The power of 'yet' with Zoe and Elmo from Sesame Street

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:01.483
- Vroom vroom, vroom vroom.

00:00:01.483 --> 00:00:03.142
Okay, Elmo's ready!

00:00:03.142 --> 00:00:04.421
- Oh wait, I'm almost ready.

00:00:04.421 --> 00:00:06.120
Um, there.

00:00:06.120 --> 00:00:06.680
Okay.

00:00:06.680 --> 00:00:07.620
- Yeah, ready?

00:00:07.620 --> 00:00:08.457
(both giggle)

00:00:08.457 --> 00:00:10.303
The Elmo-mobile.

00:00:10.303 --> 00:00:12.940
- And the Zoe-mobile!

00:00:13.600 --> 00:00:15.040
- Three, two, one!

00:00:16.140 --> 00:00:19.660
- Yeah baby! Boy, Elmo's ramp worked! Yeah (laughs).

00:00:19.660 --> 00:00:21.080
- Well mine didn't work!

00:00:21.080 --> 00:00:22.620
I need a do-over!

00:00:22.620 --> 00:00:25.160
- Okay, do-over, do-over (laughs)

00:00:25.540 --> 00:00:27.957
- All right, three, two, one, woo.

00:00:27.957 --> 00:00:29.469
What? Oh!

00:00:29.469 --> 00:00:32.113
It, it didn't work again!

00:00:32.113 --> 00:00:33.582
- Well, you know that's okay, Zoe.

00:00:33.582 --> 00:00:36.454
Zoe can play with Elmo's ramp.

00:00:36.454 --> 00:00:38.369
Elmo's ramp works great!

00:00:38.369 --> 00:00:40.252
- Well thanks, Elmo.

00:00:40.260 --> 00:00:45.240
Boy, I guess I'm just no good at building ramps!

00:00:45.280 --> 00:00:46.260
- Sorry.

00:00:46.261 --> 00:00:48.201
- Hi Elmo, hi Zoe.

00:00:48.201 --> 00:00:50.123
- Oh, hi Mr Sal.

00:00:50.123 --> 00:00:51.574
- What's wrong Zoe?

00:00:51.574 --> 00:00:53.851
- Oh, my ramp doesn't work.

00:00:53.851 --> 00:00:56.541
I'm just gonna go play with Elmo's ramp.

00:00:56.541 --> 00:00:57.970
- Oh, hold on a second.

00:00:57.970 --> 00:00:59.971
Any great engineering project is gonna involve

00:00:59.971 --> 00:01:01.630
some trial and error.

00:01:01.630 --> 00:01:03.593
It's not that your ramp doesn't work,

00:01:03.593 --> 00:01:05.512
it's just that it doesn't work yet!

00:01:05.512 --> 00:01:07.135
That's the power of 'yet'.

00:01:07.135 --> 00:01:09.164
- Woo, oh, Mr. Sal?

00:01:09.164 --> 00:01:11.058
Is that like a super power?

00:01:11.058 --> 00:01:11.891
- Kind of Elmo.

00:01:11.891 --> 00:01:14.018
It's a super power that we all have.

00:01:14.018 --> 00:01:16.265
It's the idea that mistakes aren't bad,

00:01:16.265 --> 00:01:17.616
and that we learn from them,

00:01:17.616 --> 00:01:18.908
so we keep trying.

00:01:18.908 --> 00:01:21.887
- But I tried my ramp twice already.

00:01:21.887 --> 00:01:24.419
- Well what did you try differently the second time?

00:01:24.419 --> 00:01:26.062
- Nothing.

00:01:26.062 --> 00:01:27.175
- Well why don't we look closer

00:01:27.175 --> 00:01:28.794
and see if we can try a different approach?

00:01:28.794 --> 00:01:30.627
And even if that doesn't work, it's okay.

00:01:30.627 --> 00:01:31.599
We'll learn from it.

00:01:31.599 --> 00:01:32.432
- Ooh!

00:01:32.432 --> 00:01:36.143
- Okay, well, the Zoe-mobile crashed right here.

00:01:36.143 --> 00:01:36.976
- [Elmo] Yeah?

00:01:36.976 --> 00:01:40.144
- So maybe I need to just fill this hole.

00:01:40.144 --> 00:01:41.164
- That's a good idea.

00:01:41.164 --> 00:01:44.304
- I think I have a block that'll do just the trick.

00:01:44.304 --> 00:01:45.520
Here, wait.

00:01:45.520 --> 00:01:46.745
- Ooh!

00:01:46.745 --> 00:01:49.021
- There you go, Zoe, I like the way you're thinking.

00:01:49.021 --> 00:01:50.441
Like the great engineer that you are.

00:01:50.441 --> 00:01:51.517
- Ah, all right!

00:01:51.517 --> 00:01:52.467
Here, let me try.

00:01:52.467 --> 00:01:53.300
- [Elmo] Okay.

00:01:53.300 --> 00:01:54.934
- Come here, Zoe-mobile.

00:01:54.940 --> 00:01:56.900
Here we go!

00:01:57.360 --> 00:01:58.186
- Oh boy.

00:01:58.186 --> 00:01:59.288
- Oh, no!

00:01:59.288 --> 00:02:02.190
Oh, that's it, I'm just giving up.

00:02:02.190 --> 00:02:03.873
- No, no, no, no, no!

00:02:03.873 --> 00:02:06.126
Not if you believe in the power of 'yet'.

00:02:06.126 --> 00:02:09.909
You know how your muscles get stronger when you exercise?

00:02:09.909 --> 00:02:11.850
- Oh yeah, I'm super strong.

00:02:11.850 --> 00:02:12.683
Watch this.

00:02:12.683 --> 00:02:14.497
- Oh, Elmo too.

00:02:14.497 --> 00:02:15.330
- Exactly!

00:02:15.330 --> 00:02:17.556
Making mistakes and coming up with solutions

00:02:17.556 --> 00:02:20.858
to solve your problems is exercise for your brain.

00:02:20.860 --> 00:02:24.540
- Whoa! It's brainercize!

00:02:24.540 --> 00:02:27.774
- Right! When you believe you can do it and you keep trying,

00:02:27.774 --> 00:02:29.797
that's when your brain is growing and you're learning

00:02:29.797 --> 00:02:30.630
new things.

00:02:30.630 --> 00:02:31.463
- Wow!

00:02:31.463 --> 00:02:33.169
- It's called a growth mindset.

00:02:33.169 --> 00:02:36.993
- Okay, well then, I'm gonna try again!

00:02:36.993 --> 00:02:38.141
- Okay Zoe!

00:02:38.141 --> 00:02:38.974
- Now let's see.

00:02:38.974 --> 00:02:42.495
That time the Zoe-mobile crashed right here.

00:02:42.495 --> 00:02:43.328
- Right.

00:02:43.328 --> 00:02:45.058
- So maybe if I get rid of this block.

00:02:45.058 --> 00:02:46.006
- Yeah, ooh.

00:02:46.006 --> 00:02:46.845
- Oh hey!

00:02:46.845 --> 00:02:48.979
Look at that nice straight line all the way down!

00:02:48.979 --> 00:02:49.812
- Ah, uh huh!

00:02:49.812 --> 00:02:50.843
- I'll bet that'll do it!

00:02:50.843 --> 00:02:51.703
Here let me try.

00:02:51.703 --> 00:02:52.536
- Okay.

00:02:52.536 --> 00:02:54.138
- Come here Zoe-mobile.

00:02:54.140 --> 00:02:56.140
Here we go!

00:02:56.920 --> 00:02:59.780
- Yay! Good job Zoe!

00:02:59.860 --> 00:03:03.420
Oh boy, the Zoe-mobile went so fast!

00:03:03.420 --> 00:03:04.120
- Yeah!

00:03:04.120 --> 00:03:07.960
Hey, can Zoe make Elmo's ramp taller and faster too?

00:03:07.962 --> 00:03:09.457
- Yeah, let's do it together!

00:03:09.457 --> 00:03:11.162
- Yeah, okay!

00:03:11.162 --> 00:03:12.295
- Great job guys.

00:03:12.295 --> 00:03:14.778
I'm so proud that you kept trying,

00:03:14.778 --> 00:03:16.588
and you weren't afraid to make mistakes.

00:03:16.588 --> 00:03:19.760
And because of it we all learned a ton.

00:03:19.780 --> 00:03:22.040
And that's the power of 'yet'.

00:03:22.040 --> 00:03:24.066
- Yeah! Come on Zoe, let's play.

00:03:24.066 --> 00:03:24.899
- Alright!

00:03:24.900 --> 00:03:27.180
- Okay so, maybe if there's like something here?


Khan Academy India Talent Search 2017

WEBVTT
Kind: captions
Language: en

00:00:00.450 --> 00:00:03.167
- Hi I'm Sal Khan, founder
of the Khan Academy,

00:00:03.167 --> 00:00:04.653
and I just wanted to let you know about

00:00:04.653 --> 00:00:06.580
our India Talent Search.

00:00:06.580 --> 00:00:09.134
As you might know Khan
Academy we're a not for profit

00:00:09.134 --> 00:00:11.317
with a mission of providing
a free world-class education

00:00:11.317 --> 00:00:13.360
for anyone anywhere.

00:00:13.360 --> 00:00:16.425
And to us it means that if
you are a villager someplace

00:00:16.425 --> 00:00:18.399
and you don't have access
to a formal school,

00:00:18.399 --> 00:00:20.605
that you might be able to
access a low cost smartphone

00:00:20.605 --> 00:00:22.881
and then be able to self-educate yourself

00:00:22.881 --> 00:00:24.692
and one day prove what
you know so that you could

00:00:24.692 --> 00:00:26.549
get a job or go and get
into higher education.

00:00:26.549 --> 00:00:28.570
But ideally you're using Khan Academy

00:00:28.570 --> 00:00:30.195
in conjunction with a classroom.

00:00:30.195 --> 00:00:32.424
Where the classroom can
allow students to learn

00:00:32.424 --> 00:00:35.048
and work at their own pace,
give data to teachers,

00:00:35.048 --> 00:00:38.183
free up class time for open-ended projects

00:00:38.183 --> 00:00:41.155
or peer-to-peer learning
or Socratic dialogue.

00:00:41.155 --> 00:00:43.825
And so we have a call out for the talent,

00:00:43.825 --> 00:00:45.659
the teaching talent in India,

00:00:45.659 --> 00:00:47.796
to work with us.

00:00:47.796 --> 00:00:49.746
By being part of this talent search,

00:00:49.746 --> 00:00:53.067
one, you'll get a chance to
practice making videos yourself.

00:00:53.067 --> 00:00:56.457
And we're looking for folks
in math and science initially,

00:00:56.457 --> 00:00:58.384
but eventually all subjects.

00:00:58.384 --> 00:01:00.776
But it's a way for us to find talent,

00:01:00.776 --> 00:01:03.864
talent that can help us create content

00:01:03.864 --> 00:01:07.138
that will educate tens
of millions of learners

00:01:07.138 --> 00:01:08.903
throughout India.

00:01:08.903 --> 00:01:12.084
So the opportunity here is
I think pretty exciting.

00:01:12.084 --> 00:01:15.195
There will be prizes, but
maybe the biggest prize of all

00:01:15.195 --> 00:01:17.424
is the opportunity to
contribute and to help

00:01:17.424 --> 00:01:19.328
your fellow citizens.

00:01:19.328 --> 00:01:22.115
And now I'm gonna hand it off to Aanand.

00:01:22.115 --> 00:01:23.856
who is our head of content in India.

00:01:23.856 --> 00:01:26.431
- I'm really very excited to invite you

00:01:26.431 --> 00:01:29.194
to Khan Academy India's
second talent search.

00:01:29.194 --> 00:01:32.073
We've been looking for teachers
to help us reach our mission

00:01:32.073 --> 00:01:35.626
of creating content that's
relevant to the Indian learners.

00:01:35.626 --> 00:01:38.342
Now one big piece of
this is to map a content

00:01:38.342 --> 00:01:39.759
to the Indian syllabus,

00:01:39.759 --> 00:01:41.361
which means the content that you create

00:01:41.361 --> 00:01:44.147
will be used directly by
teachers and students,

00:01:44.147 --> 00:01:47.955
millions of them, to help their
school experience directly.

00:01:47.955 --> 00:01:50.486
Now another big piece of
what we wanna do for India

00:01:50.486 --> 00:01:52.948
is to make Khan Academy's
content available

00:01:52.948 --> 00:01:55.386
in all major Indian languages.

00:01:55.386 --> 00:01:57.870
Now we already have Khan
Academy available in a few

00:01:57.870 --> 00:01:59.565
Indian languages, but
we really wanna take it

00:01:59.565 --> 00:02:00.935
to the next step over here.

00:02:00.935 --> 00:02:02.351
Now to achieve both of these,

00:02:02.351 --> 00:02:04.441
in my opinion, the most
important thing is to find

00:02:04.441 --> 00:02:06.786
the right content creators.

00:02:06.786 --> 00:02:09.247
Not just creators who are
passionate about their subjects,

00:02:09.247 --> 00:02:11.268
but also creators who
are really passionate

00:02:11.268 --> 00:02:12.986
about making education available

00:02:12.986 --> 00:02:15.052
to millions of learners.

00:02:15.052 --> 00:02:17.351
And that's the primary
purpose of this talent search.

00:02:17.351 --> 00:02:20.045
We are looking for
science and math teachers

00:02:20.045 --> 00:02:22.878
and content creators in five languages,

00:02:22.878 --> 00:02:25.060
English and Hindi, but also Kannada,

00:02:25.060 --> 00:02:26.964
Tamil and Marathi.

00:02:26.964 --> 00:02:29.263
And we're looking to give out 10 winners,

00:02:29.263 --> 00:02:30.679
give out prizes for 10 winners,

00:02:30.679 --> 00:02:32.700
one winner and one runner's up in each of

00:02:32.700 --> 00:02:34.418
these five languages.

00:02:34.418 --> 00:02:37.065
So if you are a creator
or if you know a creator,

00:02:37.065 --> 00:02:38.690
make sure you spread the word

00:02:38.690 --> 00:02:41.732
and help as many people know
about this talent search

00:02:41.732 --> 00:02:43.474
and help us find the
right content creators

00:02:43.474 --> 00:02:45.006
to get closer to our mission.

00:02:45.006 --> 00:02:48.164
The last date for sending
your entries is December 17.

00:02:48.164 --> 00:02:51.531
And now I'm happy to introduce
two of last year's winners

00:02:51.531 --> 00:02:54.039
who now work with us, Mahesh and Ram,

00:02:54.039 --> 00:02:55.734
to say a little bit about their experience

00:02:55.734 --> 00:02:56.779
with Khan Academy.

00:02:56.779 --> 00:02:58.447
- Hi my name is Mahesh Shenoy.

00:02:58.447 --> 00:03:01.930
I was the winner of the last
year's India Talent Search,

00:03:01.930 --> 00:03:04.995
and now the newest and a proud member

00:03:04.995 --> 00:03:06.992
of Khan Academy Team India.

00:03:06.992 --> 00:03:08.432
Over the past two and a half years,

00:03:08.432 --> 00:03:10.545
I've been making YouTube physics videos,

00:03:10.545 --> 00:03:13.308
and so I've learned a great
deal about video creation.

00:03:13.308 --> 00:03:16.071
However, two days with this team,

00:03:16.071 --> 00:03:19.067
and I realized I have
so much more to learn.

00:03:19.067 --> 00:03:21.575
We are a small team of passionate people

00:03:21.575 --> 00:03:23.502
but with a huge mission,

00:03:23.502 --> 00:03:26.962
a mission to educate tens of millions

00:03:26.962 --> 00:03:28.726
of young lives of India.

00:03:28.726 --> 00:03:31.420
And if you feel you too
have the same passion,

00:03:31.420 --> 00:03:33.672
here's an opportunity to join us.

00:03:33.672 --> 00:03:37.689
- Hi, I'm Ram, one of last
year's Talent Search winners.

00:03:37.689 --> 00:03:40.150
I love physics, and I've been
teaching it for a long time.

00:03:40.150 --> 00:03:42.635
What I'm excited about
is that now I can help

00:03:42.635 --> 00:03:44.934
millions of kids in the
country love physics

00:03:44.934 --> 00:03:46.188
the way I do.

00:03:46.188 --> 00:03:48.417
And since the entire content is free,

00:03:48.417 --> 00:03:50.553
that means even the kids
who do not have a shot

00:03:50.553 --> 00:03:53.223
at quality education can
now educate themselves

00:03:53.223 --> 00:03:54.686
using my videos.

00:03:54.686 --> 00:03:56.939
So if you want to help us
in achieving our mission,

00:03:56.939 --> 00:03:58.564
please do send us your videos.

00:03:58.564 --> 00:04:02.186
And trust me, video creation
process is a lot simpler

00:04:02.186 --> 00:04:05.182
and more fun than it seems like.

00:04:05.182 --> 00:04:06.946
- Now when we evaluate your videos,

00:04:06.946 --> 00:04:09.268
we will look a lot more
at their content depth

00:04:09.268 --> 00:04:11.172
and explanation rather than fancy visuals

00:04:11.172 --> 00:04:12.426
or production value,

00:04:12.426 --> 00:04:14.725
so make sure that or rather don't hesitate

00:04:14.725 --> 00:04:17.906
to just point a camera at
a piece of paper or a board

00:04:17.906 --> 00:04:19.253
as you explain your idea.

00:04:19.253 --> 00:04:20.878
Remember that the last
date is December 17,

00:04:20.878 --> 00:04:23.711
and make sure you spread the word.


Ratios for recipes

WEBVTT
Kind: captions
Language: en

00:00:00.587 --> 00:00:03.010
- [Instructor] Right over
here, we have the recipe

00:00:03.010 --> 00:00:07.176
for super cake, which you
want to make for your guests

00:00:07.176 --> 00:00:09.505
that are coming over for dinner tonight.

00:00:09.505 --> 00:00:11.630
But this recipe right over here,

00:00:11.630 --> 00:00:13.608
this is for 32 people.

00:00:13.608 --> 00:00:15.775
This would serve 32 folks.

00:00:17.070 --> 00:00:21.278
But, you only have 16 guests coming over.

00:00:21.278 --> 00:00:23.877
So, if you only have
16 guests coming over,

00:00:23.877 --> 00:00:26.181
what should be your ingredients here?

00:00:26.181 --> 00:00:29.149
How much of each of these
ingredients should you have?

00:00:29.149 --> 00:00:33.316
I encourage you to pause the
video and think about it.

00:00:34.465 --> 00:00:35.843
Right now, we're gonna think about, well,

00:00:35.843 --> 00:00:38.757
we're gonna have a slightly
smaller super cake.

00:00:38.757 --> 00:00:39.924
Smaller super,

00:00:41.863 --> 00:00:43.520
super cake.

00:00:43.520 --> 00:00:45.148
You might have reasoned that,

00:00:45.148 --> 00:00:48.247
"Look, if we're going to
have half as many guests,

00:00:48.247 --> 00:00:49.908
"then each of the ingredients,

00:00:49.908 --> 00:00:51.836
"we should just have half as much."

00:00:51.836 --> 00:00:52.804
And you would be right.

00:00:52.804 --> 00:00:55.364
Instead of eight eggs, for
our smaller super cake,

00:00:55.364 --> 00:00:56.852
you could have four eggs.

00:00:56.852 --> 00:01:00.989
Instead of six cups of flour,
in our smaller super cake,

00:01:00.989 --> 00:01:03.293
you could have three cups of flour.

00:01:03.293 --> 00:01:05.205
Instead of six cups of sugar,

00:01:05.205 --> 00:01:07.873
you could have three cups of sugar.

00:01:07.873 --> 00:01:10.093
I'm just taking half of
each of these numbers.

00:01:10.093 --> 00:01:12.502
Instead of two cups of butter,

00:01:12.502 --> 00:01:15.132
you could have one cup of butter.

00:01:15.132 --> 00:01:17.715
Instead of six teaspoons of baking soda,

00:01:17.715 --> 00:01:20.815
you could have three
teaspoons of baking soda.

00:01:20.815 --> 00:01:23.607
And, last but not least,
instead of two cups of water,

00:01:23.607 --> 00:01:26.757
you could have one cup of water.

00:01:26.757 --> 00:01:28.733
Now, this will work and this is actually

00:01:28.733 --> 00:01:30.986
how you should adjust recipes.

00:01:30.986 --> 00:01:34.017
But there's something
interesting about what's similar

00:01:34.017 --> 00:01:35.386
about these two recipes.

00:01:35.386 --> 00:01:39.117
The recipe for the main super
cake that feeds 32 people

00:01:39.117 --> 00:01:43.143
and the recipe for the smaller super cake.

00:01:43.143 --> 00:01:45.906
And that's the notion of ratios.

00:01:45.906 --> 00:01:47.508
The ratios between ingredients

00:01:47.508 --> 00:01:50.027
or the ratio of how much of an ingredient

00:01:50.027 --> 00:01:52.635
you need for given guests.

00:01:52.635 --> 00:01:57.371
For example, you can see here
that for every eight eggs,

00:01:57.371 --> 00:01:59.321
you have six cups of flour.

00:01:59.321 --> 00:02:01.209
So, let me write this down.

00:02:01.209 --> 00:02:02.042
So, for

00:02:03.900 --> 00:02:04.733
every

00:02:06.037 --> 00:02:06.870
eight eggs

00:02:08.610 --> 00:02:11.530
we have six cups of flour.

00:02:11.530 --> 00:02:12.363
We have

00:02:14.395 --> 00:02:15.895
six cups of flour.

00:02:18.562 --> 00:02:21.512
Which can be expressed as a ratio of,

00:02:21.512 --> 00:02:24.345
the ratio of eggs to flour is 8:6.

00:02:27.576 --> 00:02:30.376
Which is, once again, interpreted
as for every eight eggs,

00:02:30.376 --> 00:02:31.937
I have six cups of flour.

00:02:31.937 --> 00:02:34.770
If I said for every six cups
of flour, I have eight eggs,

00:02:34.770 --> 00:02:36.687
I would've written 6:8.

00:02:38.145 --> 00:02:39.844
So, the order here matters.

00:02:39.844 --> 00:02:41.582
But here I'm saying the ratio

00:02:41.582 --> 00:02:46.345
of eggs to flour, of eggs
to cups of flour is 8:6.

00:02:46.345 --> 00:02:50.071
For every eight eggs, I
have six cups of flour.

00:02:50.071 --> 00:02:52.510
Well, what about for the smaller cake?

00:02:52.510 --> 00:02:53.427
Well, here,

00:02:55.686 --> 00:02:57.353
for every four eggs,

00:02:59.339 --> 00:03:01.006
for every four eggs,

00:03:02.011 --> 00:03:04.725
we have three cups of flour.

00:03:04.725 --> 00:03:05.558
We have

00:03:06.684 --> 00:03:07.517
three cups

00:03:09.341 --> 00:03:10.174
of flour.

00:03:11.674 --> 00:03:13.660
So, what would this ratio be?

00:03:13.660 --> 00:03:16.628
Well, for every four eggs,

00:03:16.628 --> 00:03:18.961
we have three cups of flour.

00:03:19.975 --> 00:03:23.142
So, the ratio of eggs to flour is 4:3.

00:03:24.063 --> 00:03:27.239
Now, turns out that these
are the exact same ratio.

00:03:27.239 --> 00:03:30.284
If you have eight eggs for
every six cups of flour,

00:03:30.284 --> 00:03:32.629
or for every eight eggs
you have six cups of flour,

00:03:32.629 --> 00:03:34.858
that's the same thing
as for every four eggs,

00:03:34.858 --> 00:03:36.396
you have three cups of flour.

00:03:36.396 --> 00:03:38.615
What you're just doing is
taking each of these numbers

00:03:38.615 --> 00:03:40.766
and you are dividing it by two.

00:03:40.766 --> 00:03:43.349
So, you could say the
ratio in either case,

00:03:43.349 --> 00:03:45.402
the ratio of eggs to flour,

00:03:45.402 --> 00:03:46.946
let me write this down.

00:03:46.946 --> 00:03:47.779
The ratio

00:03:49.177 --> 00:03:50.010
of eggs,

00:03:52.008 --> 00:03:52.841
eggs,

00:03:55.325 --> 00:03:57.075
to two cups of flour.

00:03:58.150 --> 00:03:59.483
Let me write two

00:04:00.860 --> 00:04:02.027
cups of flour.

00:04:03.201 --> 00:04:04.368
Cups of flour.

00:04:06.774 --> 00:04:08.274
In either case is,

00:04:10.282 --> 00:04:11.282
is four eggs

00:04:13.129 --> 00:04:16.230
for every three cups of flour.

00:04:16.230 --> 00:04:18.976
This is going to be
true for either recipe.

00:04:18.976 --> 00:04:20.920
You have the same ratio.

00:04:20.920 --> 00:04:23.137
If you have eight eggs here,

00:04:23.137 --> 00:04:25.193
so, for every four eggs, you
have three cups of flour.

00:04:25.193 --> 00:04:28.170
Well, that means your going
to have six cups of flour.

00:04:28.170 --> 00:04:30.481
This is why ratios are helpful.

00:04:30.481 --> 00:04:32.728
This recipe has a
different number of eggs,

00:04:32.728 --> 00:04:33.976
a different number of cups of flour,

00:04:33.976 --> 00:04:36.518
a different number of cups of sugar.

00:04:36.518 --> 00:04:39.856
But the ratios between the
ingredients are the same.

00:04:39.856 --> 00:04:43.600
So, you will be able to have
a cake that tastes the same,

00:04:43.600 --> 00:04:45.649
that essentially is the same cake

00:04:45.649 --> 00:04:48.149
but just is a different size.


Equivalent ratios

WEBVTT
Kind: captions
Language: en

00:00:00.342 --> 00:00:02.683
- [Instructor] We're asked
to select three ratios

00:00:02.683 --> 00:00:06.252
that are equivalent to seven to six.

00:00:06.252 --> 00:00:08.476
So pause this video
and see if you can spot

00:00:08.476 --> 00:00:12.643
the three ratios that are
equivalent to seven to six.

00:00:13.722 --> 00:00:15.680
Alright, now let's work
through this together,

00:00:15.680 --> 00:00:18.560
and the main thing to realize
about equivalent ratios

00:00:18.560 --> 00:00:21.482
is we just have to multiply or divide

00:00:21.482 --> 00:00:23.325
the corresponding parts of the ratio

00:00:23.325 --> 00:00:24.546
by the same amount.

00:00:24.546 --> 00:00:26.277
So before I even look at these choices,

00:00:26.277 --> 00:00:28.772
for example, if I have seven to six,

00:00:28.772 --> 00:00:31.522
if I multiply the seven times two

00:00:32.495 --> 00:00:33.791
to get 14,

00:00:33.791 --> 00:00:36.566
then I would also
multiply the six times two

00:00:36.566 --> 00:00:37.731
to get 12.

00:00:37.731 --> 00:00:41.898
So, for example, 14 to 12
is the exact same ratio.

00:00:43.084 --> 00:00:46.244
Now you might be tempted to pick 12 to 14,

00:00:46.244 --> 00:00:48.512
but that is not the same ratio.

00:00:48.512 --> 00:00:50.451
Order matters in a ratio.

00:00:50.451 --> 00:00:53.422
This could be ratio of oranges to apples.

00:00:53.422 --> 00:00:55.818
And we're saying for every seven oranges,

00:00:55.818 --> 00:00:57.623
there are six apples.

00:00:57.623 --> 00:01:00.085
You wouldn't be able to say
it the other way around.

00:01:00.085 --> 00:01:01.398
So you would rule this one out

00:01:01.398 --> 00:01:03.969
even though it's dealing with
some of the right numbers.

00:01:03.969 --> 00:01:05.482
It's not in the right order.

00:01:05.482 --> 00:01:08.026
Now let's think about 21 to 18.

00:01:08.026 --> 00:01:10.693
To go from seven to 21,

00:01:10.693 --> 00:01:13.451
we would multiply by three.

00:01:13.451 --> 00:01:15.538
And to go from six to 18,

00:01:15.538 --> 00:01:17.564
you would also multiply by three.

00:01:17.564 --> 00:01:18.397
So that works.

00:01:18.397 --> 00:01:20.719
If we multiply both of
these numbers by three,

00:01:20.719 --> 00:01:22.729
we get 21 to 18.

00:01:22.729 --> 00:01:24.822
So let me circle that in.

00:01:24.822 --> 00:01:27.241
That one is for sure equivalent.

00:01:27.241 --> 00:01:28.908
What about 42 to 36?

00:01:30.030 --> 00:01:32.483
Well, to go from seven to 42,

00:01:32.483 --> 00:01:36.092
we're going to have to multiply by six.

00:01:36.092 --> 00:01:38.390
And to go from six to thirty-six,

00:01:38.390 --> 00:01:40.480
we also multiply by six.

00:01:40.480 --> 00:01:43.421
So this, once again,
is an equivalent ratio.

00:01:43.421 --> 00:01:45.667
We multiply each of these by six

00:01:45.667 --> 00:01:47.147
and we keep the same order.

00:01:47.147 --> 00:01:50.142
So that is equivalent right over there.

00:01:50.142 --> 00:01:50.975
63 to 54.

00:01:52.606 --> 00:01:57.591
Let's see, to go from seven
to 63, you multiply by nine.

00:01:57.591 --> 00:02:01.841
And to go from six to 54,
you also multiply by nine.

00:02:01.841 --> 00:02:06.456
So once again, 63 to 54
is an equivalent ratio.

00:02:06.456 --> 00:02:08.042
And so we've already selected three,

00:02:08.042 --> 00:02:10.299
but let's just verify
that this doesn't work.

00:02:10.299 --> 00:02:14.662
So to go from seven to 84,
you would multiply by 12.

00:02:14.662 --> 00:02:16.412
To go from six to 62,

00:02:18.719 --> 00:02:22.015
you multiply by 10 and 2/6

00:02:22.015 --> 00:02:25.860
or 10 1/3, so this one is definitely not

00:02:25.860 --> 00:02:27.173
an equivalent ratio.

00:02:27.173 --> 00:02:29.256
Let's do another example.

00:02:30.100 --> 00:02:33.256
So once again, we are asked
to select three ratios

00:02:33.256 --> 00:02:35.923
that are equivalent to 16 to 12.

00:02:37.167 --> 00:02:40.866
So pause this video and see
if you can work through it.

00:02:40.866 --> 00:02:42.323
Alright, let's look at this first one.

00:02:42.323 --> 00:02:44.008
So eight to six.

00:02:44.008 --> 00:02:45.370
So at first you might say well, gee,

00:02:45.370 --> 00:02:47.776
these numbers are smaller than 16 and 12.

00:02:47.776 --> 00:02:49.996
Remember, you can, to
get an equivalent ratio

00:02:49.996 --> 00:02:52.200
you can multiply or divide these numbers

00:02:52.200 --> 00:02:54.078
by the same number.

00:02:54.078 --> 00:02:56.411
So, to get from 16 to eight,

00:02:57.249 --> 00:03:00.766
you could do that as, well,
we just divided by two.

00:03:00.766 --> 00:03:04.849
And to go from 12 to six,
you also divide by two.

00:03:05.993 --> 00:03:08.365
So this actually is an equivalent ratio.

00:03:08.365 --> 00:03:09.813
I'll circle that in.

00:03:09.813 --> 00:03:11.480
What about 32 to 24?

00:03:12.896 --> 00:03:17.115
Well to go from 16 to
32, we multiply by two.

00:03:17.115 --> 00:03:20.815
To go from 12 to 24, we
also multiply by two.

00:03:20.815 --> 00:03:23.369
So this is an equivalent ratio.

00:03:23.369 --> 00:03:25.181
What about four to three?

00:03:25.181 --> 00:03:27.532
Well, to go from 16 to four,

00:03:27.532 --> 00:03:30.951
we would have to divide by four.

00:03:30.951 --> 00:03:33.006
And to go from 12 to three,

00:03:33.006 --> 00:03:35.808
we are going to divide by four as well.

00:03:35.808 --> 00:03:37.127
So we're dividing by the same thing,

00:03:37.127 --> 00:03:38.212
each of these numbers.

00:03:38.212 --> 00:03:41.048
So, this is also going to
be an equivalent ratio.

00:03:41.048 --> 00:03:44.158
So we've selected our three,
so we are essentially done.

00:03:44.158 --> 00:03:47.471
But, we might as well
see why these don't work.

00:03:47.471 --> 00:03:48.700
Now let's think about it.

00:03:48.700 --> 00:03:50.367
To go from 16 to 12,

00:03:52.064 --> 00:03:53.389
how do we do that?

00:03:53.389 --> 00:03:55.822
Well, to go from 16 to 12,

00:03:55.822 --> 00:03:58.444
you could divide by four

00:03:58.444 --> 00:04:00.002
and multiply by three.

00:04:00.002 --> 00:04:03.621
So this would be times 3/4.

00:04:03.621 --> 00:04:04.935
You would get 12.

00:04:04.935 --> 00:04:06.852
And to go from 12 to eight,

00:04:06.852 --> 00:04:09.320
so you could divide by
three and multiply by two.

00:04:09.320 --> 00:04:12.685
So this you could view as times 2/3.

00:04:12.685 --> 00:04:14.578
So you'd be multiplying or dividing

00:04:14.578 --> 00:04:17.705
by different numbers here, so
this one is not equivalent.

00:04:17.705 --> 00:04:19.680
And then 24 to 16?

00:04:19.680 --> 00:04:22.850
To go from 16 to 24,
you would multiply by,

00:04:22.850 --> 00:04:25.320
let's see, that's 1 1/2.

00:04:25.320 --> 00:04:26.505
So this right over here would be,

00:04:26.505 --> 00:04:29.231
you would multiply by 1 1/2.

00:04:29.231 --> 00:04:32.452
And to go from 12 to
16, you would multiply,

00:04:32.452 --> 00:04:34.761
that is, by 1 1/3.

00:04:34.761 --> 00:04:37.392
So, times 1 1/3.

00:04:37.392 --> 00:04:39.248
So you're not multiplying
by the same amount.

00:04:39.248 --> 00:04:42.498
So once again, not an equivalent ratio.


Ratio word problem examples

WEBVTT
Kind: captions
Language: en

00:00:00.380 --> 00:00:01.643
- [Instructor] What we're
going to do in this video

00:00:01.643 --> 00:00:06.220
is tackle some word
problems involving ratios.

00:00:06.220 --> 00:00:08.675
So here, we're told that Yoda Soda

00:00:08.675 --> 00:00:10.833
is the intergalactic party drink

00:00:10.833 --> 00:00:15.561
that will have all of your
friends saying, mm, good this is.

00:00:15.561 --> 00:00:17.185
You are throwing a party

00:00:17.185 --> 00:00:21.352
and you need five liters of
Yoda Soda for every 12 guests.

00:00:22.870 --> 00:00:25.236
If you have 36 guests,

00:00:25.236 --> 00:00:29.155
how many liters of Yoda Soda do you need?

00:00:29.155 --> 00:00:33.108
So pause this video and try
to figure it out on your own.

00:00:33.108 --> 00:00:36.525
Well, they tell us the
ratio of liters of soda

00:00:36.525 --> 00:00:38.398
to number of guests.

00:00:38.398 --> 00:00:41.935
So you need five, it's five liters

00:00:41.935 --> 00:00:44.602
for every 12 guests is the ratio

00:00:45.528 --> 00:00:47.935
but we wanna have 36 guests.

00:00:47.935 --> 00:00:52.505
So if the ratio is five liters
of soda for every 12 guests

00:00:52.505 --> 00:00:55.321
but we're in a situation
where we have 36 guests,

00:00:55.321 --> 00:00:57.928
so this is three times as many guests,

00:00:57.928 --> 00:01:02.249
we're gonna need three times
as many liters of soda.

00:01:02.249 --> 00:01:05.058
So three times five is 15.

00:01:05.058 --> 00:01:06.563
Five to 12.

00:01:06.563 --> 00:01:08.190
Five liters for 12 guests

00:01:08.190 --> 00:01:10.393
or for five liters for every 12 guests

00:01:10.393 --> 00:01:14.018
is the same thing as 15
liters for every 36 guests.

00:01:14.018 --> 00:01:15.035
So to answer that question,

00:01:15.035 --> 00:01:16.717
how many liters do you need,

00:01:16.717 --> 00:01:18.300
you need 15 liters.

00:01:19.160 --> 00:01:21.660
Let's do another one of these.

00:01:23.999 --> 00:01:25.693
Here, we just have a picture

00:01:25.693 --> 00:01:27.484
of a bunch of fish in a tank

00:01:27.484 --> 00:01:29.482
and it says there are eight big fish

00:01:29.482 --> 00:01:32.142
for every blank small fish

00:01:32.142 --> 00:01:33.607
and then it says there are four big fish

00:01:33.607 --> 00:01:35.808
for every blank small fish.

00:01:35.808 --> 00:01:36.990
So pause this video again

00:01:36.990 --> 00:01:39.683
and see if you can work through this.

00:01:39.683 --> 00:01:43.233
Alright, so let's just
count the big fish first.

00:01:43.233 --> 00:01:45.397
So there's one, two, three,

00:01:45.397 --> 00:01:46.376
wait, let me count this way.

00:01:46.376 --> 00:01:49.306
One, two, three, four,
five, six, seven, eight.

00:01:49.306 --> 00:01:52.282
So in this tank, there
actually are eight big fish

00:01:52.282 --> 00:01:53.998
and so let's see how many
small fish there are.

00:01:53.998 --> 00:01:56.569
There's one, two, three, four, five,

00:01:56.569 --> 00:01:59.819
six, seven, eight, nine, 10 small fish.

00:02:01.049 --> 00:02:03.164
So in the tank, for every eight big fish

00:02:03.164 --> 00:02:06.345
which you see in red,
there are 10 small fish

00:02:06.345 --> 00:02:08.955
but here it says, there are four big fish

00:02:08.955 --> 00:02:10.622
for every blank small fish.

00:02:10.622 --> 00:02:12.223
So what would that be?

00:02:12.223 --> 00:02:13.389
Well, one way to think about it

00:02:13.389 --> 00:02:15.722
is we have half as many fish

00:02:17.190 --> 00:02:19.931
or half as many big fish
so we divided it by two.

00:02:19.931 --> 00:02:22.536
So we're gonna have
half as many small fish.

00:02:22.536 --> 00:02:24.042
So we're gonna divide by two.

00:02:24.042 --> 00:02:28.357
So for every four big fish,
there are five small fish

00:02:28.357 --> 00:02:29.254
and one way to think about it,

00:02:29.254 --> 00:02:31.338
you could divide the fish evenly

00:02:31.338 --> 00:02:33.334
into two groups right over here.

00:02:33.334 --> 00:02:35.456
So let's see, if we can capture,

00:02:35.456 --> 00:02:37.956
so if you could have, this is,

00:02:39.453 --> 00:02:40.798
if I divide it like that,

00:02:40.798 --> 00:02:45.071
here I have one, two, three, four big fish

00:02:45.071 --> 00:02:48.170
and one, two, three, four, five small fish

00:02:48.170 --> 00:02:51.557
then in this group I have
one, two, three, four big fish

00:02:51.557 --> 00:02:54.706
and one, two, three,
four, five small fish.

00:02:54.706 --> 00:02:58.296
So every four big fish,
there are five small fish.

00:02:58.296 --> 00:03:00.459
These are equivalent ratios.

00:03:00.459 --> 00:03:01.876
Let's keep going.

00:03:04.539 --> 00:03:07.433
So here, we're told an ice cream shop

00:03:07.433 --> 00:03:11.143
uses the following ingredients
to make one sundae.

00:03:11.143 --> 00:03:13.101
So they use two scoops of ice cream,

00:03:13.101 --> 00:03:15.461
four spoonfuls of sprinkles,

00:03:15.461 --> 00:03:17.909
two tablespoons of whipped cream.

00:03:17.909 --> 00:03:20.111
How many sundaes did the shop make

00:03:20.111 --> 00:03:23.361
if they used 32 spoonfuls of sprinkles?

00:03:25.286 --> 00:03:28.793
So pause the video and
try to think about it.

00:03:28.793 --> 00:03:31.205
So there's a couple of
ways to think about it.

00:03:31.205 --> 00:03:34.059
Here, it says, let's see,
we're talking about sprinkles.

00:03:34.059 --> 00:03:35.608
So that's what's relevant here.

00:03:35.608 --> 00:03:38.752
Four spoonfuls for every one sundae.

00:03:38.752 --> 00:03:40.229
So we could say that there,

00:03:40.229 --> 00:03:45.076
so the ratio of spoonfuls
to sundaes is four to one.

00:03:45.076 --> 00:03:48.326
Four spoonfuls, spoonfuls of sprinkles,

00:03:50.325 --> 00:03:51.208
let me write it this way,

00:03:51.208 --> 00:03:54.335
let me write sprinkles, sprinkles.

00:03:54.335 --> 00:03:56.241
How many spoonfuls?

00:03:56.241 --> 00:03:59.074
How many spoonfuls for one sundae?

00:04:01.634 --> 00:04:05.908
But here we're talking about
using 32 spoonfuls of sprinkles

00:04:05.908 --> 00:04:08.146
so that is eight times as many.

00:04:08.146 --> 00:04:09.941
So you're going to be able to use,

00:04:09.941 --> 00:04:12.633
create eight times as many sundaes.

00:04:12.633 --> 00:04:15.435
So you're gonna have 32
spoonfuls of sprinkles

00:04:15.435 --> 00:04:17.656
for every eight sundaes.

00:04:17.656 --> 00:04:19.486
So how many sundaes did the shop make?

00:04:19.486 --> 00:04:21.530
Well, they made eight.

00:04:21.530 --> 00:04:23.697
Let's do one last example.

00:04:26.261 --> 00:04:29.239
At a dog park, there are 10 black dogs,

00:04:29.239 --> 00:04:33.406
five brown dogs, two white
dogs and 12 multi-color dogs.

00:04:35.563 --> 00:04:39.730
For every one brown dog,
there are two blank dogs.

00:04:41.105 --> 00:04:44.614
Pause the video and figure
out what goes in this blank.

00:04:44.614 --> 00:04:46.248
Alright, so let's see.

00:04:46.248 --> 00:04:50.286
There's five brown dogs
for every 10 black dogs,

00:04:50.286 --> 00:04:53.020
five brown dogs for every two white dogs

00:04:53.020 --> 00:04:57.672
and five brown dogs for
every 12 multi-color dogs

00:04:57.672 --> 00:04:59.747
but here you're saying
for every one brown dog,

00:04:59.747 --> 00:05:02.518
there are two blank dogs.

00:05:02.518 --> 00:05:05.210
So what type of dog is there a ratio?

00:05:05.210 --> 00:05:06.431
So for every brown dog,

00:05:06.431 --> 00:05:09.450
there's twice as many of that type of dog.

00:05:09.450 --> 00:05:13.784
Well, here, we see for
every five brown dogs,

00:05:13.784 --> 00:05:15.784
there are 10 black dogs.

00:05:16.970 --> 00:05:17.867
So one way to think about it,

00:05:17.867 --> 00:05:19.213
the number of black dogs

00:05:19.213 --> 00:05:22.470
is always gonna be twice
the number of brown dogs.

00:05:22.470 --> 00:05:24.023
So for every one brown dog,

00:05:24.023 --> 00:05:27.856
there would be two, two
black, two black dogs.

00:05:29.973 --> 00:05:30.951
One way to think about it,

00:05:30.951 --> 00:05:33.934
the ratio between brown
dogs and black dogs

00:05:33.934 --> 00:05:35.235
and it's kinda counterintuitive.

00:05:35.235 --> 00:05:36.212
I used the wrong colors here.

00:05:36.212 --> 00:05:37.801
I should have used brown and black.

00:05:37.801 --> 00:05:39.023
So let me do that.

00:05:39.023 --> 00:05:41.178
So the ratio of brown to black

00:05:41.178 --> 00:05:45.011
is five brown dogs for
every 10, 10 black dogs

00:05:47.201 --> 00:05:50.382
or if you divide both of
these numbers by five,

00:05:50.382 --> 00:05:53.049
you would get one, one brown dog

00:05:54.256 --> 00:05:58.335
for every two, for every two black dogs

00:05:58.335 --> 00:06:01.670
and that's exactly what
this statement is saying.


Ratio example problems

WEBVTT
Kind: captions
Language: en

00:00:00.432 --> 00:00:02.254
- [Instructor] Let's do
some example questions

00:00:02.254 --> 00:00:04.188
dealing with ratios.

00:00:04.188 --> 00:00:07.442
So we're told, "The table shows
the number of people waiting

00:00:07.442 --> 00:00:10.770
"in line for different
rides at an amusement park."

00:00:10.770 --> 00:00:13.363
So 15 people are waiting in
line for the roller coaster,

00:00:13.363 --> 00:00:15.235
four people for the slingshot,

00:00:15.235 --> 00:00:17.773
12 people waiting in line
for the bumper cards,

00:00:17.773 --> 00:00:20.534
and 11 people in line for the round-up.

00:00:20.534 --> 00:00:24.584
"What is the ratio of
people waiting in line

00:00:24.584 --> 00:00:26.001
"for the round-up

00:00:27.128 --> 00:00:31.954
"to the people waiting in
line for the slingshot?"

00:00:31.954 --> 00:00:35.275
Pause this video and see
if you can figure it out.

00:00:35.275 --> 00:00:38.143
So we wanna know the ratio
of the people waiting in line

00:00:38.143 --> 00:00:42.294
for the round-up, this is
the round-up right over here,

00:00:42.294 --> 00:00:46.461
to the number of people waiting
in line for the slingshot.

00:00:47.987 --> 00:00:52.644
So, there's 11 people waiting
in line for the round-up,

00:00:52.644 --> 00:00:56.843
and there are four people waiting
in line for the slingshot,

00:00:56.843 --> 00:00:59.524
so the ratio is 11 to four.

00:00:59.524 --> 00:01:02.666
Or for every 11 people
in line for the round-up,

00:01:02.666 --> 00:01:06.833
there are four people waiting
in line for the slingshot.

00:01:07.695 --> 00:01:09.778
Let's do another example.

00:01:10.762 --> 00:01:13.323
"Katie loves to read!

00:01:13.323 --> 00:01:17.335
"In the last few months, she
has read three graphic novels,

00:01:17.335 --> 00:01:20.832
"two mysteries, four
science fiction novels,

00:01:20.832 --> 00:01:23.075
"and 21 comic books.

00:01:23.075 --> 00:01:27.332
"What is the ratio of sci-fi
novels to comic books?"

00:01:27.332 --> 00:01:28.911
So once again, pause this video

00:01:28.911 --> 00:01:31.598
and try to work it out on your own.

00:01:31.598 --> 00:01:34.450
All right, so we wanted to know
the ratio of sci-fi novels,

00:01:34.450 --> 00:01:36.950
so she has four sci-fi novels,

00:01:39.382 --> 00:01:41.970
the ratio of that to comic books.

00:01:41.970 --> 00:01:43.887
She has 21 comic books.

00:01:44.744 --> 00:01:49.277
So the ratio is for
every four sci-fi novels,

00:01:49.277 --> 00:01:51.194
she has 21 comic books.

00:01:52.371 --> 00:01:54.223
Do you want me to do
that in that other color?

00:01:54.223 --> 00:01:56.118
She has 21 comic books.

00:01:56.118 --> 00:01:58.368
So the ratio is four to 21,

00:01:59.621 --> 00:02:02.616
the ratio of sci-fi novels to comic books.

00:02:02.616 --> 00:02:06.867
Four sci-fi novels for
every 21 comic books.

00:02:06.867 --> 00:02:08.363
Let's do one more example.

00:02:08.363 --> 00:02:10.196
This is strangely fun.

00:02:11.623 --> 00:02:14.113
"What is the ratio of apples to bananas?"

00:02:14.113 --> 00:02:16.906
Pause this video and try to figure it out.

00:02:16.906 --> 00:02:20.368
So let's see, there are
one, two, three apples.

00:02:20.368 --> 00:02:23.747
So for every three apples,
how many bananas are there?

00:02:23.747 --> 00:02:27.710
Well, there's one, two,
three, four bananas.

00:02:27.710 --> 00:02:29.877
So the ratio of apples to,

00:02:32.104 --> 00:02:35.937
the ratio of apples to
bananas is three apples

00:02:38.763 --> 00:02:40.679
for every four bananas.

00:02:40.679 --> 00:02:41.637
Order matters.

00:02:41.637 --> 00:02:44.087
If they said the ratio
of bananas to apples,

00:02:44.087 --> 00:02:45.640
then this would be four to three,

00:02:45.640 --> 00:02:49.106
but they say apples to
bananas, three to four.

00:02:49.106 --> 00:02:52.033
Three apples for every four bananas.


Understanding equivalent ratios

WEBVTT
Kind: captions
Language: en

00:00:00.690 --> 00:00:01.915
- [Voiceover] We're told that Burger Barn

00:00:01.915 --> 00:00:05.734
makes dipping sauce by
mixing two spoonfuls of honey

00:00:05.734 --> 00:00:09.313
with one half spoonful of mustard.

00:00:09.313 --> 00:00:11.108
Sandwich Town makes dipping sauce

00:00:11.108 --> 00:00:13.164
by mixing four spoonfuls of honey

00:00:13.164 --> 00:00:16.373
with one spoonful of mustard.

00:00:16.373 --> 00:00:21.362
Which dipping sauce has a
stronger mustard flavor?

00:00:21.362 --> 00:00:22.945
So pause this video and see if you can

00:00:22.945 --> 00:00:25.108
work through that on your own.

00:00:25.108 --> 00:00:26.772
All right, now let's
think about the ratios

00:00:26.772 --> 00:00:30.831
of honey to mustard at
each of these restaurants.

00:00:30.831 --> 00:00:34.159
So first let's think about
the scenario with Burger Barn.

00:00:34.159 --> 00:00:37.658
So I'll just say BB for
short, for Burger Burn.

00:00:37.658 --> 00:00:39.974
So they have two spoonfuls of honey

00:00:39.974 --> 00:00:42.376
for every one half spoonful of mustard,

00:00:42.376 --> 00:00:44.793
so the ratio of honey to mustard

00:00:44.793 --> 00:00:48.710
in terms of spoonfuls is
two spoonfuls of honey

00:00:50.121 --> 00:00:53.371
for every one half spoonful of mustard,

00:00:55.298 --> 00:00:58.618
so this is the ratio of honey to mustard.

00:00:58.618 --> 00:00:59.679
Let me write this.

00:00:59.679 --> 00:01:04.672
This is honey, and this
right over here is mustard.

00:01:04.672 --> 00:01:08.839
Now, let's look at Sandwich
Town, so I'll call that ST.

00:01:10.626 --> 00:01:12.083
So Sandwich Town makes dipping sauce

00:01:12.083 --> 00:01:14.552
by having four spoonfuls of honey

00:01:14.552 --> 00:01:16.894
for every one spoonful of mustard.

00:01:16.894 --> 00:01:18.996
So the ratio of honey to mustard

00:01:18.996 --> 00:01:22.599
is four spoonfuls to one spoonful,

00:01:22.599 --> 00:01:26.682
so once again, that is
honey and that is mustard.

00:01:29.251 --> 00:01:31.870
Now, can we make these equivalent ratios

00:01:31.870 --> 00:01:33.577
or can we compare them somehow?

00:01:33.577 --> 00:01:35.081
Well, let's see.

00:01:35.081 --> 00:01:37.852
We have one half spoonful of mustard here.

00:01:37.852 --> 00:01:39.602
We have one spoon of mustard here,

00:01:39.602 --> 00:01:41.342
so what if we multiplied both the mustard

00:01:41.342 --> 00:01:44.380
and the honey spoonfuls by two?

00:01:44.380 --> 00:01:45.669
That still would be an equivalent ratio

00:01:45.669 --> 00:01:48.053
because we're multiplying
by the same amount.

00:01:48.053 --> 00:01:51.934
So if we multiply by
two in both situations,

00:01:51.934 --> 00:01:54.571
you have four spoonfuls of honey

00:01:54.571 --> 00:01:57.404
for every one spoonful of mustard.

00:01:59.044 --> 00:02:00.460
Well, that's the exact same ratio

00:02:00.460 --> 00:02:02.157
that we have at Sandwich Town.

00:02:02.157 --> 00:02:04.465
So it actually turns out that they have

00:02:04.465 --> 00:02:07.960
the same concentration of mustard.

00:02:07.960 --> 00:02:11.929
They have the same ratio
of honey to mustard.

00:02:11.929 --> 00:02:15.174
Four spoonfuls of honey for
every spoonful of mustard

00:02:15.174 --> 00:02:17.434
in either situation.

00:02:17.434 --> 00:02:18.820
Let's do another example.

00:02:18.820 --> 00:02:22.987
So here, we are asked or
we are told, we are told,

00:02:25.817 --> 00:02:28.674
Patrick's favorite shade of purple paint

00:02:28.674 --> 00:02:31.343
is made with four ounces of blue paint,

00:02:31.343 --> 00:02:35.510
so underline that in blue,
four ounces of blue paint,

00:02:36.784 --> 00:02:39.312
for every three ounces of red paint,

00:02:39.312 --> 00:02:41.610
for every three ounces of red paint.

00:02:41.610 --> 00:02:44.280
So the ratio of blue paint to red paint

00:02:44.280 --> 00:02:47.947
is four ounces of blue,
four ounces of blue,

00:02:50.063 --> 00:02:54.063
for every three ounces
of red, so four to three.

00:02:55.197 --> 00:02:56.825
Which of the following paint mixtures

00:02:56.825 --> 00:03:00.223
will create the same shade of purple?

00:03:00.223 --> 00:03:01.623
All right, pause this video

00:03:01.623 --> 00:03:04.826
and see if you can figure
it out on your own.

00:03:04.826 --> 00:03:06.559
So this is three ounces of blue paint

00:03:06.559 --> 00:03:08.702
mixed with four ounces of red paint.

00:03:08.702 --> 00:03:12.369
Well, this is a ratio
here of three to four,

00:03:14.804 --> 00:03:16.739
and even though it's dealing
with the same numbers,

00:03:16.739 --> 00:03:18.023
this is a different ratio.

00:03:18.023 --> 00:03:19.238
The order matters.

00:03:19.238 --> 00:03:22.318
This is four ounces of blue
for every three ounces of red.

00:03:22.318 --> 00:03:24.489
This is saying three ounces of blue

00:03:24.489 --> 00:03:29.110
for every four ounces of red,
so we could rule this one out.

00:03:29.110 --> 00:03:30.890
Eight ounces of blue paint mixed

00:03:30.890 --> 00:03:32.372
with six ounces of red paint.

00:03:32.372 --> 00:03:35.672
So here, this ratio is
eight ounces of blue

00:03:35.672 --> 00:03:38.005
for every six ounces of red.

00:03:40.133 --> 00:03:42.252
Well, are these equivalent ratios?

00:03:42.252 --> 00:03:45.153
Well, the difference, or you can go,

00:03:45.153 --> 00:03:48.320
if you multiply by two in either case,

00:03:49.527 --> 00:03:52.056
you will get to eight to six.

00:03:52.056 --> 00:03:55.677
Four times two is eight,
three times two is six.

00:03:55.677 --> 00:03:57.917
So this is indeed an equivalent ratio,

00:03:57.917 --> 00:03:59.971
so we would select this one.

00:03:59.971 --> 00:04:02.173
All right, here they say
six ounces of blue paint

00:04:02.173 --> 00:04:04.906
mixed with eight ounces of red paint.

00:04:04.906 --> 00:04:08.221
So this is, they've swapped
the blues and the red

00:04:08.221 --> 00:04:11.293
relative to this one, so this
is a ratio of six to eight,

00:04:11.293 --> 00:04:13.238
so let me write this down.

00:04:13.238 --> 00:04:15.439
So this is a ratio, six
ounces of blue paint

00:04:15.439 --> 00:04:18.409
for every eight ounces of red paint.

00:04:18.409 --> 00:04:20.064
So just like we ruled out that first one,

00:04:20.064 --> 00:04:22.001
this is dealing with the same numbers

00:04:22.001 --> 00:04:23.935
but in a different order
and the order matters,

00:04:23.935 --> 00:04:25.374
so we'll rule that out.

00:04:25.374 --> 00:04:29.783
20 ounces of blue paint,
20 ounces of blue paint,

00:04:29.783 --> 00:04:33.176
for every 15 ounces of red paint.

00:04:33.176 --> 00:04:35.381
So are these equivalent?

00:04:35.381 --> 00:04:37.319
Well, let's think about it.

00:04:37.319 --> 00:04:41.555
To go from four to 20,
you can multiply by five,

00:04:41.555 --> 00:04:44.546
and to go from three to 15,
you could multiply by five,

00:04:44.546 --> 00:04:45.999
so we can multiply by the same factor

00:04:45.999 --> 00:04:48.738
to go from four to three to 20 to 15,

00:04:48.738 --> 00:04:51.905
so this is indeed an equivalent ratio.

00:04:53.060 --> 00:04:57.649
12 ounces of blue paint mixed
with 16 ounces of red paint.

00:04:57.649 --> 00:04:59.368
All right, so this is a ratio here

00:04:59.368 --> 00:05:03.368
of 12 ounces of blue for
every 16 ounces of red.

00:05:04.302 --> 00:05:06.728
So let's think about this.

00:05:06.728 --> 00:05:10.895
To go from four to 12, you
would multiply by three.

00:05:14.600 --> 00:05:16.255
Now, if you multiplied three by three,

00:05:16.255 --> 00:05:18.547
you would have a nine here, not a 16,

00:05:18.547 --> 00:05:20.732
so this is definitely
not an equivalent ratio.

00:05:20.732 --> 00:05:21.805
Another way of thinking about it,

00:05:21.805 --> 00:05:23.851
you have, in terms of ounces,

00:05:23.851 --> 00:05:26.275
you have more ounces of
blue than you have of red

00:05:26.275 --> 00:05:27.827
for any of the equivalent ratios,

00:05:27.827 --> 00:05:30.088
but here you have more
ounces of red than blue,

00:05:30.088 --> 00:05:32.005
so once again, another way of realizing

00:05:32.005 --> 00:05:33.440
that that is not equivalent,

00:05:33.440 --> 00:05:37.740
so only B and D are
the equivalent mixtures

00:05:37.740 --> 00:05:40.840
that will provide the
same shade of purple.

00:05:40.840 --> 00:05:41.875
To have that same shade,

00:05:41.875 --> 00:05:44.441
you need the same ratio of blue to red.


Dilations and shape properties

WEBVTT
Kind: captions
Language: en

00:00:00.749 --> 00:00:02.104
- [Instructor] What we're
going to do in this video

00:00:02.104 --> 00:00:05.815
is think about how shapes' properties

00:00:05.815 --> 00:00:09.667
might be preserved or not
preserved from dilations

00:00:09.667 --> 00:00:11.378
and so here we have this quadrilateral

00:00:11.378 --> 00:00:14.206
and we're going to dilate
it about point P here

00:00:14.206 --> 00:00:17.104
and I have this little Dilation tool.

00:00:17.104 --> 00:00:18.422
So the first question is

00:00:18.422 --> 00:00:21.756
are the coordinates of the
vertices going to be preserved?

00:00:21.756 --> 00:00:24.249
Well, pause the video and
try to think about that.

00:00:24.249 --> 00:00:26.165
Let's just try it out experimentally.

00:00:26.165 --> 00:00:29.185
We can see under an
arbitrary dilation here,

00:00:29.185 --> 00:00:30.906
the coordinates are not preserved.

00:00:30.906 --> 00:00:32.577
The point that corresponds to D

00:00:32.577 --> 00:00:34.382
now has a different coordinate.

00:00:34.382 --> 00:00:37.155
The vertices, the vertex
that corresponds to A

00:00:37.155 --> 00:00:38.460
now has different coordinates.

00:00:38.460 --> 00:00:40.049
Same thing for B and C.

00:00:40.049 --> 00:00:42.372
The corresponding points
after the dilation

00:00:42.372 --> 00:00:46.164
now sit on a different part
of the coordinate plane.

00:00:46.164 --> 00:00:48.030
So in this case, the
coordinates of the vertices

00:00:48.030 --> 00:00:49.988
are not preserved.

00:00:49.988 --> 00:00:53.528
Now, the next question, let
me go back to where we were.

00:00:53.528 --> 00:00:54.694
So the next question,

00:00:54.694 --> 00:00:57.937
the corresponding line
segments after dilation,

00:00:57.937 --> 00:01:00.997
are they sitting on the same line

00:01:00.997 --> 00:01:03.164
and so let me dilate again

00:01:04.094 --> 00:01:07.440
and so you can see if you
consider this point B prime

00:01:07.440 --> 00:01:09.191
'cause it corresponds to point B,

00:01:09.191 --> 00:01:11.837
the segment B prime C prime,

00:01:11.837 --> 00:01:15.170
this does not sit on the same line as BC

00:01:16.278 --> 00:01:18.278
but the segment D prime,

00:01:19.500 --> 00:01:22.764
the corresponding line
segment to line segment AD,

00:01:22.764 --> 00:01:24.930
that does sit on the same line

00:01:24.930 --> 00:01:27.131
and if you think about why that is,

00:01:27.131 --> 00:01:30.464
well, if we originally draw a line that,

00:01:31.700 --> 00:01:36.308
if we look at the line
that contains segment AD,

00:01:36.308 --> 00:01:40.180
it also goes through point
P and so as we expand out,

00:01:40.180 --> 00:01:41.767
this segment right over here

00:01:41.767 --> 00:01:45.926
is going to expand and shift
outward along the same lines

00:01:45.926 --> 00:01:48.938
but that's not going to be
true of these other segments

00:01:48.938 --> 00:01:50.407
because they don't,

00:01:50.407 --> 00:01:53.265
because the point P
does not sit on the line

00:01:53.265 --> 00:01:55.959
that those segments sit on

00:01:55.959 --> 00:01:57.838
and so let's just expand it again

00:01:57.838 --> 00:02:00.082
so you see that right over there.

00:02:00.082 --> 00:02:03.424
Now, the next question, are
angle measures preserved?

00:02:03.424 --> 00:02:04.770
Well, it looks like they are

00:02:04.770 --> 00:02:05.626
and this is one of the things

00:02:05.626 --> 00:02:07.786
that is true about a dilation

00:02:07.786 --> 00:02:10.150
is that you're going to
preserve angle measures.

00:02:10.150 --> 00:02:11.905
This angle is still a right angle.

00:02:11.905 --> 00:02:14.751
This angle here, I guess
you can call it angle,

00:02:14.751 --> 00:02:16.094
the measure of angle B

00:02:16.094 --> 00:02:18.468
is the same as the
measure of angle B prime

00:02:18.468 --> 00:02:21.809
and you can see it with all of
these points right over there

00:02:21.809 --> 00:02:22.814
and then the last question.

00:02:22.814 --> 00:02:27.113
Are side lengths, perimeter
and area preserved?

00:02:27.113 --> 00:02:30.175
Well, we can immediately
see as we dilate outwards,

00:02:30.175 --> 00:02:32.913
for example, the segment
corresponding to AD

00:02:32.913 --> 00:02:34.011
has gotten longer.

00:02:34.011 --> 00:02:37.078
In fact, if we dilate
outwards, all of the segments,

00:02:37.078 --> 00:02:39.041
the corresponding segments
are getting larger

00:02:39.041 --> 00:02:40.504
and if they're all getting larger

00:02:40.504 --> 00:02:41.975
then the perimeter's getting larger

00:02:41.975 --> 00:02:43.358
and the area's getting larger.

00:02:43.358 --> 00:02:45.766
Likewise, if we dilate in like this,

00:02:45.766 --> 00:02:47.193
they're all getting smaller.

00:02:47.193 --> 00:02:51.232
So side lengths, perimeter
and area are not preserved.

00:02:51.232 --> 00:02:54.536
Now, let's ask the same
questions with another dilation

00:02:54.536 --> 00:02:55.676
and this is going to be interesting

00:02:55.676 --> 00:02:57.389
because we're going to look at a dilation

00:02:57.389 --> 00:03:01.270
that is centered at one of
the vertices of our shape.

00:03:01.270 --> 00:03:03.437
So let me scroll down here

00:03:04.775 --> 00:03:07.913
and so I have the same tool again

00:03:07.913 --> 00:03:10.484
and now here we have a
triangle, triangle ABC

00:03:10.484 --> 00:03:13.906
and we're gonna dilate about point C.

00:03:13.906 --> 00:03:16.359
So first of all, do we think the vertices,

00:03:16.359 --> 00:03:19.625
the coordinates of the vertices
are going to be preserved?

00:03:19.625 --> 00:03:21.414
Let's dilate out.

00:03:21.414 --> 00:03:24.729
Well, you can see point C is preserved.

00:03:24.729 --> 00:03:26.526
When it gets mapped after the dilation,

00:03:26.526 --> 00:03:28.484
it sits in the exact same place

00:03:28.484 --> 00:03:32.482
but the things that correspond
to A and B are not preserved.

00:03:32.482 --> 00:03:33.835
You could call this A prime

00:03:33.835 --> 00:03:36.119
and this definitely has
different coordinates than A

00:03:36.119 --> 00:03:39.670
and B prime definitely has
different coordinates than B.

00:03:39.670 --> 00:03:42.319
Now, what about
corresponding line segments?

00:03:42.319 --> 00:03:44.560
Are they on the same line?

00:03:44.560 --> 00:03:46.887
Well, some of them are
and some of them aren't.

00:03:46.887 --> 00:03:50.016
So for example, when we dilate,

00:03:50.016 --> 00:03:54.460
so let's look at the segment
AC and the segment BC,

00:03:54.460 --> 00:03:57.605
when we dilate, we can see, whoops,

00:03:57.605 --> 00:04:00.226
when we dilate, we can see
the corresponding segments,

00:04:00.226 --> 00:04:04.533
you could call this A prime
C prime or B prime C prime,

00:04:04.533 --> 00:04:06.991
do still sit on that same line

00:04:06.991 --> 00:04:10.622
and that's because the point
that we are dilating about,

00:04:10.622 --> 00:04:13.434
point C, sat on those original segments.

00:04:13.434 --> 00:04:15.845
So we're essentially just lengthening out

00:04:15.845 --> 00:04:18.655
on the point that is not
the center of dilation.

00:04:18.655 --> 00:04:20.490
We're lengthening out away from it

00:04:20.490 --> 00:04:22.857
or if the dilation is going in,

00:04:22.857 --> 00:04:27.099
we would be shortening
along that same line

00:04:27.099 --> 00:04:28.612
but some of the segments

00:04:28.612 --> 00:04:30.985
are not overlapping on the same line.

00:04:30.985 --> 00:04:33.432
So for example, A prime B prime

00:04:33.432 --> 00:04:36.682
does not sit along the same line as AB.

00:04:37.796 --> 00:04:39.718
Now, what about the angle measures?

00:04:39.718 --> 00:04:41.346
Well, we already talked about it.

00:04:41.346 --> 00:04:43.882
Angle measures are
preserved under dilations.

00:04:43.882 --> 00:04:47.120
The measure of angle C here,
this is the exact same angle

00:04:47.120 --> 00:04:50.092
and so is the measure of angle
you could call this A prime

00:04:50.092 --> 00:04:52.652
and B prime right over here.

00:04:52.652 --> 00:04:54.978
And then finally, what about side lengths?

00:04:54.978 --> 00:04:58.397
Well, you can clearly see
that when I dilate out,

00:04:58.397 --> 00:05:01.090
my side lengths increase
or if I dilate in,

00:05:01.090 --> 00:05:02.677
my side lengths decrease

00:05:02.677 --> 00:05:05.168
and so side lengths are not preserved

00:05:05.168 --> 00:05:06.842
and if side lengths are not preserved

00:05:06.842 --> 00:05:08.597
then the perimeter is not preserved

00:05:08.597 --> 00:05:10.754
and also the area is not preserved.

00:05:10.754 --> 00:05:13.891
You could view area as a
function of the side lengths.

00:05:13.891 --> 00:05:15.115
As we dilate out like this,

00:05:15.115 --> 00:05:17.314
the perimeter grows and so does the area.

00:05:17.314 --> 00:05:18.748
If we dilate in like this,

00:05:18.748 --> 00:05:22.265
the perimeter shrinks
and so does the area.


Happy Mole Day!

WEBVTT
Kind: captions
Language: en

00:00:00.480 --> 00:00:02.660
Hey everybody! Rocco T. Mole here

00:00:02.660 --> 00:00:04.660
to wish you a Happy Mole Day

00:00:04.680 --> 00:00:06.680
from all of us at Khan Academy!

00:00:07.349 --> 00:00:09.360
Yes, moles!

00:00:09.370 --> 00:00:11.749
The chemistry concept, not the critter.

00:00:11.749 --> 00:00:14.900
Now, in case you’ve been living under a rock (like me)

00:00:14.900 --> 00:00:17.700
a mole is another name for Avogadro’s number

00:00:17.700 --> 00:00:20.700
which is (approximately) 6.022 times 10 to the 23rd.

00:00:20.700 --> 00:00:23.740
Kinda like how a “dozen” is another name for 12.

00:00:23.740 --> 00:00:26.980
So why do we need a name for such a big number?!

00:00:26.980 --> 00:00:32.540
Well, we could write it like this: 602,214,129,000,000,000,000,000

00:00:32.540 --> 00:00:33.840
(Thank you)

00:00:33.840 --> 00:00:35.380
But that would take a while!

00:00:35.380 --> 00:00:37.820
Moles make counting easier for chemists,

00:00:37.820 --> 00:00:40.800
particularly when talking about atoms or molecules.

00:00:40.820 --> 00:00:43.520
So for the number of molecules in a cup of water,

00:00:43.520 --> 00:00:47.340
you could write an 8 with 24 zeros after it...

00:00:47.340 --> 00:00:52.280
OR you could just call it 13 moles of water instead!

00:00:52.280 --> 00:00:52.920
(Thank you Yuki)

00:00:52.920 --> 00:00:55.260
Isn't that easier?

00:00:55.260 --> 00:00:59.280
Now, the moral of this story is: moles are the best!

00:00:59.280 --> 00:01:01.680
And if you want to learn more about chemistry,

00:01:01.720 --> 00:01:06.770
or anything, really, head to our website: khanacademy.org

00:01:06.770 --> 00:01:11.740
That's Khan as in Ghenghis, no relation; and Academy, as in academy.

00:01:11.740 --> 00:01:13.240
Happy Mole Day everyone!

00:01:13.240 --> 00:01:14.800
You can learn anything!

00:01:22.880 --> 00:01:24.300
Are we still–we're not recording, right?


Liters to milliliters examples

WEBVTT
Kind: captions
Language: en

00:00:00.296 --> 00:00:01.576
- [Instructor] What we're
going to do in this video

00:00:01.576 --> 00:00:05.419
is some examples converting
between liters and milliliters

00:00:05.419 --> 00:00:10.080
and just as a reminder,
milli means one-thousandth

00:00:10.080 --> 00:00:13.817
so a milliliter is
one-thousandth of a liter,

00:00:13.817 --> 00:00:14.957
or another way to think about it,

00:00:14.957 --> 00:00:17.457
one liter is 1000 milliliters.

00:00:19.873 --> 00:00:23.989
So given that, how many
milliliters would seven liters be?

00:00:23.989 --> 00:00:26.233
Pause the video and think about that.

00:00:26.233 --> 00:00:29.129
Well if one liter is 1000 milliliters,

00:00:29.129 --> 00:00:33.298
then seven liters would
be 7000 milliliters.

00:00:33.298 --> 00:00:34.972
And what about 18 liters?

00:00:34.972 --> 00:00:36.699
Pause the video and think about it.

00:00:36.699 --> 00:00:39.866
Well that would be 18,000 milliliters.

00:00:42.484 --> 00:00:44.676
So however many liters you've got

00:00:44.676 --> 00:00:47.563
it would be a thousand
times as many milliliters

00:00:47.563 --> 00:00:51.760
because each milliliter is
one-thousandth of a liter.

00:00:51.760 --> 00:00:53.861
Let's do some more examples.

00:00:53.861 --> 00:00:58.026
So here it says blank
milliliters equals 15 liters.

00:00:58.026 --> 00:01:01.268
Pause the video again, see
if you can figure this out.

00:01:01.268 --> 00:01:05.271
Well remember, every liter
is a thousand milliliters.

00:01:05.271 --> 00:01:08.688
So 15 liters would be 15,000 milliliters.

00:01:11.173 --> 00:01:13.653
Remember, if you have a smaller unit,

00:01:13.653 --> 00:01:15.979
and here you're smaller
by a factor of a thousand,

00:01:15.979 --> 00:01:18.054
the number that you would need of it

00:01:18.054 --> 00:01:20.917
to have the same as a
large unit would be larger.

00:01:20.917 --> 00:01:22.799
So you have a smaller unit,

00:01:22.799 --> 00:01:24.941
so you have a larger number here.

00:01:24.941 --> 00:01:27.582
Let's do one more example.

00:01:27.582 --> 00:01:30.845
Compare using greater than,
less than, or equal to.

00:01:30.845 --> 00:01:35.466
So nine liters, how does that
compare to 90 milliliters?

00:01:35.466 --> 00:01:39.500
Pause this video and try
to answer it for yourself.

00:01:39.500 --> 00:01:42.548
Well how many milliliters is nine liters?

00:01:42.548 --> 00:01:47.372
Nine liters is the same
thing as 9,000 milliliters

00:01:47.372 --> 00:01:50.196
and 9,000 milliliters is clearly

00:01:50.196 --> 00:01:52.529
greater than 90 milliliters.

00:01:53.862 --> 00:01:55.661
So what you want to do
in a problem like this

00:01:55.661 --> 00:01:57.508
is convert both to milliliters.

00:01:57.508 --> 00:02:00.427
9,000 milliliters, that's
what nine liters is,

00:02:00.427 --> 00:02:03.086
that's 9,000 milliliters,
that's going to be

00:02:03.086 --> 00:02:05.419
greater than 90 milliliters.


Counting by tens

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:03.220
- [Tutor] So we are
told let's count by tens

00:00:03.220 --> 00:00:05.887
and we go 10, 20, blank, 40, 50,

00:00:07.593 --> 00:00:08.510
60, 70, 80,

00:00:09.508 --> 00:00:11.146
90, 100,

00:00:11.146 --> 00:00:12.871
what number did we miss?

00:00:12.871 --> 00:00:16.457
Pause the video, what number
did we miss right over here?

00:00:16.457 --> 00:00:18.107
Well, if we're counting by tens,

00:00:18.107 --> 00:00:19.690
we would go 10, 20,

00:00:20.895 --> 00:00:23.271
30, 40, 50, 60, 70,

00:00:23.271 --> 00:00:26.072
80, 90, 100, so we're missing 30,

00:00:26.072 --> 00:00:28.673
so which choice right over here has 30?

00:00:28.673 --> 00:00:31.837
Well, if we scroll down a
little bit, we see right there,

00:00:31.837 --> 00:00:33.070
that is our choice.

00:00:33.070 --> 00:00:35.564
Let's do another example.

00:00:35.564 --> 00:00:37.231
So here we are asked

00:00:38.305 --> 00:00:40.388
which ten frames show 20?

00:00:41.724 --> 00:00:44.292
A ten frame is just a fancy word

00:00:44.292 --> 00:00:47.042
for one of these blocks or these frames,

00:00:47.042 --> 00:00:48.109
that have 10 objects in them,

00:00:48.109 --> 00:00:51.108
you can see it right over here,
one, two, three, four, five,

00:00:51.108 --> 00:00:52.977
six, seven, eight, nine, 10,

00:00:52.977 --> 00:00:56.837
so which of these ten frames show 20?

00:00:56.837 --> 00:00:59.803
Well, 20 is two groups of 10,

00:00:59.803 --> 00:01:03.771
so this is 10 and then 20, so
that's 20 right over there,

00:01:03.771 --> 00:01:05.354
choice B is 10, 20,

00:01:06.505 --> 00:01:07.791
30, 40,

00:01:07.791 --> 00:01:10.490
choice C is 10, 20, 30,

00:01:10.490 --> 00:01:13.797
so we can feel good about choice A.

00:01:13.797 --> 00:01:18.592
Here we're told drag the ten
frames into the box to make 40.

00:01:18.592 --> 00:01:21.962
So let's see, here this
is 10, right over there,

00:01:21.962 --> 00:01:24.817
then we get another 10, gets us to 20,

00:01:24.817 --> 00:01:27.203
then another 10 gets us to 30

00:01:27.203 --> 00:01:30.560
and then finally another 10 gets us to 40,

00:01:30.560 --> 00:01:32.810
10, 20, 30, 40, we're done.


Estimating adding and subtracting 3 digit numbers

WEBVTT
Kind: captions
Language: en

00:00:00.226 --> 00:00:01.631
- [Instructor] What we're
going to do in this video

00:00:01.631 --> 00:00:04.312
is get some practice estimating adding

00:00:04.312 --> 00:00:06.798
and subtracting three digit numbers

00:00:06.798 --> 00:00:09.798
and so here it says 398 plus 251 is,

00:00:11.121 --> 00:00:13.451
and this squiggly equal sign means

00:00:13.451 --> 00:00:15.082
we just need to make an estimate.

00:00:15.082 --> 00:00:18.026
We wanna know what is
this roughly equal to?

00:00:18.026 --> 00:00:19.963
So normally I say pause the video

00:00:19.963 --> 00:00:21.905
but here I want you to
work it out in your head.

00:00:21.905 --> 00:00:23.173
So I'm just gonna pause.

00:00:23.173 --> 00:00:25.424
I'm just gonna stop
talking for like a second

00:00:25.424 --> 00:00:27.587
and see if you can come
up with what this is

00:00:27.587 --> 00:00:30.444
or maybe I'll give you three seconds

00:00:30.444 --> 00:00:31.995
'cause the whole point
here is to estimate,

00:00:31.995 --> 00:00:34.765
not get the exact right answer.

00:00:34.765 --> 00:00:37.308
Okay, so I'm assuming
you've had a go at it.

00:00:37.308 --> 00:00:38.732
Now, I'll tell you how I think about it.

00:00:38.732 --> 00:00:41.013
We of course could maybe
take out some paper

00:00:41.013 --> 00:00:42.037
or you might even be able to get

00:00:42.037 --> 00:00:44.171
the exact answer in your head

00:00:44.171 --> 00:00:46.610
but in everyday life, if
you're at the supermarket

00:00:46.610 --> 00:00:47.934
and you're like, okay,

00:00:47.934 --> 00:00:49.873
I guess it would be an
expensive supermarket,

00:00:49.873 --> 00:00:53.867
something is $398, something else is $251.

00:00:53.867 --> 00:00:55.333
Roughly how much would I be spending

00:00:55.333 --> 00:00:56.881
if I bought both of them?

00:00:56.881 --> 00:00:58.564
Well, my head would say, alright,

00:00:58.564 --> 00:01:02.064
398, I would round to nearest 10 at least,

00:01:02.964 --> 00:01:04.029
maybe the nearest 100.

00:01:04.029 --> 00:01:05.741
So let's round to the nearest 10.

00:01:05.741 --> 00:01:09.792
In the case of 398, the
nearest 10 is the nearest 100.

00:01:09.792 --> 00:01:12.731
And so we would get to,
this is approximately 400.

00:01:12.731 --> 00:01:16.314
And then this is, 251
is approximately 250.

00:01:17.460 --> 00:01:19.622
So if you were to add these two things up,

00:01:19.622 --> 00:01:20.610
you're going to get something

00:01:20.610 --> 00:01:23.527
that is approximately equal to 650.

00:01:25.509 --> 00:01:28.734
And lucky for us, that
is one of the choices

00:01:28.734 --> 00:01:31.107
and what I'm about to do is not estimate

00:01:31.107 --> 00:01:33.270
but just see how far off we were.

00:01:33.270 --> 00:01:37.437
So if we were to just
actually do it, 398 plus 251.

00:01:39.401 --> 00:01:41.241
Eight plus one is nine.

00:01:41.241 --> 00:01:43.563
Nine plus five is 14.

00:01:43.563 --> 00:01:44.995
This is 14 10s.

00:01:44.995 --> 00:01:46.100
We put four 10s here,

00:01:46.100 --> 00:01:49.267
and the other 10 10s we regroup as 100

00:01:50.220 --> 00:01:54.193
and then one plus three plus 200 is 600.

00:01:54.193 --> 00:01:55.866
So in this case, in this particular case,

00:01:55.866 --> 00:01:58.273
we got awfully close with our estimation

00:01:58.273 --> 00:02:00.199
and if you don't need
to get the exact number,

00:02:00.199 --> 00:02:02.428
well, that'll be fine.

00:02:02.428 --> 00:02:04.018
Let's do another example.

00:02:04.018 --> 00:02:06.908
In here, we are going to do
a little bit of subtraction.

00:02:06.908 --> 00:02:08.546
So once again, pause this video

00:02:08.546 --> 00:02:10.626
or try to do it as quickly as you can.

00:02:10.626 --> 00:02:13.206
Try to estimate what this
difference is going to be.

00:02:13.206 --> 00:02:14.373
678 minus 273.

00:02:17.037 --> 00:02:18.262
Alright, let's do it together.

00:02:18.262 --> 00:02:21.398
So there's a couple of ways to tackle it.

00:02:21.398 --> 00:02:23.642
You could round to the nearest 10

00:02:23.642 --> 00:02:26.038
and you could say, well,
this is approximately 600,

00:02:26.038 --> 00:02:27.580
let's see, to round to the nearest 10,

00:02:27.580 --> 00:02:29.102
you would round up right over here

00:02:29.102 --> 00:02:31.602
so you'd say this is 680 minus

00:02:33.018 --> 00:02:34.435
you could say 270

00:02:36.359 --> 00:02:38.234
which is going to give you

00:02:38.234 --> 00:02:40.554
and here you're still gonna
have to do some mental math.

00:02:40.554 --> 00:02:41.494
This would be what?

00:02:41.494 --> 00:02:43.161
600 minus 200 is 400

00:02:44.388 --> 00:02:46.912
and 80 minus 70 is 10.

00:02:46.912 --> 00:02:48.310
So that's one way to do it

00:02:48.310 --> 00:02:49.572
or you could do it even rougher.

00:02:49.572 --> 00:02:51.735
You could just do to the nearest 100.

00:02:51.735 --> 00:02:53.855
So you could say, look, 678,

00:02:53.855 --> 00:02:56.018
the nearest 100 is 700

00:02:56.018 --> 00:03:00.138
and then minus 273, the
nearest 100 there is 300

00:03:00.138 --> 00:03:02.040
and so this is even rougher

00:03:02.040 --> 00:03:05.679
but it gets us actually
still similar answers

00:03:05.679 --> 00:03:07.424
and either way we estimated,

00:03:07.424 --> 00:03:09.184
either the kind of rougher way

00:03:09.184 --> 00:03:11.060
or the slightly less rough way,

00:03:11.060 --> 00:03:13.914
we got to something around 400.

00:03:13.914 --> 00:03:16.238
So you could feel good
that this is your choice.

00:03:16.238 --> 00:03:17.256
The reason why we even have to make

00:03:17.256 --> 00:03:19.008
multiple choice questions for estimation

00:03:19.008 --> 00:03:21.575
is not everyone is gonna
get the exact same estimate

00:03:21.575 --> 00:03:24.013
but the correct choice should be the one

00:03:24.013 --> 00:03:28.096
that any reasonable estimate
would be closest to.


Associative property of multiplication

WEBVTT
Kind: captions
Language: en

00:00:00.546 --> 00:00:01.379
- [Instructor] So, what we're gonna do

00:00:01.379 --> 00:00:04.327
is get a little bit of practicing
multiple numbers together

00:00:04.327 --> 00:00:06.310
and we're gonna discover some things.

00:00:06.310 --> 00:00:08.155
So, first I want you to figure out

00:00:08.155 --> 00:00:10.988
what four times five times two is.

00:00:13.638 --> 00:00:17.516
Pause the video and try to
figure it out on your own.

00:00:17.516 --> 00:00:19.141
Alright, so whatever your answer is,

00:00:19.141 --> 00:00:20.828
some of you might have done it this way,

00:00:20.828 --> 00:00:22.220
some of you might have said hey,

00:00:22.220 --> 00:00:23.805
what is four times five

00:00:23.805 --> 00:00:25.945
and then you multiplied it by two,

00:00:25.945 --> 00:00:27.161
so what you would really have done

00:00:27.161 --> 00:00:30.556
is you would have done
four times five first,

00:00:30.556 --> 00:00:32.411
so that's why I put
parentheses around that

00:00:32.411 --> 00:00:34.927
and then you would have multiplied by two

00:00:34.927 --> 00:00:36.325
and what would you have gotten?

00:00:36.325 --> 00:00:39.384
Weil, the four times five part,

00:00:39.384 --> 00:00:41.412
that is of course 20

00:00:41.412 --> 00:00:44.520
and then you multiply that times two

00:00:44.520 --> 00:00:46.958
and you would get 40

00:00:46.958 --> 00:00:48.493
which of course would be correct,

00:00:48.493 --> 00:00:50.118
four times five times two

00:00:50.118 --> 00:00:52.404
is indeed equal to 40.

00:00:52.404 --> 00:00:54.262
Now, what I want you to do now

00:00:54.262 --> 00:00:55.937
is as quickly as possible

00:00:55.937 --> 00:00:59.755
try to figure out what five times two

00:00:59.755 --> 00:01:01.382
times four is.

00:01:01.382 --> 00:01:04.467
Really quick, pause the
video, try to figure that out.

00:01:04.467 --> 00:01:06.646
Well, some of you might have tried

00:01:06.646 --> 00:01:08.627
and you might have done
it in a similar way

00:01:08.627 --> 00:01:12.039
where you tried to figure
out five times two is first

00:01:12.039 --> 00:01:14.128
and you said okay, five times two

00:01:14.128 --> 00:01:15.794
is equal to 10

00:01:15.794 --> 00:01:18.730
and then I'd multiply that times four

00:01:18.730 --> 00:01:19.744
and then you would say well, gee,

00:01:19.744 --> 00:01:21.998
this is same thing as I got last time.

00:01:21.998 --> 00:01:24.685
Is there something interesting going on?

00:01:24.685 --> 00:01:25.610
And the interesting thing

00:01:25.610 --> 00:01:27.518
that you might realize is in both cases

00:01:27.518 --> 00:01:29.660
we're multiplying the same three numbers.

00:01:29.660 --> 00:01:31.637
We are just doing it in a different order.

00:01:31.637 --> 00:01:32.587
Here we multiplied four times,

00:01:32.587 --> 00:01:34.450
we wrote it out in a different order,

00:01:34.450 --> 00:01:35.847
four times five times two.

00:01:35.847 --> 00:01:38.101
Here we wrote five times two times four.

00:01:38.101 --> 00:01:40.333
Here we did the four times five first,

00:01:40.333 --> 00:01:42.487
here we did the five times two first

00:01:42.487 --> 00:01:45.053
but notice we got the same result.

00:01:45.053 --> 00:01:46.699
Now, I'd encourage you, pause this video.

00:01:46.699 --> 00:01:48.920
Try to multiply these numbers

00:01:48.920 --> 00:01:50.216
in any order,

00:01:50.216 --> 00:01:53.290
maybe you do two times four first.

00:01:53.290 --> 00:01:54.636
In fact, let's just do that.

00:01:54.636 --> 00:01:56.636
Let's do two times four,

00:01:58.302 --> 00:01:59.613
two times four

00:01:59.613 --> 00:02:01.579
and then multiply that by five.

00:02:01.579 --> 00:02:04.010
What is this going to be equal to?

00:02:04.010 --> 00:02:05.321
Well, you might notice again

00:02:05.321 --> 00:02:08.130
this is two times four is eight,

00:02:08.130 --> 00:02:10.460
you multiply that times five.

00:02:10.460 --> 00:02:13.432
Well, once again, we got 40,

00:02:13.432 --> 00:02:15.397
so you might see a pattern here.

00:02:15.397 --> 00:02:19.793
It doesn't matter which order
we multiply these things in.

00:02:19.793 --> 00:02:23.960
In fact, you could write
four times five times two.

00:02:25.615 --> 00:02:28.554
You could do the four times five first,

00:02:28.554 --> 00:02:31.063
four times fives times two

00:02:31.063 --> 00:02:34.563
or you could do four times five times two,

00:02:35.706 --> 00:02:38.439
so you could do four times five times two.

00:02:38.439 --> 00:02:40.190
So, it doesn't matter which order

00:02:40.190 --> 00:02:41.866
you multiply these things in.

00:02:41.866 --> 00:02:44.287
In every case you are going to get 40.

00:02:44.287 --> 00:02:45.872
Now, there's a very fancy term for this,

00:02:45.872 --> 00:02:48.418
the associative property of multiplication

00:02:48.418 --> 00:02:51.805
but the main realization
is and it's not just true

00:02:51.805 --> 00:02:52.788
with the three numbers,

00:02:52.788 --> 00:02:54.445
in fact, you've seen something similar

00:02:54.445 --> 00:02:56.199
with two numbers where it doesn't matter

00:02:56.199 --> 00:02:57.987
what order you multiply them in

00:02:57.987 --> 00:02:59.549
but what you see with three numbers

00:02:59.549 --> 00:03:01.110
and even if you tried it with four or five

00:03:01.110 --> 00:03:03.228
or really 1,000 numbers

00:03:03.228 --> 00:03:04.563
being multiplied together,

00:03:04.563 --> 00:03:06.594
as long as you're just
multiplying them all,

00:03:06.594 --> 00:03:09.315
it doesn't matter what
order you're doing it with.

00:03:09.315 --> 00:03:10.725
It doesn't matter in what order

00:03:10.725 --> 00:03:12.251
you associate them with.

00:03:12.251 --> 00:03:13.900
Here we did four times five first,

00:03:13.900 --> 00:03:15.535
four times five first,

00:03:15.535 --> 00:03:16.971
here we did five times two first

00:03:16.971 --> 00:03:18.107
but in either case

00:03:18.107 --> 00:03:19.335
we got the same result

00:03:19.335 --> 00:03:21.130
and I'd encourage you, after this video,

00:03:21.130 --> 00:03:22.182
try to draw it out.

00:03:22.182 --> 00:03:24.871
Try to think about why that
actually makes intuitive sense,

00:03:24.871 --> 00:03:27.252
why this is true in the world

00:03:27.252 --> 00:03:29.422
and it's nice because
it simplifies our life

00:03:29.422 --> 00:03:31.195
when we're doing mathematics

00:03:31.195 --> 00:03:34.363
and not only now but in our
future mathematical career.


Khan Academy view of mastery learning

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:01.965
- [Instructor] The terms mastery learning

00:00:01.965 --> 00:00:05.459
are used a lot these days
but I wanna do a video

00:00:05.459 --> 00:00:08.232
on 'em because they can
mean different things

00:00:08.232 --> 00:00:09.961
to different people and
I wanna just talk about

00:00:09.961 --> 00:00:12.542
what it means at least in
a Khan Academy context.

00:00:12.542 --> 00:00:14.838
So to give us some perspective,
let's actually just start

00:00:14.838 --> 00:00:18.603
with traditional learning and
think about where it works

00:00:18.603 --> 00:00:20.425
and maybe where it doesn't work

00:00:20.425 --> 00:00:22.730
and then we could think
about why mastery learning

00:00:22.730 --> 00:00:24.651
might address some of those issues.

00:00:24.651 --> 00:00:27.707
So let's say we are in a
middle school math class

00:00:27.707 --> 00:00:31.874
and right now, the classroom
is focused on negative numbers.

00:00:32.990 --> 00:00:35.550
We're gonna work on that
for a couple of weeks.

00:00:35.550 --> 00:00:39.133
So this is negative
numbers right over here

00:00:40.099 --> 00:00:42.368
and after a couple of weeks
of lecture and homework,

00:00:42.368 --> 00:00:44.713
we give a task and lets
say a certain student

00:00:44.713 --> 00:00:48.225
that we're following
gets an 80% on that test.

00:00:48.225 --> 00:00:51.558
So he or she knows a lot of the material

00:00:52.648 --> 00:00:55.755
but doesn't know some of the material here

00:00:55.755 --> 00:00:58.520
maybe doesn't know some
of the material here

00:00:58.520 --> 00:01:02.412
maybe doesn't know some
of the material over here.

00:01:02.412 --> 00:01:04.006
So these are gaps.

00:01:04.006 --> 00:01:07.135
These are gaps in their understanding.

00:01:07.135 --> 00:01:11.198
So these, we label these
correctly, these are gaps.

00:01:11.198 --> 00:01:13.242
And even though we've taken the trouble

00:01:13.242 --> 00:01:15.720
of giving an assessment, a quiz a test,

00:01:15.720 --> 00:01:17.153
and we identified these gaps,

00:01:17.153 --> 00:01:19.298
the whole class including that student

00:01:19.298 --> 00:01:21.502
will then move on to the next concept.

00:01:21.502 --> 00:01:24.460
So let's say the next
concept that we now work on

00:01:24.460 --> 00:01:26.877
maybe we do it for a few more weeks

00:01:26.877 --> 00:01:30.633
according to the lesson
plan, is now basic exponents.

00:01:30.633 --> 00:01:32.800
So this is basic exponents

00:01:35.205 --> 00:01:36.861
and the same thing happens.

00:01:36.861 --> 00:01:39.197
We have some lecture and
homework for a few weeks

00:01:39.197 --> 00:01:41.097
and then at the end of that we have a test

00:01:41.097 --> 00:01:42.539
and let's say on the that test,

00:01:42.539 --> 00:01:45.363
the student gets a 70%.

00:01:45.363 --> 00:01:48.788
So he or she knows a
good bit of the material

00:01:48.788 --> 00:01:52.149
but there's still some
pretty significant gaps.

00:01:52.149 --> 00:01:53.705
Let me color in these gaps.

00:01:53.705 --> 00:01:55.429
So the white is what they were actually

00:01:55.429 --> 00:01:56.780
able to perform on these tests

00:01:56.780 --> 00:01:58.181
and even these tests are imperfect,

00:01:58.181 --> 00:01:59.989
they're just sampling
the students' knowledge

00:01:59.989 --> 00:02:01.687
and so what happen to be on the test

00:02:01.687 --> 00:02:04.267
they still didn't know
some of the material.

00:02:04.267 --> 00:02:05.669
Some of it might've been careless mistakes

00:02:05.669 --> 00:02:07.894
but some of it might've
been pretty important.

00:02:07.894 --> 00:02:10.211
For example, this gap right over here

00:02:10.211 --> 00:02:14.803
might be what happens if I raise
something to the zero power

00:02:14.803 --> 00:02:18.906
or maybe it's building on top
of a gap with negative numbers

00:02:18.906 --> 00:02:21.393
maybe this gap was happening,

00:02:21.393 --> 00:02:23.589
not just 'cause basic
exponents are difficult

00:02:23.589 --> 00:02:25.571
but because there's a
gap in negative numbers

00:02:25.571 --> 00:02:27.429
so the student doesn't
know what does it mean

00:02:27.429 --> 00:02:31.310
if I take a negative number
to a positive exponent.

00:02:31.310 --> 00:02:33.698
So maybe that's a gap there.

00:02:33.698 --> 00:02:35.251
But even though we've taken the trouble

00:02:35.251 --> 00:02:37.907
of identifying those gaps,
the class will then move on

00:02:37.907 --> 00:02:39.402
to the next concept.

00:02:39.402 --> 00:02:41.759
The amount of time is what's fixed

00:02:41.759 --> 00:02:43.451
and what's variable is how well

00:02:43.451 --> 00:02:46.664
the students understand
it, A, B, C, D, or F.

00:02:46.664 --> 00:02:49.825
And then the next concept, let's say

00:02:49.825 --> 00:02:51.317
we'll do this in another color,

00:02:51.317 --> 00:02:54.701
so the next concept here,
we are building on top of

00:02:54.701 --> 00:02:56.274
everything that we've learned so far,

00:02:56.274 --> 00:02:59.191
let's say it is negative exponents.

00:03:01.365 --> 00:03:03.205
So I think you can see
where this is going.

00:03:03.205 --> 00:03:06.607
This is trouble now for the student.

00:03:06.607 --> 00:03:08.975
There's lecture and homework,
the student is trying

00:03:08.975 --> 00:03:12.215
the best they can but things
are just not really gelling.

00:03:12.215 --> 00:03:14.751
And so all of a sudden,
when you take the quiz,

00:03:14.751 --> 00:03:17.495
the student just hits a wall
after two or three weeks

00:03:17.495 --> 00:03:20.963
and let's say they get a 30%

00:03:20.963 --> 00:03:23.531
and so they're only able to get 30%

00:03:23.531 --> 00:03:26.620
of the material right that
happened to be on the test,

00:03:26.620 --> 00:03:28.907
the rest they got wrong.

00:03:28.907 --> 00:03:30.947
Now, in a traditional system, we say

00:03:30.947 --> 00:03:34.087
"alright, the student just
failed this exam quite badly.

00:03:34.087 --> 00:03:36.241
"Maybe the student needs to work harder.

00:03:36.241 --> 00:03:39.309
"Maybe they need to be put
into a different track.

00:03:39.309 --> 00:03:44.043
"Maybe the subject is just too
difficult for this student."

00:03:44.043 --> 00:03:45.750
but when you look at what's going on,

00:03:45.750 --> 00:03:47.274
it's pretty clear that
it had nothing to do

00:03:47.274 --> 00:03:49.189
with the ability level of the student

00:03:49.189 --> 00:03:51.561
and it didn't have anything
to do with the difficulty

00:03:51.561 --> 00:03:52.931
necessarily of the subject matter

00:03:52.931 --> 00:03:54.942
but it's more that they
just kept accumulating

00:03:54.942 --> 00:03:57.391
these gaps all along the way

00:03:57.391 --> 00:04:00.216
so at some point, those
gaps become so debilitating

00:04:00.216 --> 00:04:02.033
that the student hits a wall

00:04:02.033 --> 00:04:03.089
and starts failing the class

00:04:03.089 --> 00:04:05.863
and if they're not able to
remediate these gaps go back,

00:04:05.863 --> 00:04:08.056
well they're never going to really be able

00:04:08.056 --> 00:04:09.623
to understand negative exponents

00:04:09.623 --> 00:04:11.228
and then they're never going
to be able to understand

00:04:11.228 --> 00:04:13.543
logarithms properly and
more advanced algebra

00:04:13.543 --> 00:04:16.125
and so on and so forth
and we've all seen this

00:04:16.125 --> 00:04:18.107
either for ourselves
or some of our friends

00:04:18.107 --> 00:04:18.972
and family members.

00:04:18.972 --> 00:04:20.015
They hit walls.

00:04:20.015 --> 00:04:22.311
And the argument that we
believe at Khan Academy

00:04:22.311 --> 00:04:25.941
it is not because they're not bright,

00:04:25.941 --> 00:04:28.570
it's not because the
subject matter is difficult,

00:04:28.570 --> 00:04:31.566
it's because we're forcing
them through at a fixed pace.

00:04:31.566 --> 00:04:34.100
And to realize how absurd
this is on some level,

00:04:34.100 --> 00:04:36.863
imagine if we did other
things in our life that way,

00:04:36.863 --> 00:04:38.874
say home building.

00:04:38.874 --> 00:04:41.443
So you tell the contractor
we have two weeks

00:04:41.443 --> 00:04:44.326
to build this foundation, do what you can.

00:04:44.326 --> 00:04:45.863
And so they build a foundation

00:04:45.863 --> 00:04:47.924
but then two weeks later,
the inspector comes

00:04:47.924 --> 00:04:51.155
and says "Okay, the concrete's
still wet right over here.

00:04:51.155 --> 00:04:53.126
"This part isn't quite up to code.

00:04:53.126 --> 00:04:56.417
"I will give this an 80%"

00:04:56.417 --> 00:04:57.526
and you say, "Great, that's a C.

00:04:57.526 --> 00:04:59.008
"Let's build the first floor."

00:04:59.008 --> 00:05:01.244
and so again, you try to
build the first floor,

00:05:01.244 --> 00:05:03.519
maybe it rains, some of
the supplies don't show up,

00:05:03.519 --> 00:05:05.743
and so the inspector comes
after a couple of weeks

00:05:05.743 --> 00:05:08.761
and says, "Alright, I'll give that 70%"

00:05:08.761 --> 00:05:09.745
and you say "Great, that's a D

00:05:09.745 --> 00:05:11.342
"Now let's build the second floor"

00:05:11.342 --> 00:05:12.862
so on and so forth then all of a sudden

00:05:12.862 --> 00:05:14.093
while you're building that second floor,

00:05:14.093 --> 00:05:17.315
the whole structure comes collapsing down.

00:05:17.315 --> 00:05:19.405
And if our reaction to
that is the reaction

00:05:19.405 --> 00:05:20.542
we typically have in education,

00:05:20.542 --> 00:05:22.358
we say "Oh, we needed more inspection"

00:05:22.358 --> 00:05:25.108
or "we needed better contractors"

00:05:26.870 --> 00:05:28.536
but the problem was the process.

00:05:28.536 --> 00:05:30.231
We are artificially constraining

00:05:30.231 --> 00:05:32.173
how long you have to do something

00:05:32.173 --> 00:05:34.672
which pretty much ensures
a variable outcome.

00:05:34.672 --> 00:05:37.679
You take the trouble of
identifying those gaps

00:05:37.679 --> 00:05:39.902
but then you build right on top of it.

00:05:39.902 --> 00:05:41.934
So this is traditional learning

00:05:41.934 --> 00:05:44.230
and one could argue that if
you're just pushing people

00:05:44.230 --> 00:05:45.988
ahead at some pace like this,

00:05:45.988 --> 00:05:48.366
gaps will accumulate for everyone

00:05:48.366 --> 00:05:50.316
and they will all hit a wall at some point

00:05:50.316 --> 00:05:51.941
and we've all felt that.

00:05:51.941 --> 00:05:54.333
And so mastery learning says,
"Look, instead of making

00:05:54.333 --> 00:05:57.521
"everyone go at the same
pace, let us personalize."

00:05:57.521 --> 00:06:00.284
and personalization in this context means

00:06:00.284 --> 00:06:02.447
let people go at their own pace.

00:06:02.447 --> 00:06:05.780
So traditional learning, it's fixed pace

00:06:08.167 --> 00:06:10.417
and variable understanding,

00:06:15.060 --> 00:06:18.643
while mastery learning
has personalization.

00:06:19.838 --> 00:06:22.505
So it's more of a variable pace,

00:06:25.284 --> 00:06:27.173
and then we assume students get

00:06:27.173 --> 00:06:29.825
to a high level of proficiency or mastery.

00:06:29.825 --> 00:06:31.492
So high expectations

00:06:37.675 --> 00:06:40.536
around proficiency or mastery

00:06:40.536 --> 00:06:42.719
and those words can mean different things

00:06:42.719 --> 00:06:47.065
in different context,
proficiency or mastery.

00:06:47.065 --> 00:06:51.128
So in a mastery learning
system, you first would

00:06:51.128 --> 00:06:54.480
maybe the student would be
ready for the negative numbers

00:06:54.480 --> 00:06:56.474
and maybe after a few weeks,

00:06:56.474 --> 00:06:58.293
they take some type of assessment,

00:06:58.293 --> 00:07:00.405
to get much as much practice
and feedback as possible

00:07:00.405 --> 00:07:03.433
and they perform similarly
to that first example,

00:07:03.433 --> 00:07:04.825
the student in the first example,

00:07:04.825 --> 00:07:07.284
maybe they get that 80% there.

00:07:07.284 --> 00:07:09.174
In a mastery learning system,

00:07:09.174 --> 00:07:10.372
we wouldn't just tell that student,

00:07:10.372 --> 00:07:13.664
"Alright, let's move
on to basic exponents"

00:07:13.664 --> 00:07:16.694
what we would do is, hey,
why don't you keep working

00:07:16.694 --> 00:07:19.027
on the negative numbers here

00:07:20.037 --> 00:07:22.482
and so that you can address those gaps.

00:07:22.482 --> 00:07:24.595
And so it takes the student
maybe a little bit more time

00:07:24.595 --> 00:07:28.597
but eventually, they're
able to fill in those gaps.

00:07:28.597 --> 00:07:30.823
There might be still a few small gaps

00:07:30.823 --> 00:07:34.285
but the whole point is that
they can always go back

00:07:34.285 --> 00:07:36.999
and revisit and ensure that
they fill in those gaps

00:07:36.999 --> 00:07:39.124
so that they don't become debilitating.

00:07:39.124 --> 00:07:41.196
Ideally, they'll fill in all the gaps.

00:07:41.196 --> 00:07:43.470
And now, they're ready for basic exponents

00:07:43.470 --> 00:07:46.020
and I'd argue that now that
you're tackling basic exponents,

00:07:46.020 --> 00:07:48.185
one, the student actually
might be able to even learn it

00:07:48.185 --> 00:07:50.104
faster 'cause they're
gonna get less confused

00:07:50.104 --> 00:07:52.948
by the negative exponents
but if they still end up

00:07:52.948 --> 00:07:55.955
having a gap when they take
some type of an assessment

00:07:55.955 --> 00:07:57.064
or while they're doing practice,

00:07:57.064 --> 00:07:58.861
they have as much time as they need

00:07:58.861 --> 00:08:01.929
to go back and fill in those gaps

00:08:01.929 --> 00:08:03.972
and so the whole principle here is

00:08:03.972 --> 00:08:06.041
in mastery learning,
the student is building

00:08:06.041 --> 00:08:08.003
a really, really solid foundation

00:08:08.003 --> 00:08:09.771
so that they never hit that wall

00:08:09.771 --> 00:08:11.122
when they get to negative exponents.

00:08:11.122 --> 00:08:12.798
They understand their
negative numbers well,

00:08:12.798 --> 00:08:14.131
they understand their exponents well

00:08:14.131 --> 00:08:16.833
and so then they can just keep on going

00:08:16.833 --> 00:08:19.055
and going and going and at Khan Academy

00:08:19.055 --> 00:08:21.494
we believe that if you learn this way,

00:08:21.494 --> 00:08:22.806
yes, certain subjects might take you

00:08:22.806 --> 00:08:25.535
a little bit longer, but
then if you invest there,

00:08:25.535 --> 00:08:27.384
the future subjects will take less time

00:08:27.384 --> 00:08:29.653
and you will understand more and overall

00:08:29.653 --> 00:08:31.369
and we've seen efficacy
studies to this effect,

00:08:31.369 --> 00:08:33.757
you'll actually learn better, faster

00:08:33.757 --> 00:08:37.279
and you won't eventually
hit some type of a barrier

00:08:37.279 --> 00:08:41.191
like the first student did
with negative exponents.


Subtracting multi digit numbers with regrouping

WEBVTT
Kind: captions
Language: en

00:00:00.482 --> 00:00:01.959
- [Instructor] What we're
gonna do in this video

00:00:01.959 --> 00:00:04.126
is figure out what 389,002

00:00:06.066 --> 00:00:07.399
minus 76,151 is.

00:00:10.385 --> 00:00:12.665
Like always, I encourage
you to pause the video

00:00:12.665 --> 00:00:14.295
and try to figure it out on your own.

00:00:14.295 --> 00:00:15.726
That's the best way to really,

00:00:15.726 --> 00:00:16.974
even if you're not able to figure out,

00:00:16.974 --> 00:00:18.272
or if you get a different answer,

00:00:18.272 --> 00:00:19.737
then when I work through it with you

00:00:19.737 --> 00:00:23.719
it will really stick in
your brain that much more.

00:00:23.719 --> 00:00:25.156
Alright, now let's work
through it together.

00:00:25.156 --> 00:00:27.173
The way I'm gonna do
it is sometimes called

00:00:27.173 --> 00:00:29.971
the standard method or
the standard algorithm,

00:00:29.971 --> 00:00:33.412
algorithm being a fancy word for a method.

00:00:33.412 --> 00:00:37.928
What I'm gonna do is
first write the 389,002.

00:00:37.928 --> 00:00:38.761
389,002.

00:00:42.601 --> 00:00:44.851
And I'm subtracting 76,151.

00:00:48.494 --> 00:00:50.048
You notice the first thing that I did

00:00:50.048 --> 00:00:53.399
is I aligned the digits to
the appropriate place value.

00:00:53.399 --> 00:00:55.820
I put the ones below the ones.

00:00:55.820 --> 00:00:59.179
The 10s below the 10s,
the 100s below the 100s,

00:00:59.179 --> 00:01:00.949
the 1,000s below the 1,000s,

00:01:00.949 --> 00:01:04.176
the 10,000s below the
10,000s, so on and so forth.

00:01:04.176 --> 00:01:06.137
And now we're ready to subtract.

00:01:06.137 --> 00:01:07.671
So the first thing we might do is well,

00:01:07.671 --> 00:01:09.361
let's look at the ones place.

00:01:09.361 --> 00:01:13.581
Here I have two ones, and
I'm gonna take away one one.

00:01:13.581 --> 00:01:15.426
So I'm gonna be left with one one.

00:01:15.426 --> 00:01:17.044
That was pretty straightforward.

00:01:17.044 --> 00:01:18.834
But then things get a
little bit more difficult

00:01:18.834 --> 00:01:20.454
when we get to the 10s place.

00:01:20.454 --> 00:01:23.350
How do I take five 10s from zero 10s?

00:01:23.350 --> 00:01:26.253
So let me just not think
about that for a second,

00:01:26.253 --> 00:01:28.314
but I have the same
problem in the 100s place.

00:01:28.314 --> 00:01:31.442
How do I take away one 100 from zero 100s?

00:01:31.442 --> 00:01:33.264
Now when I go to the 1,000s place,

00:01:33.264 --> 00:01:36.771
I can take away six
1,000s from nine 1,000s,

00:01:36.771 --> 00:01:40.056
but before I do that what
I want to do is regroup

00:01:40.056 --> 00:01:41.601
so that I don't have zeros here

00:01:41.601 --> 00:01:46.013
so that I can take away from
the 100s and the 10s place.

00:01:46.013 --> 00:01:50.367
And so what I can do is I
can rewrite nine 1,000s,

00:01:50.367 --> 00:01:52.672
so I'm gonna take away
one of those 1,000s,

00:01:52.672 --> 00:01:54.309
so I'm gonna have eight 1,000s.

00:01:54.309 --> 00:01:57.853
And I'm gonna regroup it as 10 100s.

00:01:57.853 --> 00:02:01.436
So this can be that
1,000 would be 10 100s.

00:02:03.301 --> 00:02:06.770
Now that solves a problem,
except for the 10s place.

00:02:06.770 --> 00:02:08.708
But what I can then do
is I could take away

00:02:08.708 --> 00:02:12.014
one of those 100s so I
only have nine 100s now,

00:02:12.014 --> 00:02:16.304
and I could regroup that
extra 100 as 10 10s.

00:02:16.304 --> 00:02:17.387
So as 10 10s.

00:02:18.449 --> 00:02:20.440
And now I can keep subtracting.

00:02:20.440 --> 00:02:24.607
So in the 10s place, 10 10s
minus five 10s, is five 10s.

00:02:27.285 --> 00:02:31.452
I go to the 100s place,
nine 100s minus 100 is 800.

00:02:34.386 --> 00:02:35.930
I go to the 1,000s place.

00:02:35.930 --> 00:02:38.180
8,000 minus 6,000 is 2,000.

00:02:40.702 --> 00:02:44.011
And then I can go to the 10,000s place.

00:02:44.011 --> 00:02:45.898
This is essentially eight 10,000s,

00:02:45.898 --> 00:02:50.394
or 80,000 minus 70,000
is going to be 10,000.

00:02:50.394 --> 00:02:52.097
One 10,000.

00:02:52.097 --> 00:02:56.334
And then last but not least,
I have my three 100,000s.

00:02:56.334 --> 00:02:57.454
So there you go.

00:02:57.454 --> 00:02:58.287
We're done.

00:02:58.287 --> 00:02:59.620
This is 312,851.

00:03:01.734 --> 00:03:03.601
This is the standard method.

00:03:03.601 --> 00:03:05.051
I started at the ones place.

00:03:05.051 --> 00:03:07.072
Sometimes it's good to just do a check

00:03:07.072 --> 00:03:10.735
to make sure every digit on
top in the appropriate place

00:03:10.735 --> 00:03:13.065
is at least equal to the digit

00:03:13.065 --> 00:03:14.746
that you're subtracting from it.

00:03:14.746 --> 00:03:16.831
And so you can do the
regrouping ahead of time.

00:03:16.831 --> 00:03:20.500
But either way, you will end
up with a similar process.