Khan for Educators: Khan Academy’s learning experience

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Language: en

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- So at Khan Academy,

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we are striving to create personalized

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mastery based learning that
transforms student's mindsets.

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And within that I think
there's a three things

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that make our value proposition unique.

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The first is that our content
is provided free of charge

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for teachers and students.

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The second is that we have custom content

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that's aligned to standards
in different countries.

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So in Brazil, to the BNCC.

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Or in the US, to the common core.

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And the third is that

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we are a technology that's not just

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a substitute for paper and pencil,

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and not such a dramatic change

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that it'd be overwhelming

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and you'd have to rethink
everything in your classroom,

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but right in the middle

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to offer an innovative change

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that is not too overwhelming for teachers.

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For us at Khan Academy,

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mastery learning is fairly simple.

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It's that the incentives,
the decisions in class

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should be made based on what students

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are proving they understand consistently.

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And in many cases that happens in tests,

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maybe not 'til the end of year tests,

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but we think it should
be a full year process

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building up to that point.

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Really it's not like a yes or no,

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are you fully mastery based

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or are you not at all mastery based,

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there's a spectrum of ways you can

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change over your classroom
to be more mastery based.

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When it comes to personalization though,

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there's a few things that
are really important.

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The first is that there's the
right content for students.

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And that might not be the same

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for all students in the class.

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And we can help personalize that content,

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but at the end of the
day it is the teacher

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that's going to be most effective

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at personalizing the
content using Khan Academy.

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And second, it's self-paced.

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So that if I need more
practice on a given topic,

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I can have it.

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I can have what we sometimes call

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a functionally infinite
amount of practice.

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If you're not getting it,

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try again, no problem.

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Well when we think about
the student mindset

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that we'd all hope to have,

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both for ourselves and for our students,

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I think it's a student
that believes strongly

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in their own potential,

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and has the learning strategies

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to actually understand difficult material.

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And so there's a few ways we
try to enable that mindset

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for learners on our platform.

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The first is to remove
all barriers to learning.

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So there's the content accessible

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for all students at all times,

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and then there's support
while you're practicing

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if you get stuck.

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And so there's no excuse
to not start learning,

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and to not persist when you're stuck.

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The focus is on you.

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The second though is
processes to get unstuck,

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for lack of a better word.

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And so you're in the middle
of learning and you're stuck,

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which is totally fine.

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It's normal, happens to everyone.

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But right below the practice

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it's gonna say are you stuck?

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Get help.

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There's multiple ways
that you might need help.

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You maybe need a hint, you
maybe need to watch a video,

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you might need to ask your teacher.

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But by going through that process,

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you figure out when the right time is

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to use each of those strategies.

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And then the third is
through encouragement

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that we give on the site,

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whether you're getting
problems right or wrong,

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that reinforces the message

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that it's the effort that counts.

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Student agency is a really popular

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topic right now in education,

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and I think that sometimes
there's a mistake

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that it's going from no
agency to total agency.

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But we really see it as a spectrum.

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And on Khan Academy at a minimum,

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the agency that we think is
important for students to have

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would be to answer some questions like

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am I on track to complete
these assignments?

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What order am I gonna work on them?

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And when do I know if I need help?

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But as you start to show more maturity,

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being able to take
control a little bit more

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of the learning process,

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then you can start to make
some bigger decisions.

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Like what's my actual goal for this week,

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or this month, or the whole school year?

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What matters to me?

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And when I'm done with this content,

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are there other subjects
that I want to explore

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on my own that aren't even required?

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So the learning experience
on Khan Academy.

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Well it could be different
from student to student,

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I like to think of one student's
experience in particular.

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So his name is Damien,

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he's an 11 year old in southern
California, Los Angeles,

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but I think his experience could

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be typical of students in Sao Paolo,

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or anywhere around the world.

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But there were a few
things about his experience

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that I think were really important,

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and that I took away from

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the ideal experience on Khan Academy.

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So the first is that he had a
really clear goal for the year

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that his teacher had provided
for him on Khan Academy.

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And every time he logged in,

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the first thing he saw was

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his progress toward that big goal.

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But combined with that big goal,

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each day as he was practicing,

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he had really detailed support,

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both instructional support

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through the videos and articles,

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and then the practice support

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through the exercises and
challenges and unit tests.

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And not only that,

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but he also had his
teacher there as a resource

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if the instructional
resources weren't enough.

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And there was this combination
of his teacher, Ms Choo

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being an expert about
how to use Khan Academy,

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but also Damien having
some freedom and choice

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and agency to move on if he was done.

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To have his own freedom to choose

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what he was gonna work on that day.

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So that balance between the teacher

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really being able to guide
Damien towards the right material

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but him also having freedom and control

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over his learning process.

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So you've got the big goal
and the detailed support,

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and you've got the teacher as the expert,

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but the student still having the freedom.

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And that's I think what makes

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the learning experience
distinct on Khan Academy.


Khan for Educators: Khan Academy's Mission

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Language: en

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- I am Sal Khan, founder of the
not-for-profit Khan Academy.

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As you probably know,
we have a big mission,

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to provide a free world-class education

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for anyone, anywhere.

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And we know that the most important people

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in that mission are you, the teacher.

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And so that's why from the beginning,

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Khan Academy has always
worked closely with teachers

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to be able to create tools for teachers

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so that they can use
it with their students

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and allow the students' learning

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to happen as well as possible.

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And so that's why we're excited

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that you are a part of this training.

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Because I've always said, if I had to pick

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between an amazing teacher
and amazing technology,

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I would pick the amazing
teacher every time.

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The good thing is we don't
have to make that trade-off.

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And so, here at Khan Academy,

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we are trying to build tools for you,

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tools that will make your life easier,

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that will save you time,

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and will help you serve
your students better.

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- So Khan Academy is an online
educational set of resources.

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It is a combination of world-class content

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that spans from kindergarten
all the way to 12th grade,

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and in some cases, the first
and second year of college.

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And then we span across many subjects.

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There's two pieces that I
think makes it very unique.

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One is not just world-class content,

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but it's taught in a way that
is very easy to understand.

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We also build a lot of what we call

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social-emotional learning
elements into the platform.

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'Cause learning is hard.

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It can be intimidating.

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You could feel under-confident,

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you could feel not very smart,

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learning something that's very new to you.

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So our product of content and software,

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the combination of both,

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we try to make it so
it's easy to understand,

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that it's fun, that's it's
engaging, that it motivates you,

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that it helps build your self-confidence

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so that you can start
to be a self-motivated,

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independent learner, to
be a lifelong learner.

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And what makes us unique

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is those elements of not just the content

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but the social-emotional
learning part of the software,

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as well as we have a lot
of built-in intelligence

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to know exactly where you are

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and all the steps that you need to learn.

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So we have this thing
called a Knowledge Map

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inside our product that let's you say,

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"Gosh, if I wanna learn calculus some day,

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"I need to know these
foundational elements first,

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"and then I can build on
top," sort of like a house.

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We have the foundational elements,

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and then you know how to
build the first story,

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and then you put the second story,

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and we connect all those dots for you.

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Our reach and our scale today,

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we are in over 190
countries across the world.

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We are translated in over 30
languages across the world

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by amazing advocates,
volunteers that help us do this

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because they believe
so much in our mission.

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And it does really take a
village to make that happen.

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It is unfortunate there's a misconception

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of us wanting to replace the teacher.

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Absolutely not.

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There is no way that we
can replace the teacher.

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They are such an important
part of the student's life.

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For us, it's about providing tools

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and functionality for the teacher

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to empower them, to give them agency,

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to be better than they can ever be,

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to be more efficient,
to be more effective.

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So tools and insights that we can do

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to help the teacher so that they can

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be the best that they can
be for these students.

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The people at Khan Academy are amazing.

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I am so blessed to run this company

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because the people, I have 200 plus people

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whose sole goal is to enable
this mission to happen.

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They just want to really
transform the educational industry

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to really help those
under-served children.

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And that's what they eat,
breathe, and sleep, every day.

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- So we're excited that
you're part of this training.

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Hopefully, you will find everything

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that we are able to provide
to you to be of use.

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And we are looking forward

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to getting your feedback
about how together

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we can better serve you and your students.

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Thank you.


Khan for Educators: Welcome to Khan for Educators

WEBVTT
Kind: captions
Language: en

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- Hello teachers, I'm Meaghan.

00:00:05.670 --> 00:00:07.420
Welcome to Khan for Educators,

00:00:07.420 --> 00:00:10.830
initial course for
teachers on Khan Academy.

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You are about to begin an
exciting learning journey.

00:00:13.800 --> 00:00:17.583
But first, let's look together
at the path that lies ahead.

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To get started click the
start training button

00:00:22.710 --> 00:00:24.430
to begin learning.

00:00:24.430 --> 00:00:27.890
This course has one unit
composed of seven lessons

00:00:27.890 --> 00:00:29.500
in which we explore everything

00:00:29.500 --> 00:00:31.760
from getting started on Khan Academy

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to classroom implementation

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and diving deeper into Khan
Academy's teacher reports.

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The course begins with the lesson

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Getting to know Khan Academy.

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Which shares a little about our commitment

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to high quality education,
and the learning experience

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we hope to provide.

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Then we have the lesson
Setting up you teacher account,

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which covers the main teacher functions,

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setting up classes, an overview
of Khan Academy content,

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and a walkthrough of
the student experience.

00:01:01.760 --> 00:01:04.350
The third lesson, Introduction
to mastery learning

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provides a broad overview
of mastery learning

00:01:07.280 --> 00:01:09.420
and address frequently asked questions

00:01:09.420 --> 00:01:11.590
relating to mastery learning.

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The fourth lesson, Using
course mastery on Khan Academy

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dives deeper into Khan Academy's
mastery learning system.

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This lesson includes a cursory look

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at Khan Academy's progress reports

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and showcases teacher insights

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on using progress data with students.

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Lesson five, Using assignments
to support mastery learning

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details how to create and
manage student assignments

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and how to leverage Khan
Academy's assignment report

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to support mastery learning with students.

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Lesson six focuses on implementing

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Khan Academy with students.

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In this lesson we go
further into the logistics

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of using Khan Academy with students

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including our recommended
implementation model,

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classroom best practices,
and student motivation.

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In lesson seven, teaching
remotely with Khan Academy,

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we explore implementation recommendations

00:02:03.150 --> 00:02:04.730
and tips for teaching students

00:02:04.730 --> 00:02:07.370
beyond the walls of your classroom.

00:02:07.370 --> 00:02:09.930
These resources are
designed to support teachers

00:02:09.930 --> 00:02:12.570
and students in remote
learning experiences

00:02:12.570 --> 00:02:15.673
using Khan Academy and
other educational tools.

00:02:16.600 --> 00:02:19.480
The course concludes
with a next step section

00:02:19.480 --> 00:02:21.420
that explores the different opportunities

00:02:21.420 --> 00:02:24.400
for further education so
you can continue to learn

00:02:24.400 --> 00:02:26.610
and innovate in your classes.

00:02:26.610 --> 00:02:28.820
Khan for Educators was designed

00:02:28.820 --> 00:02:31.960
so teachers, coaches, and administrators

00:02:31.960 --> 00:02:35.290
could experience Khan Academy as students.

00:02:35.290 --> 00:02:37.620
So in order to complete the course

00:02:37.620 --> 00:02:39.890
you'll need to engage with exercises,

00:02:39.890 --> 00:02:44.090
master skills, and perform
well on the final assessment.

00:02:44.090 --> 00:02:46.320
But don't worry, there's
a reward for those

00:02:46.320 --> 00:02:47.763
who complete this journey.

00:02:48.689 --> 00:02:50.630
Your professional
learning is in your hands,

00:02:50.630 --> 00:02:53.740
start Khan for Educators
initial course right now

00:02:53.740 --> 00:02:56.290
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00:02:56.290 --> 00:02:58.403
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00:02:59.340 --> 00:03:01.350
Do you have any questions
about the course?

00:03:01.350 --> 00:03:04.230
Access the help center
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00:03:04.230 --> 00:03:05.063
See you soon.


Incorporating opposing viewpoints

WEBVTT
Kind: captions
Language: en

00:00:01.630 --> 00:00:03.080
- [David] Hello, readers.

00:00:03.080 --> 00:00:05.060
Let's argue.

00:00:05.060 --> 00:00:07.580
In writing, argument is a kind of fight.

00:00:07.580 --> 00:00:09.210
But I think it is unwise

00:00:09.210 --> 00:00:13.050
to think of it as a one-way conversation.

00:00:13.050 --> 00:00:16.150
The best arguments do not
plunge forward heedlessly.

00:00:16.150 --> 00:00:18.440
They do not steamroll opposition.

00:00:18.440 --> 00:00:21.220
Rather, they seek out opposing arguments

00:00:21.220 --> 00:00:22.930
and incorporate them.

00:00:22.930 --> 00:00:25.670
Good readers pay attention
to how authors acknowledge

00:00:25.670 --> 00:00:28.100
opposing viewpoints in an argument.

00:00:28.100 --> 00:00:29.980
Doing this makes it easier to decide

00:00:29.980 --> 00:00:31.750
how well thought out an argument is

00:00:31.750 --> 00:00:34.320
and determine whether the
author is knowledgeable

00:00:34.320 --> 00:00:36.970
and thoughtful in their position.

00:00:36.970 --> 00:00:39.820
Now, I do not practice the
martial art of Wing Chun.

00:00:39.820 --> 00:00:43.470
But that style of self-defense
is famous for techniques

00:00:43.470 --> 00:00:46.590
that block and strike at the same time.

00:00:46.590 --> 00:00:48.100
Your opponent's fist comes in,

00:00:48.100 --> 00:00:49.720
you redirect it away from your body,

00:00:49.720 --> 00:00:52.680
and in that same motion
continue your momentum

00:00:52.680 --> 00:00:55.610
into its own immediate counterstrike.

00:00:55.610 --> 00:00:57.970
Acknowledging the existence
of opposing viewpoints

00:00:57.970 --> 00:01:01.370
has two main applications,
which are pretty different.

00:01:01.370 --> 00:01:04.250
First, maybe you're not on
any side of the argument

00:01:04.250 --> 00:01:07.660
and you wish to straightforwardly
describe the conflict,

00:01:07.660 --> 00:01:10.010
like a journalist reporting on a lawsuit.

00:01:10.010 --> 00:01:11.640
It's a journalist's responsibility

00:01:11.640 --> 00:01:14.400
to truthfully portray the
full scope of information

00:01:14.400 --> 00:01:17.310
on a topic, bringing
every piece of relevant

00:01:17.310 --> 00:01:19.850
and plausible information to bear.

00:01:19.850 --> 00:01:22.220
The author provides equal
time to the disputants

00:01:22.220 --> 00:01:25.230
and tries not to provide
their own opinion here.

00:01:25.230 --> 00:01:27.010
That could look like this.

00:01:27.010 --> 00:01:30.170
Ms. Adeyemi contended that
Mr. Dupont stole the cookies

00:01:30.170 --> 00:01:32.110
from her cookie jar, and that furthermore,

00:01:32.110 --> 00:01:34.340
she had baked those
cookies in the first place,

00:01:34.340 --> 00:01:37.450
thus strengthening her
claim to the said cookies.

00:01:37.450 --> 00:01:39.750
Of the 24 cookies baked by Ms. Adeyemi,

00:01:39.750 --> 00:01:43.340
she alleges that 10 of them
were taken by Mr. Dupont.

00:01:43.340 --> 00:01:46.180
Mr. Dupont, however, contended
that as he was the person

00:01:46.180 --> 00:01:48.220
who made the cookie jar for Ms. Adeyemi

00:01:48.220 --> 00:01:49.610
in the ceramics class he took,

00:01:49.610 --> 00:01:52.240
he is entitled to the occasional cookie.

00:01:52.240 --> 00:01:54.480
He does not dispute the 10-cookie figure,

00:01:54.480 --> 00:01:57.110
adding only that they were "delicious."

00:01:57.110 --> 00:02:00.110
Judge Huang, upon reviewing
testimony from both parties,

00:02:00.110 --> 00:02:01.620
sided with Ms. Adeyemi,

00:02:01.620 --> 00:02:03.800
saying that you are not
entitled to a cookie

00:02:03.800 --> 00:02:05.800
just for being a good friend one time,

00:02:05.800 --> 00:02:09.690
and that next time, Mr. Dupont
should ask for permission.

00:02:09.690 --> 00:02:11.350
Now, looking at that situation,

00:02:11.350 --> 00:02:13.710
my personal opinion is
that it is inappropriate

00:02:13.710 --> 00:02:14.950
to steal your friend's cookies.

00:02:14.950 --> 00:02:17.700
An opinion that any right-thinking
person should share.

00:02:17.700 --> 00:02:22.300
But injecting opinion may not
be appropriate in all cases.

00:02:22.300 --> 00:02:24.200
So okay, that's the first case.

00:02:24.200 --> 00:02:26.010
Reporting on multiple sides of a dispute

00:02:26.010 --> 00:02:28.470
without getting involved yourself.

00:02:28.470 --> 00:02:29.610
Now, the second reason,

00:02:29.610 --> 00:02:32.800
the second application for
including opposing viewpoints

00:02:32.800 --> 00:02:34.440
in an argumentative piece of writing

00:02:34.440 --> 00:02:38.240
is that Wing Chun thing, the
block as you strike technique.

00:02:38.240 --> 00:02:39.620
It makes your argument stronger

00:02:39.620 --> 00:02:42.020
if you anticipate
possible objections to it,

00:02:42.020 --> 00:02:44.190
address them, and strike them down

00:02:44.190 --> 00:02:48.000
all the while still making your
argument in the first place.

00:02:48.000 --> 00:02:50.090
Let's take this example from the website.

00:02:50.090 --> 00:02:53.080
This piece is about the
lost colony at Roanoke.

00:02:53.080 --> 00:02:55.380
A bunch of English settlers disappeared

00:02:55.380 --> 00:02:59.240
under uncertain circumstances
for reasons still unknown.

00:02:59.240 --> 00:03:00.570
And the author's trying to make the case

00:03:00.570 --> 00:03:03.140
that although theories for
the disappearance exist,

00:03:03.140 --> 00:03:05.850
the truth is still beyond our grasp.

00:03:05.850 --> 00:03:07.270
So in order to make that case,

00:03:07.270 --> 00:03:08.930
they address several different theories

00:03:08.930 --> 00:03:11.123
that attempt to explain the disappearance.

00:03:12.410 --> 00:03:14.710
Many people have tried
to solve the mystery

00:03:14.710 --> 00:03:16.280
of the lost colony.

00:03:16.280 --> 00:03:19.060
Historians and archeologists
have searched for answers

00:03:19.060 --> 00:03:20.600
for hundreds of years.

00:03:20.600 --> 00:03:22.310
Some possible solutions are:

00:03:22.310 --> 00:03:25.660
A, Native people killed the
colonists on Roanoke Island.

00:03:25.660 --> 00:03:27.400
B, the colonists were all killed

00:03:27.400 --> 00:03:29.070
on Roanoke Island by disease.

00:03:29.070 --> 00:03:31.410
C, their town was washed
away by a hurricane,

00:03:31.410 --> 00:03:32.550
and the people drowned.

00:03:32.550 --> 00:03:34.720
Or D, they all left Roanoke Island

00:03:34.720 --> 00:03:37.310
and went to live in some other place.

00:03:37.310 --> 00:03:39.790
Now, watch what the author
does as they systematically

00:03:39.790 --> 00:03:42.010
go through each theory and address it.

00:03:42.010 --> 00:03:44.220
I've only excepted the first two,

00:03:44.220 --> 00:03:46.170
so let's look at those first two.

00:03:46.170 --> 00:03:50.030
A, when John White got back
to Roanoke Island in 1590

00:03:50.030 --> 00:03:52.350
he did not find any bones or bodies

00:03:52.350 --> 00:03:54.200
or any signs of fighting.

00:03:54.200 --> 00:03:56.090
Bones last a long time.

00:03:56.090 --> 00:03:58.070
If Native people had killed the colonists,

00:03:58.070 --> 00:03:59.930
there would probably
have been some remains

00:03:59.930 --> 00:04:01.980
or other signs of violence.

00:04:01.980 --> 00:04:03.270
We can guess that the colonists

00:04:03.270 --> 00:04:06.060
were not killed on Roanoke Island.

00:04:06.060 --> 00:04:09.040
B, when the English
first came to Virginia,

00:04:09.040 --> 00:04:10.790
they're using a 16th-century spelling,

00:04:10.790 --> 00:04:14.520
they brought diseases with
them, such as flu and smallpox,

00:04:14.520 --> 00:04:16.460
that were new to the Native communities.

00:04:16.460 --> 00:04:17.960
They had no immunity against them

00:04:17.960 --> 00:04:19.820
and many died very quickly.

00:04:19.820 --> 00:04:21.390
Letters written by the colonists

00:04:21.390 --> 00:04:23.350
tell us that the English remained healthy.

00:04:23.350 --> 00:04:26.970
And remember, no bones or
bodies or graves were found.

00:04:26.970 --> 00:04:30.330
We can guess that the colonists
did not all die of disease.

00:04:30.330 --> 00:04:33.300
So the author's saying that
these events are unlikely,

00:04:33.300 --> 00:04:34.760
taking the theories seriously,

00:04:34.760 --> 00:04:37.030
and then thinking them
through to their conclusions.

00:04:37.030 --> 00:04:38.730
But demonstrating why they don't seem

00:04:38.730 --> 00:04:40.500
very likely explanations.

00:04:40.500 --> 00:04:42.040
Why do they think it's unlikely

00:04:42.040 --> 00:04:44.110
that Native people killed those colonists?

00:04:44.110 --> 00:04:46.653
There aren't any remains
or signs of combat.

00:04:47.500 --> 00:04:50.290
Why does it seem unlikely
that they died of diseases?

00:04:50.290 --> 00:04:52.270
There are no graves or remains.

00:04:52.270 --> 00:04:54.310
The thesis is, nobody knows why.

00:04:54.310 --> 00:04:57.030
Here are two counters to it
basically saying here's why,

00:04:57.030 --> 00:04:59.880
and the author says here's why
these are unlikely to be true

00:04:59.880 --> 00:05:01.580
which weakens those counterarguments

00:05:01.580 --> 00:05:03.620
and strengthens the original.

00:05:03.620 --> 00:05:05.900
Block, strike.

00:05:05.900 --> 00:05:07.940
My overall point is this.

00:05:07.940 --> 00:05:11.250
Don't ignore the potential
counters to your argument.

00:05:11.250 --> 00:05:13.300
Incorporate them, analyze them,

00:05:13.300 --> 00:05:16.740
and redirect their energy
into your own position.

00:05:16.740 --> 00:05:17.870
And when you read,

00:05:17.870 --> 00:05:20.430
notice if the author is
acknowledging counters

00:05:20.430 --> 00:05:21.840
or ignoring them.

00:05:21.840 --> 00:05:25.520
If they ignore them, you
should be suspicious.

00:05:25.520 --> 00:05:27.970
Why are they ignoring them?

00:05:27.970 --> 00:05:31.053
If you can answer that,
then you can learn anything.

00:05:31.890 --> 00:05:32.723
David out.


Analyzing tone through word choice

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:03.080
- [David] Hello readers,
I suppose it's time,

00:00:03.080 --> 00:00:06.470
if we have to to talk about tone.

00:00:06.470 --> 00:00:10.900
You see, if I were feeling snide
or dismissive or sarcastic,

00:00:10.900 --> 00:00:13.060
I'd use a lot of disdainful language

00:00:13.060 --> 00:00:15.240
to talk about how little
I valued this topic,

00:00:15.240 --> 00:00:17.990
which is a piddling trifle, a Bagatelle,

00:00:17.990 --> 00:00:19.363
a trivial, little nothing.

00:00:20.260 --> 00:00:23.520
Far more likely though,
considering my love of languages,

00:00:23.520 --> 00:00:27.000
the notion that I'd be
enthusiastic and encouraging,

00:00:27.000 --> 00:00:28.880
I would say understanding tone

00:00:28.880 --> 00:00:31.670
unlocks a treasure house of understanding,

00:00:31.670 --> 00:00:34.040
it is a feast of knowledge.

00:00:34.040 --> 00:00:35.756
Tone communicates how an author feels

00:00:35.756 --> 00:00:37.940
about the topic they're writing about,

00:00:37.940 --> 00:00:40.100
this can come across in a
number of different ways,

00:00:40.100 --> 00:00:43.270
it can reflect their
enthusiasm or skepticism,

00:00:43.270 --> 00:00:46.650
it can also communicate
formality or informality,

00:00:46.650 --> 00:00:48.882
an academic paper or a
speech before the UN,

00:00:48.882 --> 00:00:51.230
for example are very different things

00:00:51.230 --> 00:00:53.190
from a toast at a wedding

00:00:53.190 --> 00:00:55.670
or a thank you card for a birthday gift

00:00:55.670 --> 00:00:57.700
and this kind of difference
in tone is something

00:00:57.700 --> 00:01:01.170
that sociologists and
linguists call register.

00:01:01.170 --> 00:01:02.870
Social conventions and customs

00:01:02.870 --> 00:01:06.390
call for different registers
in different circumstances,

00:01:06.390 --> 00:01:09.090
just as it would be
inappropriate in most situations

00:01:09.090 --> 00:01:11.060
to wear a tuxedo at the beach,

00:01:11.060 --> 00:01:12.850
so too would it be incongruous

00:01:12.850 --> 00:01:16.470
to use extremely formal
language in an informal setting?

00:01:16.470 --> 00:01:17.617
(melodic orchestral music)

00:01:17.617 --> 00:01:20.250
(clearing throat) Dear honored sir,

00:01:20.250 --> 00:01:22.610
it was the privilege of my very life

00:01:22.610 --> 00:01:25.660
to have you attend my 14th birthday party.

00:01:25.660 --> 00:01:29.250
I am grateful beyond words
for your most generous gift,

00:01:29.250 --> 00:01:31.553
a check for $36 American.

00:01:32.420 --> 00:01:36.480
Your humble and obedient servant, David.

00:01:36.480 --> 00:01:38.910
In fact using extremely formal language

00:01:38.910 --> 00:01:40.310
and high-minded gratitude

00:01:40.310 --> 00:01:43.226
for something as relatively
small as a birthday gift

00:01:43.226 --> 00:01:46.541
might even come across as
sarcastic or insulting.

00:01:46.541 --> 00:01:48.950
But this is sort of an extreme example,

00:01:48.950 --> 00:01:52.320
let's pull back and discuss
how an understanding of tone

00:01:52.320 --> 00:01:56.010
can aid you in making sense
of informational texts.

00:01:56.010 --> 00:01:59.740
One great way to do that
is to analyze word choice,

00:01:59.740 --> 00:02:01.690
we can look at a writer's language

00:02:01.690 --> 00:02:04.130
and determine their
attitude towards the subject

00:02:04.130 --> 00:02:06.763
based on the words they've
chosen to describe it.

00:02:07.640 --> 00:02:09.550
Oceans of ink have been spilled

00:02:09.550 --> 00:02:12.100
over comparisons between
a Chicago style hotdog

00:02:12.100 --> 00:02:13.870
and a New York style hotdog.

00:02:13.870 --> 00:02:16.470
The first with its
garden's worth of toppings,

00:02:16.470 --> 00:02:19.270
but a holier than now
prohibition of ketchup,

00:02:19.270 --> 00:02:21.390
the latter with its sauerkraut, mustard

00:02:21.390 --> 00:02:24.070
and dubious dirty water cooking style.

00:02:24.070 --> 00:02:27.650
But scant attention, a droplet
of ink before the ocean

00:02:27.650 --> 00:02:30.060
has been paid to the half-smoke,

00:02:30.060 --> 00:02:35.060
the unsung but mighty regional
sausage of Washington DC.

00:02:35.130 --> 00:02:38.370
Now how does the author
think about the subject?

00:02:38.370 --> 00:02:39.350
Well, we know that they think

00:02:39.350 --> 00:02:40.820
that not enough writing has been done

00:02:40.820 --> 00:02:43.040
about DC's regional
sausage, the half-smoke,

00:02:43.040 --> 00:02:44.751
but how do they feel about it?

00:02:44.751 --> 00:02:47.840
How do the words they use
express their feelings?

00:02:47.840 --> 00:02:49.520
Let's break it down bit by bit.

00:02:49.520 --> 00:02:52.830
So right out of the gate,
we have oceans of ink,

00:02:52.830 --> 00:02:54.293
this is a deliberate
piece of overstatement,

00:02:54.293 --> 00:02:56.312
there are no literal oceans made of ink,

00:02:56.312 --> 00:03:00.100
but it's being set up in
opposition to the droplet of ink

00:03:00.100 --> 00:03:03.066
used to describe half-smokes
later in the paragraph.

00:03:03.066 --> 00:03:06.480
Half-smokes are described
as unsung, but mighty,

00:03:06.480 --> 00:03:08.377
which suggests that they
haven't been given their due,

00:03:08.377 --> 00:03:10.885
there hasn't been enough
praise for half-smokes

00:03:10.885 --> 00:03:12.870
and that therefore the amount of attention

00:03:12.870 --> 00:03:14.980
given to Chicago and New York hotdogs

00:03:14.980 --> 00:03:18.216
is unfair or even disproportionate.

00:03:18.216 --> 00:03:20.309
I think we can also
determine from word choice,

00:03:20.309 --> 00:03:22.730
that the author thinks a Chicago hot dog

00:03:22.730 --> 00:03:23.780
is a little ridiculous

00:03:23.780 --> 00:03:25.955
and that a New York hot
dog is a little gross.

00:03:25.955 --> 00:03:27.890
How do we know this?

00:03:27.890 --> 00:03:30.530
Chicagoans generally don't
like ketchup on their hotdogs

00:03:30.530 --> 00:03:32.211
and the way the author
phrases this is by saying,

00:03:32.211 --> 00:03:35.722
that they have a holier than
thou prohibition on ketchup,

00:03:35.722 --> 00:03:38.618
which is to say they get all
haughty and upset about it,

00:03:38.618 --> 00:03:41.100
which is weird because it's ketchup,

00:03:41.100 --> 00:03:42.410
listen, I'm a Chicagoan by birth,

00:03:42.410 --> 00:03:45.450
I used to feel this way
and I'm not even sure why.

00:03:45.450 --> 00:03:47.879
Similarly the word
dubious in the description

00:03:47.879 --> 00:03:50.350
of the New York hotdog, meaning doubtful

00:03:50.350 --> 00:03:52.630
suggests that the dirty
water cooking method

00:03:52.630 --> 00:03:56.150
is kind of nasty sounding,
why would the author do this?

00:03:56.150 --> 00:03:58.210
Is it to say these are terrible hot dogs

00:03:58.210 --> 00:03:59.090
and nobody should eat them?

00:03:59.090 --> 00:04:00.500
No, I don't think so,

00:04:00.500 --> 00:04:03.430
The author is trying to
make room for the half-smoke

00:04:03.430 --> 00:04:06.147
in the national sausage
conversation and to do that,

00:04:06.147 --> 00:04:08.960
they're first trying to
dismantle the importance

00:04:08.960 --> 00:04:12.212
of New York and Chicago
style by making fun of them.

00:04:12.212 --> 00:04:13.860
These are tactical choices,

00:04:13.860 --> 00:04:16.460
not to be confused with authorial voice,

00:04:16.460 --> 00:04:20.090
which is a different concept entirely

00:04:20.090 --> 00:04:22.950
an author's voice is their style,

00:04:22.950 --> 00:04:25.460
it's much more consistent across topics,

00:04:25.460 --> 00:04:28.023
whereas a tone is specific to a topic.

00:04:29.120 --> 00:04:31.170
So I might have an authorial voice,

00:04:31.170 --> 00:04:33.120
that uses a lot of goofy wordplay,

00:04:33.120 --> 00:04:35.980
but I use a sympathetic
tone to talk about bears

00:04:35.980 --> 00:04:39.480
and a hostile tone to talk
about, I don't know, whales,

00:04:39.480 --> 00:04:43.090
yeah, boo whales, I said it.

00:04:43.090 --> 00:04:45.290
I do not actually hate
whales, I love whales.

00:04:45.290 --> 00:04:49.250
But my point is this, use
your knowledge of words,

00:04:49.250 --> 00:04:51.881
of the connotation and
implications of the language,

00:04:51.881 --> 00:04:53.700
that an author might use

00:04:53.700 --> 00:04:56.940
to unlock your
understanding of their tone,

00:04:56.940 --> 00:04:59.500
because if you can do that, my friend,

00:04:59.500 --> 00:05:02.233
you can learn anything, David out.


Free live tutoring at schoolhouse.world

WEBVTT
Kind: captions
Language: en

00:00:00.870 --> 00:00:03.000
- Hi, everyone, Sal here from Khan Academy

00:00:03.000 --> 00:00:04.790
and I just wanted to make an announcement

00:00:04.790 --> 00:00:07.670
of something that I think
many of you will find useful.

00:00:07.670 --> 00:00:09.820
I have a little bit of
a side project going on

00:00:09.820 --> 00:00:12.140
called schoolhouse.world.

00:00:12.140 --> 00:00:14.780
It isn't an official Khan Academy project,

00:00:14.780 --> 00:00:16.990
but it's a way to get free tutoring.

00:00:16.990 --> 00:00:20.140
Yes, I'm talking about free live tutoring.

00:00:20.140 --> 00:00:23.240
What happens on schoolhouse.world
is you as a student

00:00:23.240 --> 00:00:25.390
can go and say what areas

00:00:25.390 --> 00:00:26.850
and we're starting with high school math,

00:00:26.850 --> 00:00:29.170
what areas of high school
math you need help in

00:00:29.170 --> 00:00:31.820
and you can see existing tutoring sessions

00:00:31.820 --> 00:00:35.030
that are scheduled in the
coming days and coming weeks

00:00:35.030 --> 00:00:38.040
and on the other side,
we have volunteer tutors

00:00:38.040 --> 00:00:42.230
who look at what students,
what you, might need help in

00:00:42.230 --> 00:00:45.010
and will schedule these
group tutoring sessions.

00:00:45.010 --> 00:00:47.810
So whether you're interested
in being a student

00:00:47.810 --> 00:00:50.010
and getting some free live help

00:00:50.010 --> 00:00:52.550
or that you're interested
in being a tutor or both,

00:00:52.550 --> 00:00:54.030
check out schoolhouse.world.

00:00:54.030 --> 00:00:55.930
There's a little bit of
a registration process.

00:00:55.930 --> 00:00:59.010
This is really a startup project right now

00:00:59.010 --> 00:00:59.950
where we're trying to make sure

00:00:59.950 --> 00:01:02.200
we balance the tutors and the students,

00:01:02.200 --> 00:01:03.340
but I'll tell you right now

00:01:03.340 --> 00:01:06.360
we have an incredible
number of amazing tutors

00:01:06.360 --> 00:01:08.960
and actually we're looking
for more students to tutor.

00:01:08.960 --> 00:01:11.400
So check it out, fill out the form

00:01:11.400 --> 00:01:14.127
and you will be able to get some help

00:01:14.127 --> 00:01:15.560
and the view is you can learn

00:01:15.560 --> 00:01:17.870
at your own time and pace on Khan Academy.

00:01:17.870 --> 00:01:20.950
Obviously we have the
exercises, the feedback there.

00:01:20.950 --> 00:01:22.240
You have the videos.

00:01:22.240 --> 00:01:24.500
We just launched our Get
Ready for Grade Level courses.

00:01:24.500 --> 00:01:25.770
You can use that as well.

00:01:25.770 --> 00:01:28.070
And then when you need in-person help,

00:01:28.070 --> 00:01:30.423
you can go to schoolhouse.world.


Interpreting trigonometric graphs in context

WEBVTT
Kind: captions
Language: en

00:00:00.310 --> 00:00:02.570
- [Instructor] We're told Alexa
is riding on a Ferris wheel.

00:00:02.570 --> 00:00:04.400
Her height above the ground in meters

00:00:04.400 --> 00:00:08.010
is modeled by H of t where
t is the time in seconds.

00:00:08.010 --> 00:00:10.670
And we can see that right over here.

00:00:10.670 --> 00:00:12.900
Now what I want to focus on this video

00:00:12.900 --> 00:00:14.900
is some features of this graph.

00:00:14.900 --> 00:00:16.620
And the features we're gonna focus on,

00:00:16.620 --> 00:00:19.790
actually the first of them,
is going to be the midline.

00:00:19.790 --> 00:00:21.810
So pause this video and
see if you can figure out

00:00:21.810 --> 00:00:25.450
the midline of this graph, or
the midline of this function.

00:00:25.450 --> 00:00:26.440
And then we're going to think about

00:00:26.440 --> 00:00:28.073
what it actually represents.

00:00:29.500 --> 00:00:33.020
Well, Alexia starts off at
five meters above the ground

00:00:33.020 --> 00:00:34.590
and then she goes higher,
and higher, and higher,

00:00:34.590 --> 00:00:36.330
and gets as high as 25 meters,

00:00:36.330 --> 00:00:39.410
and then goes back as low as
five meters above the ground,

00:00:39.410 --> 00:00:41.030
and as high as 25 meters.

00:00:41.030 --> 00:00:43.080
And what we can view the midline as

00:00:43.080 --> 00:00:45.890
is the midpoint between these extremes,

00:00:45.890 --> 00:00:48.080
or the average of these extremes.

00:00:48.080 --> 00:00:50.720
Well, the extremes are
she goes as low as five

00:00:50.720 --> 00:00:52.290
and as high as 25.

00:00:52.290 --> 00:00:54.540
So what's the average of five and 25?

00:00:54.540 --> 00:00:56.120
Well, that would be 15.

00:00:56.120 --> 00:00:59.430
So the midline would
look something like this.

00:00:59.430 --> 00:01:01.950
And I'm actually gonna
keep going off the graph.

00:01:01.950 --> 00:01:03.840
And the reason is is
to help us think about

00:01:03.840 --> 00:01:07.110
what does that midline even represent.

00:01:07.110 --> 00:01:09.170
And one way to think about it is

00:01:09.170 --> 00:01:13.720
it represents the center of
our rotation in this situation,

00:01:13.720 --> 00:01:15.620
or how high above the ground

00:01:15.620 --> 00:01:18.160
is the center of our Ferris wheel?

00:01:18.160 --> 00:01:21.060
And to help us visualize that,
let me draw a Ferris wheel.

00:01:22.350 --> 00:01:27.023
So I'm going to draw a circle
with this as the center.

00:01:28.520 --> 00:01:33.520
And so the Ferris wheel would
look something like this.

00:01:36.060 --> 00:01:39.493
And it has some type of
maybe support structure.

00:01:40.910 --> 00:01:45.890
So the Ferris wheel might
look something like that.

00:01:45.890 --> 00:01:48.623
And this height above the ground,

00:01:49.720 --> 00:01:54.720
that is 15 meters, that is what
the midline is representing.

00:01:55.690 --> 00:02:00.690
Now the next feature I want
to explore is the amplitude.

00:02:01.440 --> 00:02:04.650
Pause this video and think
about what is the amplitude

00:02:04.650 --> 00:02:06.660
of this oscillating
function right over here

00:02:06.660 --> 00:02:08.640
and then we'll think about
what does that represent

00:02:08.640 --> 00:02:09.670
in the real world,

00:02:09.670 --> 00:02:11.920
or where does it come
from in the real world?

00:02:13.150 --> 00:02:17.300
Well the amplitude is
the maximum difference

00:02:17.300 --> 00:02:20.290
or the maximum magnitude
away from that midline.

00:02:20.290 --> 00:02:21.851
And you can see it right over here.

00:02:21.851 --> 00:02:25.690
Actually right when Alexa starts

00:02:25.690 --> 00:02:30.690
we have starting 10
meters below the midline,

00:02:30.990 --> 00:02:32.740
10 meters below the center,

00:02:32.740 --> 00:02:36.770
and this is when Alexa is right over here.

00:02:36.770 --> 00:02:40.210
She is 10 meters below the midline.

00:02:40.210 --> 00:02:44.550
And then after, it looks like 10 seconds,

00:02:44.550 --> 00:02:46.780
she is right at the midline.

00:02:46.780 --> 00:02:49.290
So that means that she is right over here.

00:02:49.290 --> 00:02:51.050
Maybe the Ferris wheel is going this way,

00:02:51.050 --> 00:02:53.970
at least in my imagination
it's going clockwise.

00:02:53.970 --> 00:02:57.510
And then after another 10
seconds she is at 25 meters.

00:02:57.510 --> 00:03:01.300
So she is right over there.

00:03:01.300 --> 00:03:02.190
And you could see that.

00:03:02.190 --> 00:03:05.140
She is right over there, I
drew that circle intentionally

00:03:05.140 --> 00:03:06.600
of that size.

00:03:06.600 --> 00:03:10.700
And so we see the
amplitude in full effect.

00:03:10.700 --> 00:03:14.380
10 meters below to begin the
midline and 10 meters above.

00:03:14.380 --> 00:03:18.070
And so it's the maximum displacement

00:03:18.070 --> 00:03:22.190
or the maximum change from that midline.

00:03:22.190 --> 00:03:27.150
And so over here it really
represents the radius

00:03:27.150 --> 00:03:30.180
of our Ferris wheel, 10 meters.

00:03:30.180 --> 00:03:33.450
And then from this part she
starts going back down again.

00:03:33.450 --> 00:03:37.100
And then over here she's
back to where she started.

00:03:37.100 --> 00:03:40.160
Now the last feature I want to explore

00:03:40.160 --> 00:03:42.720
is the notion of a period.

00:03:42.720 --> 00:03:45.500
What is the period of
this periodic function?

00:03:45.500 --> 00:03:47.383
Pause this video and think about that.

00:03:48.280 --> 00:03:50.350
Well the period is how
much time does it take

00:03:50.350 --> 00:03:51.940
to complete one cycle.

00:03:51.940 --> 00:03:54.010
So here she's starting at the bottom.

00:03:54.010 --> 00:03:56.550
And let's see, after 10
seconds, not at the bottom yet.

00:03:56.550 --> 00:03:58.180
After 20 seconds, not at the bottom yet.

00:03:58.180 --> 00:03:59.870
After 30 seconds, not at the bottom yet.

00:03:59.870 --> 00:04:01.980
And then here she is, after 40 seconds,

00:04:01.980 --> 00:04:04.940
she's back at the bottom
and about to head up again.

00:04:04.940 --> 00:04:09.710
And so this time right
over here, that 40 seconds,

00:04:09.710 --> 00:04:11.160
that is the period.

00:04:11.160 --> 00:04:13.010
And if you think about
what's going on over here,

00:04:13.010 --> 00:04:15.580
she starts over here five
meters above the ground.

00:04:15.580 --> 00:04:18.867
After 10 seconds she is right over here,

00:04:18.867 --> 00:04:21.250
and that corresponds to
this point right over here.

00:04:21.250 --> 00:04:23.200
After 10 more seconds
she's right over there.

00:04:23.200 --> 00:04:24.690
That corresponds to that point.

00:04:24.690 --> 00:04:26.760
After 10 more seconds she's over here.

00:04:26.760 --> 00:04:28.080
That corresponds to that.

00:04:28.080 --> 00:04:31.120
And after 10 more seconds,
or total of 40 seconds,

00:04:31.120 --> 00:04:33.540
she's back to where she started.

00:04:33.540 --> 00:04:35.770
So the period in this example

00:04:35.770 --> 00:04:39.930
shows how long does it take
to complete one full rotation.

00:04:39.930 --> 00:04:41.350
Now we have to be careful sometimes

00:04:41.350 --> 00:04:44.170
when we're trying to
visually inspect the period

00:04:44.170 --> 00:04:45.650
because sometimes it might be tempting

00:04:45.650 --> 00:04:47.557
to say, "Start right over here,

00:04:47.557 --> 00:04:49.857
"and say okay, we're 15
meters above the ground.

00:04:49.857 --> 00:04:51.647
"All right, let's see, we're going down.

00:04:51.647 --> 00:04:53.057
"Now we're going up again.

00:04:53.057 --> 00:04:55.257
"And look, we're 15
meters above the ground.

00:04:55.257 --> 00:04:58.090
"Maybe this 20 seconds is a period."

00:04:58.090 --> 00:04:59.710
But when you look at it over here

00:04:59.710 --> 00:05:01.530
it's clear that that is not the case.

00:05:01.530 --> 00:05:03.790
This point represents this point

00:05:03.790 --> 00:05:05.700
at being 15 meters above the ground,

00:05:05.700 --> 00:05:08.800
going down, that's
getting us to this point,

00:05:08.800 --> 00:05:11.670
and then after another 10
seconds we get back over here.

00:05:11.670 --> 00:05:14.290
Notice, all this is
measuring is half of a cycle

00:05:14.290 --> 00:05:15.950
going halfway around.

00:05:15.950 --> 00:05:17.210
In order to go all the way around

00:05:17.210 --> 00:05:19.850
not only do we have to get
to the same exact height,

00:05:19.850 --> 00:05:21.790
but we have to be moving
in the same direction.

00:05:21.790 --> 00:05:23.570
We're at 15 meters and going down.

00:05:23.570 --> 00:05:25.940
Here we're at 15 meters and going up.

00:05:25.940 --> 00:05:27.980
So we have to keep going anther 20 seconds

00:05:27.980 --> 00:05:32.883
in order to be 15 meters
in the air, and going down.


Graph labels and scales

WEBVTT
Kind: captions
Language: en

00:00:00.669 --> 00:00:03.840
- [Instructor] We're told that
Chloe takes a slice of pizza

00:00:03.840 --> 00:00:07.700
out of the freezer and leaves
it on the counter to defrost.

00:00:07.700 --> 00:00:09.819
She models the relationship

00:00:09.819 --> 00:00:12.980
between the temperature P of the pizza.

00:00:12.980 --> 00:00:14.430
This seems like it's
going to be interesting.

00:00:14.430 --> 00:00:18.312
The temperature P of the
pizza in degrees Celsius,

00:00:18.312 --> 00:00:23.312
and time T since she took it
out of the freezer in minutes.

00:00:24.200 --> 00:00:29.200
As P is equal to 20 minus 25 times 0.8

00:00:30.510 --> 00:00:31.720
to the T power.

00:00:31.720 --> 00:00:36.430
So that's how she's modeling
her temperature of the pizza.

00:00:36.430 --> 00:00:39.960
P as a function of time.

00:00:39.960 --> 00:00:42.040
She wants to graph the relationship

00:00:42.040 --> 00:00:45.110
over the first 25 minutes.

00:00:45.110 --> 00:00:47.291
So what we're going to do
here is not so much focus

00:00:47.291 --> 00:00:48.780
on the graph itself

00:00:48.780 --> 00:00:50.640
although we will look at that.

00:00:50.640 --> 00:00:52.550
I'm actually just going to
use a graphing calculator

00:00:52.550 --> 00:00:55.200
in order to have access to the graph.

00:00:55.200 --> 00:00:57.403
But I wanna look at the
graph in the context

00:00:57.403 --> 00:00:59.760
of what we are trying to model

00:00:59.760 --> 00:01:02.870
and carefully think about
what should be the labels

00:01:02.870 --> 00:01:04.320
for the axes,

00:01:04.320 --> 00:01:07.073
what parts of the graph are interesting?

00:01:08.270 --> 00:01:09.103
So this is right

00:01:09.103 --> 00:01:12.570
over here is this function
graphed on Desmos.

00:01:12.570 --> 00:01:14.570
You can see I typed it in right over here.

00:01:14.570 --> 00:01:15.403
P is equal

00:01:15.403 --> 00:01:19.300
to 20 minus 25 times 0.8 to the T power.

00:01:19.300 --> 00:01:22.521
Exactly what we had down here.

00:01:22.521 --> 00:01:25.950
Now remember, this is
modeling the temperature

00:01:25.950 --> 00:01:29.300
of our pizza as a function of time.

00:01:29.300 --> 00:01:33.550
So to help us remember that,
let's put in some labels

00:01:33.550 --> 00:01:35.280
for our axes.

00:01:35.280 --> 00:01:37.720
So to graph, settings.

00:01:37.720 --> 00:01:40.340
If I go down here, our x-axis.

00:01:40.340 --> 00:01:43.980
Now our x-axis is really the T-axis.

00:01:43.980 --> 00:01:46.360
That's our independent variable over here.

00:01:46.360 --> 00:01:49.183
And what is it measuring?

00:01:49.183 --> 00:01:51.080
Well it says it right over here.

00:01:51.080 --> 00:01:54.064
It's measuring time T in minutes.

00:01:54.064 --> 00:01:55.970
So we could write it like this.

00:01:55.970 --> 00:01:59.973
T, which is measured in minutes.

00:02:00.810 --> 00:02:03.942
And then, what about our y-axis?

00:02:03.942 --> 00:02:07.510
Well this is really our P-axis

00:02:07.510 --> 00:02:10.580
and that's measuring degrees Celsius.

00:02:10.580 --> 00:02:12.055
So that's our P-axis,

00:02:12.055 --> 00:02:16.330
and it's measuring degrees Celsius.

00:02:21.560 --> 00:02:22.393
All right.

00:02:22.393 --> 00:02:25.140
So let's just look at what
our graph looks like so far.

00:02:25.140 --> 00:02:26.100
So there we have it.

00:02:26.100 --> 00:02:28.650
We've put in our axes and we
have already typed this part

00:02:28.650 --> 00:02:31.810
in so I can focus on the graph itself.

00:02:31.810 --> 00:02:32.890
Now are we done?

00:02:32.890 --> 00:02:35.570
Is this all we need to really think about?

00:02:35.570 --> 00:02:38.050
Well the next part to
think about is the domain

00:02:38.050 --> 00:02:40.150
and what part of the y-axis.

00:02:40.150 --> 00:02:43.870
So what part of the range
are we really interested in?

00:02:43.870 --> 00:02:46.440
Well the first thing to realize
is we're modeling something

00:02:46.440 --> 00:02:47.910
as a function of time.

00:02:47.910 --> 00:02:51.740
And so we really shouldn't
be having negative time here.

00:02:51.740 --> 00:02:53.260
And we wanna think about the relationship

00:02:53.260 --> 00:02:55.570
over the first 25 minutes.

00:02:55.570 --> 00:02:59.910
So let's go back here.

00:02:59.910 --> 00:03:03.108
And when we look at the range of x values

00:03:03.108 --> 00:03:04.180
that we care about,

00:03:04.180 --> 00:03:06.408
and really that we could think
about the part of the domain

00:03:06.408 --> 00:03:08.030
that we care about,

00:03:08.030 --> 00:03:09.917
we wanna restrict to x being greater than

00:03:09.917 --> 00:03:11.690
or equal to zero.

00:03:11.690 --> 00:03:13.480
And obviously in this situation,

00:03:13.480 --> 00:03:16.410
x is really T and then we
can also think about it

00:03:16.410 --> 00:03:17.380
as less than 25.

00:03:17.380 --> 00:03:19.150
We don't have to restrict the upper bound,

00:03:19.150 --> 00:03:23.020
but these are the first 25
minutes that she cares about.

00:03:23.020 --> 00:03:24.620
So let's do it like that.

00:03:24.620 --> 00:03:28.330
And now let's look at our graph.

00:03:28.330 --> 00:03:29.680
And the important things

00:03:29.680 --> 00:03:33.610
to appreciate is that we have the axes.

00:03:33.610 --> 00:03:35.130
We can see them.

00:03:35.130 --> 00:03:38.240
And so at time T is equal to zero,

00:03:38.240 --> 00:03:40.700
we see that we actually
have a negative temperature

00:03:40.700 --> 00:03:42.470
in degrees Celsius, and that makes sense.

00:03:42.470 --> 00:03:43.570
It came out of the freezer

00:03:43.570 --> 00:03:45.510
so it's below freezing.

00:03:45.510 --> 00:03:47.608
And then we see that the pizza is warming

00:03:47.608 --> 00:03:51.130
up as it gets closer and
closer to room temperature,

00:03:51.130 --> 00:03:51.963
which over here,

00:03:51.963 --> 00:03:55.520
looks like it's pretty
close to 20 degrees Celsius.

00:03:55.520 --> 00:03:59.180
And so now it looks like
we have been able to graph

00:03:59.180 --> 00:04:01.650
what Chloe is trying to look at.

00:04:01.650 --> 00:04:03.210
It looks like we have modeled it well,

00:04:03.210 --> 00:04:05.050
we have labeled it accordingly,

00:04:05.050 --> 00:04:09.240
and we have set the ranges
of x values and the ranges

00:04:09.240 --> 00:04:11.220
of y values that we'd wanna look at.

00:04:11.220 --> 00:04:14.415
The y values we just wanna
make sure that over the range

00:04:14.415 --> 00:04:16.280
of x values, and it's really a subset

00:04:16.280 --> 00:04:18.740
of the domain not to confuse
the term range too much.

00:04:18.740 --> 00:04:22.230
The subset of the domain of the
x values that we care about,

00:04:22.230 --> 00:04:24.680
that we can see the
corresponding y values.

00:04:24.680 --> 00:04:27.250
And we very clearly can see them.

00:04:27.250 --> 00:04:28.940
And we're essentially done.

00:04:28.940 --> 00:04:30.370
We've thought about how to best look

00:04:30.370 --> 00:04:31.720
at the graph of this model.


Interpreting expressions with multiple variables: Resistors

WEBVTT
Kind: captions
Language: en

00:00:00.170 --> 00:00:01.940
- [Lecturer] We're told
an electronic circuit

00:00:01.940 --> 00:00:06.320
has two resistors with
resistances R one and R two

00:00:06.320 --> 00:00:08.690
connected in parallel.

00:00:08.690 --> 00:00:10.620
The circuit's total resistance,

00:00:10.620 --> 00:00:15.500
R sub t or Rt is given by this formula.

00:00:15.500 --> 00:00:18.240
Suppose we increase the value R one

00:00:18.240 --> 00:00:20.483
while keeping R two constant.

00:00:22.474 --> 00:00:25.360
Does the value of R sub
t increase, decrease,

00:00:25.360 --> 00:00:27.290
or stay the same?

00:00:27.290 --> 00:00:30.720
So pause the video and see if
you can answer this question.

00:00:30.720 --> 00:00:32.410
All right, now let's work
through this together,

00:00:32.410 --> 00:00:33.980
and some of you might be familiar

00:00:33.980 --> 00:00:37.510
with the idea of an electronic
circuit and resistors,

00:00:37.510 --> 00:00:38.710
and what they represent,

00:00:38.710 --> 00:00:40.920
but you really don't
need to understand that

00:00:40.920 --> 00:00:45.010
in order to understand what's
going on in this expression.

00:00:45.010 --> 00:00:47.850
There's some quantity, R sub t,

00:00:47.850 --> 00:00:49.920
that's equal to 1 over,

00:00:49.920 --> 00:00:52.490
and then in the denominator
we have 1 over R one

00:00:52.490 --> 00:00:54.350
plus 1 over R two.

00:00:54.350 --> 00:00:56.410
So if we increase the value of R one

00:00:56.410 --> 00:00:59.850
So if we increase the value of R one

00:00:59.850 --> 00:01:03.400
while keeping R two
constant, what happens?

00:01:03.400 --> 00:01:05.140
So this is going to increase,

00:01:05.140 --> 00:01:07.790
and R two is going to be constant.

00:01:07.790 --> 00:01:08.840
So one way to think about it,

00:01:08.840 --> 00:01:10.810
we have two variables here,

00:01:10.810 --> 00:01:11.850
especially in this denominator,

00:01:11.850 --> 00:01:13.720
but really, in this entire expression,

00:01:13.720 --> 00:01:16.130
but if R two is going to be constant,

00:01:16.130 --> 00:01:19.750
we really just have to
focus our analysis on R one.

00:01:19.750 --> 00:01:22.000
If R two is constant, that
means it's just a number.

00:01:22.000 --> 00:01:24.600
It could be two, it could
be five, it could be pi.

00:01:24.600 --> 00:01:27.360
Whatever, but that is not going to change

00:01:27.360 --> 00:01:30.070
as we increase the value of R one.

00:01:30.070 --> 00:01:32.060
So let's think about
what's happening here.

00:01:32.060 --> 00:01:33.601
If R sub 1 increases,

00:01:33.601 --> 00:01:36.130
If R sub 1 increases,

00:01:36.130 --> 00:01:40.560
then what does that do to 1 over R one?

00:01:40.560 --> 00:01:42.680
Well, if you increase the denominator,

00:01:42.680 --> 00:01:46.230
then you're going to decrease
the reciprocal of that.

00:01:46.230 --> 00:01:49.240
So that means that this
whole thing right over here

00:01:49.240 --> 00:01:51.670
is going to decrease.

00:01:51.670 --> 00:01:55.040
Now, if 1 over R one is decreasing,

00:01:55.040 --> 00:01:58.810
if 1 over R one is decreasing,

00:01:58.810 --> 00:02:02.619
what's going to happen to 1
over R one plus 1 over R two?

00:02:02.619 --> 00:02:04.680
what's going to happen to 1
over R one plus 1 over R two?

00:02:04.680 --> 00:02:08.600
Will this entire expression
increase or decrease?

00:02:08.600 --> 00:02:10.760
Well, this part is staying constant.

00:02:10.760 --> 00:02:11.850
R two is constant.

00:02:11.850 --> 00:02:13.450
So 1 over R two is constant.

00:02:13.450 --> 00:02:15.180
Just imagine, R two could be two or three.

00:02:15.180 --> 00:02:18.140
So this should just be 1/2
or 1/3 or whatever it is,

00:02:18.140 --> 00:02:22.170
while over here, this part of
the expression is going down.

00:02:22.170 --> 00:02:23.790
So if you're taking the sum of two things,

00:02:23.790 --> 00:02:25.620
one part's going down,
the other part's constant,

00:02:25.620 --> 00:02:28.570
then that means this whole
thing is going to be going down.

00:02:28.570 --> 00:02:30.310
So the entire denominator

00:02:30.310 --> 00:02:33.560
of this entire thing is going down.

00:02:33.560 --> 00:02:36.950
Now, if the entire
denominator is going down,

00:02:36.950 --> 00:02:41.050
if 1 over R one plus 1 over R two,

00:02:41.050 --> 00:02:44.990
if this whole thing is going down,

00:02:44.990 --> 00:02:47.210
what's going to happen to
the reciprocal of that?

00:02:47.210 --> 00:02:51.390
1 over 1 over R one plus 1 over R two.

00:02:51.390 --> 00:02:52.970
Well, if something is going down,

00:02:52.970 --> 00:02:56.610
the reciprocal of that is going to go up.

00:02:56.610 --> 00:02:59.130
If you get smaller and
smaller denominators,

00:02:59.130 --> 00:03:02.320
1 over that is going to be
a larger and larger value.

00:03:02.320 --> 00:03:06.150
So the value or Rt increases

00:03:06.150 --> 00:03:06.983
if R one increases and R two is constant.

00:03:06.983 --> 00:03:11.320
if R one increases and R two is constant.

00:03:11.320 --> 00:03:13.330
And for those of you who
know about resistance,

00:03:13.330 --> 00:03:16.660
which is really how well

00:03:16.660 --> 00:03:18.400
a current can flow through a circuit,

00:03:18.400 --> 00:03:19.940
that will also make intuitive sense,

00:03:19.940 --> 00:03:22.930
but you don't need to
understand resistance

00:03:22.930 --> 00:03:25.953
to analyze this mathematically.


Modeling with multiple variables: Pancakes

WEBVTT
Kind: captions
Language: en

00:00:00.570 --> 00:00:01.680
- [Instructor] We are told that Jade

00:00:01.680 --> 00:00:04.760
is making pancakes using
flour, eggs and milk.

00:00:04.760 --> 00:00:08.530
This table gives the cost per
kilogram of each ingredient

00:00:08.530 --> 00:00:12.920
and the amount in
kilograms that Jade uses.

00:00:12.920 --> 00:00:13.753
All right,

00:00:13.753 --> 00:00:16.713
the total amount Jade
spends on ingredients is $6.

00:00:17.640 --> 00:00:20.820
Write an equation that
relates a, b, c, and d.

00:00:20.820 --> 00:00:23.520
Pause this video and see if
you can have a go at this.

00:00:24.500 --> 00:00:26.480
All right, now let's go
through this together.

00:00:26.480 --> 00:00:28.010
So I like to do these in real time

00:00:28.010 --> 00:00:30.130
so that you can see my thought process.

00:00:30.130 --> 00:00:32.270
So I'm here with you right now.

00:00:32.270 --> 00:00:34.970
So let's see, the total Jade spends,

00:00:34.970 --> 00:00:37.010
and this is going to be
on flour, eggs and milk,

00:00:37.010 --> 00:00:38.560
is going to be $6.

00:00:38.560 --> 00:00:40.990
So one way to think about it is,

00:00:40.990 --> 00:00:42.520
and I'll do this in different colors,

00:00:42.520 --> 00:00:47.520
the flour dollars plus the eggs.

00:00:50.410 --> 00:00:55.210
Eggs dollars, or the amount
that Jade's gonna spend on eggs,

00:00:55.210 --> 00:00:57.800
plus the amount that Jade spends on milk,

00:00:57.800 --> 00:01:00.290
I'll call that the milk dollars,

00:01:00.290 --> 00:01:02.210
is going to be equal to the total amount,

00:01:02.210 --> 00:01:04.783
is going to be equal to $6.

00:01:05.900 --> 00:01:07.350
And so what's the total amount

00:01:07.350 --> 00:01:10.310
that Jade is going to spend on flour?

00:01:10.310 --> 00:01:12.300
Well, we can just look right over here.

00:01:12.300 --> 00:01:16.950
0.9 dollars per kilogram
times a kilograms.

00:01:16.950 --> 00:01:20.490
So Jade's going to spend 0.9a dollars.

00:01:20.490 --> 00:01:22.510
I'm just going to
multiply these two things

00:01:22.510 --> 00:01:25.250
to figure out how much
Jade spends on flour.

00:01:25.250 --> 00:01:28.470
And so this is going to be equal to,

00:01:28.470 --> 00:01:29.930
and I'll lose the dollar symbol

00:01:29.930 --> 00:01:32.540
just so that we can focus on
the numbers and the variables,

00:01:32.540 --> 00:01:37.300
0.9a, 0.9a, and this is, of course,

00:01:37.300 --> 00:01:38.930
is going to be in dollars,
which is important.

00:01:38.930 --> 00:01:40.640
I'm going to add dollars
plus dollars plus dollars

00:01:40.640 --> 00:01:42.090
to get dollars.

00:01:42.090 --> 00:01:43.810
Now what about eggs?

00:01:43.810 --> 00:01:45.435
Well, the same notion.

00:01:45.435 --> 00:01:48.220
0.2 kilograms times b
dollars per kilogram.

00:01:48.220 --> 00:01:50.170
If I take the product of these two,

00:01:50.170 --> 00:01:52.270
I'm gonna get 0.2b dollars.

00:01:54.220 --> 00:01:55.970
Or I could just think of it as 0.2b

00:01:56.948 --> 00:01:58.840
if I don't write the dollar symbol.

00:01:58.840 --> 00:02:01.590
And then last but not least, on milk.

00:02:01.590 --> 00:02:04.510
Let me look at the product
of these two things,

00:02:04.510 --> 00:02:06.560
of this and of this.

00:02:06.560 --> 00:02:09.320
So d kilograms at c dollars per kilogram,

00:02:09.320 --> 00:02:13.783
that's just going to be
cd dollars, so plus cd,

00:02:15.070 --> 00:02:20.070
and all of that is going to be
equal to $6, and we're done.

00:02:20.560 --> 00:02:23.273
We wrote an equation that
relates a, b, c, and d.


Modeling with multiple variables: Roller coaster

WEBVTT
Kind: captions
Language: en

00:00:00.320 --> 00:00:02.940
- [Narrator] We're told a
rollercoaster has C cars,

00:00:02.940 --> 00:00:07.940
each containing 20 seats, and
it completes r rides a day.

00:00:08.360 --> 00:00:12.970
Assuming that no one can
ride it more than once a day,

00:00:12.970 --> 00:00:15.510
the maximum number of people that can ride

00:00:15.510 --> 00:00:18.980
the rollercoaster in a single day is P.

00:00:18.980 --> 00:00:22.620
Write an equation that relates P, c and r.

00:00:22.620 --> 00:00:24.820
Pause this video and
see if you can do that.

00:00:25.760 --> 00:00:27.300
All right, before I even
look at the variables,

00:00:27.300 --> 00:00:29.230
I'm just gonna try to think
it out in plain language.

00:00:29.230 --> 00:00:30.870
So what we want to think about is

00:00:30.870 --> 00:00:35.870
what is the max number of
people per day, people per day,

00:00:39.900 --> 00:00:43.440
and so that's going to be equal to

00:00:43.440 --> 00:00:46.910
the number of cars in our rollercoaster,

00:00:46.910 --> 00:00:49.963
so number of cars,

00:00:50.960 --> 00:00:54.960
times the maximum number
of people per car,

00:00:54.960 --> 00:00:59.960
times the max number per car.

00:01:01.280 --> 00:01:03.000
So this would just tell you

00:01:03.000 --> 00:01:05.770
the maximum number of people per ride.

00:01:05.770 --> 00:01:06.780
So then we have to multiply,

00:01:06.780 --> 00:01:09.330
times the number of rides per day.

00:01:09.330 --> 00:01:12.680
So times we do this in a new color,

00:01:12.680 --> 00:01:17.680
times number of rides per day.

00:01:19.450 --> 00:01:20.670
Now, what are each of these things?

00:01:20.670 --> 00:01:22.050
They would have either given us numbers

00:01:22.050 --> 00:01:23.570
or variables for each of them.

00:01:23.570 --> 00:01:25.150
The max number of people per day,

00:01:25.150 --> 00:01:28.050
that's what we're trying to set
on one side of the equation,

00:01:28.050 --> 00:01:30.940
that is this variable P, right over here.

00:01:30.940 --> 00:01:33.010
So we'll take capital P is equal to

00:01:33.010 --> 00:01:36.280
what's the number of cars per coaster?

00:01:36.280 --> 00:01:37.520
I guess you could say.

00:01:37.520 --> 00:01:42.180
Let me write it this way, per
coaster, per rollercoaster.

00:01:42.180 --> 00:01:43.690
So they give us that right over here,

00:01:43.690 --> 00:01:45.730
rollercoaster has c cars.

00:01:45.730 --> 00:01:48.100
So that's going to be this
variable here in orange

00:01:48.100 --> 00:01:50.450
or this part of it, that's c.

00:01:50.450 --> 00:01:53.350
Now what's the maximum
number of people per car?

00:01:53.350 --> 00:01:55.720
Well, they say each containing 20 seats.

00:01:55.720 --> 00:01:58.550
So I'd multiply that
times 20 for this part,

00:01:58.550 --> 00:02:00.030
and then I want to multiply that

00:02:00.030 --> 00:02:02.460
times the number of rides per day

00:02:02.460 --> 00:02:04.040
for the entire rollercoaster.

00:02:04.040 --> 00:02:06.620
So that's going to be
times r, and we're done.

00:02:06.620 --> 00:02:07.940
We can rearrange this a little bit,

00:02:07.940 --> 00:02:12.660
We can write this as P is equal to 20

00:02:12.660 --> 00:02:17.660
times cr, and we're done.


How the delivery of a speech affects the impact of the words

WEBVTT
Kind: captions
Language: en

00:00:00.250 --> 00:00:02.030
- [Narrator] Hello readers,

00:00:02.030 --> 00:00:05.050
today we're talking
about how the delivery of

00:00:05.050 --> 00:00:08.930
the speech affects the
impact of the words.

00:00:08.930 --> 00:00:10.750
So what do I mean by that?

00:00:10.750 --> 00:00:12.140
It's all the ways that

00:00:12.140 --> 00:00:16.600
how a person says something
affects what they mean.

00:00:16.600 --> 00:00:20.510
Words on a page may have
a certain definition,

00:00:20.510 --> 00:00:23.540
but we humans use all
sorts of different ways

00:00:23.540 --> 00:00:26.140
to show what we really mean.

00:00:26.140 --> 00:00:28.930
We can say something quietly

00:00:28.930 --> 00:00:33.200
or really loudly to emphasize a point.

00:00:33.200 --> 00:00:38.200
We can emphasize some
words, but not others.

00:00:38.640 --> 00:00:42.960
We can pause, to create dramatic tension.

00:00:42.960 --> 00:00:46.460
We know that how something
is said is important

00:00:46.460 --> 00:00:48.960
because when we don't
have that information,

00:00:48.960 --> 00:00:50.280
sometimes it's hard to know

00:00:50.280 --> 00:00:52.610
what another person is really saying.

00:00:52.610 --> 00:00:57.000
Say that you forgot about your
friend Eli's birthday party.

00:00:57.000 --> 00:01:02.000
So you text them, "hey,
sorry I missed your party."

00:01:05.820 --> 00:01:07.500
Seriously for me this is one

00:01:07.500 --> 00:01:10.580
of the most anxiety-inducing situations

00:01:10.580 --> 00:01:12.950
that I encounter on a regular basis.

00:01:12.950 --> 00:01:15.500
What does Eli actually mean here?

00:01:15.500 --> 00:01:16.760
It's fine.

00:01:16.760 --> 00:01:19.340
Or it's fine

00:01:19.340 --> 00:01:22.810
or it's fine.

00:01:22.810 --> 00:01:24.480
Is it fine or isn't it?

00:01:24.480 --> 00:01:26.660
Gang, I don't know.

00:01:26.660 --> 00:01:29.810
Eli's tone and body language,

00:01:29.810 --> 00:01:33.150
which we can't see in just a text message,

00:01:33.150 --> 00:01:36.500
add in important elements of meaning.

00:01:36.500 --> 00:01:39.770
We can apply that
knowledge to how we speak

00:01:39.770 --> 00:01:42.870
and how we assess the speech of others.

00:01:42.870 --> 00:01:47.250
Good public speakers use
a range of techniques

00:01:47.250 --> 00:01:50.210
to convey their message to their audience,

00:01:50.210 --> 00:01:52.970
which goes beyond just
the words that they say.

00:01:52.970 --> 00:01:57.970
They become actors who are
telling us a story on stage,

00:01:58.000 --> 00:01:59.610
not just with their lines,

00:01:59.610 --> 00:02:02.090
but with their physical presence.

00:02:02.090 --> 00:02:04.360
So, let's talk about
some of these techniques

00:02:04.360 --> 00:02:06.210
and then we'll watch a
little bit of a speech

00:02:06.210 --> 00:02:08.480
so you can spot some examples.

00:02:08.480 --> 00:02:11.670
First, there's vocal variety.

00:02:11.670 --> 00:02:14.760
This means using different speaking speeds

00:02:14.760 --> 00:02:19.120
and changing between soft
and loud speaking volumes.

00:02:19.120 --> 00:02:21.190
When people don't do this,

00:02:21.190 --> 00:02:25.456
we say that they're speaking
in a monotone, you know.

00:02:25.456 --> 00:02:27.726
Bueller?

00:02:27.726 --> 00:02:28.663
Bueller?

00:02:30.500 --> 00:02:35.190
Vocal variation adds excitement
and emphasis to speech.

00:02:35.190 --> 00:02:37.920
Then there's language.

00:02:37.920 --> 00:02:40.910
Here I mean the choice of words

00:02:40.910 --> 00:02:44.400
and the rhetorical
devices the speaker uses

00:02:44.400 --> 00:02:46.470
to appeal to their audience

00:02:46.470 --> 00:02:50.020
and make the audience
agree with their points.

00:02:50.020 --> 00:02:53.390
So, for example, if you're
at a business convention,

00:02:53.390 --> 00:02:58.220
you would expect a speaker
to use pretty formal language

00:02:58.220 --> 00:03:01.770
like, good evening my esteemed colleagues,

00:03:01.770 --> 00:03:05.600
tonight I want to discuss the
importance of market research

00:03:05.600 --> 00:03:08.240
and connecting with our customer base.

00:03:08.240 --> 00:03:11.347
You wouldn't expect the speaker to say,

00:03:11.347 --> 00:03:14.467
"(indistinct), I'm a Hanker
and (indistinct) tonight.

00:03:14.467 --> 00:03:16.720
"Let's go mine some gold."

00:03:16.720 --> 00:03:18.870
But if you were at a
gold miners convention,

00:03:18.870 --> 00:03:21.300
maybe that's exactly what
you would expect to hear.

00:03:21.300 --> 00:03:25.560
Language also includes
the rhetorical devices

00:03:25.560 --> 00:03:28.690
that help to structure an argument.

00:03:28.690 --> 00:03:30.780
For example, repetition.

00:03:30.780 --> 00:03:35.720
Repeating the same word or
phrase can help hammer it home

00:03:35.720 --> 00:03:39.280
or make the speaker's
point feel more urgent.

00:03:39.280 --> 00:03:43.090
In Martin Luther King Jr's
"I have a dream" speech,

00:03:43.090 --> 00:03:46.227
he starts eight sentences
in a row with the phrase,

00:03:46.227 --> 00:03:47.860
"I have a dream."

00:03:47.860 --> 00:03:52.130
So these two points cover
how a speaker talks,

00:03:52.130 --> 00:03:55.740
but there are also physical
aspects to giving a speech.

00:03:55.740 --> 00:04:00.570
Gestures and eye contact, visual aids,

00:04:00.570 --> 00:04:04.110
and the use of the stage area itself.

00:04:04.110 --> 00:04:06.360
The speaker can pace back and forth

00:04:06.360 --> 00:04:08.070
to show they're feeling agitated,

00:04:08.070 --> 00:04:12.270
or throw their shoulders back
to show they're feeling proud.

00:04:12.270 --> 00:04:15.610
They can use their hands to
emphasize what they're saying.

00:04:15.610 --> 00:04:18.470
Speakers can use props if they want to,

00:04:18.470 --> 00:04:22.250
a chart or image or an object.

00:04:22.250 --> 00:04:25.890
And just like actors can have
performances that are great,

00:04:25.890 --> 00:04:28.510
and performances that are only so, so.

00:04:28.510 --> 00:04:32.210
Speakers can use all of these
techniques to great effect,

00:04:32.210 --> 00:04:36.930
or they can miss the mark by
seeming phony or uncomfortable.

00:04:36.930 --> 00:04:41.000
So let's take a look at
a speech and its delivery

00:04:41.000 --> 00:04:43.570
to see if we can spot
any of these techniques

00:04:43.570 --> 00:04:45.890
and what messages they convey.

00:04:45.890 --> 00:04:48.800
This is a speech from 1988

00:04:48.800 --> 00:04:52.620
by the then governor of Texas Ann Richards

00:04:52.620 --> 00:04:55.150
at the Democratic National Convention.

00:04:55.150 --> 00:04:57.010
I'll fast forward to the good parts.

00:04:57.010 --> 00:04:59.950
- Those were real people
with real problems

00:04:59.950 --> 00:05:01.410
and they had real dreams

00:05:01.410 --> 00:05:03.210
about getting out of the depression.

00:05:04.350 --> 00:05:06.960
I can remember summer
nights when we had put down

00:05:06.960 --> 00:05:09.280
what we call the Baptist palette

00:05:10.240 --> 00:05:12.693
and we listened to the grownups talk.

00:05:14.170 --> 00:05:16.370
I can still hear the sound of the dominoes

00:05:16.370 --> 00:05:17.960
clicking on the marble slab

00:05:17.960 --> 00:05:20.470
my daddy had found for a tabletop.

00:05:20.470 --> 00:05:21.860
- [Narrator] Did you
see what she did there?

00:05:21.860 --> 00:05:25.450
What's her language telling
us about who she is?

00:05:25.450 --> 00:05:27.460
What did she do with her hands there

00:05:27.460 --> 00:05:29.770
when she talked about the dominoes?

00:05:29.770 --> 00:05:31.810
She's telling us she's not fancy,

00:05:31.810 --> 00:05:33.860
she's from an ordinary background

00:05:33.860 --> 00:05:36.530
and she helps us visualize the scene

00:05:36.530 --> 00:05:39.900
by wiggling her fingers like
she's putting down dominoes.

00:05:39.900 --> 00:05:41.310
- I got a letter last week

00:05:41.310 --> 00:05:43.830
from a young mother in Lorena, Texas,

00:05:43.830 --> 00:05:47.438
and I wanna read part of it to you.

00:05:47.438 --> 00:05:49.260
- [Narrator] Okay. How about that?

00:05:49.260 --> 00:05:52.290
What did you think about
her opening up that letter?

00:05:52.290 --> 00:05:54.750
Is that actually the letter she received

00:05:54.750 --> 00:05:56.440
from the young mother?

00:05:56.440 --> 00:05:59.210
Probably not. I think I
can see the text on it

00:05:59.210 --> 00:06:00.160
and it's really big.

00:06:00.160 --> 00:06:03.210
So, she's probably
reading from a typed copy.

00:06:03.210 --> 00:06:05.080
It's folded in thirds though,

00:06:05.080 --> 00:06:07.430
like a letter that came in an envelope.

00:06:07.430 --> 00:06:10.970
It gives you the impression
that this is a real letter,

00:06:10.970 --> 00:06:12.280
something she got in the mail,

00:06:12.280 --> 00:06:15.040
and she's telling you
the plain truth from it.

00:06:15.040 --> 00:06:17.600
This is a visual aid. Okay.

00:06:17.600 --> 00:06:19.020
Let's skip the middle of the letter

00:06:19.020 --> 00:06:23.047
and see how Governor Richards
delivers the end of it.

00:06:23.047 --> 00:06:26.733
- We plot along trying to
make it better for ourselves

00:06:26.733 --> 00:06:31.060
and our children and our parents.

00:06:31.060 --> 00:06:32.470
We aren't vocal anymore.

00:06:32.470 --> 00:06:36.173
I think maybe we're too tired.

00:06:38.290 --> 00:06:43.290
I believe that people like
us are forgotten in America.

00:06:45.130 --> 00:06:46.370
- [Narrator] What did you notice about

00:06:46.370 --> 00:06:50.990
how Governor Richards delivered
those last two sentences?

00:06:50.990 --> 00:06:54.740
I think maybe we're too tired.

00:06:54.740 --> 00:06:56.970
She sounds tired.

00:06:56.970 --> 00:06:59.390
And she pauses between the words.

00:06:59.390 --> 00:07:04.390
I believe that people like
us are forgotten in America.

00:07:05.550 --> 00:07:08.990
All of those pauses
give weight and emphasis

00:07:08.990 --> 00:07:11.030
to the experience of the young mother.

00:07:11.030 --> 00:07:13.720
This is vocal variety.

00:07:13.720 --> 00:07:15.932
Okay. This is the last
one we'll talk about.

00:07:15.932 --> 00:07:18.719
- They've told farmers
that they were selfish,

00:07:18.719 --> 00:07:21.230
that they would drive up food prices

00:07:21.230 --> 00:07:23.080
if they asked the government to intervene

00:07:23.080 --> 00:07:25.150
on behalf of the family farm

00:07:25.150 --> 00:07:27.730
and we watch farms go on the auction block

00:07:27.730 --> 00:07:30.620
while we bought food
from foreign countries.

00:07:30.620 --> 00:07:31.804
Well, that's wrong.

00:07:31.804 --> 00:07:34.554
(crowd applauds)

00:07:44.150 --> 00:07:48.630
They told working mothers
it's all their fault

00:07:48.630 --> 00:07:50.560
that families are falling apart

00:07:50.560 --> 00:07:53.510
because they had to go to work
to keep their kids in jeans

00:07:53.510 --> 00:07:56.140
and tennis shoes in
college and they're wrong.

00:07:56.140 --> 00:07:58.890
(crowd applauds)

00:08:04.860 --> 00:08:06.420
They told American labor

00:08:06.420 --> 00:08:09.210
they were trying to ruin free enterprise

00:08:09.210 --> 00:08:13.690
by asking for 60 days
notice of plant closings

00:08:13.690 --> 00:08:14.913
and that's wrong.

00:08:14.913 --> 00:08:17.370
(crowd applauds)

00:08:17.370 --> 00:08:20.370
- [Narrator] What did you
hear repeated several times

00:08:20.370 --> 00:08:21.630
in this section?

00:08:21.630 --> 00:08:23.320
That's wrong.

00:08:23.320 --> 00:08:25.960
This is a rhetorical device.

00:08:25.960 --> 00:08:27.320
What does it make you feel

00:08:27.320 --> 00:08:30.700
about the points Governor
Richards was making here?

00:08:30.700 --> 00:08:34.220
It kind of feels like they're
piling on each other, right?

00:08:34.220 --> 00:08:38.810
She's adding more and
more evidence to her case.

00:08:38.810 --> 00:08:41.560
So the next time you watch a speech,

00:08:41.560 --> 00:08:43.970
keep these techniques in mind.

00:08:43.970 --> 00:08:46.940
They'll help you see
how a compelling speaker

00:08:46.940 --> 00:08:49.820
can transform the text of the speech

00:08:49.820 --> 00:08:52.593
with vocal and physical effects.


Mapping shapes

WEBVTT
Kind: captions
Language: en

00:00:00.240 --> 00:00:02.040
- [Instructor] We're told that triangles,

00:00:02.040 --> 00:00:03.700
let's see, we have triangle PQR

00:00:03.700 --> 00:00:07.040
and triangle ABC are congruent.

00:00:07.040 --> 00:00:11.780
The side length of each square
on the grid is one unit.

00:00:11.780 --> 00:00:14.320
So each of these is one unit.

00:00:14.320 --> 00:00:17.650
Which of the following
sequences of transformations

00:00:17.650 --> 00:00:22.567
maps triangle PQR onto triangle ABC?

00:00:23.480 --> 00:00:27.780
So we have four different
sequences of transformations,

00:00:27.780 --> 00:00:29.560
and so why don't you pause this video

00:00:29.560 --> 00:00:32.725
and figure out which of
these actually does map

00:00:32.725 --> 00:00:36.210
triangle PQR, so this is PQR,

00:00:36.210 --> 00:00:40.410
onto ABC, and it could be
more than one of these.

00:00:40.410 --> 00:00:43.290
So pause this video and have a go at that.

00:00:43.290 --> 00:00:45.270
All right, now let's do this together.

00:00:45.270 --> 00:00:47.820
So let's first think about Sequence A,

00:00:47.820 --> 00:00:50.670
and I will do Sequence
A in this purple color.

00:00:50.670 --> 00:00:53.210
So remember, we're
starting with triangle PQR.

00:00:53.210 --> 00:00:55.880
So first it says a rotation 90 degrees

00:00:55.880 --> 00:01:00.880
about the point, about the
point R, so let's do that.

00:01:01.160 --> 00:01:02.950
And then we'll do the
rest of this sequence.

00:01:02.950 --> 00:01:05.890
So if we rotate this 90 degrees,

00:01:05.890 --> 00:01:07.790
so one way to think about it is,

00:01:07.790 --> 00:01:12.190
a line like that is then
going to be like that.

00:01:12.190 --> 00:01:13.690
So we're going to go like that.

00:01:13.690 --> 00:01:17.080
And so R is going to stay where it is.

00:01:17.080 --> 00:01:18.830
You're rotating about it.

00:01:18.830 --> 00:01:23.520
But P is now going to be right over here.

00:01:23.520 --> 00:01:26.440
One way to think about
it is to go from R to P,

00:01:26.440 --> 00:01:29.380
we went down one and three to the right.

00:01:29.380 --> 00:01:31.110
Now when you do the rotation,

00:01:31.110 --> 00:01:35.130
you're going to go to the
right one and then up three.

00:01:35.130 --> 00:01:37.460
So P is going to be there
and you can see that.

00:01:37.460 --> 00:01:39.510
That's the rotation.

00:01:39.510 --> 00:01:43.340
So that side will look like this.

00:01:43.340 --> 00:01:45.030
So that is P.

00:01:45.030 --> 00:01:50.030
And then Q is going to go right over here.

00:01:51.710 --> 00:01:52.760
It's going to, once again,

00:01:52.760 --> 00:01:56.500
also do a 90-degree rotation about R.

00:01:56.500 --> 00:01:59.730
And so after you do
the 90-degree rotation,

00:01:59.730 --> 00:02:02.550
PQR is going to look like this.

00:02:02.550 --> 00:02:04.510
So that is Q.

00:02:04.510 --> 00:02:05.630
So we've done that first part.

00:02:05.630 --> 00:02:09.580
Then a translation six units to the left

00:02:09.580 --> 00:02:11.294
and seven units up.

00:02:11.294 --> 00:02:15.060
So each of these points
are going to go six units

00:02:15.060 --> 00:02:16.780
to the left and seven up.

00:02:16.780 --> 00:02:18.550
So if we take point P,

00:02:18.550 --> 00:02:22.720
six to the left, one, two,
three, four, five, six,

00:02:22.720 --> 00:02:27.720
seven units up, one, two,
three, four, five, six, seven.

00:02:28.060 --> 00:02:31.710
It'll put it right over
there, so that is point P.

00:02:31.710 --> 00:02:34.790
If we take point R, we
take six units to the left,

00:02:34.790 --> 00:02:38.510
one, two, three, four, five, six,

00:02:38.510 --> 00:02:43.510
seven up, one, two, three,
four, five, six, seven.

00:02:43.730 --> 00:02:46.330
It gets us right over there.

00:02:46.330 --> 00:02:49.328
And then point Q, if we
go six units to the left,

00:02:49.328 --> 00:02:53.110
one, two, three, four, five, six,

00:02:53.110 --> 00:02:58.110
seven up is one, two, three,
four, five, six, seven.

00:02:58.400 --> 00:03:00.870
Puts us right over there.

00:03:00.870 --> 00:03:02.630
So this looks like it worked.

00:03:02.630 --> 00:03:05.164
Sequence A is good.

00:03:05.164 --> 00:03:09.167
It maps PQR onto ABC.

00:03:10.580 --> 00:03:14.060
This last one isn't an R,
this is a Q right over here.

00:03:14.060 --> 00:03:17.070
So that worked, Sequence A.

00:03:17.070 --> 00:03:19.210
Now let's work on Sequence B.

00:03:19.210 --> 00:03:20.620
I'll do this in different color.

00:03:20.620 --> 00:03:24.140
A translation eight units to the left

00:03:24.140 --> 00:03:26.330
and three up, so let's do that first.

00:03:26.330 --> 00:03:30.060
So if we take point Q eight
to the left and three up,

00:03:30.060 --> 00:03:32.820
one, two, three, four,

00:03:32.820 --> 00:03:35.000
five, six, seven, eight,

00:03:35.000 --> 00:03:38.360
three up, one, two, three.

00:03:38.360 --> 00:03:41.310
So this'll be my red Q for now.

00:03:41.310 --> 00:03:43.880
And now if I do this point R,

00:03:43.880 --> 00:03:45.799
one, two, three, four,

00:03:45.799 --> 00:03:49.180
five, six, seven, eight.

00:03:49.180 --> 00:03:50.080
Let me make sure I did that right.

00:03:50.080 --> 00:03:54.274
One, two, three, four, five,
six, seven, eight, three up,

00:03:54.274 --> 00:03:55.970
one, two, three.

00:03:55.970 --> 00:03:59.030
So my new R is going to be there.

00:03:59.030 --> 00:04:02.780
And then last but not least, point P,

00:04:02.780 --> 00:04:05.760
eight to the left, one, two, three, four,

00:04:05.760 --> 00:04:07.690
five, six, seven, eight,

00:04:07.690 --> 00:04:11.440
three up, one, two,
three, goes right there.

00:04:11.440 --> 00:04:14.870
So just that translation

00:04:14.870 --> 00:04:17.550
will get us

00:04:17.550 --> 00:04:19.560
to this point.

00:04:19.560 --> 00:04:21.010
It'll get us to that point,

00:04:21.010 --> 00:04:22.590
so we're clearly not done mapping yet,

00:04:22.590 --> 00:04:26.540
but there's more
transformation to be done.

00:04:26.540 --> 00:04:27.970
So it looks something like that.

00:04:27.970 --> 00:04:31.890
Says then a reflection
over the horizontal line

00:04:31.890 --> 00:04:33.900
through point A.

00:04:33.900 --> 00:04:36.940
So point A is right over here.

00:04:36.940 --> 00:04:40.420
The horizontal line is right like that.

00:04:40.420 --> 00:04:42.630
So if I were to reflect,
point A wouldn't change.

00:04:42.630 --> 00:04:45.840
Point R right now is three
below that horizontal line.

00:04:45.840 --> 00:04:48.470
Point R will then be three
above that horizontal line.

00:04:48.470 --> 00:04:52.700
So point R will then go right over there.

00:04:52.700 --> 00:04:55.750
Just from that, I can
see that this sequence

00:04:55.750 --> 00:04:57.730
of transformations is not going to work.

00:04:57.730 --> 00:04:59.880
It's putting R in the wrong place.

00:04:59.880 --> 00:05:03.580
So I'm going to rule out Sequence B.

00:05:03.580 --> 00:05:08.100
Sequence C, let me do
that with another color.

00:05:08.100 --> 00:05:10.870
I don't know, I will do
it with this orange color.

00:05:10.870 --> 00:05:15.870
A reflection over the vertical
point through point Q.

00:05:16.210 --> 00:05:19.660
Sorry, a reflection over the
vertical line through point Q.

00:05:19.660 --> 00:05:20.570
So let me do that.

00:05:20.570 --> 00:05:24.120
So the vertical line through
point Q looks like this,

00:05:24.120 --> 00:05:26.150
just gonna draw that vertical line.

00:05:26.150 --> 00:05:28.810
So if you reflect it, Q is going to be,

00:05:28.810 --> 00:05:30.290
it's going to stay in place.

00:05:30.290 --> 00:05:32.320
R is one to the right of that,

00:05:32.320 --> 00:05:34.040
so now it's going to be one to the left

00:05:34.040 --> 00:05:35.330
once you do the reflection.

00:05:35.330 --> 00:05:38.390
And point P is four to the right,

00:05:38.390 --> 00:05:39.540
so now it's gonna be four to the left.

00:05:39.540 --> 00:05:42.930
One, two, three, four,
so P is going to be there

00:05:42.930 --> 00:05:44.450
after the reflection.

00:05:44.450 --> 00:05:47.660
And so it's going to
look something like this

00:05:47.660 --> 00:05:49.610
after that first transformation,

00:05:49.610 --> 00:05:51.970
and this is getting a little bit messy.

00:05:51.970 --> 00:05:54.680
But this is what you'll probably
have to go through as well,

00:05:54.680 --> 00:05:56.640
so I'll go through it with you.

00:05:56.640 --> 00:05:58.660
All right, so we did that
first part, the reflection.

00:05:58.660 --> 00:06:02.100
Then a translation four to
the left and seven units up.

00:06:02.100 --> 00:06:04.680
So four to the left and seven up.

00:06:04.680 --> 00:06:06.310
So let me try that.

00:06:06.310 --> 00:06:09.060
So four to the left,
one, two, three, four,

00:06:09.060 --> 00:06:14.060
seven up, one, two, three,
four, five, six, seven.

00:06:14.580 --> 00:06:17.570
So it's putting Q right over here.

00:06:17.570 --> 00:06:20.280
I'm already suspicious of
it because Sequence A worked

00:06:20.280 --> 00:06:22.100
where we put P right over there.

00:06:22.100 --> 00:06:24.820
So I'm already suspicious of
this, but let's keep trying.

00:06:24.820 --> 00:06:27.490
So four to the left and seven up,

00:06:27.490 --> 00:06:29.930
one, two, three, four, seven up,

00:06:29.930 --> 00:06:34.070
one, two, three, four, five, six, seven.

00:06:34.070 --> 00:06:38.060
So R is going to the same
place as Sequence A put it.

00:06:38.060 --> 00:06:41.783
And then point P, one, two, three, four,

00:06:41.783 --> 00:06:46.220
one, two, three, four, five, six, seven.

00:06:46.220 --> 00:06:47.681
Actually, it worked.

00:06:47.681 --> 00:06:52.681
So it works because this is
actually an isosceles triangle.

00:06:53.867 --> 00:06:55.670
And so this one actually worked out.

00:06:55.670 --> 00:07:00.270
We were able to map PQR
onto ABC with Sequence C.

00:07:00.270 --> 00:07:03.710
So I like, I like this one as well.

00:07:03.710 --> 00:07:07.200
And then last but not
least, let's try Sequence D.

00:07:07.200 --> 00:07:09.740
I'll do that in black
so that we can see it.

00:07:09.740 --> 00:07:12.200
So first we do a translation
eight units to the left

00:07:12.200 --> 00:07:13.250
and three up.

00:07:13.250 --> 00:07:14.740
Eight to the left and three up.

00:07:14.740 --> 00:07:16.090
So we'll start here.

00:07:16.090 --> 00:07:17.940
One, two, three, four,

00:07:17.940 --> 00:07:19.850
five, six, seven, eight,

00:07:19.850 --> 00:07:22.580
three up, one, two, three.

00:07:22.580 --> 00:07:26.070
So I'll put my black Q right over there.

00:07:26.070 --> 00:07:30.450
So eight to the left,
one, two, three, four,

00:07:30.450 --> 00:07:32.360
five, six, seven, eight,

00:07:32.360 --> 00:07:34.880
three up, one, two, three.

00:07:34.880 --> 00:07:37.630
I'll put my black R right over there.

00:07:37.630 --> 00:07:39.900
It's actually exactly
what we did in Sequence B

00:07:39.900 --> 00:07:40.733
the first time.

00:07:40.733 --> 00:07:43.480
So P is going to show up right over there.

00:07:43.480 --> 00:07:45.320
So after that translation,

00:07:45.320 --> 00:07:48.380
sequence, that first
translation in Sequence D

00:07:48.380 --> 00:07:50.130
gets us right over there.

00:07:50.130 --> 00:07:55.130
Then it says a rotation
-270 degrees about point A.

00:07:56.880 --> 00:07:59.300
So this is point A right over here.

00:07:59.300 --> 00:08:03.450
And -270 degrees, it's negative,

00:08:03.450 --> 00:08:05.490
so it's going to go clockwise.

00:08:05.490 --> 00:08:08.390
And let's see, 180 degrees,
let's say if we were to take

00:08:08.390 --> 00:08:10.340
this line right over here,

00:08:10.340 --> 00:08:12.440
if we were to go 180 degrees,

00:08:12.440 --> 00:08:17.380
it would go to this line like that.

00:08:17.380 --> 00:08:19.600
And then if you were to
go another 90 degrees,

00:08:19.600 --> 00:08:21.884
it actually does look like it would,

00:08:21.884 --> 00:08:25.200
it would map onto that.

00:08:25.200 --> 00:08:28.030
So this is actually looking pretty good.

00:08:28.030 --> 00:08:31.110
If you were to, this line
right over here will then,

00:08:31.110 --> 00:08:36.110
if you go -270 degrees, will
map onto this right over here,

00:08:37.186 --> 00:08:40.810
and then that point R will
kinda go along for the ride

00:08:40.810 --> 00:08:41.710
is one way to think about it,

00:08:41.710 --> 00:08:43.690
and so it'll go right over there as well.

00:08:43.690 --> 00:08:46.400
So I'm actually liking Sequence D as well.

00:08:46.400 --> 00:08:49.763
So all of these work
except for Sequence B.