Khan Academy in Idaho

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Language: en

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Kelly: I've never seen this.

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This has been so impressive and amazing,

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and leaving teachers with wanting more.

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(hip hop music)

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Joshua: When I first
knew about Khan Academy,

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it was mostly like, "Uh, my
teacher said this in class,

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"but I can't remember what he said,

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"so I'm going to go check
out on Khan Academy."

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So, it was more of a personal resource,

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and that's kinda where I
was thinking it would be

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in my classroom down the line, and say,

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"If you're struggling with this,

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"go check out Khan Academy."

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But now, after coming to this,
it can be that first step.

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It can be the go-to, "Hey, go learn this,

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"go learn the foundations,"
and then we can take it

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to the next level in our classroom.

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We can put those hands-on activities.

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(hip hop music)

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David: [Thinking] it will take a child,

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and look and say, "Wow, they're
really struggling here,"

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so, now when I've got
everybody else doing this,

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I can slip around back
without anybody noticing

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that I'm helping somebody
because they're slower

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and allowing that child
to keep their dignity,

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because I was able to privately
identify what there was

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that they needed help
with; and that was awesome.

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(hip hop music)

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Jeannie: I love this whole concept.

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This is so life-changing
in the way that you teach,

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because then it gives you
time to work with the students

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and it gives you time to
understand what they know

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and clear up misconceptions.

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It gives you time to just really encourage

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those students to go on.

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(hip hop music)

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Teri: I have a very
unique set of students.

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They happen to be behind bars.

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In my classroom, I might have a guy

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that's functioning at his 2nd grade level,

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and I may have a guy that has his PhD,

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sitting in the same classroom,

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and how do you bridge
that gap as a teacher?

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And yet, I saw the Khan
Academy being a tool

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that we could implement at a very low cost

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with our economy the way it is

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and provide the biggest bang for the buck.

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(hip hop music)

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David: Empowering the student to learn

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is what the key is to
making them learn for life,

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so I think this is a great
aspect and a great tool of that,

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and I think it'll actually
start helping them to say,

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"Hey, if I don't know the
answer, I can find it."

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Because that's kinda what I
try to do in my classroom,

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and I think we need to do more of that.

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Al: It's the way kids learn now.

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It's the way kind of education is going.

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It's been kind of status
quo for many years now,

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and I think that we really
are on the front edge

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of some new, innovative
solutions to helping kids learn,

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and catching up, with not
only the rest of the nation,

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but the rest of the world.

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Kelly: I feel like my students
are the [revolutioni].

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(hip hop music)


Sal on AirTalk talking about his new book

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Larry: It started with just a
few little videos on algebra

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to help out a cousin who
needed assistance in school,

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and, from there, it grew
and grew and grew into more

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than 3,200 YouTube videos,
giving all kinds of instruction.

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It's known as the Khan Academy,
but, more than just that,

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it's leading to a rethinking
of how education is

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delivered in the nation's
classrooms and at home.

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Salman Khan's new book, The One World

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School House: Education Reimagined.

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Sal, thank you for joining us.

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We appreciate it very much.

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Sal: Thanks for having me.

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Larry: Take us back to what was going on.

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Here you are, you're doing your

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hedge fund management and research,

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and you have a cousin who needs some help.

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How does it all spring from this?

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Sal: Yeah; she needed help.

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She's 12 years old.

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She was in New Orleans,
which is where I grew up.

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I was in Boston at the time.

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I offered to tutor her
everyday after work for me,

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after school for her; she agreed.

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It worked out.

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We just work out, do it
over the phone, and we used

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a little bit of this Yahoo
Chat to kind of communicate.

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She eventually got into the kind of

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the more appropriate math track for her,

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and I start tutoring her brothers.

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Word got around in the family
that free tutoring was happening.

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So, you fast forward about 18 months,

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and I was tutoring about
10 or 15 family members

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everyday after work; and it was a friend-

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By this point, I had moved
out to Northern California,

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and a friend said, "Well,
to help yoursef scale,

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"why don't you put some
of these on YouTube?"

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and I thought it was a silly
idea, that YouTube was for

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cats playing piano, but I gave it a shot.

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>From there, it just caught on, I guess.

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Larry: How long did it take
for the word to get out

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and for people to start
using these videos?

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Sal: It was just this I
think word of mouth thing,

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that starting in 2006 a parent
would tell another parent,

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a student would tell another student,

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a teacher would tell another teacher.

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By 2009, there were several
hundreds of thousands

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of people using it on a regular basis.

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That's when I quit my day
job to start this as a

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not for profit and work on this full time,

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and then, by 2010, it had grown.

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By that point, we started to get
a little bit of press as well.

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We're now at about
almost 7 million students

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every month are using it.

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Larry: Wow.

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There's a criticism from
The Washington Post,

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where this teacher has his
own company, I guess it is,

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and was featured in a blog
in The Washington Post,

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and part of the knock was
that you said you spend

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a couple of minutes researching and do it,

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but I thought part of the
appeal of the videos is

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there is a sort of a naturalness there.

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It's the less formal aspect of
it I think is part of the appeal.

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Sal: Yeah.

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I think there's two
dimensions to preparation.

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I think one dimension is
preparation of your mind,

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which is hopefully happened
over your entire lifetime,

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but obviously if I go
into a topic that I'm not

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expert in at the moment,
I will spend hours on it.

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But I agree with you.

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I think what people connected to
was it was very conversational.

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They could tell it was some guy
making this for his cousins.

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I didn't edit out my thought processes.

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You could kind of hear
me thinking in real time.

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Sometimes I would go down one avenue,

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that was a logical avenue, but say,

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"Well actually, this isn't working out.

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"Let's back up."

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Too often in math and science,

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you just get the final
solution, and it seems

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so easy and perfect, but
it seems impossible to you.

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I think people appreciated
that it felt much more human,

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much more approachable in this way.

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Larry: Much like it is
in a show like this,

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which is unscripted and a conversation,

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or a program like Morning Edition,

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where it's all scripted
and you have two anchors.

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Both have their place.

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They're just different approaches.

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Sal: Exactly.

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I think when I talk to a lot of
... and I've had the privilege of

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working with a lot of amazing
teachers, and they tell me.

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I mean, the things that
connect with students more

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are the ones that are unscripted.

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Your mind has to be very
clear and very distilled about

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what you want to talk
about and how you might

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communicate it, but
humans realize when you're

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reading something versus
when you're actually

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thinking and communicating
from your heart.

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Larry: Let's talk about
taking this as a model

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and incorporating it into
the classroom in Los Altos,

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up in the Bay Area, where you reside.

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They're actually incorporating this.

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How does it work?

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Sal: They first reached out to us 2010,

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when we got our first real funding from

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Google and the Gates
Foundation to work on this.

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At the time, we thought it was
a completely supplemental thing.

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Khan Academy is your free tutor out there.

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But, as I write about in the book,

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they kind of reached out to us and said,

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"What would you do with a
5th grade math classroom,

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"now that you exist, your tools exist?"

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I said, "I don't think
it makes sense to use

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"class time to give lectures anymore.

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"Lectures might be useful, but now you can

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"pause and repeat and
watch them on demand.

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"Let's use class time for
something more constructive.

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"Why don't we ask student
teaching each other?

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"Why don't we have more one
on one time with the teacher?"

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And as soon as you also remove
lectures from the classroom,

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now, all of a sudden,
you don't have to have

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every student working at the same pace.

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You could have them all kind of

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mastering concepts then moving on.

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They thought it was an interesting
idea, so they gave it a shot.

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This was two years ago, and since
then it's been district-wide,

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and they've been seeing some
pretty interesting results.

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Larry: You know the
criticism that some have,

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the concern is that for the students

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who don't have much parental support,

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have difficult time
getting access to computer,

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they're going to be left behind,

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and the whiz kids are going to do great

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because they can go at their own pace.

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Sal: Well, I think this addresses that

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more than the traditional model does.

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The traditional model
that we all grew up in,

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you go home, you have homework,

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and that's where frankly
a lot of the learning

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should happen, when you're
doing the problem solving.

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It's the educated kids
who have older siblings,

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or who have parents who might be able to

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help them on the
schoolwork, or whose parents

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are even home and they're not at work,

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and then they go to class
and they do something

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very passive and they get frustrated.

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What we're advocating is
that actually doing the

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problem-solving, which is
a much more important part,

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in class, where they're
surrounded by peers

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and they have a support network,

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so you don't have the child whose parents

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aren't home from work or
whose parents don't have

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a high school diploma, who can't help them

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on an algebra homework,
getting frustrated.

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Now they're in class; they're surrounded.

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They have the teacher, the
peers, there's a ton of help.

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There's one classroom
where there was a student

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who spoke very little English.

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In a traditional classroom,
that kid would just be

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left behind, even though
actually we found out

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he was quite good at mathematics.

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What allowed to happen
in this model is that

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the teacher was able to
spend extra time with him.

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The teacher didn't speak Spanish,

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but several of the students
did, and so the students

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were able to be peer tutors and make sure

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that the student could keep up.

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I think there is an issue
about access to technology,

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and we are working at
charter schools in San Jose

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and Oakland, places that
are more underserved,

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but actually they were seeing
some of the biggest gains.

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The trick is how do we give
access to the technology?

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But you could do it by keeping
computer labs open longer,

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by having after school
programs and other things.

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Larry: So even if they're
not a quiet space at home,

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there's another place that kids can go

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to see those lectures.

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We're talking with Salman Khan.

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He's the founder of the
nonprofit Khan Academy,

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and author of The One World School House:

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Education Reimagined;
and part of the case that

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he makes in this book is that the kind of

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low cost delivery of
education in this model

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could revolutionize
underdeveloped countries,

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those that just don't
have access to education,

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that this could be a huge
way of addressing that.

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How would you, though, deal with

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that kind of problem
solving, the in classroom,

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the need for the educated professional?

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Sal: Yeah, well, in the developed world,

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where students have access to a teacher,

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I think this supercharges
that physical part of it.

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This isn't about virtual versus physical.

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It's not Amazon.com
versus Barnes and Noble's.

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This is about let's take
lecture off the table,

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because lecture, and we have
in the book a study that proved

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that lecture is probably the
worst possible use of time

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and very little learning actually goes on,

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make that on demand, at a student's time,

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they can remediate and not be embarassed,

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and make class time all
about problem solving,

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all about interaction with the teachers.

00:07:53.287 --> 00:07:54.954
So, in our mind, if you have a teacher,

00:07:54.954 --> 00:07:56.751
they become that much more valuable

00:07:56.751 --> 00:07:58.371
because you get to interact with them.

00:07:58.371 --> 00:08:01.151
In the developing world, you
have a different problem.

00:08:01.151 --> 00:08:03.452
Even if you have the
resources, you might not have

00:08:03.452 --> 00:08:06.551
a teacher in the village
who can address that topic.

00:08:06.551 --> 00:08:09.648
Even if you do, the students are
at all different skill levels.

00:08:09.648 --> 00:08:10.783
Some might be illiterate.

00:08:10.783 --> 00:08:13.146
Some might be somehow roughly
at their own grade level.

00:08:13.146 --> 00:08:15.440
What we say is, in those context,

00:08:15.440 --> 00:08:16.877
and there's an orphanage in Mongolia,

00:08:16.877 --> 00:08:19.223
actually several that
are using us in this way,

00:08:19.223 --> 00:08:21.646
it's better than nothing.

00:08:21.646 --> 00:08:23.957
It can give you a very
strong academic scaffold.

00:08:23.957 --> 00:08:26.375
You have a community of learners
online who can help you.

00:08:26.375 --> 00:08:27.569
And sometimes you're getting help

00:08:27.569 --> 00:08:29.952
from a teacher on the
other side of the planet,

00:08:29.952 --> 00:08:31.576
or another student on the
other side of the planet.

00:08:31.576 --> 00:08:32.936
Or some of these kids are actually

00:08:32.936 --> 00:08:34.451
helping kids in the developed world.

00:08:34.451 --> 00:08:37.653
So, for us, it's not an either/or.

00:08:37.653 --> 00:08:39.683
The ideal is you have amazing teachers,

00:08:39.683 --> 00:08:41.897
but if you have nothing,
like these orphanages

00:08:41.897 --> 00:08:43.650
in Mongolia, you're getting something.

00:08:43.650 --> 00:08:46.250
Larry: You can use
webcams, things like that

00:08:46.250 --> 00:08:48.486
to be able to make a two-way,

00:08:48.486 --> 00:08:51.393
interactive followup to online lectures?

00:08:51.393 --> 00:08:53.064
Sal: Yeah, that's stuff
that we have planned.

00:08:53.064 --> 00:08:54.750
I talk a lot about it in the book.

00:08:54.750 --> 00:08:57.394
I think Khan Academy is in
very, very early stages,

00:08:57.394 --> 00:08:58.985
and we set it up as a not for profit,

00:08:58.985 --> 00:09:01.342
so it really has this potential
to be this institution

00:09:01.342 --> 00:09:03.897
to deliver education
for the world for free.

00:09:03.897 --> 00:09:06.144
I hope in 50 or 100 years, well after ...

00:09:06.144 --> 00:09:07.853
well, hopefully I'm around in 50 years,

00:09:07.853 --> 00:09:11.250
but even after I'm gone,
people will still be

00:09:11.250 --> 00:09:13.066
working on the problem
of how can we make this

00:09:13.066 --> 00:09:14.393
more interactive, more engaging,

00:09:14.393 --> 00:09:15.751
and connect more learners
around the world?

00:09:15.751 --> 00:09:17.752
Larry: Salman Khan,
author of The One World

00:09:17.752 --> 00:09:20.650
School House: Education Reimagined.

00:09:20.650 --> 00:09:23.254
I'd love to hear from you
your questions or comments

00:09:23.254 --> 00:09:26.051
about Khan Academy, about the more than

00:09:26.051 --> 00:09:29.293
3,200 YouTube teaching
videos that are there,

00:09:29.293 --> 00:09:31.230
how it's being used by school districts,

00:09:31.230 --> 00:09:33.329
by individual schools as well.

00:09:33.329 --> 00:09:40.230
We're at 866-893-KPCC, 866-893-5722,

00:09:40.230 --> 00:09:43.871
or the AirTalk page at KPCC.org.

00:09:43.871 --> 00:09:46.530
TR asked an interesting
question he has on the page,

00:09:46.530 --> 00:09:48.956
"Are there tests that an
adult can take to assess

00:09:48.956 --> 00:09:52.230
their math shortcomings
on the Khan Academy site?"

00:09:52.230 --> 00:09:53.126
Sal: Yeah.

00:09:53.126 --> 00:09:54.829
That's what we're working on right now.

00:09:54.829 --> 00:09:56.552
We already have a significant exercise.

00:09:56.552 --> 00:09:58.380
Anyone can go to Khan Academy, log in.

00:09:58.380 --> 00:10:00.728
Actually, our team now, we're
36 people; it's not just me.

00:10:00.728 --> 00:10:03.041
Most of them are software
engineers and educators

00:10:03.041 --> 00:10:05.557
who are working on exactly
what's being described.

00:10:05.557 --> 00:10:07.329
You get as many problems as you need.

00:10:07.329 --> 00:10:08.289
It assesses you.

00:10:08.289 --> 00:10:09.742
It keeps progressing you forward.

00:10:09.742 --> 00:10:11.295
You get feedback on what you're doing.

00:10:11.295 --> 00:10:13.629
What we want to do is
broaden that to well beyond

00:10:13.629 --> 00:10:15.631
mathematics, so you can
get assessment on things,

00:10:15.631 --> 00:10:17.785
diagnostics, and then show what you know,

00:10:17.785 --> 00:10:19.329
and if you're having
trouble in a certain domain,

00:10:19.329 --> 00:10:21.372
there are these tutorials
that can help you out.

00:10:21.372 --> 00:10:22.631
Larry: One thing I forgot to mention,

00:10:22.631 --> 00:10:25.230
because this is really a
central part of your approach,

00:10:25.230 --> 00:10:27.929
is that everybody needs to be able to show

00:10:27.929 --> 00:10:30.036
that they've mastered a step before

00:10:30.036 --> 00:10:31.459
they move on to the next one,

00:10:31.459 --> 00:10:34.542
and schools are in a tough
spot trying to do that.

00:10:34.542 --> 00:10:37.290
Sal: I talked about in
the book pretty heavily is

00:10:37.290 --> 00:10:40.829
all the debate about education
essentially misses the point.

00:10:40.829 --> 00:10:43.729
It's all kind of on the fringes
of this model that we have

00:10:43.729 --> 00:10:46.131
that few people realize we
inherited from the Prussians,

00:10:46.131 --> 00:10:49.630
a country that does not
exist anymore, 200 years ago.

00:10:49.630 --> 00:10:52.547
The Prussian model was based on how do we

00:10:52.547 --> 00:10:54.527
educate a lot of people cost effectively?

00:10:54.527 --> 00:10:56.638
Well, it was the beginning
of the industrial revolution,

00:10:56.638 --> 00:10:57.835
so we'll do the same thing.

00:10:57.835 --> 00:11:00.223
We'll bash them together
in these age cohorts.

00:11:00.223 --> 00:11:01.545
They go to the same pace.

00:11:01.545 --> 00:11:03.837
They go to these stations,
which are these classes.

00:11:03.837 --> 00:11:05.553
Knowledge is applied to them.

00:11:05.553 --> 00:11:07.736
Some, it sticks; some, it doesn't.

00:11:07.736 --> 00:11:10.637
Then you sift out the product,
and some become doctors

00:11:10.637 --> 00:11:13.337
and some don't become
doctors or engineers.

00:11:13.337 --> 00:11:15.964
What we're saying is we think we can

00:11:15.964 --> 00:11:17.543
break out of that
Prussian model now because

00:11:17.543 --> 00:11:19.882
that Prussian model
pretty much dooms people

00:11:19.882 --> 00:11:21.969
to hit walls in their understanding.

00:11:21.969 --> 00:11:25.336
Right now, in the model,
you get a C on your exam

00:11:25.336 --> 00:11:28.337
on basic exponents, it moves you
to the next topic the next week,

00:11:28.337 --> 00:11:30.238
where you go to negative
exponents or logarithms,

00:11:30.238 --> 00:11:31.936
somehow expecting you to master that,

00:11:31.936 --> 00:11:34.480
even though you had that weak foundation.

00:11:34.480 --> 00:11:36.401
And so, we say no.

00:11:36.401 --> 00:11:39.067
Master that concept, at least
get a basic proficiency in it,

00:11:39.067 --> 00:11:42.096
and only then is it realistic
for you to be able to

00:11:42.096 --> 00:11:43.800
understand something
that builds on top of it.

00:11:43.800 --> 00:11:46.932
Larry: It's funny, when I was in
6th grade, it was way pre-Internet,

00:11:46.932 --> 00:11:50.047
I was in an experimental
classroom public school

00:11:50.047 --> 00:11:51.738
in Inglewood here in Southern California.

00:11:51.738 --> 00:11:54.139
They were trying something
where they combine

00:11:54.139 --> 00:11:57.939
5th and 6th grade, so it
was a joint classroom,

00:11:57.939 --> 00:12:00.337
and there was almost no lecture.

00:12:00.337 --> 00:12:01.837
The teacher sat in the middle of the room,

00:12:01.837 --> 00:12:05.462
and we had work stations in
different subject areas, again,

00:12:05.462 --> 00:12:09.430
so there are no videos, essentially,
but all kinds of stations.

00:12:09.430 --> 00:12:10.337
You work at your own pace.

00:12:10.337 --> 00:12:11.966
There were tests along
the way to make sure

00:12:11.966 --> 00:12:13.547
you had mastery before you moved on;

00:12:13.547 --> 00:12:15.960
and it was my favorite
year of school, because

00:12:15.960 --> 00:12:19.138
in areas where I was good,
I could go really fast;

00:12:19.138 --> 00:12:22.046
in areas where I needed more
help, I had the teacher available,

00:12:22.046 --> 00:12:24.882
one on one, to be able
to help me through it.

00:12:24.882 --> 00:12:28.230
I don't know how long that ever
last or what happened to it,

00:12:28.230 --> 00:12:30.551
but for me it was perfect
for my learning style.

00:12:30.551 --> 00:12:34.137
It just seems like those
kinds of experiments

00:12:34.137 --> 00:12:36.048
were often very hard to
come by when you've got

00:12:36.048 --> 00:12:39.298
such disparate student
level of achievement.

00:12:39.298 --> 00:12:40.138
Sal: Yeah.

00:12:40.138 --> 00:12:43.380
I think what you're describing,
it's not just for you.

00:12:43.380 --> 00:12:44.635
I think almost any human being

00:12:44.635 --> 00:12:46.138
would say that is how
they naturally learn.

00:12:46.138 --> 00:12:48.633
In the book, I talk about that
is how people naturally learn,

00:12:48.633 --> 00:12:50.952
through activity, through personalization,

00:12:50.952 --> 00:12:52.537
through interaction
with other human beings.

00:12:52.537 --> 00:12:55.036
What I think is special
about this time in history

00:12:55.036 --> 00:12:56.567
is that there are many
experiments like the one

00:12:56.567 --> 00:12:58.536
you were a part of in your childhood.

00:12:58.536 --> 00:12:59.779
There are a lot of schools that are moving

00:12:59.779 --> 00:13:01.279
in that direction, but
it's not mainstream.

00:13:01.279 --> 00:13:03.445
What we're seeing now is
because of the technology,

00:13:03.445 --> 00:13:05.635
because of this broad
adoption that things like

00:13:05.635 --> 00:13:08.452
Khan Academy are seeing, it's
starting to be mainstream.

00:13:08.452 --> 00:13:11.370
The coordination is starting
to empower teachers to do that.

00:13:11.370 --> 00:13:13.038
Larry: We still do group projects, too,

00:13:13.038 --> 00:13:14.250
which I know your summer camp,

00:13:14.250 --> 00:13:16.365
that's a big part of it, right?

00:13:16.365 --> 00:13:17.137
Sal: Right.

00:13:17.137 --> 00:13:19.638
One thing I talk a lot about
in the book is everyone's

00:13:19.638 --> 00:13:21.736
all paranoid about are we
falling behind Estonia or

00:13:21.736 --> 00:13:25.362
South Korea or Finland because
of our algebra test scores,

00:13:25.362 --> 00:13:28.236
and it's worth not being
complacent about that,

00:13:28.236 --> 00:13:32.137
but what I emphasize
is America is becoming

00:13:32.137 --> 00:13:34.036
more and more the center
of the world's innovation,

00:13:34.036 --> 00:13:36.336
and that's because we have
this culture of creativity.

00:13:36.336 --> 00:13:38.638
Failure isn't stigmatized.

00:13:38.638 --> 00:13:40.538
What I see, instead of
making our Prussian model

00:13:40.538 --> 00:13:42.737
more like the one in
Finland or South Korea or

00:13:42.737 --> 00:13:45.452
Singapore, let's make ours more American,

00:13:45.452 --> 00:13:47.365
where it's more personalized, more time

00:13:47.365 --> 00:13:49.870
with other human beings,
and time for creativity.

00:13:49.870 --> 00:13:50.946
Creativity is probably the single

00:13:50.946 --> 00:13:53.452
most important thing today,
but our current model

00:13:53.452 --> 00:13:55.947
completely squeezes time
for it out of the equation.

00:13:55.947 --> 00:13:58.236
Larry: Bill in Huntington
Beach, you're on AirTalk.

00:13:58.236 --> 00:13:59.290
Bill: Hi.

00:13:59.290 --> 00:14:04.037
I want to express my
gratitude for the Khan Academy

00:14:04.037 --> 00:14:07.784
and all the tapes that are out there.

00:14:07.784 --> 00:14:14.537
I'm a 55-year-old grad student,
returning to civil engineering.

00:14:14.537 --> 00:14:19.567
It's been 30 years since I first
took calculus and I'd lost it all.

00:14:19.567 --> 00:14:22.952
And so, I really literally
relearned the subject

00:14:22.952 --> 00:14:25.427
over the span of a few months.

00:14:25.427 --> 00:14:28.565
Thanks to Sal and his great tapes.

00:14:28.565 --> 00:14:30.738
Larry: Wow; so not just kids?

00:14:30.738 --> 00:14:31.738
Sal: No.

00:14:31.738 --> 00:14:32.951
We see that in the data.

00:14:32.951 --> 00:14:35.788
Stories like that is what
keep our whole team motivated.

00:14:35.788 --> 00:14:38.536
Larry: Maurice in San Dimas, welcome.

00:14:38.536 --> 00:14:40.135
Maurice: Hi, Larry.

00:14:40.135 --> 00:14:42.447
My wife is a teacher
in San Gabriel Valley,

00:14:42.447 --> 00:14:45.788
teaching chemistry, and
she loved the videos,

00:14:45.788 --> 00:14:49.639
and actually uses it
as homework assignments

00:14:49.639 --> 00:14:52.038
as a review, more than anything.

00:14:52.038 --> 00:14:54.866
The main problem that I see
is that the school district

00:14:54.866 --> 00:14:56.837
doesn't let her actually play the videos

00:14:56.837 --> 00:14:59.227
in the classroom because it's on YouTube.

00:14:59.227 --> 00:15:00.429
Sal: Yeah.

00:15:00.429 --> 00:15:03.777
That's a very real issue.

00:15:03.777 --> 00:15:05.302
A lot of classrooms block YouTube.

00:15:05.302 --> 00:15:07.016
Some countries block YouTube.

00:15:07.016 --> 00:15:10.961
On Khan Academy, there's
like a little link where

00:15:10.961 --> 00:15:13.545
you can acces it on mirrored
sites, some of the videos,

00:15:13.545 --> 00:15:16.881
but I think school districts are ...
and that's a short term solution.

00:15:16.881 --> 00:15:18.244
The school districts
are starting to realize

00:15:18.244 --> 00:15:20.045
that YouTube does have educational value,

00:15:20.045 --> 00:15:22.543
and YouTube is starting
to realize that as well.

00:15:22.543 --> 00:15:24.964
I think collectively we're
all working on solutions

00:15:24.964 --> 00:15:26.545
to address exactly what you described.

00:15:26.545 --> 00:15:28.047
Larry: Roxanne in West Lake Village

00:15:28.047 --> 00:15:30.373
says she's a math tutor, refers students

00:15:30.373 --> 00:15:31.962
to Khan Academy all the time.

00:15:31.962 --> 00:15:34.460
Then parents ask, "Why do
I need to hire tutors?"

00:15:34.460 --> 00:15:36.345
But there's still a great need because

00:15:36.345 --> 00:15:38.373
kids need to practice the hands on,

00:15:38.373 --> 00:15:40.243
just like when learning baseball.

00:15:40.243 --> 00:15:42.043
Sal: Once again, Khan
Academy is not there to

00:15:42.043 --> 00:15:43.845
replace humans; it's there
to supercharge humans.

00:15:43.845 --> 00:15:46.435
All of this started off as me
being a tutor, and it wasn't

00:15:46.435 --> 00:15:49.834
to replace myself, it was
really to allow my ...

00:15:49.834 --> 00:15:51.850
and get the half an hour
that I had with Nadia

00:15:51.850 --> 00:15:53.543
to be more constructive,
so I didn't have to lecture

00:15:53.543 --> 00:15:55.380
for things for her and
she didn't have to be

00:15:55.380 --> 00:15:57.243
embarassed to ask a
question from 4th grade.

00:15:57.243 --> 00:15:58.446
She could get it on demand.

00:15:58.446 --> 00:16:00.544
And so, yeah, that's what
you've got to tell parents,

00:16:00.544 --> 00:16:02.944
that the tutor is now more valuable

00:16:02.944 --> 00:16:04.648
and can take things to
another level with students.

00:16:04.648 --> 00:16:06.212
Larry: Jennifer in Fullerton,

00:16:06.212 --> 00:16:09.446
wondering about translation
for other countries.

00:16:09.446 --> 00:16:11.172
You're looking at new videos to serve in

00:16:11.172 --> 00:16:13.079
other languages or dubbing yourself?

00:16:13.079 --> 00:16:15.613
Sal: We actually have a
fairly extensive project.

00:16:15.613 --> 00:16:19.447
We've translated and
redone 7,000 videos into

00:16:19.447 --> 00:16:21.843
other languages, the 12
major languages of the world.

00:16:21.843 --> 00:16:24.090
If you go to the bottom of the
site, you see a little drop down.

00:16:24.090 --> 00:16:25.590
We have actually 1,000 in Spanish,

00:16:25.590 --> 00:16:27.127
1,000 in Portuguese,
and a bunch of others.

00:16:27.127 --> 00:16:27.448
Larry: Wow.

00:16:27.448 --> 00:16:28.739
Jonathan in Long Beach says,

00:16:28.769 --> 00:16:31.662
"The technology really
streamlined the college system."

00:16:31.662 --> 00:16:33.844
He's a student at Long Beach City College.

00:16:33.844 --> 00:16:35.537
He says, "Lectures go on and on,

00:16:35.537 --> 00:16:37.839
"regurgitation and inefficient."

00:16:37.839 --> 00:16:39.938
Salman Khan, thank you for being with us.

00:16:39.938 --> 00:16:41.351
Appreciate it very much.

00:16:41.351 --> 00:16:43.269
We'll see how much your
ideas make their way

00:16:43.269 --> 00:16:45.037
into mainstream American education.

00:16:45.037 --> 00:16:45.855
Sal: Thank you.

00:16:45.855 --> 00:16:47.941
Larry: The One World School House:

00:16:47.941 --> 00:16:50.264
Education Reimagined, by the founder of

00:16:50.264 --> 00:16:52.770
the nonprofit Khan Academy, Salman Khan.

00:16:52.770 --> 00:16:55.441
It's AirTalk on 89.3 KPCC.

00:16:55.441 --> 00:16:56.936
Have a great afternoon.

00:16:56.936 --> 00:17:00.936
BBC News Hour comes up
next, and then The World-


Solving the troll riddle visually

WEBVTT
Kind: captions
Language: en

00:00:00.690 --> 00:00:04.420
Where we left off, we
were trying our very best

00:00:04.420 --> 00:00:06.890
to get to the castle
and save whomever

00:00:06.890 --> 00:00:08.660
we were needing to save.

00:00:08.660 --> 00:00:11.660
But we had to cross the
bridge and the troll

00:00:11.660 --> 00:00:14.290
gave us these clues because
we had no money in our pocket.

00:00:14.290 --> 00:00:15.789
And if we don't
solve his riddle,

00:00:15.789 --> 00:00:17.330
he's going to push
us into the water.

00:00:17.330 --> 00:00:21.024
So we are under pressure.

00:00:21.024 --> 00:00:23.190
And at least we made some
headway in the last video.

00:00:23.190 --> 00:00:25.880
We were able to represent
his clues mathematically

00:00:25.880 --> 00:00:28.020
as a system of equations.

00:00:28.020 --> 00:00:30.020
What I want to do in
this video is think about

00:00:30.020 --> 00:00:32.650
whether we can solve for
this system of equations.

00:00:32.650 --> 00:00:34.970
And you'll see that
there are many ways

00:00:34.970 --> 00:00:38.026
of solving a system
of equations.

00:00:38.026 --> 00:00:39.650
But this time I want
to do it visually.

00:00:39.650 --> 00:00:41.483
Because at least in my
mind, it helps really

00:00:41.483 --> 00:00:44.780
get the intuition of what
these things are saying.

00:00:44.780 --> 00:00:47.110
So let's draw some
axes over here.

00:00:47.110 --> 00:00:49.490
Let's draw an f-axis.

00:00:49.490 --> 00:00:51.430
That's the number of
fives that I have.

00:00:51.430 --> 00:00:53.310
And let's draw a t-axis.

00:00:53.310 --> 00:00:55.720
That is the number
of tens I have.

00:00:55.720 --> 00:01:00.680
And let's say that this
right over here is 500 tens.

00:01:00.680 --> 00:01:03.350
That is 1,000 tens.

00:01:03.350 --> 00:01:06.480
And let's say this is-- oh,
sorry, that's 500 fives.

00:01:06.480 --> 00:01:08.270
That's 1,000 fives.

00:01:08.270 --> 00:01:14.790
This is 500 tens, And
this is 1,000 tens.

00:01:14.790 --> 00:01:17.860
So let's think about all of
the combinations of f's and t's

00:01:17.860 --> 00:01:20.790
that satisfy this
first equation.

00:01:20.790 --> 00:01:24.050
If we have no tens, then
we're going to have 900 fives.

00:01:29.000 --> 00:01:31.100
So that looks like
it's right about there.

00:01:31.100 --> 00:01:37.049
So that's the point
0 tens, 900 fives.

00:01:37.049 --> 00:01:38.340
But what if went the other way?

00:01:38.340 --> 00:01:41.770
If we have no fives, we're
going to have 900 tens.

00:01:41.770 --> 00:01:46.230
So that's going to be the
point 900 tens, 0 fives.

00:01:46.230 --> 00:01:50.310
So all the combinations of
f's and t's that satisfy this

00:01:50.310 --> 00:01:54.830
are going to be on this
line right over there.

00:01:54.830 --> 00:01:57.520
And I'll just draw a dotted line
just because it's easier for me

00:01:57.520 --> 00:01:58.460
to draw it straight.

00:01:58.460 --> 00:02:01.780
So that represents all the
f's and t's that satisfy

00:02:01.780 --> 00:02:02.800
the first constraint.

00:02:02.800 --> 00:02:04.430
Obviously, there's
a bunch of them,

00:02:04.430 --> 00:02:06.520
so we don't know
which is the one that

00:02:06.520 --> 00:02:08.870
is actually what the troll has.

00:02:08.870 --> 00:02:11.420
But lucky for us, we have
a second constraint--

00:02:11.420 --> 00:02:12.580
this one right over here.

00:02:12.580 --> 00:02:14.470
So let's do the same thing.

00:02:14.470 --> 00:02:18.280
In this constraint, what
happens if we have no tens?

00:02:18.280 --> 00:02:21.569
If tens are 0, then we
have 5f is equal to 5,500.

00:02:21.569 --> 00:02:23.360
Let me do a little
table here, because this

00:02:23.360 --> 00:02:26.450
is a little bit more involved.

00:02:26.450 --> 00:02:30.260
So for the second
equation, tens and fives.

00:02:30.260 --> 00:02:35.440
If I have no tens, I have
5f is equal to 5,500,

00:02:35.440 --> 00:02:37.870
f will be 1,100.

00:02:37.870 --> 00:02:40.320
I must have 1,100 fives.

00:02:40.320 --> 00:02:44.750
If I have no fives,
then this is 0,

00:02:44.750 --> 00:02:46.770
and I have 10t is
equal to 5,500,

00:02:46.770 --> 00:02:50.520
that means I have 550 tens.

00:02:50.520 --> 00:02:52.150
So let's plot both
at those point.

00:02:52.150 --> 00:02:54.420
t equals 0, f is 11.

00:02:54.420 --> 00:02:56.120
That's right about there.

00:02:56.120 --> 00:02:57.860
So that is 0.

00:02:57.860 --> 00:03:02.700
1,100 is on the line that
represents this equation.

00:03:02.700 --> 00:03:05.860
And that when f is 0, t is 550.

00:03:05.860 --> 00:03:11.230
So let's see, this is about--
this would be 6, 7, 8, 9,

00:03:11.230 --> 00:03:14.010
so 550 is going to
be right over here.

00:03:14.010 --> 00:03:19.430
So that is the
point 550 comma 0.

00:03:19.430 --> 00:03:23.110
And all of these
points-- let me try

00:03:23.110 --> 00:03:24.384
to draw a straight line again.

00:03:24.384 --> 00:03:25.800
I could do a better
job than that.

00:03:28.510 --> 00:03:32.530
So all of these points
are the points--

00:03:32.530 --> 00:03:34.957
let me try one more time.

00:03:34.957 --> 00:03:36.040
We want to get this right.

00:03:36.040 --> 00:03:39.120
We don't want to get pushed
into the water by the troll.

00:03:39.120 --> 00:03:40.340
So there you go.

00:03:40.340 --> 00:03:41.470
That looks pretty good.

00:03:41.470 --> 00:03:46.170
So every point on this blue line
represents an ft combination

00:03:46.170 --> 00:03:48.860
that satisfies the
second constraint.

00:03:48.860 --> 00:03:51.620
So what is an f and t, or
number of fives and number

00:03:51.620 --> 00:03:53.640
of tens that satisfy
both constraints?

00:03:53.640 --> 00:03:55.620
Well, it would be
a point that is

00:03:55.620 --> 00:03:58.710
sitting on both of the lines.

00:03:58.710 --> 00:04:01.460
And what is a point that is
sitting on both of the lines?

00:04:01.460 --> 00:04:02.876
Well, that's where
they intersect.

00:04:02.876 --> 00:04:05.750
This point right over here
is clearly on the blue line

00:04:05.750 --> 00:04:08.840
and is clearly on
the yellow line.

00:04:08.840 --> 00:04:11.950
And what we can do is, if
we drew this graph really,

00:04:11.950 --> 00:04:16.320
really precisely, we could
see how many fives that is

00:04:16.320 --> 00:04:18.140
and how many tens that is.

00:04:18.140 --> 00:04:20.779
And if you look at it, if
you look at very precisely,

00:04:20.779 --> 00:04:24.560
and actually I encourage you
to graph it very precisely

00:04:24.560 --> 00:04:29.330
and come up with how many fives
and how many tens that is.

00:04:29.330 --> 00:04:33.256
Well, when we do it right over
here, I'm going to eyeball it.

00:04:33.256 --> 00:04:34.630
If we look at it
right over here,

00:04:34.630 --> 00:04:39.600
it looks like we
have about 700 fives,

00:04:39.600 --> 00:04:42.180
and it looks like we
have about 200 tens.

00:04:42.180 --> 00:04:44.490
And this is based on
my really rough graph.

00:04:44.490 --> 00:04:45.960
But let's see if that worked.

00:04:45.960 --> 00:04:51.130
700 plus 200 is equal to 900.

00:04:51.130 --> 00:04:54.840
And if I have 700 fives--
let me write this down.

00:04:54.840 --> 00:04:59.090
5 times 700 is going to be
the value of the fives, which

00:04:59.090 --> 00:05:00.970
is $3,500.

00:05:00.970 --> 00:05:10.300
And then 10 plus 10 times
200, which is $2,000, $2,000

00:05:10.300 --> 00:05:11.540
is the value of the 10s.

00:05:11.540 --> 00:05:13.200
And if you add up
the two values,

00:05:13.200 --> 00:05:16.280
you indeed get to $ 5,500

00:05:16.280 --> 00:05:17.810
So this looks right.

00:05:17.810 --> 00:05:20.000
And so we can tell
the troll-- Troll!

00:05:20.000 --> 00:05:20.780
I know!

00:05:20.780 --> 00:05:23.692
I know how many $5
and $10 bills you.

00:05:23.692 --> 00:05:30.530
You have 700 $5 bills, and
you have 200 $10 bills.

00:05:30.530 --> 00:05:33.000
The troll is
impressed, and he lets

00:05:33.000 --> 00:05:38.390
you cross the bridge to be the
hero or heroine of this fantasy

00:05:38.390 --> 00:05:39.671
adventure.


Trolls, tolls, and systems of equations

WEBVTT
Kind: captions
Language: en

00:00:00.730 --> 00:00:04.090
You are traveling in some type
of a strange fantasy land.

00:00:04.090 --> 00:00:06.530
And you're trying
to get to the castle

00:00:06.530 --> 00:00:08.600
up here to save the
princess or the prince

00:00:08.600 --> 00:00:10.700
or whomever you're
trying to save.

00:00:10.700 --> 00:00:13.010
But to get there, you
have to cross this river.

00:00:13.010 --> 00:00:14.125
You can't swim across it.

00:00:14.125 --> 00:00:15.356
It's a very rough river.

00:00:15.356 --> 00:00:16.730
So you have to
cross this bridge.

00:00:16.730 --> 00:00:20.510
And so as you approach the
bridge, this troll shows up.

00:00:20.510 --> 00:00:21.540
That's the troll.

00:00:21.540 --> 00:00:23.910
And he says, well, I'm
a reasonable troll.

00:00:23.910 --> 00:00:24.910
You just have to pay $5.

00:00:24.910 --> 00:00:26.826
And when you look a
little bit more carefully,

00:00:26.826 --> 00:00:28.960
you see that there
actually was a sign there

00:00:28.960 --> 00:00:33.440
that says $5 toll
to cross the bridge.

00:00:33.440 --> 00:00:35.120
Now, unfortunately
for you, you do not

00:00:35.120 --> 00:00:37.400
have any money in your pocket.

00:00:37.400 --> 00:00:39.890
And so the troll says,
well, you can't cross.

00:00:39.890 --> 00:00:42.650
But you say, I need to really,
really get to that castle.

00:00:42.650 --> 00:00:46.220
And so the troll says, well,
I'll take some pity on you.

00:00:46.220 --> 00:00:53.640
Instead of paying the $5,
I will give you a riddle.

00:00:53.640 --> 00:00:55.130
And the riddle is this.

00:00:55.130 --> 00:00:56.870
And now, I'm speaking
as the troll.

00:00:56.870 --> 00:01:00.150
I am a rich troll
because I get to charge

00:01:00.150 --> 00:01:02.090
from everyone who
crosses the bridge.

00:01:02.090 --> 00:01:04.900
And actually, I only
accept $5 or $10 bills.

00:01:04.900 --> 00:01:06.800
It's a bit of a
riddle why they accept

00:01:06.800 --> 00:01:08.800
American currency in
this fantasy land.

00:01:08.800 --> 00:01:11.060
But let's just take
that as a given for now.

00:01:11.060 --> 00:01:13.200
So I only take $5 or $10 bills.

00:01:13.200 --> 00:01:15.100
I'm being the troll.

00:01:15.100 --> 00:01:17.760
Obviously, if you give me a
$10, I'll give you $5 back.

00:01:17.760 --> 00:01:22.190
And I know, because I count
my money on a daily basis.

00:01:22.190 --> 00:01:24.280
I like to save my
money as the troll.

00:01:24.280 --> 00:01:30.270
I know that I have a
total of 900 bills.

00:01:30.270 --> 00:01:32.200
So let me write that down.

00:01:32.200 --> 00:01:41.090
I have a total of 900 bills, a
total of 900 $5 and $10 bills.

00:01:44.760 --> 00:01:46.869
And he says, because
I'm very sympathetic,

00:01:46.869 --> 00:01:48.660
I'll give you another
piece of information.

00:01:48.660 --> 00:01:51.740
He says, if you were to
add up the value of all

00:01:51.740 --> 00:02:02.910
of my money, which is all in
$5 and $10 bills that I have,

00:02:02.910 --> 00:02:10.000
I, speaking as the troll about
dollars bills, is $5,500.

00:02:10.000 --> 00:02:10.940
This is a rich troll.

00:02:13.930 --> 00:02:16.810
And so the riddle
is-- exactly, exactly.

00:02:16.810 --> 00:02:19.000
And if you give the wrong
answer and if you're not

00:02:19.000 --> 00:02:20.185
able to solve it
in 10 minutes, he's

00:02:20.185 --> 00:02:21.400
just going to push
you into the river

00:02:21.400 --> 00:02:22.990
or do something horrible to you.

00:02:22.990 --> 00:02:37.344
He says, exactly how many 5's
and 10's do I, the troll, have?

00:02:37.344 --> 00:02:39.510
So the first thing I'm going
to have you think about

00:02:39.510 --> 00:02:41.595
is, is this even a
solvable problem?

00:02:41.595 --> 00:02:43.220
Because if it's not
a solvable problem,

00:02:43.220 --> 00:02:44.970
you should probably
run as fast as you can

00:02:44.970 --> 00:02:47.370
in the other direction.

00:02:47.370 --> 00:02:50.014
So now, I will tell you, yes,
it is a solvable problem.

00:02:50.014 --> 00:02:52.555
And let's start thinking about
it a little bit algebraically.

00:02:52.555 --> 00:02:55.440
And to do that, let's
just set some variables.

00:02:55.440 --> 00:02:57.347
And I will set the
variables to be

00:02:57.347 --> 00:02:58.930
what we're really
trying to solve for.

00:02:58.930 --> 00:03:02.050
We're trying to solve for the
number of $5 bills we have

00:03:02.050 --> 00:03:05.320
and the number of $10
bills that we have.

00:03:05.320 --> 00:03:07.110
So let's just define
some variables.

00:03:07.110 --> 00:03:08.580
I'll say f for 5.

00:03:08.580 --> 00:03:20.200
Let's let f equal the number
of $5 bills that we have.

00:03:20.200 --> 00:03:22.400
And I'll use the same idea.

00:03:22.400 --> 00:03:30.990
Let's let t is equal to the
number $10 bills that we have.

00:03:30.990 --> 00:03:32.775
Now, given this
information, and now

00:03:32.775 --> 00:03:34.400
I'm not sure if I'm
speaking as-- well,

00:03:34.400 --> 00:03:35.640
let's say I'm still
speaking as the troll.

00:03:35.640 --> 00:03:36.840
I'm a very sympathetic
troll, and I'm

00:03:36.840 --> 00:03:38.180
going to give you hints.

00:03:38.180 --> 00:03:40.400
Given this information and
setting these variables

00:03:40.400 --> 00:03:43.670
in this way, can I represent
the clues in the riddle

00:03:43.670 --> 00:03:44.580
mathematically?

00:03:44.580 --> 00:03:46.240
So let's focus on
the first clue.

00:03:46.240 --> 00:03:51.180
Can I represent this clue that
the total of 900 $5 and $10

00:03:51.180 --> 00:03:54.150
bills, or can I represent
that mathematically,

00:03:54.150 --> 00:03:58.870
that I have a total of
900 $5 and $10 bills?

00:03:58.870 --> 00:04:01.400
Well, what's going to
be our total of bills?

00:04:01.400 --> 00:04:04.310
It's going to be the number of
5's that we have, which is f.

00:04:04.310 --> 00:04:06.530
The number of 5's
that we have is f.

00:04:06.530 --> 00:04:09.150
And then the number of
10s that we have is t.

00:04:09.150 --> 00:04:11.160
The total number of 5's
plus the total number

00:04:11.160 --> 00:04:13.160
of 10s, that's our
total number of bills.

00:04:13.160 --> 00:04:17.959
So that's going to
be equal to 900.

00:04:17.959 --> 00:04:22.580
So this statement, this
first clue in our riddle,

00:04:22.580 --> 00:04:24.670
can be written
mathematically like this

00:04:24.670 --> 00:04:26.490
if we defined the
variables like that.

00:04:26.490 --> 00:04:30.790
And I just said f for 5,
because f for 5 in t for 10.

00:04:30.790 --> 00:04:32.780
Now, let's look at
the second clue.

00:04:32.780 --> 00:04:38.210
Can we represent this
one mathematically given

00:04:38.210 --> 00:04:42.790
these variable definitions
that we created?

00:04:42.790 --> 00:04:47.420
Well, let's think separately
about the value of the $5 bills

00:04:47.420 --> 00:04:49.440
and the value of the $10 bills.

00:04:49.440 --> 00:04:52.500
What's the value of
all of the $5 bills?

00:04:52.500 --> 00:04:55.100
Well, each $5 bill is worth $5.

00:04:55.100 --> 00:04:58.170
So it's going to be 5 times
the number of $5 bills

00:04:58.170 --> 00:04:58.820
that we have.

00:04:58.820 --> 00:05:02.610
So if I have one $5
bill, it will be $5.

00:05:02.610 --> 00:05:06.560
If I have 100 $5 bills,
then it's going to be $500.

00:05:06.560 --> 00:05:09.180
How ever many $5 bills,
I just multiply it by 5.

00:05:09.180 --> 00:05:11.060
That's the value
of the $5 bills.

00:05:11.060 --> 00:05:12.440
Let me write that down.

00:05:12.440 --> 00:05:18.330
Value of the $5 bills.

00:05:18.330 --> 00:05:19.600
Now, same logic.

00:05:19.600 --> 00:05:22.030
What's the value
of the $10 bills?

00:05:22.030 --> 00:05:23.750
Well, the value of
the $10 bills is just

00:05:23.750 --> 00:05:26.030
going to be 10 times
however many bills

00:05:26.030 --> 00:05:31.847
I have-- value of the $10 bills.

00:05:31.847 --> 00:05:33.930
So what's going to be the
total value of my bills?

00:05:33.930 --> 00:05:36.100
Well, it's going to be
the value of the $5 bills

00:05:36.100 --> 00:05:40.472
plus the value of the $10 bills?

00:05:40.472 --> 00:05:42.180
And he tells me what
that total value is.

00:05:42.180 --> 00:05:43.489
It's $5,500.

00:05:43.489 --> 00:05:45.030
So if I add these
two things, they're

00:05:45.030 --> 00:05:50.700
going to add up to be $5,500.

00:05:50.700 --> 00:05:54.380
So this second statement we
can represent mathematically

00:05:54.380 --> 00:05:59.720
with this second
equation right over here.

00:05:59.720 --> 00:06:01.900
And what we essentially
have right over here,

00:06:01.900 --> 00:06:03.840
we have two equations.

00:06:03.840 --> 00:06:05.780
Each of them have two unknowns.

00:06:05.780 --> 00:06:07.680
And just using one
of these equations,

00:06:07.680 --> 00:06:10.084
we can't really figure
out what f and t are.

00:06:10.084 --> 00:06:12.000
You can pick a bunch of
different combinations

00:06:12.000 --> 00:06:13.450
that add up to 900 here.

00:06:13.450 --> 00:06:16.410
You could pick a bunch of
different combinations, where

00:06:16.410 --> 00:06:19.300
if you work out all the
math, you get $5,500.

00:06:19.300 --> 00:06:22.650
So independently,
these equations,

00:06:22.650 --> 00:06:24.440
you don't know what f and t are.

00:06:24.440 --> 00:06:27.580
But what we will see over
the next several videos

00:06:27.580 --> 00:06:30.060
is that if you use both of
this information, if you

00:06:30.060 --> 00:06:31.590
say that there's
an f and a t that

00:06:31.590 --> 00:06:34.760
has to satisfy both
of these equations,

00:06:34.760 --> 00:06:37.420
then you can find a solution.

00:06:37.420 --> 00:06:40.040
And this is called a
system of equations.

00:06:43.270 --> 00:06:48.550
Let me write that down--
system of equations.


Hundred days and Waterloo

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:03.703
So let's review how we got to where we are right now.

00:00:03.703 --> 00:00:06.283
In 1789 you have the Revolution in France.

00:00:06.283 --> 00:00:11.016
This makes the French very proud, a lot of nationalistic pride.

00:00:11.016 --> 00:00:13.591
It also makes the rest of Europe a little worried.

00:00:13.591 --> 00:00:17.851
They're all monarchies, they don't like this idea of overthrowing your kings.

00:00:17.851 --> 00:00:22.169
And so during this revolutionary period you have a series of wars with the rest of Europe.

00:00:22.169 --> 00:00:25.968
Revolutionary France does, essentially, the French Revolutionary Wars.

00:00:25.968 --> 00:00:30.033
And during that period Napoleon becomes quite famous as the French

00:00:30.033 --> 00:00:33.431
and maybe the best European military commander.

00:00:33.431 --> 00:00:37.337
So, now Napoleon is starting to become essentialy a hero in France.

00:00:37.337 --> 00:00:40.555
And by 1799 he is able to come to power in a coup d'état

00:00:40.555 --> 00:00:43.709
with a couple of other people and then he outmaneuvers them

00:00:43.709 --> 00:00:46.986
and then by 1804 he becomes the emperor Napoleon

00:00:46.986 --> 00:00:51.157
and in this whole period he is now trying to expand the Empire

00:00:51.157 --> 00:00:55.304
so these were the Revolutionary Wars, and these you can consider right over here

00:00:55.304 --> 00:00:59.903
are the Napoleonic Wars and the pic of the French Empire under Napoleon

00:00:59.903 --> 00:01:02.595
happens in 1812 and the real downfall

00:01:02.595 --> 00:01:05.608
if you ask my opinion and many other people

00:01:05.608 --> 00:01:07.181
would be when he invaded Russia

00:01:07.181 --> 00:01:10.145
that really decimated the French Grand Armée

00:01:10.145 --> 00:01:13.966
and we saw in the last video that by April 1814,

00:01:13.966 --> 00:01:18.305
the 6th coalition was finally succesfull against Napoleon

00:01:18.305 --> 00:01:21.251
and then he was exiled

00:01:21.251 --> 00:01:28.109
to the island of Elba where we're taking up the story

00:01:28.109 --> 00:01:32.687
he only hung out there for a little under 10 months

00:01:32.687 --> 00:01:34.897
he was separated from his family

00:01:34.897 --> 00:01:38.262
so that even though he was put in charge of this litle island

00:01:38.262 --> 00:01:40.499
it wouldn't have been what he wanted

00:01:40.499 --> 00:01:42.819
and he obviously was an ambitious person on top of that

00:01:42.819 --> 00:01:45.843
He caught wind of what was happening in France.

00:01:45.843 --> 00:01:48.239
Louis the 18th was there, the nobility returned

00:01:48.239 --> 00:01:52.301
they weren't treating the old Army veterans well which made him suspect

00:01:52.301 --> 00:01:55.983
that he may be able to retake control somehow

00:01:55.983 --> 00:01:58.392
On top of that the French Empire

00:01:58.392 --> 00:02:01.502
was being shrunken back to its original boundaries

00:02:01.502 --> 00:02:04.835
which made many people in France a lot less proud so Napoleon

00:02:04.835 --> 00:02:06.924
started to sense that maybe he could do something.

00:02:06.924 --> 00:02:09.994
On top of that, he caught wind that people might not

00:02:09.994 --> 00:02:14.287
leave him in Elba because he is Napoleon and they were afraid that he may come back

00:02:14.287 --> 00:02:17.284
so they might banish him to someplace even more remote,

00:02:17.284 --> 00:02:21.122
or there might be some attempts to assassinate him

00:02:21.122 --> 00:02:25.690
So with that in mind, being who he is, and being as creative as he is

00:02:25.690 --> 00:02:29.307
he's able to somehow escape from Elba, he's able to get a boat,

00:02:29.307 --> 00:02:33.021
land on the Southern shores of France. The French

00:02:33.021 --> 00:02:36.847
authorities are able to catch wind of this, they send the military

00:02:36.847 --> 00:02:39.718
to engage with him, this is the French military

00:02:39.718 --> 00:02:40.963
to essentially confront

00:02:40.963 --> 00:02:45.669
capture, kill Napoleon on the Southern shores of France

00:02:45.669 --> 00:02:49.326
and when he sees them, he dismounts from the horse that he's got,

00:02:49.326 --> 00:02:52.888
he walks up to them completely unarmed and he says,

00:02:52.888 --> 00:02:55.970
"go ahead, shoot your emperor"

00:02:55.970 --> 00:02:58.908
which is in my mind a fairly gutsy move to do

00:02:58.908 --> 00:03:02.370
And they rally around him and he's able to actually take control

00:03:02.370 --> 00:03:06.427
of the army that was sent to capture or kill him

00:03:06.427 --> 00:03:08.472
and he starts marching to Paris

00:03:08.472 --> 00:03:13.480
He starts marching to Paris, and Louis the 18th, the brave man that he is

00:03:13.480 --> 00:03:15.661
catches wind of this and escapes

00:03:15.661 --> 00:03:23.635
and so by March of 1815 Napoleon is able to retake control

00:03:23.635 --> 00:03:25.804
of Paris and essentially, France.

00:03:25.804 --> 00:03:29.587
And this is the beginning of what is known as the Hundred Days.

00:03:29.587 --> 00:03:38.235
It actually is about a 111 days, but it doesn't sound that good.

00:03:38.235 --> 00:03:43.036
So between March 1815, and July 1815

00:03:43.036 --> 00:03:46.502
You can imagine, even before Napoleon was able to reach Paris

00:03:46.502 --> 00:03:51.491
word got around about what was going on

00:03:51.491 --> 00:03:54.513
That Napoleon was back, they didn't like it

00:03:54.513 --> 00:03:58.003
They essentially announced that they wouldn't stand by there

00:03:58.003 --> 00:04:00.521
and that were going to form a new coalition to stop him

00:04:00.521 --> 00:04:04.001
So Napoleon had two options once he gets in Paris,

00:04:04.001 --> 00:04:08.003
He could essentially sit and wait

00:04:08.003 --> 00:04:13.554
wait for the combined forces of Europe to reorganize and then attack him.

00:04:13.554 --> 00:04:17.388
Or he could go on the offensive,

00:04:17.388 --> 00:04:20.800
he could attack before they had a chance to fully regroup

00:04:20.800 --> 00:04:24.842
you can imagine, he viewed this as being his best shot

00:04:24.842 --> 00:04:30.219
so he starts going after the combined forces of Great Britain

00:04:30.219 --> 00:04:33.454
and Prussia in what is now Belgium

00:04:33.454 --> 00:04:36.840
And over there is where he engaged in probably some of the most

00:04:36.840 --> 00:04:43.224
decisive battles, the most decisive one was the battle of Waterloo

00:04:43.224 --> 00:04:46.810
which is possibly one of the most famous battles in history

00:04:46.810 --> 00:04:50.455
maybe due to also the Abba song about it

00:04:50.455 --> 00:04:53.833
and that is where he met the Duke of Wellington on the British side,

00:04:53.833 --> 00:04:57.778
and Blücher on the Prussian side

00:04:57.778 --> 00:05:01.274
Napoleon had seventy or eighty thousand troops

00:05:01.274 --> 00:05:04.758
The other side had a hundred and twenty/thirty thousand troops

00:05:04.758 --> 00:05:10.373
A extremely bloody battle, more than forty/fifty thousand people killed,

00:05:10.373 --> 00:05:13.352
injured, missing on and on and on.

00:05:13.352 --> 00:05:15.655
But in the end, Napoleon lost and many historians,

00:05:15.655 --> 00:05:18.093
there's different reasons for why he lost

00:05:18.093 --> 00:05:20.920
he actually did a pretty good job considering the scenario

00:05:20.920 --> 00:05:23.315
the ground because of the weather was very muddy

00:05:23.315 --> 00:05:26.702
and actually was not good for being on the offense

00:05:26.702 --> 00:05:28.651
It was very good conditions for being on the defense

00:05:28.651 --> 00:05:32.308
And you know, Napoleon was essentially trying to take out

00:05:32.308 --> 00:05:37.155
these somewhat remnant armies before the Coalition,

00:05:37.155 --> 00:05:43.745
the 7th Coalition essentially had a chance to fully get back to full force

00:05:43.745 --> 00:05:46.930
But he loses at Waterloo, there are a few skirmishes after that,

00:05:46.930 --> 00:05:49.761
but the French retreat back to Paris

00:05:49.761 --> 00:05:53.312
At this point Napoleon sees the writing on the wall

00:05:53.312 --> 00:05:55.602
He's not completely delusional

00:05:55.602 --> 00:05:58.681
He sees that if they were able to, especially if the Prussians

00:05:58.681 --> 00:06:00.294
are able to get him again, they might not let him live

00:06:00.294 --> 00:06:02.645
They might really do something crazy

00:06:02.645 --> 00:06:04.830
with him, so he surrenders himself to the British

00:06:04.830 --> 00:06:10.415
And then they exile him to the isle of Saint Helena

00:06:10.415 --> 00:06:14.343
which is one of the very remote island which is afraid to be exiled to

00:06:14.343 --> 00:06:17.228
to begin with. An just to give a sense of how remote it is

00:06:17.228 --> 00:06:19.208
This right over here

00:06:19.208 --> 00:06:22.029
is the South West coast of Africa

00:06:22.029 --> 00:06:23.690
This is Africa right over here.

00:06:23.690 --> 00:06:27.072
Saint Helena is right out over here

00:06:27.072 --> 00:06:29.164
Almost in the middle of the Atlantic

00:06:29.164 --> 00:06:31.497
between Africa and South America

00:06:31.497 --> 00:06:33.065
And that's where Napoleon would

00:06:33.065 --> 00:06:34.841
live out the rest of his life

00:06:34.841 --> 00:06:36.711
In a very uncomfortable situation

00:06:36.711 --> 00:06:39.447
much worse than what he had going on in Elba

00:06:39.447 --> 00:06:41.303
Separated from everyone else.

00:06:41.303 --> 00:06:44.916
And then he dies in 1821

00:06:44.916 --> 00:06:46.801
The official cause and this is what many historians

00:06:46.801 --> 00:06:48.491
do believe actually happened

00:06:48.491 --> 00:06:50.443
Is that he died of stomach cancer

00:06:50.443 --> 00:06:54.397
Bu there are many theories that there might

00:06:54.397 --> 00:06:56.848
have been some type of assassination

00:06:56.848 --> 00:06:58.350
Some slow arsenic poisoning

00:06:58.350 --> 00:07:00.917
There was a lot of arsenic in his tissues

00:07:00.917 --> 00:07:04.508
His body was unusually well preserved after his death

00:07:04.508 --> 00:07:04.509
That's one of the things arsenic does

00:07:06.649 --> 00:07:08.794
Some people think that it might have been

00:07:08.794 --> 00:07:10.538
an inadvertent arsenic poisoning

00:07:10.538 --> 00:07:12.081
because of the environment that he was in

00:07:12.081 --> 00:07:14.061
Of the conditions he might have been in,

00:07:14.061 --> 00:07:14.224
of the paint in the walls,

00:07:14.224 --> 00:07:18.778
but either way, he really lived roughly

00:07:18.778 --> 00:07:21.117
throught the last six years

00:07:21.117 --> 00:07:24.300
in pretty unpleasant conditions, and then

00:07:24.300 --> 00:07:28.054
died of stomach cancer.

00:07:28.054 --> 00:07:32.054
And that was essentially the final end of Napoleon


Transfer pricing and tax havens

WEBVTT
Kind: captions
Language: en

00:00:00.243 --> 00:00:04.123
- Let's say that I run a company

00:00:04.123 --> 00:00:06.749
that is based inside of the United States.

00:00:06.749 --> 00:00:09.563
So this right over here is my company.

00:00:09.563 --> 00:00:12.736
Maybe I have some
smokestacks of some kind.

00:00:12.736 --> 00:00:14.283
So that is my company,

00:00:14.283 --> 00:00:17.770
and it makes a million
dollars in pre-tax profits.

00:00:17.770 --> 00:00:21.336
One million dollars,
and this is before tax.

00:00:21.336 --> 00:00:23.575
So, pre-tax profits.

00:00:23.575 --> 00:00:25.406
And let's say that the
country that I'm in,

00:00:25.406 --> 00:00:27.323
and the way I've drawn it,
this is the United States,

00:00:27.323 --> 00:00:30.263
let's say at the time that
I make those pre-tax profits

00:00:30.263 --> 00:00:35.263
the corporate tax rate
is 35%, 35% tax rate.

00:00:36.423 --> 00:00:38.243
So, it's pretty
straightforward to think about

00:00:38.243 --> 00:00:40.303
how much taxes I would have to pay.

00:00:40.303 --> 00:00:43.703
I would pay 35% on this
one million dollars,

00:00:43.703 --> 00:00:47.403
or essentially I would
pay $350,000 in taxes.

00:00:47.403 --> 00:00:52.023
Three-hundred and fifty
thousand dollars in taxes,

00:00:52.023 --> 00:00:55.546
and I would have 650,000 left in profit.

00:00:55.546 --> 00:01:00.546
So, 650,000 left in profit.

00:01:00.823 --> 00:01:02.163
Now what I want to think about,

00:01:02.163 --> 00:01:04.743
let's say my company wants to
get a little bit more creative

00:01:04.743 --> 00:01:07.263
about how it might save on taxes.

00:01:07.263 --> 00:01:09.723
So what it does is, it
realizes that there's an island

00:01:09.723 --> 00:01:11.683
not too far off the U.S. Coast,

00:01:11.683 --> 00:01:13.199
and there are actually several of them,

00:01:13.199 --> 00:01:16.295
that has a substantively lower tax rate.

00:01:16.295 --> 00:01:17.543
And I'm just picking it arbitrarily,

00:01:17.543 --> 00:01:22.543
but let's say it has a 5%
corporate tax rate, 5% tax rate.

00:01:25.083 --> 00:01:27.165
So how can this company,
which is physically

00:01:27.165 --> 00:01:29.383
or for the most part
based in this country,

00:01:29.383 --> 00:01:32.483
somehow benefit from this lower tax rate

00:01:32.483 --> 00:01:34.723
that is happening offshore?

00:01:34.723 --> 00:01:36.196
Well, what they'll typically do is

00:01:36.196 --> 00:01:37.923
set up another subsidiary,

00:01:37.923 --> 00:01:40.043
one that this company owns and controls,

00:01:40.043 --> 00:01:43.443
but it is set up in this
little island nation.

00:01:43.443 --> 00:01:45.756
So let's set it up right over here.

00:01:45.756 --> 00:01:47.067
So that's the other company.

00:01:47.067 --> 00:01:48.843
And what it'll do is,
it'll tend to give it maybe

00:01:48.843 --> 00:01:51.403
often times it'll give it
some intellectual property,

00:01:51.403 --> 00:01:54.123
maybe patents, trademarks,
things like this.

00:01:54.123 --> 00:01:56.063
So it gets all of the
intellectual property

00:01:56.063 --> 00:01:57.181
of the parent company.

00:01:57.181 --> 00:02:02.181
So, given the intellectual property.

00:02:03.363 --> 00:02:04.803
And then, what it can say is--

00:02:04.803 --> 00:02:07.784
And this is owned by the parent entity,

00:02:07.784 --> 00:02:09.066
so I'll draw a little dotted line here.

00:02:09.066 --> 00:02:12.035
It's owned and controlled by this company

00:02:12.035 --> 00:02:14.869
that's based in the U.S.,
and what they'll say is,

00:02:14.869 --> 00:02:16.912
look, we don't have a million
dollar pre-tax profit anymore,

00:02:16.912 --> 00:02:19.969
because we had to
essentially license the use

00:02:19.969 --> 00:02:23.444
of this intellectual property,

00:02:23.444 --> 00:02:26.949
whether it's trademarks,
copyrights, patents,

00:02:26.949 --> 00:02:29.021
we've got to pay this
entity right over here

00:02:29.021 --> 00:02:32.449
some amount of money to use
that intellectual property.

00:02:32.449 --> 00:02:33.504
So let's say that they say,

00:02:33.504 --> 00:02:38.424
we're going to pay them,
I don't know, $800,000,

00:02:38.424 --> 00:02:40.429
and this is essentially transfer pricing.

00:02:40.429 --> 00:02:43.215
In theory, there should
be a way of deciding

00:02:43.215 --> 00:02:46.249
what is the fair rate for
that intellectual property,

00:02:46.249 --> 00:02:48.896
but often times that intellectual
property is fairly unique,

00:02:48.896 --> 00:02:50.809
so it's hard to determine a market rate,

00:02:50.809 --> 00:02:52.309
which really just leaves this company

00:02:52.309 --> 00:02:54.029
to decide it for itself.

00:02:54.029 --> 00:02:56.809
So let's go into that reality,

00:02:56.809 --> 00:02:58.956
where instead of this reality,

00:02:58.956 --> 00:03:02.524
this company, before it had
a million in pre-tax profits,

00:03:02.524 --> 00:03:06.161
but now it's paying 800,000
in royalties and licensing

00:03:06.161 --> 00:03:08.001
to this entity right over here.

00:03:08.001 --> 00:03:13.001
So out of that one million, you
have 800,000 going offshore.

00:03:13.490 --> 00:03:18.356
You have 800,000 goes offshore.

00:03:18.356 --> 00:03:21.210
And so, the real pre-tax
profit for this company now,

00:03:21.210 --> 00:03:23.489
based on accounting for it this way,

00:03:23.489 --> 00:03:26.969
based on paying this
subsidiary that's offshore

00:03:26.969 --> 00:03:30.049
for use of the intellectual property,

00:03:30.049 --> 00:03:35.049
the company now has 200K
in pre-tax profits, 200K.

00:03:37.223 --> 00:03:39.604
So that was before the licensing.

00:03:39.604 --> 00:03:41.090
Now this is after the licensing.

00:03:41.090 --> 00:03:43.589
This is the new pre-tax number.

00:03:43.589 --> 00:03:45.645
This is the new pre-tax number.

00:03:45.645 --> 00:03:50.613
And so in the U.S., it would
only pay 35% of the $200,000.

00:03:50.613 --> 00:03:53.709
Instead of paying $350,000 in taxes,

00:03:53.709 --> 00:03:55.489
it would now pay--

00:03:55.489 --> 00:03:57.575
So it's no longer 350 in taxes.

00:03:57.575 --> 00:04:02.575
Thirty-five percent of 200K
is 70K in taxes, 70K in taxes,

00:04:03.829 --> 00:04:07.149
and the U.S., I guess you
could say parent company,

00:04:07.149 --> 00:04:12.149
would show a profit of 200K
minus the 70K of $130,000.

00:04:13.389 --> 00:04:17.115
So, 130,000, I would call it net profit,

00:04:17.115 --> 00:04:20.409
or we could say post-tax profit.

00:04:20.409 --> 00:04:21.969
And then, this character right over here,

00:04:21.969 --> 00:04:23.335
let's say it has very minimal costs.

00:04:23.335 --> 00:04:25.588
Let's say it has no
costs, for simplification.

00:04:25.588 --> 00:04:27.989
It would have some, to do some paperwork.

00:04:27.989 --> 00:04:29.941
All of this would essentially be profit.

00:04:29.941 --> 00:04:32.116
Maybe have a few thousand
dollars in costs,

00:04:32.116 --> 00:04:34.116
but we'll ignore that for now.

00:04:34.116 --> 00:04:36.329
So all of this would
be its pre-tax profit.

00:04:36.329 --> 00:04:38.533
It would have to pay 5% of it.

00:04:38.533 --> 00:04:42.329
Five percent in taxes to
this country right over here.

00:04:42.329 --> 00:04:46.509
So 5% of 800,000 is $40,000.

00:04:46.509 --> 00:04:49.107
So it would pay 40,000 in taxes

00:04:49.107 --> 00:04:52.732
to the government of this
island right over here,

00:04:52.732 --> 00:04:57.049
and then it would be left
with the remainder, $760,000.

00:04:57.049 --> 00:05:00.192
So, it would have 760,000.

00:05:00.192 --> 00:05:02.384
I guess you could call
that it's net profit,

00:05:02.384 --> 00:05:06.629
after paying taxes, net profit.

00:05:06.629 --> 00:05:08.409
So you can see here the company saved

00:05:08.409 --> 00:05:10.389
substantially on taxes.

00:05:10.389 --> 00:05:14.169
It paid 70,000 in the
U.S. and 40,000 abroad.

00:05:14.169 --> 00:05:17.069
So it paid a total of 110,000 in taxes

00:05:17.069 --> 00:05:20.669
versus the 350,000 it
would have had to pay

00:05:20.669 --> 00:05:24.882
if it was based purely,
purely in the United States.

00:05:24.882 --> 00:05:26.929
So you might say, hey,
this is a great thing.

00:05:26.929 --> 00:05:29.849
Companies, why even have
an 800,000 transfer price?

00:05:29.849 --> 00:05:30.653
Why not do a million?

00:05:30.653 --> 00:05:33.809
And, obviously, if you do it
a little bit too ridiculously,

00:05:33.809 --> 00:05:35.341
it'll get more and more scrutiny.

00:05:35.341 --> 00:05:38.412
So there's some balancing influence there,

00:05:38.412 --> 00:05:39.804
and obviously if there is a market

00:05:39.804 --> 00:05:41.282
for this intellectual property

00:05:41.282 --> 00:05:43.329
or that type of intellectual property,

00:05:43.329 --> 00:05:45.189
or if you are licensing to other people,

00:05:45.189 --> 00:05:46.739
that might dictate what this is,

00:05:46.739 --> 00:05:49.529
but you might say, why
not do this night and day?

00:05:49.529 --> 00:05:51.649
Well, the question is,
you now have this profit,

00:05:51.649 --> 00:05:53.964
and it might be in the form of cash.

00:05:53.964 --> 00:05:56.609
We go into other videos in more
depth when it might not be.

00:05:56.609 --> 00:05:58.289
But you have essentially this profit,

00:05:58.289 --> 00:06:00.589
but you won't be able to get
it back into the United States

00:06:00.589 --> 00:06:02.909
without paying a tax on it.

00:06:02.909 --> 00:06:04.219
So if you want to get it
back in the United States,

00:06:04.219 --> 00:06:05.387
and that's actually the check.

00:06:05.387 --> 00:06:09.829
The reason why we do tax
repatriation of funds

00:06:09.829 --> 00:06:12.369
is so that companies can't
do this night and day,

00:06:12.369 --> 00:06:13.973
essentially transfer profits abroad

00:06:13.973 --> 00:06:15.909
and then bring the cash back in.

00:06:15.909 --> 00:06:17.849
In order to close this loophole,

00:06:17.849 --> 00:06:22.849
that's why the repatriation of these funds

00:06:23.679 --> 00:06:25.532
are actually taxed.

00:06:25.532 --> 00:06:26.432
And I'll let you think about,

00:06:26.432 --> 00:06:27.344
and it obviously depends on

00:06:27.344 --> 00:06:30.012
what the transfer prices
are and things like that,

00:06:30.012 --> 00:06:33.692
but essentially what this
tax rate would have to be

00:06:33.692 --> 00:06:36.627
in order for a company
to come out neutral.

00:06:36.627 --> 00:06:38.232
And there's other ways
of getting around it,

00:06:38.232 --> 00:06:39.862
and I'll do other videos later,

00:06:39.862 --> 00:06:43.412
of ways that this cash can be put to use,

00:06:43.412 --> 00:06:45.812
and it still is not actually taxed.


Monte Carlo Simulation to Answer LeBron's Question

WEBVTT
Kind: captions
Language: en

00:00:02.469 --> 00:00:04.694
LeBron: It's LeBron here. I got
a quick brain teaser for you.

00:00:04.694 --> 00:00:07.076
If I'm down 3 with 30 seconds left

00:00:07.076 --> 00:00:09.029
is it better to take the 3?

00:00:09.029 --> 00:00:12.230
Or is it easier to take
the 2 and attempt to fowl a

00:00:12.230 --> 00:00:15.197
bad free throw shooter and
get another possession?

00:00:15.197 --> 00:00:18.096
Here's my friend Sal with an answer.

00:00:18.096 --> 00:00:21.697
Sal: That's a very very
interesting question, LeBron.

00:00:21.697 --> 00:00:24.139
Calculating the probabilities
of if you were to take a 3

00:00:24.139 --> 00:00:25.954
what's your probability of tying the game

00:00:25.954 --> 00:00:27.442
and then being able to win in overtime

00:00:27.442 --> 00:00:29.199
that can be done on paper

00:00:29.199 --> 00:00:32.231
but the scenario where you take
a 2 and you attempt to fowl

00:00:32.231 --> 00:00:34.445
the opposing team and
they might make none or 1

00:00:34.445 --> 00:00:36.810
or two free-throws and then
you might get another posession

00:00:36.810 --> 00:00:37.971
and then you take another 2

00:00:37.971 --> 00:00:40.171
That's more complicated. You
could attempt to do it on paper

00:00:40.171 --> 00:00:43.407
but instead, I've written a
little computer simulation here

00:00:43.407 --> 00:00:46.972
and this type of a simulation is called
a Monte-Carlo simulation and literally,

00:00:46.972 --> 00:00:49.696
it'll run the scenarios and
it will do it as many times

00:00:49.696 --> 00:00:52.844
as we put in this variable over
here. So we're gonna set it up

00:00:52.844 --> 00:00:55.174
so we get an accurate number.
We're gonna do it a THOUSAND times

00:00:55.174 --> 00:00:58.798
for each of those scenarios and
see what fraction in each scenario

00:00:58.798 --> 00:01:02.365
which fraction do we end up winning?
And that's a pretty good estimate

00:01:02.365 --> 00:01:05.450
of the probability of us
actually winning the game

00:01:05.450 --> 00:01:08.030
depending on which strategy we choose.

00:01:08.030 --> 00:01:11.804
The rest of these things, these
variables that we set right over here

00:01:11.804 --> 00:01:14.605
these are the parameters
that will essentially drive

00:01:14.605 --> 00:01:17.279
the outcomes. This three-point
percentage, this is your

00:01:17.279 --> 00:01:19.774
three-point percentage, I have
it low here because I'm assuming

00:01:19.774 --> 00:01:22.231
it's going to be a hard 3.
It's going to be lower than

00:01:22.231 --> 00:01:24.530
a typical 3 point percentage.

00:01:24.530 --> 00:01:25.844
But obviously if this
number, if you set it higher

00:01:25.844 --> 00:01:27.947
than the three will look
better. If you set it lower

00:01:27.947 --> 00:01:29.576
than the 2 is going to look better.

00:01:29.576 --> 00:01:32.357
This is your 2 point
percentage. I'm assuming here

00:01:32.357 --> 00:01:35.128
it's going to be a relatively
easy 2 because the other

00:01:35.128 --> 00:01:37.698
team isn't going to be defending
as heavily against a 2.

00:01:37.698 --> 00:01:40.664
So I put it a little higher but
you can play with the numbers

00:01:40.664 --> 00:01:42.809
to see what you get in
different scenarios.

00:01:42.809 --> 00:01:46.309
This is the probability of
the opponent taking a 2,

00:01:46.309 --> 00:01:47.822
this is the opponent's
free-throw percentage.

00:01:47.822 --> 00:01:50.087
Once again if this is very
high than the fowling is not

00:01:50.087 --> 00:01:53.211
going to look as good. If this is
low the fowling might make sense.

00:01:53.211 --> 00:01:55.792
And I put this a little bit
lower than the league average

00:01:55.792 --> 00:01:58.370
because I'm assuming
you'll attempt to fowl

00:01:58.370 --> 00:02:00.714
or you have a reasonable chance of fowling
one of the weaker free-throw shooters.

00:02:00.714 --> 00:02:04.214
This is how much time goes off
the clock when you take a 2

00:02:04.214 --> 00:02:09.375
This is how long it takes you to
fowl. This is offensive rebound

00:02:09.375 --> 00:02:10.270
percentage. And then I have a slightly

00:02:10.270 --> 00:02:12.017
different thing that I separated out is

00:02:12.017 --> 00:02:17.637
the, the percent chance of
a team taking a free-throw.

00:02:17.637 --> 00:02:20.898
If they miss their second free-throw the
percent chance that they'll actually be

00:02:20.898 --> 00:02:23.690
able to rebound it. So that's
15% you can play with that

00:02:23.690 --> 00:02:26.140
And this is just a probability,or
your percent chance of

00:02:26.140 --> 00:02:29.352
winning in overtime. And
I just put that at 50/50

00:02:29.352 --> 00:02:32.074
and the rest of this really
just uses those parameters

00:02:32.074 --> 00:02:34.938
to go through the simulations.
This is a little code

00:02:34.938 --> 00:02:37.943
right over here just to draw the
background or actually load the images

00:02:37.943 --> 00:02:40.609
This is the meat. These two functions.

00:02:40.609 --> 00:02:42.835
So take 3 is a scenario
where we go for the 3.

00:02:42.835 --> 00:02:46.187
So we try to make the 3,
if we make the 3 then we

00:02:46.187 --> 00:02:49.185
have essentially tied the game
and now we're going into overtime

00:02:49.185 --> 00:02:51.798
and if we win in overtime, then we win!

00:02:51.798 --> 00:02:53.628
If neither of those things are true,

00:02:53.628 --> 00:02:55.185
or if one of those things
end up not being true

00:02:55.185 --> 00:02:57.235
either we make the 3 and
we lose in overtime, or we

00:02:57.235 --> 00:03:00.357
don't make the 3, then
false, we didn't win.

00:03:00.357 --> 00:03:03.109
And this function is going to
be called as many times as that

00:03:03.109 --> 00:03:05.138
variable trials. So it could
be called a thousand times

00:03:05.138 --> 00:03:07.467
a million times, whatever we
set it to, to figure out what

00:03:07.467 --> 00:03:09.688
fraction of the scenarios do we win in?

00:03:09.688 --> 00:03:13.963
This does the same thing for the
taking the 2 and trying to fowl.

00:03:13.963 --> 00:03:16.690
It gets a little bit more
complicated but it's not too bad.

00:03:16.690 --> 00:03:19.328
And it's a very simple simulation, I
think a lot of people listening might

00:03:19.328 --> 00:03:23.718
be able to add some,
little bit more complexity

00:03:23.718 --> 00:03:26.048
to maybe make it a
little bit more accurate.

00:03:26.048 --> 00:03:28.330
But what it does, it keeps
of who has the posession,

00:03:28.330 --> 00:03:30.722
how many points you're
down,how much time is left,

00:03:30.722 --> 00:03:33.721
and the way I implimented it, it
really only works for specific

00:03:33.721 --> 00:03:35.716
scenario we talked about. You would
probably want to make it fancier

00:03:35.716 --> 00:03:38.268
if you had more time on
the clock or if you wanted

00:03:38.268 --> 00:03:43.121
to cover more scenarios of different

00:03:43.121 --> 00:03:45.140
point spreads. But this
is essentially saying,

00:03:45.140 --> 00:03:47.463
look, while we're gonna
keep running this scenario,

00:03:47.463 --> 00:03:51.094
while there's time left on the
clock, this clause is talking about

00:03:51.094 --> 00:03:53.017
what do we do if we have the possession?

00:03:53.017 --> 00:03:58.465
If we're down by more than 3,
then we're gonna want to take

00:03:58.480 --> 00:04:00.041
it as quickly as possible and
we just take the minimum time

00:04:00.041 --> 00:04:05.087
off necessary to shoot a 2.
Otherwise, we would acutally

00:04:05.117 --> 00:04:07.517
want to run down the
clock. So if we happened,

00:04:07.547 --> 00:04:09.594
for whatever reason while going
through this over and over again

00:04:09.594 --> 00:04:12.395
to be up, we would probably
want to run the clock down

00:04:12.395 --> 00:04:15.760
before we take a shot. Now
this right over here says,

00:04:15.760 --> 00:04:17.923
remember, this is a scenario
where we're taking a 2,

00:04:17.923 --> 00:04:21.666
so this says, okay, lets try
to go for the 2 if we make it,

00:04:21.666 --> 00:04:26.726
then we're down by 2 less. And then we,
the possession goes to the other team.

00:04:26.726 --> 00:04:33.222
If we do not make it, does
the opposing team rebound it?

00:04:33.222 --> 00:04:35.801
So this is essentially
saying, if the opposing team

00:04:35.801 --> 00:04:38.416
makes the rebound, so we
did not make the offensive

00:04:38.416 --> 00:04:41.501
rebound, then they now
have the possession.

00:04:41.501 --> 00:04:45.895
This clause over is, what about the
cases where we don't have the possession?

00:04:45.895 --> 00:04:52.368
This is essentially what we say
if we're down by a more than

00:04:52.368 --> 00:04:55.425
zero points than we're
going to try to fowl.

00:04:55.425 --> 00:04:57.925
We're going to take the
time off the clock to fowl.

00:04:57.925 --> 00:05:02.146
Then the opponent is going
to take their two free-throws

00:05:02.146 --> 00:05:04.402
right over here, and there's
a little bit of code to see

00:05:04.402 --> 00:05:08.897
if in the situation that they
missed the second free-throw,

00:05:08.897 --> 00:05:12.202
there's some probability that
the opponant might actually

00:05:12.202 --> 00:05:15.493
be able to get the offensive rebound, so
we actually put that in there as well.

00:05:15.493 --> 00:05:21.282
Then there's the scenarios where
maybe we just happen not to be down,

00:05:21.282 --> 00:05:26.948
in which case, the opponent
is likely to take a 2.

00:05:26.948 --> 00:05:29.278
At least we assume that.
This is a case where I think

00:05:29.278 --> 00:05:32.118
other people could modify
it more. The bottom line is

00:05:32.118 --> 00:05:35.892
if we're not down, we
definitely do not want to fowl.

00:05:35.892 --> 00:05:38.162
So we're not fowling in this scenario.

00:05:38.162 --> 00:05:41.268
Remember, we're in this 2 point scenario.

00:05:41.268 --> 00:05:45.201
This essentially says,
look, when the clock ends,

00:05:45.201 --> 00:05:48.225
when time goes to zero, if
we're down by more than zero

00:05:48.225 --> 00:05:50.278
we lost. If we're down by
less than zero, we won.

00:05:50.278 --> 00:05:54.068
Otherwise, it's tied
and we go into overtime.

00:05:54.068 --> 00:05:58.832
So this clause right over here
tests to see if we win in overtime.

00:05:58.832 --> 00:06:01.059
All of the other things
are really just to draw.

00:06:01.059 --> 00:06:03.802
This draws the bars, this draws
some of the numbers on top of it

00:06:03.802 --> 00:06:07.355
Then, this is we actually run the trial.

00:06:07.355 --> 00:06:10.633
So we call this as many
times as there are trials

00:06:10.633 --> 00:06:13.256
that trials variables, and
we count how many times

00:06:13.256 --> 00:06:15.633
do we win taking a 3? How many
times do we lose taking a 3?

00:06:15.633 --> 00:06:18.292
How many times do we win
taking a 2? How many times

00:06:18.292 --> 00:06:22.353
lose taking a 2? Then we just
display everything right over there.

00:06:22.353 --> 00:06:25.767
Now that we have a decent
understanding of the program

00:06:25.767 --> 00:06:29.066
itself, let's get a
little bit of a drumroll,

00:06:29.066 --> 00:06:31.061
and see whether it makes
sense to take the 3,

00:06:31.061 --> 00:06:33.032
given these assumptions.
Instead of having ten trials

00:06:33.032 --> 00:06:35.736
let's give it a big number.
Let's say a thousand trials,

00:06:35.736 --> 00:06:39.047
let me reset this this thing.
So restart it right over here.

00:06:39.047 --> 00:06:42.629
You see its getting better approximations.

00:06:42.629 --> 00:06:45.794
This is what fraction of
the trial so far resulted in

00:06:45.794 --> 00:06:48.592
a victory. So right now taking
a 2, looks like it's about

00:06:48.592 --> 00:06:54.049
15-16%, looks like we got
a victory. Here its 12-13%

00:06:54.049 --> 00:06:56.547
As we got more and more trials
we're more likely to have

00:06:56.547 --> 00:07:00.901
a much much more accurate
sense of our probabilities.

00:07:00.901 --> 00:07:02.992
A more accurate approximation
of the probabilities.

00:07:02.992 --> 00:07:06.157
But let's see, it's getting close...

00:07:06.157 --> 00:07:15.546
And we get... 2. Well based on
this, it looks like there's...

00:07:15.546 --> 00:07:17.956
Based on the assumptions that
we made, and this is important,

00:07:17.956 --> 00:07:20.290
based on these assumptions, it
looks like we were better off

00:07:20.290 --> 00:07:25.545
by a little bit, slightly higher,
taking the easy 2 then trying to fowl.

00:07:25.545 --> 00:07:28.590
But if we change things, and
I'll make it lower trials

00:07:28.590 --> 00:07:32.714
so that we don't have to wait all
day, let's make it 300 trials,

00:07:32.714 --> 00:07:35.762
if you were to raise your
3 point percentage to say,

00:07:35.762 --> 00:07:40.376
let's say it's 35% and let's
say the 2 is much harder

00:07:40.376 --> 00:07:43.792
than we had before, let's
say its 40% and let's say

00:07:43.792 --> 00:07:45.994
your opponent is a really
good free-throw shooter

00:07:45.994 --> 00:07:50.506
so let's say it's 80%, I suspect that
you will have a different outcome.

00:07:50.506 --> 00:07:53.400
Let's restart it and see what happens.

00:07:53.400 --> 00:07:58.925
Now all of a sudden, it looks
like you're much better off

00:07:58.925 --> 00:08:03.999
given these assumptions. You're much
better off going for the 3 to tie.

00:08:03.999 --> 00:08:07.212
and go into overtime. So these
are really the assumptions

00:08:07.212 --> 00:08:11.000
that drive it for this simulation.


How to solve one-step equations

WEBVTT
Kind: captions
Language: en

00:00:00.042 --> 00:00:05.042
Now that we're comfortable with the "why" of why we do something to both sides of an equation,

00:00:05.203 --> 00:00:07.678
let's see if we can apply it to some equations to solve for

00:00:07.678 --> 00:00:16.544
an unknown variable. So let's say that you have x plus seven is equal to ten, and I want to solve for x.

00:00:16.544 --> 00:00:20.329
All its saying is something plus seven is equal to ten, and you might be able to figure that out in your head,

00:00:20.329 --> 00:00:22.873
but if you want to do it a little bit more systematically, you're like well just

00:00:22.873 --> 00:00:26.781
all I want on the left hand side is an x. Well if all I want on the left hand side is an x

00:00:26.781 --> 00:00:33.023
I'd want to get rid of the seven. I want to subtract seven from the left-hand side, but if I want to maintain an equality

00:00:33.023 --> 00:00:38.729
here, whatever I do to the left-hand side I also have to do to the right-hand side going back to our scales

00:00:38.729 --> 00:00:43.677
that's so that we can keep our scale balanced, so that we can say that the left is still equal to the right.

00:00:43.677 --> 00:00:50.564
And so what we're going to be left with is x and then the sevens cancel out

00:00:50.564 --> 00:00:56.493
is equal to ten minus seven is equal to three. So that unknown is three,

00:00:56.493 --> 00:01:01.562
and you can verify it, three plus seven is indeed equal to ten.

00:01:01.562 --> 00:01:10.749
Let's try one more. Let's say we have a minus five is equal to negative two.

00:01:10.749 --> 00:01:15.395
So this is a little bit more interesting since we have all of these negative numbers here, but we can use

00:01:15.395 --> 00:01:19.727
the exact same logic. We just want an a over here on the left-hand side

00:01:19.727 --> 00:01:23.023
so we have to get rid of this negative five somehow.

00:01:23.023 --> 00:01:26.244
Well the best way of getting rid of a negative 5 is to add five to it.

00:01:26.244 --> 00:01:30.630
So I'll do that. So I will add five to the left-hand side.

00:01:30.630 --> 00:01:34.311
But if I want the left-hand side to stay equal to the right-hand side,

00:01:34.311 --> 00:01:36.348
whatever I do to the left I have to do the right.

00:01:36.348 --> 00:01:40.193
So I'm going to have to add five on the right-hand side as well,

00:01:40.193 --> 00:01:48.755
and so on the left-hand side I'm left with a, and then the negative five and the positive five cancel out

00:01:48.755 --> 00:01:53.179
and on the right hand side, and they're going to stay equal because I did the same thing to both sides,

00:01:53.179 --> 00:01:57.424
we have negative two plus five which is equal to three.

00:01:57.424 --> 00:02:02.362
So a is equal to three. Once again you can verify it.

00:02:02.362 --> 00:02:06.362
Three minus five is indeed equal to negative two.


How to use the one-step equation intuition exercise

WEBVTT
Kind: captions
Language: en

00:00:00.650 --> 00:00:03.544
Now you've got your
chance to use this scale

00:00:03.544 --> 00:00:05.210
to figure out how
much something weighs.

00:00:05.210 --> 00:00:08.310
So we're asked, how much
does Old Spice Man weigh?

00:00:08.310 --> 00:00:11.750
We have Old Spice Man,
this little guy here, plus

00:00:11.750 --> 00:00:12.900
you have 3 blocks.

00:00:12.900 --> 00:00:14.316
So on the left-hand
side, you have

00:00:14.316 --> 00:00:15.746
Old Spice Man plus 3 blocks.

00:00:15.746 --> 00:00:17.370
And you see that the
scale is balanced.

00:00:17.370 --> 00:00:19.170
On the right hand side,
you have 8 blocks.

00:00:19.170 --> 00:00:23.049
So Old Spice Man plus
3 is equal to 8 blocks.

00:00:23.049 --> 00:00:25.090
And you can see what
happens when we do something

00:00:25.090 --> 00:00:26.950
to one side of the
scale or another.

00:00:26.950 --> 00:00:30.060
If we were to take a block
from the right-hand side, all

00:00:30.060 --> 00:00:32.100
of a sudden, the right-hand
side becomes lighter

00:00:32.100 --> 00:00:33.260
and it tilts up.

00:00:33.260 --> 00:00:35.140
And our scale is
no longer balanced,

00:00:35.140 --> 00:00:37.090
and we can no longer
say that the left

00:00:37.090 --> 00:00:38.540
and the right-hand
side is equal.

00:00:38.540 --> 00:00:41.390
And there's an explanation
of it below here.

00:00:41.390 --> 00:00:43.464
So what we want to do
is add or remove blocks

00:00:43.464 --> 00:00:44.880
from the left or
right-hand sides.

00:00:44.880 --> 00:00:46.480
So essentially we're
just left with Old Spice

00:00:46.480 --> 00:00:48.900
Man on the left-hand side,
but the scale is balanced.

00:00:48.900 --> 00:00:50.540
So whatever is on
the right-hand side

00:00:50.540 --> 00:00:53.150
is how much he weighs in blocks.

00:00:53.150 --> 00:00:54.530
So let's see if we can do that.

00:00:54.530 --> 00:00:57.050
So let me add that block back.

00:00:57.050 --> 00:00:58.810
That's where we started from.

00:00:58.810 --> 00:01:01.060
So let's see, I want
to get rid of these 3.

00:01:01.060 --> 00:01:03.450
So if I take 1 away
from the left-hand side,

00:01:03.450 --> 00:01:05.209
well, I can't just do it there,
because now, all of a sudden,

00:01:05.209 --> 00:01:06.410
the left-hand side is too light.

00:01:06.410 --> 00:01:09.020
So I'm going to have to take 1
away from the right-hand side

00:01:09.020 --> 00:01:10.160
as well.

00:01:10.160 --> 00:01:11.270
Well, let me do it again.

00:01:11.270 --> 00:01:12.770
Take 1 away from
the left-hand side.

00:01:12.770 --> 00:01:15.860
We'll have to do 1 from the
right-hand side as well.

00:01:15.860 --> 00:01:18.720
And I'm getting close-- 1
from the left-hand side,

00:01:18.720 --> 00:01:20.160
now 1 from the right-hand side.

00:01:20.160 --> 00:01:21.520
And it is a balanced.

00:01:21.520 --> 00:01:25.100
Old Spice Man is
equal to 5 blocks.

00:01:25.100 --> 00:01:27.470
And you see what happened
here algebraically.

00:01:27.470 --> 00:01:29.700
I took 1 from the left
and right-hand side.

00:01:29.700 --> 00:01:30.830
I did it 3 times.

00:01:30.830 --> 00:01:33.500
So we started with
essentially Old Spice Man,

00:01:33.500 --> 00:01:35.720
or you could call it x, plus 3.

00:01:35.720 --> 00:01:38.480
But then we ended up subtracting
3 from the left-hand side

00:01:38.480 --> 00:01:40.740
and subtracting 3 from
the right-hand side.

00:01:40.740 --> 00:01:43.400
So we subtracted the same
number from both sides

00:01:43.400 --> 00:01:46.250
to get the weight
of Old Spice Man.

00:01:46.250 --> 00:01:48.490
And we could check
it right over here.

00:01:48.490 --> 00:01:50.680
And very good.