

00:07:26.936 --> 00:07:28.895
Is knowledge fact information?

00:07:28.895 --> 00:07:32.073
Is it a specific skill set?

00:07:32.073 --> 00:07:35.130
Is it a medal level skill of
kind of knowing how to learn

00:07:35.130 --> 00:07:37.333
and some would say it's all of the above.

00:07:37.333 --> 00:07:41.456
What I would say is what I think
are the most important things

00:07:41.456 --> 00:07:45.628
in a modern education, I think
it's the ability to be creative.

00:07:45.628 --> 00:07:50.652
I think it's the ability to
kind of go into an open space

00:07:50.652 --> 00:07:55.198
where nothing is defined and
be able to look at the tools

00:07:55.198 --> 00:07:58.864
that are available to you and put
something together that meets a problem.

00:07:58.864 --> 00:08:03.097
Actually this could be in a technical
sense or it could be in a business sense

00:08:03.097 --> 00:08:04.972
or a market, whatever sense.

00:08:04.972 --> 00:08:09.799
I think the most important thing is that
people should get from their education

00:08:09.799 --> 00:08:12.466
is the ability to make things,
the ability to create things.

00:08:12.466 --> 00:08:16.066
Unfortunately that's the thing
that I think is completely absent

00:08:16.066 --> 00:08:18.170
from our current education.

00:08:18.170 --> 00:08:20.239
One example is Math and
there's a huge debate

00:08:20.239 --> 00:08:22.201
about what's the best way to
teach Math is and all the rest.

00:08:22.201 --> 00:08:25.319
What's shocking is that no one ever says,

00:08:25.319 --> 00:08:29.458
"Well maybe there should be engineering
in education to some degree,"

00:08:29.458 --> 00:08:31.328
that's limited by people's perception

00:08:31.328 --> 00:08:34.401
of whether we can get proper
engineering even taught.

00:08:34.401 --> 00:08:37.646
Whether we can find a talented
teacher in the engineering in schools.

00:08:37.646 --> 00:08:40.066
But no one ever says, because
frankly the ability to engineer,

00:08:40.066 --> 00:08:42.403
and I'm saying engineering in
the broadest sense of the word,

00:08:42.403 --> 00:08:44.336
not what people normally
associate with engineering.

00:08:44.336 --> 00:08:46.558
I'm saying engineering which is really,

00:08:46.558 --> 00:08:50.066
most people don't normally associate
it as a deeply creative field,

00:08:50.066 --> 00:08:51.475
but it is a deeply creative.

00:08:51.475 --> 00:08:54.895
In fact engineering is, by
it's very nature, it's creating
things that never existed before.

00:08:54.895 --> 00:08:59.277
Engineering is not something
that's emphasized right now.

00:08:59.277 --> 00:09:04.933
There might be music class and music
class is focused on playing things

00:09:04.933 --> 00:09:09.835
but you see very little composition at
especially at the K through 12 level.

00:09:09.835 --> 00:09:13.175
Everything is focused on playing
things that someone else has written.

00:09:13.175 --> 00:09:16.798
So the creativity is
de-emphasized in school right now.

00:09:16.798 --> 00:09:20.745
I think that's the very thing
that has to be emphasized a lot,

00:09:20.745 --> 00:09:23.079
a lot more heavily, not just ability.

00:09:23.079 --> 00:09:25.757
Because frankly and this is
the reality of the modern world

00:09:25.757 --> 00:09:28.496
is that the tools are going to
change, the jobs are going to change,

00:09:28.496 --> 00:09:31.080
the information you need to know
for that job are going to change

00:09:31.080 --> 00:09:33.175
but what you really need
to do is that ability to

00:09:33.175 --> 00:09:35.702
one, create something out of
nothing, so that's the creativity.

00:09:35.702 --> 00:09:40.452
I would say the second thing is this
ability to kind of self-teach yourself.

00:09:40.452 --> 00:09:42.874
Look at the resources
that are in the world

00:09:42.874 --> 00:09:47.451
to give yourself the tools you need
to be able to create that thing.

00:09:47.451 --> 00:09:51.388
The next question, if the
era of a job for life is over

00:09:51.388 --> 00:09:53.034
and we need to be more adaptable,

00:09:53.034 --> 00:09:56.261
do you foresee a future of people
self-educating through their life?

00:09:58.214 --> 00:10:01.365
My peripheral vision was
reading this question.

00:10:01.365 --> 00:10:05.124
So yes, I think self-educating
throughout life,

00:10:05.124 --> 00:10:10.725
beyond just the economic aspects of
it, maybe being a requirement now

00:10:10.725 --> 00:10:13.585
because the world is changing so
fast and jobs are changing so fast,

00:10:13.585 --> 00:10:17.992
but I also just think it's helpful,
healthy from a happiness point of view.

00:10:17.992 --> 00:10:22.949
Just as people go to the
gym, they do exercise

00:10:22.949 --> 00:10:24.985
and not because they're going
to compete in some sport.

00:10:24.985 --> 00:10:27.054
Not because they're paid
to compete in exercises,

00:10:27.054 --> 00:10:28.992
they do it because it's
good for their health

00:10:28.992 --> 00:10:31.988
and they do it because they
know it makes them happy.

00:10:31.988 --> 00:10:33.654
There's even these studies,

00:10:33.654 --> 00:10:35.945
endorphins get released in
your brain and all of that.

00:10:35.945 --> 00:10:37.859
I think the exact same
thing is to of learning,

00:10:37.859 --> 00:10:40.793
I mean you're just exercising a different
part of what it means to the human.

00:10:40.793 --> 00:10:42.360
You're exercising your brain.

00:10:42.360 --> 00:10:46.195
One, I think is going to
be an economic imperative.

00:10:46.195 --> 00:10:48.077
You will need to self-educate
through your life.

00:10:48.077 --> 00:10:50.945
I mean going back to this answer, the
context is going to keep changing,

00:10:50.945 --> 00:10:57.518
the only skill that will
really be valuable is the
ability to learn very quickly

00:10:57.518 --> 00:10:59.720
and then apply it in a creative way

00:10:59.720 --> 00:11:02.132
to create something that
has never existed before.

00:11:02.793 --> 00:11:04.853
I also think hopefully people
will start to recognize

00:11:04.853 --> 00:11:08.523
that self-education is
an economic imperative

00:11:08.523 --> 00:11:12.523
but it's also a really satisfying thing
that will give people more happiness

00:11:12.523 --> 00:11:15.942
than many of the things that people
perceive will give them happiness.

00:11:15.942 --> 00:11:18.440
Like more square footage or a fancier car.

00:11:19.240 --> 00:11:20.831
Now Khan Academy related,

00:11:20.831 --> 00:11:23.593
what are your aspirations for
the growth of the khan Academy?

00:11:25.039 --> 00:11:27.400
Our attitude towards growth is,

00:11:27.400 --> 00:11:30.640
I mean we'd obviously love as many
students as possible to use it,

00:11:30.640 --> 00:11:35.799
but our attitude is let's
focus on what we are producing.

00:11:35.799 --> 00:11:38.801
Let's make sure it's this
compelling of an experience

00:11:38.801 --> 00:11:40.335
for the people who are using
it as right now as possible.

00:11:40.335 --> 00:11:44.975
If we do that, other people
will find it compelling as well.

00:11:44.975 --> 00:11:47.669
Those people who are using it and
finding it valuable right now,

00:11:47.669 --> 00:11:49.198
will tell other people.

00:11:49.198 --> 00:11:53.195
In terms of user growth, I mean I
can hope that it continues to grow

00:11:53.195 --> 00:11:55.672
at the rate it's doing, it
grew tenfold this past year

00:11:55.672 --> 00:11:57.593
and we're about two million
unique students a month.

00:11:57.593 --> 00:12:03.344
We don't want to get to 20 million or
200 million and have a bad experience.

00:12:03.344 --> 00:12:06.679
Our main focus is keep
tight on the experience.

00:12:06.679 --> 00:12:09.260
If you talk about growth
from a future point of view,

00:12:09.260 --> 00:12:12.802
we hope to expand the faculty

00:12:12.802 --> 00:12:15.855
and this is something I've
started hinting at a little bit.

00:12:15.855 --> 00:12:18.140
I don't want to be the
only person teaching.

00:12:18.140 --> 00:12:20.664
I do want to teach on Khan
Academy the rest of my life

00:12:20.664 --> 00:12:21.971
but I think there's other people

00:12:21.971 --> 00:12:24.139
who will bring super
valuable voices to the table.

00:12:24.139 --> 00:12:26.145
We're going to expand the faculty

00:12:26.145 --> 00:12:29.005
and you'll hear more about
this in the coming months.

00:12:29.005 --> 00:12:33.976
We're also going to expand kind
of what the platform that we have.

00:12:33.976 --> 00:12:36.664
We hope to enable students to
communicate with each other,

00:12:36.664 --> 00:12:38.735
and to turn really into
a community experience

00:12:38.735 --> 00:12:40.932
and we just have to think
of a good way to do that.

00:12:40.932 --> 00:12:42.982
Obviously expanding the faculty

00:12:42.982 --> 00:12:44.957
but this also goes with
the software part of it.

00:12:44.957 --> 00:12:48.342
We want to expand the content
base of both the video side

00:12:48.342 --> 00:12:49.813
but also the exercises.

00:12:49.813 --> 00:12:55.547
Eventually you can also use Khan
Academy as a way to learn art history,

00:12:55.547 --> 00:12:59.865
or to learn chemistry, whatever,
to actually practice those things.

00:12:59.865 --> 00:13:04.401
Your thoughts on flipping the
classroom, I thought this was fantastic.

00:13:04.401 --> 00:13:05.752
Well thank you for
thinking it was fantastic

00:13:05.752 --> 00:13:07.211
but one thing I want to emphasize

00:13:07.211 --> 00:13:09.340
because I talk about flipping
the classroom in that Ted talk

00:13:09.340 --> 00:13:12.213
and got a lot of press,
and the notion is that

00:13:12.213 --> 00:13:14.339
these high school teachers were saying,

00:13:14.339 --> 00:13:15.550
"Hey, Sal gave a lecture so let's ..."

00:13:15.550 --> 00:13:17.547
My students watch Sal's video

00:13:17.547 --> 00:13:20.214
and then the teacher can use
class time for interaction,

00:13:20.214 --> 00:13:23.379
I 110% agree with that idea.

00:13:25.179 --> 00:13:27.470
What we're advocating now
is taking that even further.

00:13:27.470 --> 00:13:29.137
It's not even a pure flip,

00:13:29.137 --> 00:13:32.883
it's now every student whether
they're at home or at the classroom,

00:13:32.883 --> 00:13:34.949
working at their own
pace at their own time

00:13:34.949 --> 00:13:36.795
and then the teacher intervenes

00:13:36.795 --> 00:13:41.664
either when there's a need to do the
interactive project or a conversation,

00:13:41.664 --> 00:13:44.947
or the teacher intervenes when
they see a student being stuck.

00:13:44.947 --> 00:13:48.526
You can go to a pure
flip then when you go,

00:13:48.526 --> 00:13:50.864
what we're talking about it becomes
a little less pure of a flip.

00:13:50.864 --> 00:13:53.792
We're saying, "Look if a
kid needs to watch a video"

00:13:53.792 --> 00:13:55.559
"in the classroom, that's okay."

00:13:55.559 --> 00:13:58.336
We don't think that the classroom
should be about watching videos

00:13:58.336 --> 00:13:59.989
but if that's what they
need at that moment,

00:13:59.989 --> 00:14:02.913
or that kid, not all the kids,
that kid they can watch the video.

00:14:02.913 --> 00:14:05.497
If they want to do exercise
at home that's great.

00:14:05.497 --> 00:14:08.255
But the important thing is
that they can fully leverage

00:14:08.255 --> 00:14:11.044
the humans in the classroom,
their peers and the teacher.

00:14:11.044 --> 00:14:13.494
Then the teacher spending
every moment of his or her time

00:14:13.494 --> 00:14:15.163
in meaningful interaction with students

00:14:15.163 --> 00:14:17.001
and really taking them to the next level.

00:14:17.001 --> 00:14:19.189
Then the last question is,

00:14:19.189 --> 00:14:23.054
your thoughts on the potential
of game mechanics and ICT,

00:14:23.054 --> 00:14:25.854
in general to encourage
the learning process.

00:14:25.854 --> 00:14:27.793
Any clear evidence in the Khan Academy?

00:14:27.793 --> 00:14:31.459
There is this layer of points
and badges, and streaks

00:14:31.459 --> 00:14:33.461
and things like that in the Khan Academy.

00:14:33.461 --> 00:14:37.055
Anecdotaly it seems like a lot
of kids find it compelling,

00:14:37.055 --> 00:14:42.119
even the data in the school
it looks like a lot of kids

00:14:42.119 --> 00:14:44.523
became more engaged when
we threw this layer on.

00:14:44.523 --> 00:14:46.503
But we're constantly
experimenting with it,

00:14:46.503 --> 00:14:49.253
we're constantly making sure that
it's driving the right behaviors,

00:14:49.253 --> 00:14:54.170
that the kids aren't just looking
at the badges or the points

00:14:54.170 --> 00:14:55.707
but they really are getting good gains

00:14:55.707 --> 00:14:58.095
and they're trying to enjoy
the learning process itself.

00:14:59.326 --> 00:15:02.195
The evidence, we saw really
good results from Los Altos.

00:15:02.195 --> 00:15:05.504
I actually put some of those results
in a previous video that I made today,

00:15:05.504 --> 00:15:06.916
so you can look at that.

00:15:06.916 --> 00:15:08.751
That's why Los Altos
is going district wide.

00:15:08.751 --> 00:15:11.081
Not clear if that's due to the
game mechanics or due the content

00:15:11.081 --> 00:15:13.196
or some combination of both of them.

00:15:13.196 --> 00:15:15.084
We hope to continue to explore this

00:15:15.084 --> 00:15:18.591
and we're talking to teachers and students
constantly about how to tweak this,

00:15:18.591 --> 00:15:20.194
so we can make it a better experience.

00:15:20.194 --> 00:15:23.591
We also hope to put a lot of
our game mechanics right now

00:15:23.591 --> 00:15:26.595
for the most part extrinsic, so they're
independent of the subject at hand.

00:15:26.595 --> 00:15:28.928
We also want to put a lot
of intrinsic motivator,

00:15:28.928 --> 00:15:32.158
so some of the exercises
themselves are like games

00:15:32.158 --> 00:15:36.238
but their games that are where deep
subject matter help you solve the game.

00:15:36.238 --> 00:15:38.927
This is something that we're
just going to constantly try

00:15:38.927 --> 00:15:40.995
to iterate on it and address.

00:15:40.995 --> 00:15:43.592
This brings to an important issue
as we've gotten a lot of press

00:15:43.592 --> 00:15:49.682
and we think hopefully that we
are having an impact right now.

00:15:49.682 --> 00:15:51.436
But we think we're very
early on in the process,

00:15:51.436 --> 00:15:53.174
so we don't think that we
have all the solutions.

00:15:53.174 --> 00:15:57.628
I think what is kind of the opportunity
that we have in the Khan Academy,

00:15:57.628 --> 00:15:59.524
what excites me is that
we do have the traction

00:15:59.524 --> 00:16:03.786
that we can now become the best lab
for really figuring out what works

00:16:03.786 --> 00:16:05.918
and then getting traction on that.

00:16:05.918 --> 00:16:08.798
We view ourselves where
we're early in the game

00:16:08.798 --> 00:16:12.676
and the baseball now is your top
of the first inning right now.

00:16:12.676 --> 00:16:15.731
Maybe I should make a cricket analogy
but I don't understand cricket.

00:16:15.731 --> 00:16:20.192
We think we're really early on and so
we think it's a very open ended question

00:16:20.192 --> 00:16:21.553
on where we're going to take this.

00:16:21.553 --> 00:16:25.337
We really just want to be open minded
about building stuff, looking at the data,

00:16:25.337 --> 00:16:28.004
looking at the feedback and
then taking that seriously

00:16:28.004 --> 00:16:30.607
and then continuing to refine it.