Advanced (plural) possession

WEBVTT
Kind: captions
Language: en

00:00:00.422 --> 00:00:01.973
- [Paige] Hello grammarians, hello David.

00:00:01.973 --> 00:00:03.139
- [David] Hello Paige.

00:00:03.139 --> 00:00:05.905
- [Paige] So today we're gonna
talk about Plural Possession.

00:00:05.905 --> 00:00:10.424
Meaning when more than one
person, or thing, or animal,

00:00:10.424 --> 00:00:12.091
owns something else.

00:00:13.258 --> 00:00:16.661
And this, like most other
types of possession,

00:00:16.661 --> 00:00:18.904
tends to involve apostrophes.

00:00:18.904 --> 00:00:20.138
- [David] Makes sense, checks out.

00:00:20.138 --> 00:00:21.857
- [Paige] Yeah, cool.

00:00:21.857 --> 00:00:23.312
- [David] So it's just
apostrophe, S, right?

00:00:23.312 --> 00:00:24.991
Like, I mean, why are we
even making this video?

00:00:24.991 --> 00:00:26.008
- [Paige] Well, no.

00:00:26.008 --> 00:00:26.841
- [David] Oh.

00:00:26.841 --> 00:00:28.319
- [Paige] Apostrophe, S,
is a rule that applies when

00:00:28.319 --> 00:00:30.486
the possessive noun is singular.

00:00:30.486 --> 00:00:33.173
So for example, the dog's bone.

00:00:33.173 --> 00:00:35.761
Right, that's one dog's bone.

00:00:35.761 --> 00:00:38.301
- [David] One singular
dog possessing one bone.

00:00:38.301 --> 00:00:39.134
- [Paige] Exactly.

00:00:39.134 --> 00:00:40.173
- [David] What if I
wanted to talk about like,

00:00:40.173 --> 00:00:42.378
five dogs' bones?

00:00:42.378 --> 00:00:44.865
Like they had a big old pile of bones?

00:00:44.865 --> 00:00:47.225
- [Paige] Right, so that is a case where

00:00:47.225 --> 00:00:48.845
we will not use apostrophe, S.

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- [David] What?

00:00:50.162 --> 00:00:52.066
- [Paige] I'm sorry to disappoint.

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- [David] I'm not disappointed,
I'm just surprised.

00:00:54.312 --> 00:00:57.810
Not actually surprised,
that's just a stage trick.

00:00:57.810 --> 00:01:00.303
- [Paige] So, if we're
talking about five dogs,

00:01:00.303 --> 00:01:02.176
and their bones,

00:01:02.176 --> 00:01:05.176
we say five dogs, apostrophe, bones,

00:01:06.254 --> 00:01:08.228
and there's no S after the apostrophe.

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- [David] So it goes S, apostrophe?

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So we have the S for the plural,

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and then an apostrophe for possession,

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but not a second S for possession?

00:01:18.733 --> 00:01:20.080
- [Paige] Right, we don't want like,

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the dogs's bones.

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- [David] Okay.

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Okay, but the apostrophe
at the end isn't about

00:01:28.676 --> 00:01:30.249
there being multiple bones, right?

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It's about there being multiple dogs?

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- [Paige] Yeah, so even
if it's multiple dogs,

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and they're possessing a singular thing,

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- [David] So if five dogs
all had the same favorite

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dog park.

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- [Paige] Right, because
it's the best dog park

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in the world.

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- [David] Okay.

00:01:47.872 --> 00:01:49.524
- [Paige] So in that case
you would say something like,

00:01:49.524 --> 00:01:51.455
the dogs' favorite park.

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Right, park is still
singular, but dogs' is plural.

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So that's why it's just
apostrophe, and no S afterwards.

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- [David] So this also only
applies to plural nouns that

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end in S, right?

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So if I'm talking about one
of our irregular plural nouns,

00:02:08.888 --> 00:02:09.721
like mice,

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or geese,

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or men, or women,

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I would still add apostrophe, S, right?

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Like, okay, so I'm imagining
a department store,

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and there's a men's
section, a women's section,

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and a mice's section.

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- [Paige] (laughs) Okay,
that is an interesting

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department store.

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- [David] Well it doesn't
take up that much floor space

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for the mouse section.

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So, I get that if there's
more than one dog,

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it's D-O-G-S, apostrophe.

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If it's a plural irregular
noun that doesn't end in S,

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then it's still just apostrophe, S,

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like regular possession.

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What about family names?

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- [Paige] Oh, okay,
that's a good question.

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So, let's say there's a family
with the last name, Harper.

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- [David] Okay.

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- [Paige] And I am going to
visit the Harpers' house.

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- [David] Okay.

00:03:03.049 --> 00:03:05.101
- [Paige] Right, so that's
the house that belongs to

00:03:05.101 --> 00:03:08.814
all of the Harpers, the Harper family.

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- [David] Okay, so that seems
pretty straight forward,

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but what if we're talking
about a name that ends in S?

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Like Burns?

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- [Paige] Okay, yeah.

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That can make things a
little bit complicated.

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The way that names that
end in S become plural is

00:03:21.855 --> 00:03:24.723
by adding ES to the end of them.

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So Burns becomes Burnses.

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- [David] And so Burnses,
without the apostrophe,

00:03:30.251 --> 00:03:34.702
is how I would refer to that
family unit in total also.

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Right, like it's Mr Burns and the Burnses?

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Or Dr Jones and the Joneses?

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- [Paige] Exactly.

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- [David] Okay.

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- [Paige] So then when you
wanna make that possessive,

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as in, the Burnses' house,

00:03:48.789 --> 00:03:52.223
you make it plural by adding that ES,

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and then put the apostrophe after that.

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- [David] Cool, so plural
things that end in S

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don't have a second S
after the apostrophe?

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- [Paige] Yeah.

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- [David] But irregular plurals,

00:04:01.830 --> 00:04:04.492
like men, women, mice, do?

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- [Paige] Yeah.

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- [David] Thank you, Paige.

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- [Paige] You're welcome.

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You can learn anything.

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- [David] David out.

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- [Paige] Paige out.


Introduction to the apostrophe

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:01.421
- [Voiceover] Hello Grammarians

00:00:01.421 --> 00:00:02.303
Hello Paige,

00:00:02.303 --> 00:00:03.136
- [Voiceover] Hi, David.

00:00:03.136 --> 00:00:05.026
- [Voiceover] Hello apostrophe!

00:00:05.026 --> 00:00:06.199
Today we're going to start talking about

00:00:06.199 --> 00:00:08.866
a different piece of punctuation

00:00:09.767 --> 00:00:13.833
and that piece of
punctuation is the apostrophe

00:00:13.833 --> 00:00:15.084
it kind of looks like a comma,

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but it's one that floats in the air

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Here's the ground, here's the word ground,

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And if we say Paige's dog Atti

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we're using the apostrophe,
not shown to scale obviously

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in one of its three
different applications.

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So the apostrophe can do three things.

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Thing number one: it can
stand in for missing letters.

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- [Voiceover] So when
an apostrophe stands in

00:00:48.082 --> 00:00:51.883
for missing letters that's
called a contraction

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- [Voiceover] So what does that look like,

00:00:54.549 --> 00:00:57.688
what does a contraction
look like in context?

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- [Voiceover] So another
way to say something like

00:00:59.351 --> 00:01:01.588
"I did not eat the cookie." Is to say

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"I didn't eat the cookie."

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- [Voiceover] So that
apostrophe there represents

00:01:11.055 --> 00:01:13.048
the 'O' being taken out
and everything being

00:01:13.048 --> 00:01:15.795
squished together into
this new word 'didn't'

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So "Did not" gets (sucks) together,

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and then we attach this
apostrophe to show that

00:01:21.531 --> 00:01:26.389
we've contracted, or shortened
or shrunk, these two words.

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- [Voiceover] Right.

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- [Voiceover] Paige, join
me on screen number two

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and let's talk about thing number two.

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- [Voiceover] Let's go.

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- [Voiceover] So the second
thing that an apostrophe can do

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is show that something belongs to someone,

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what we call possession.

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- [Voiceover] So you
can use an apostrophe to

00:01:41.935 --> 00:01:46.018
say something like "That's
David's cursed skull."

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- [Voiceover] It's true.

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It's been in my family for generations.

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But what is going on here?

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What is this doing the same work as?

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- [Voiceover] So the
sentence basically means

00:02:01.300 --> 00:02:04.448
that cursed skull belongs to David.

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This first sentence, "That's
David's cursed skull"

00:02:07.260 --> 00:02:09.898
is kind of just an easier way to say that.

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- [Voiceover] So apostrophes
can show contraction

00:02:12.947 --> 00:02:14.227
much like we're also doing

00:02:14.227 --> 00:02:17.414
in this part of the sentence
as well with "That's",

00:02:17.414 --> 00:02:19.879
because this is a shorter version of

00:02:19.879 --> 00:02:22.462
"That is David's cursed skull."

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but we're condensing that or
contracting that into "That's"

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but it's also being used
for its second purpose here

00:02:29.434 --> 00:02:32.117
which is "David's", and
this is what we call

00:02:32.117 --> 00:02:34.379
the possessive or the genitive case.

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Saying that, this cursed
skull belongs to me.

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Paige, what's the third
use of apostrophes?

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It's pretty rare.

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- [Voiceover] The third use
does not happen very often,

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but apostrophes can occasionally be used

00:02:48.870 --> 00:02:51.212
to make words plural.

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- [Voiceover] Okay,
because I was always taught

00:02:52.864 --> 00:02:56.052
never to use apostrophes
to pluralize stuff.

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Like the plural of book is books,

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not "Book's". That's wrong.

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- [Voiceover] Yeah, so there a--

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- [Voiceover] This is the plural,

00:03:04.599 --> 00:03:08.182
and this is something belonging to a book.

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- [Voiceover] Right, the book's pages.

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- [Voiceover] Right.

00:03:13.230 --> 00:03:16.057
- [Voiceover] So there's
really only one case

00:03:16.057 --> 00:03:17.820
where you'd want to use an apostrophe

00:03:17.820 --> 00:03:19.090
to make something plural.

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- [Voiceover] What is that case?

00:03:20.459 --> 00:03:22.624
- [Voiceover] That case is when you're

00:03:22.624 --> 00:03:26.169
trying to make the plural
of lower case letter.

00:03:26.169 --> 00:03:30.336
- [Voiceover] Like, "I'm
really bad at drawing 's's."

00:03:31.363 --> 00:03:32.740
- [Voiceover] Right. If you
didn't have that apostrophe

00:03:32.740 --> 00:03:36.439
there, it might kinda
just look like (hisses)

00:03:36.439 --> 00:03:38.821
- [Voiceover] So I could say, for example,

00:03:38.821 --> 00:03:40.488
"I like to draw j's"

00:03:42.452 --> 00:03:45.619
and "Remember to dot your j's and i's"

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Like that, to denote that their plural,

00:03:49.871 --> 00:03:51.947
to indicate there's
some kind of separation

00:03:51.947 --> 00:03:54.912
between this lowercase letter
and this lowercase letter.

00:03:54.912 --> 00:03:56.029
And that we're trying to say that

00:03:56.029 --> 00:03:57.958
there are multiple j's and i's.

00:03:57.958 --> 00:04:01.278
- [Voiceover] Right. Especially
with something like i's,

00:04:01.278 --> 00:04:02.620
if you didn't have that apostrophe there,

00:04:02.620 --> 00:04:03.572
it would probably just look like

00:04:03.572 --> 00:04:05.080
you were trying to write the word is.

00:04:05.080 --> 00:04:06.133
- [Voiceover] Sure.

00:04:06.133 --> 00:04:07.714
So this is kind of a work-around.

00:04:07.714 --> 00:04:10.280
- [Voiceover] Exactly.

00:04:10.280 --> 00:04:12.203
- [Voiceover] So this
usage is extremely rare,

00:04:12.203 --> 00:04:13.719
that's why I put it in parentheses,

00:04:13.719 --> 00:04:17.886
because I really want to
de-emphasize this last usage.

00:04:19.180 --> 00:04:20.406
Super rare.

00:04:20.406 --> 00:04:21.762
So more importantly the first

00:04:21.762 --> 00:04:23.657
two things are the most important.

00:04:23.657 --> 00:04:26.310
Number one, contractions
make stuff shorter like

00:04:26.310 --> 00:04:27.739
"I did not eat the cookie." to

00:04:27.739 --> 00:04:29.368
"I didn't eat the cookie."

00:04:29.368 --> 00:04:32.293
And possession, showing ownership.

00:04:32.293 --> 00:04:35.697
So instead of saying "That
cursed skull belongs to David"

00:04:35.697 --> 00:04:39.353
you would say "That is
David's cursed skull."

00:04:39.353 --> 00:04:41.096
- [Voiceover] Exactly.

00:04:41.096 --> 00:04:41.931
- [Voiceover] And that's an overview

00:04:41.931 --> 00:04:44.634
of the three powers of the apostrophe.

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You can learn anything, David out.

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- [Voiceover] Paige out.


Introduction to contractions

WEBVTT
Kind: captions
Language: en

00:00:00.584 --> 00:00:01.751
- [Voiceover] Hello
Grammarians, hello David.

00:00:01.751 --> 00:00:02.826
- [David] Hello Paige!

00:00:02.826 --> 00:00:05.212
- [Paige] So today we're
gonna talk about contractions

00:00:05.212 --> 00:00:09.379
which are another use for
our friend, the apostrophe.

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So David, what is a contraction?

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- [David] So something that apostrophes

00:00:15.324 --> 00:00:16.961
are really good at doing is showing when

00:00:16.961 --> 00:00:19.276
letters are missing from a word.

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Right, so let's say we have something

00:00:21.824 --> 00:00:24.657
like the two word phrase "I will".

00:00:27.088 --> 00:00:30.042
So in linguistics, I'm
told there's this idea

00:00:30.042 --> 00:00:30.875
called the principle of least effort,

00:00:30.875 --> 00:00:33.980
but I'm not a linguist, Paige, you are.

00:00:33.980 --> 00:00:36.590
What is the principle of least effort?

00:00:36.590 --> 00:00:38.904
- [Paige] So that's kind
of a fancy way of saying

00:00:38.904 --> 00:00:41.340
people like to be lazy.

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- [David] Sure.

00:00:42.173 --> 00:00:44.785
- [Paige] Which is, you
know, tends to be accurate

00:00:44.785 --> 00:00:48.458
across language, so you know,
we can say something like

00:00:48.458 --> 00:00:51.820
"I will", but honestly that kind of takes

00:00:51.820 --> 00:00:54.218
a lot of effort to say, right?

00:00:54.218 --> 00:00:55.205
- [David] I have to articulate the mouth

00:00:55.205 --> 00:00:57.030
in this particular way.

00:00:57.030 --> 00:01:00.939
It's just easier to just
collapse all of that

00:01:00.939 --> 00:01:05.139
into one, you know,
one syllable, one sound

00:01:05.139 --> 00:01:06.306
to say "I'll".

00:01:07.344 --> 00:01:10.086
And when we do that, we use an apostrophe

00:01:10.086 --> 00:01:12.751
to indicate the missing letters.

00:01:12.751 --> 00:01:15.257
That missing "w" sound.

00:01:15.257 --> 00:01:16.778
That's a contraction.

00:01:16.778 --> 00:01:19.440
So most model verbs,
right, if you remember

00:01:19.440 --> 00:01:22.552
model auxiliaries from the verb section.

00:01:22.552 --> 00:01:25.052
We use those a lot in English.

00:01:26.479 --> 00:01:28.915
And so it's really easy to combine those

00:01:28.915 --> 00:01:32.832
with most words or pronouns
into a contraction.

00:01:33.748 --> 00:01:37.695
So you could take the phrase "she would",

00:01:37.695 --> 00:01:40.791
which is a lot of letters to say.

00:01:40.791 --> 00:01:42.622
Takes a lot of letters to write.

00:01:42.622 --> 00:01:44.004
And we can turn that into, with the help

00:01:44.004 --> 00:01:45.497
of our friend the apostrophe,

00:01:45.497 --> 00:01:48.542
the word "she'd" means the same thing.

00:01:48.542 --> 00:01:49.425
- [Paige] Yeah, that's pretty amazing.

00:01:49.425 --> 00:01:54.043
I mean this tiny apostrophe
stands in the place

00:01:54.043 --> 00:01:56.458
of all of these letters.

00:01:56.458 --> 00:01:57.736
- [David] Yeah it's doing a lot of work.

00:01:57.736 --> 00:02:00.048
Have I got a deal for your, Paige.

00:02:00.048 --> 00:02:02.780
How would you like three
letters for the price of four?

00:02:02.780 --> 00:02:05.444
'Cause you can shorten, you know,

00:02:05.444 --> 00:02:08.330
something like "he is" to "he's".

00:02:08.330 --> 00:02:09.624
- [Paige] Right.

00:02:09.624 --> 00:02:11.372
Yeah, I mean, that's what the principle

00:02:11.372 --> 00:02:13.503
we were talking about is all about.

00:02:13.503 --> 00:02:16.022
Like "he is" isn't that hard to say,

00:02:16.022 --> 00:02:17.663
but "he's" is a lot easier.

00:02:17.663 --> 00:02:20.558
- [David] So this is
pretty straightforward,

00:02:20.558 --> 00:02:23.992
but there are some kind of
strange uses of contractions.

00:02:23.992 --> 00:02:26.252
Some strange uses of the apostrophe

00:02:26.252 --> 00:02:30.178
that don't seem as immediately
evident on their face.

00:02:30.178 --> 00:02:33.758
So for example if you
contract the phrase "will not"

00:02:33.758 --> 00:02:38.734
into a single contraction, it
doesn't turn into "willn't",

00:02:38.734 --> 00:02:40.567
it turns into "won't".

00:02:42.413 --> 00:02:44.685
- [Paige] So in this case the
apostrophe stands in the place

00:02:44.685 --> 00:02:48.435
of this "o", but all
these letters disappear,

00:02:49.541 --> 00:02:53.225
and they're kind of unaccounted for.

00:02:53.225 --> 00:02:54.906
- [David] It's weird, it's
like the Bermuda Triangle

00:02:54.906 --> 00:02:56.318
of punctuation marks.

00:02:56.318 --> 00:02:59.176
They all just kind of got
sucked up into that apostrophe.

00:02:59.176 --> 00:03:00.231
- [Paige] Yeah.

00:03:00.231 --> 00:03:01.180
- [David] Never to be seen again.

00:03:01.180 --> 00:03:02.013
- [Paige] Who knows where they went.

00:03:02.013 --> 00:03:03.507
- [David] But there aren't a ton of those.

00:03:03.507 --> 00:03:06.065
There's "won't", there's "don't",

00:03:06.065 --> 00:03:08.479
but not to take away
from our original point.

00:03:08.479 --> 00:03:10.620
This is what the apostrophe does

00:03:10.620 --> 00:03:12.482
when it's working to contract.

00:03:12.482 --> 00:03:15.232
Right, it just takes letters
from the middle of the word,

00:03:15.232 --> 00:03:17.754
and it takes them away, it stands in

00:03:17.754 --> 00:03:20.188
for the fact that there
are letters missing.

00:03:20.188 --> 00:03:21.938
- [Paige] You got it.

00:03:22.836 --> 00:03:24.061
- [David] Cool.

00:03:24.061 --> 00:03:25.542
- [Paige] So "I will" goes to "I'll",

00:03:25.542 --> 00:03:27.549
"She would" becomes "she'd",

00:03:27.549 --> 00:03:29.224
"He is" becomes "he's",

00:03:29.224 --> 00:03:30.203
and "will not" becomes "won't".

00:03:30.203 --> 00:03:32.496
So that's contractions.

00:03:32.496 --> 00:03:33.402
You can learn anything.

00:03:33.402 --> 00:03:34.399
- [David] David out.

00:03:34.399 --> 00:03:35.709
- [Paige] Paige out.


Finding missing side when given area

WEBVTT
Kind: captions
Language: en

00:00:00.653 --> 00:00:01.991
- [Voiceover] The picture has an

00:00:01.991 --> 00:00:04.772
area of 80 square centimeters.

00:00:04.772 --> 00:00:07.234
What is the width of the picture?

00:00:07.234 --> 00:00:09.329
So here's our picture, this super

00:00:09.329 --> 00:00:11.884
fun giraffe listening to music

00:00:11.884 --> 00:00:14.666
and our picture's shape is a rectangle

00:00:14.666 --> 00:00:19.507
and we're asked to find the
width of that rectangle.

00:00:19.507 --> 00:00:22.107
Well, maybe we don't
know a special formula

00:00:22.107 --> 00:00:25.063
or a special equation to find width,

00:00:25.063 --> 00:00:29.390
but we do know one to
find area of a rectangle,

00:00:29.390 --> 00:00:33.346
so let's use that formula
and see how it can help us.

00:00:33.346 --> 00:00:37.074
We know that area of a
rectangle can be found

00:00:37.074 --> 00:00:40.559
by multiplying the
length of the rectangle,

00:00:40.559 --> 00:00:43.809
over here, the length, times the width.

00:00:46.700 --> 00:00:49.160
So if we multiply the two side lengths

00:00:49.160 --> 00:00:52.126
of a rectangle, we get its area.

00:00:52.126 --> 00:00:54.713
And on this picture, in this rectangle,

00:00:54.713 --> 00:00:58.173
we are told that our area
is 80 square centimeters,

00:00:58.173 --> 00:01:01.132
so we already know the area,

00:01:01.132 --> 00:01:02.960
and we can use that to help us.

00:01:02.960 --> 00:01:04.754
We also know the length.

00:01:04.754 --> 00:01:07.053
We're told that this
distance from here to here,

00:01:07.053 --> 00:01:11.987
this length is 10 centimeters,
so the length is 10.

00:01:11.987 --> 00:01:14.645
Times the width, we don't know the width.

00:01:14.645 --> 00:01:16.815
That's what we're looking for.

00:01:16.815 --> 00:01:20.393
So what we do know though,
is that we need our width

00:01:20.393 --> 00:01:23.785
to be a number that when
it's multiplied times 10,

00:01:23.785 --> 00:01:26.050
we get 80 for an answer.

00:01:26.050 --> 00:01:29.633
So what number times
10 equals 80 is eight.

00:01:31.711 --> 00:01:33.374
Eight time 10 equals 80.

00:01:33.374 --> 00:01:36.187
So that means the width of our picture

00:01:36.187 --> 00:01:37.937
is eight centimeters.

00:01:41.744 --> 00:01:43.476
Let's try one more.

00:01:43.476 --> 00:01:47.143
A rectangle has an area
of 24 square meters.

00:01:48.093 --> 00:01:50.436
The width of the rectangle is four meters.

00:01:50.436 --> 00:01:53.096
What is the length of the rectangle?

00:01:53.096 --> 00:01:55.855
So this time we don't even
have a picture to look at,

00:01:55.855 --> 00:01:59.011
but we have enough information
up here to solve this.

00:01:59.011 --> 00:02:01.837
Again, we can use our
formula that tells us

00:02:01.837 --> 00:02:06.004
area of a rectangle is the
length times the width.

00:02:11.781 --> 00:02:13.411
Now we could draw this rectangle.

00:02:13.411 --> 00:02:15.014
It might be helpful to visualize it,

00:02:15.014 --> 00:02:17.111
but I'm gonna show you here,
we can actually solve it

00:02:17.111 --> 00:02:19.674
without ever even seeing the rectangle,

00:02:19.674 --> 00:02:23.424
because we know the area
is 24 square meters,

00:02:24.666 --> 00:02:28.289
so the space the rectangle
covers is 24 square meters,

00:02:28.289 --> 00:02:31.617
and the length, we don't know the length.

00:02:31.617 --> 00:02:33.759
We're asked what is the length.

00:02:33.759 --> 00:02:37.846
But we do know that the
width is four meters.

00:02:37.846 --> 00:02:40.967
So our length has to be some number

00:02:40.967 --> 00:02:43.935
that when it's multiplied times four,

00:02:43.935 --> 00:02:46.018
we get 24 for the answer.

00:02:47.022 --> 00:02:49.355
And that number must be six,

00:02:50.313 --> 00:02:53.506
because six times four equals 24.

00:02:53.506 --> 00:02:56.720
So the length of our rectangle is six,

00:02:56.720 --> 00:03:00.887
and in this case we're
talking about meters, meters.


Creating rectangles with a given area 2

WEBVTT
Kind: captions
Language: en

00:00:08.566 --> 00:00:10.865
- So, here is our given rectangle,

00:00:10.865 --> 00:00:14.813
and we want to draw a
rectangle with the same area,

00:00:14.813 --> 00:00:15.840
the same area,

00:00:15.840 --> 00:00:19.647
so what is the area of this rectangle?

00:00:19.647 --> 00:00:23.230
Area is the amount of
space a shape covers,

00:00:24.924 --> 00:00:26.327
so how much space,

00:00:26.327 --> 00:00:29.797
or how many square units
does this shape cover,

00:00:29.797 --> 00:00:32.515
does our rectangle cover?

00:00:32.515 --> 00:00:34.130
Each of these is one square unit,

00:00:34.130 --> 00:00:38.297
so our rectangle covers
one, two, three, four, five,

00:00:41.380 --> 00:00:43.963
six, seven, eight square units.

00:00:46.027 --> 00:00:48.444
It has an area of eight square units.

00:00:48.444 --> 00:00:51.434
So, we want to draw another rectangle

00:00:51.434 --> 00:00:53.864
that also covers eight square units.

00:00:53.864 --> 00:00:56.293
If it covers eight square units,

00:00:56.293 --> 00:01:00.098
than it has an area of eight square units,

00:01:00.098 --> 00:01:04.331
but we can't just draw
the identical rectangle,

00:01:04.331 --> 00:01:06.350
because we're also told
that it should have,

00:01:06.350 --> 00:01:10.517
our rectangle should have
no side lengths the same,

00:01:12.403 --> 00:01:14.266
so what are the side
lengths of our rectangle?

00:01:14.266 --> 00:01:15.349
Over here on the left,

00:01:15.349 --> 00:01:16.932
it's one unit long,

00:01:18.078 --> 00:01:21.592
and going across the
top is eight units long.

00:01:21.592 --> 00:01:24.353
This rectangle had eight square units,

00:01:24.353 --> 00:01:28.541
and they were broken up
into one row of eight,

00:01:28.541 --> 00:01:31.885
so we need to think of another
way that we can break up

00:01:31.885 --> 00:01:34.192
eight square units.

00:01:34.192 --> 00:01:37.192
One idea would be two rows of four,

00:01:38.776 --> 00:01:42.404
'cause two rows of four
would also cover eight,

00:01:42.404 --> 00:01:43.904
so let's try that.

00:01:44.994 --> 00:01:48.238
Let's create a rectangle here,

00:01:48.238 --> 00:01:49.655
two rows of four,

00:01:51.765 --> 00:01:54.004
and we can just spread
this out a little bit

00:01:54.004 --> 00:01:57.004
so it covers the whole square units,

00:01:58.234 --> 00:02:02.401
and so this rectangle also
covers one, two, three, four,

00:02:06.731 --> 00:02:09.814
five, six, seven, eight square units,

00:02:11.599 --> 00:02:12.992
so the given rectangle,

00:02:12.992 --> 00:02:15.544
and our rectangle have the same area

00:02:15.544 --> 00:02:19.211
because they cover the
same amount of space,

00:02:20.599 --> 00:02:23.682
but they have different side lengths,

00:02:25.336 --> 00:02:27.753
because our new rectangle is,

00:02:29.145 --> 00:02:31.424
has a side length of two
over here on the side,

00:02:31.424 --> 00:02:33.344
it's two units long,

00:02:33.344 --> 00:02:36.509
and going across the
top is four units long,

00:02:36.509 --> 00:02:39.406
so it has new side lengths,

00:02:39.406 --> 00:02:43.385
so here's one way that
we could draw a rectangle

00:02:43.385 --> 00:02:44.260
with the same area,

00:02:44.260 --> 00:02:46.510
but different side lengths.


Creating rectangles with a given area 1

WEBVTT
Kind: captions
Language: en

00:00:01.102 --> 00:00:02.648
- [Voiceover] Each
small square on the grid

00:00:02.648 --> 00:00:05.375
has an area of one square unit.

00:00:05.375 --> 00:00:08.993
So, each of these small
squares is one square unit.

00:00:08.993 --> 00:00:10.740
This square is one square unit,

00:00:10.740 --> 00:00:14.038
and this square is one
square unit, and so on.

00:00:14.038 --> 00:00:17.413
And now we're asked to draw a rectangle

00:00:17.413 --> 00:00:20.080
with an area of 10 square units.

00:00:22.047 --> 00:00:24.240
Well, this word "area" here

00:00:24.240 --> 00:00:28.323
is talking about how much
space our shape covers.

00:00:29.199 --> 00:00:32.123
So, our shape in this case is a rectangle,

00:00:32.123 --> 00:00:33.911
so we're being asked to draw a rectangle

00:00:33.911 --> 00:00:36.244
that covers 10 square units,

00:00:38.260 --> 00:00:41.066
and we know that each of
these is one square unit,

00:00:41.066 --> 00:00:45.233
so we want a rectangle that
covers 10 of the square units.

00:00:46.841 --> 00:00:48.634
We could try just drawing a rectangle

00:00:48.634 --> 00:00:50.543
right across this top row

00:00:50.543 --> 00:00:53.064
until we get 10 square units,

00:00:53.064 --> 00:00:54.368
but the problem there is there's only

00:00:54.368 --> 00:00:57.618
one, two, three, four, five, six, seven

00:01:00.425 --> 00:01:02.174
square units going across the top.

00:01:02.174 --> 00:01:06.118
So we can't just do one
long row of 10 square units.

00:01:06.118 --> 00:01:07.828
We can't do one long column either,

00:01:07.828 --> 00:01:11.245
because one, two, three, four, five, six.

00:01:12.196 --> 00:01:13.158
Only six square units,

00:01:13.158 --> 00:01:16.532
so we can't draw a rectangle
going down like that either

00:01:16.532 --> 00:01:19.579
because we need 10 square units.

00:01:19.579 --> 00:01:23.308
So that means we're gonna
have to break up our 10

00:01:23.308 --> 00:01:25.064
into equal groups.

00:01:25.064 --> 00:01:26.976
Since it can't all fit on one row,

00:01:26.976 --> 00:01:29.989
we're gonna have to break up
the unit squares into groups.

00:01:29.989 --> 00:01:34.072
So, we can break up a 10
into two groups of five,

00:01:35.472 --> 00:01:37.466
or five groups of two.

00:01:37.466 --> 00:01:39.818
Either one of those will work.

00:01:39.818 --> 00:01:40.651
So let's do that.

00:01:40.651 --> 00:01:43.848
Let's draw ourselves a rectangle,

00:01:43.848 --> 00:01:46.170
and we'll start up here.

00:01:46.170 --> 00:01:47.719
Here's a rectangle.

00:01:47.719 --> 00:01:49.969
And let's see, that's five.

00:01:51.744 --> 00:01:53.733
And we can space and make sure

00:01:53.733 --> 00:01:57.391
that covers the whole square unit.

00:01:57.391 --> 00:01:58.900
There we go.

00:01:58.900 --> 00:02:00.817
So here's our rectangle,

00:02:00.817 --> 00:02:03.257
and this rectangle covers

00:02:03.257 --> 00:02:05.590
one, two, three, four, five,

00:02:07.157 --> 00:02:08.906
there's the first row of five.

00:02:08.906 --> 00:02:11.508
And the second row of
five has unit squares

00:02:11.508 --> 00:02:14.258
six, seven, eight, nine, and ten.

00:02:16.429 --> 00:02:18.059
So, here's one perfect answer,

00:02:18.059 --> 00:02:20.664
a rectangle that has two rows

00:02:20.664 --> 00:02:22.538
of five square units,

00:02:22.538 --> 00:02:25.139
and we could've drawn this rectangle

00:02:25.139 --> 00:02:26.889
anywhere on the grid.

00:02:26.889 --> 00:02:27.722
It doesn't matter.

00:02:27.722 --> 00:02:30.104
We could've drawn it down here

00:02:30.104 --> 00:02:32.056
with two rows of five,

00:02:32.056 --> 00:02:34.785
or right here with two rows of five.

00:02:34.785 --> 00:02:37.272
Any rectangle covering two rows of five

00:02:37.272 --> 00:02:39.774
has an area of 10 unit squares.

00:02:39.774 --> 00:02:43.941
Similarly, any rectangle
covering five rows of two,

00:02:44.881 --> 00:02:49.278
let's look and see if
we can try to show that.

00:02:49.278 --> 00:02:50.786
Here we go.

00:02:50.786 --> 00:02:52.369
Here's a rectangle.

00:02:53.882 --> 00:02:55.799
And this one will cover

00:02:58.453 --> 00:03:00.811
one, two, so we have rows of two,

00:03:00.811 --> 00:03:01.826
and there's five rows.

00:03:01.826 --> 00:03:04.909
So, one, two, three, four, five, six,

00:03:06.183 --> 00:03:08.100
seven, eight, nine, 10.

00:03:09.761 --> 00:03:12.817
So again, this rectangle
covers 10 square units.

00:03:12.817 --> 00:03:15.414
So any rectangle you can draw on the grid

00:03:15.414 --> 00:03:19.414
that either covers two
rows of five square units

00:03:20.383 --> 00:03:23.027
or five rows of two square units

00:03:23.027 --> 00:03:27.027
is a rectangle with an
area of 10 square units.


Multiplying by tens word problem

WEBVTT
Kind: captions
Language: en

00:00:01.575 --> 00:00:03.302
- [Voiceover] A volunteer
group is planting trees

00:00:03.302 --> 00:00:05.110
at five different parks.

00:00:05.110 --> 00:00:07.382
They planted 90 trees at each park.

00:00:07.382 --> 00:00:11.672
How many trees did the group plant in all?

00:00:11.672 --> 00:00:13.730
Here's what we know,

00:00:13.730 --> 00:00:16.722
we know that this group went
to five different parks,

00:00:16.722 --> 00:00:18.117
very kind of them,

00:00:18.117 --> 00:00:21.784
and planted 90 trees
at each of those parks.

00:00:23.286 --> 00:00:24.674
If we want to know the total amount,

00:00:24.674 --> 00:00:25.729
we could do a couple things.

00:00:25.729 --> 00:00:29.905
We could say they planted
90 trees at park one,

00:00:29.905 --> 00:00:32.338
plus 90 more at park two,

00:00:32.338 --> 00:00:36.033
plus, you see where this is
going, 90 more at park three,

00:00:36.033 --> 00:00:38.369
plus 90 more at park four,

00:00:38.369 --> 00:00:41.217
and finally 90 more at park five.

00:00:41.217 --> 00:00:44.962
One way to solve this would
be to add all those 90s.

00:00:44.962 --> 00:00:48.321
We could do it, it'll take a
while, but we could get there.

00:00:48.321 --> 00:00:52.898
Or, we could say that the
group planted 90 trees,

00:00:52.898 --> 00:00:53.815
five times.

00:00:55.186 --> 00:00:58.801
Five times, they planted 90 trees.

00:00:58.801 --> 00:01:00.301
So, 90 times five.

00:01:01.490 --> 00:01:02.706
Let's solve both of these.

00:01:02.706 --> 00:01:05.073
Either are great ways
to get to our solution,

00:01:05.073 --> 00:01:06.482
but maybe solving both of 'em

00:01:06.482 --> 00:01:08.481
will help us see if we
liked one way better

00:01:08.481 --> 00:01:11.361
or if one felt simpler for us.

00:01:11.361 --> 00:01:13.111
So, 90, the number 90

00:01:14.946 --> 00:01:17.276
we can think of as nine 10s,

00:01:17.276 --> 00:01:19.116
I'll write that up there,

00:01:19.116 --> 00:01:20.588
and that'll help us add

00:01:20.588 --> 00:01:23.967
nine 10s plus nine 10s is 18 10s,

00:01:23.967 --> 00:01:27.293
plus nine more 10s is 27 10s,

00:01:27.293 --> 00:01:30.204
plus nine more 10s is 36 10s,

00:01:30.204 --> 00:01:33.954
and the last nine 10s
gets us 45 10s, or 450.

00:01:35.662 --> 00:01:37.965
That zero is because
we're talking about 10s,

00:01:37.965 --> 00:01:39.215
45 10s, or 450.

00:01:42.700 --> 00:01:45.033
The group planted 450 trees.

00:01:46.524 --> 00:01:49.404
Let's try the multiplication
way and see how that goes.

00:01:49.404 --> 00:01:53.237
Again, 90 10 90, we could
think of as nine 10s

00:01:55.895 --> 00:01:59.334
times five, so if you
have nine 10s five times,

00:01:59.334 --> 00:02:00.667
you have 45 10s,

00:02:03.430 --> 00:02:04.786
and 45 10s

00:02:04.786 --> 00:02:05.869
is again 450.

00:02:07.843 --> 00:02:09.394
Get that zero on the end.

00:02:09.394 --> 00:02:11.782
Both ways, we see this
is a very generous group.

00:02:11.782 --> 00:02:13.699
They planted 450 trees.

00:02:16.067 --> 00:02:18.307
Either way, we could add
or we could multiply,

00:02:18.307 --> 00:02:21.220
for me, the multiplication
gets me there faster.

00:02:21.220 --> 00:02:23.748
I like the multiplication
way, but either way,

00:02:23.748 --> 00:02:27.915
we can see 90 trees at five
parks is 450 total trees.


Interpreting picture graphs (paint)

WEBVTT
Kind: captions
Language: en

00:00:01.061 --> 00:00:03.931
- [Voiceover] Jacob charges
$9.00 an hour to paint.

00:00:03.931 --> 00:00:06.291
The graph below shows the
number of hours he spent

00:00:06.291 --> 00:00:09.358
painting different rooms of one house.

00:00:09.358 --> 00:00:12.910
How much did Jacob charge
for painting the living room?

00:00:12.910 --> 00:00:16.426
So here's the graph, this is a
picture graph, or pictograph,

00:00:16.426 --> 00:00:19.113
and it shows us how much
time Jacob spent painting

00:00:19.113 --> 00:00:21.765
different rooms of a house.

00:00:21.765 --> 00:00:24.967
One super important thing is
this little key right here

00:00:24.967 --> 00:00:27.527
that tells us each of these paint buckets

00:00:27.527 --> 00:00:29.444
is three hours of time.

00:00:30.986 --> 00:00:34.022
We're asked about the living room.

00:00:34.022 --> 00:00:37.242
On the graph, we can find
where it says living room

00:00:37.242 --> 00:00:39.322
and see how many buckets.

00:00:39.322 --> 00:00:42.147
Remember, each of these buckets

00:00:42.147 --> 00:00:44.397
equals three hours of time.

00:00:46.048 --> 00:00:48.786
He spent three hours,
plus another three hours,

00:00:48.786 --> 00:00:52.953
so he spent a total of six
hours painting the living room.

00:00:54.125 --> 00:00:58.292
But the question asks us,
how much did Jacob charge.

00:00:59.220 --> 00:01:02.137
Jacob charges $9.00 for every hour,

00:01:03.651 --> 00:01:05.287
and he worked for six hours,

00:01:05.287 --> 00:01:08.581
so he charged $9.00 six times.

00:01:08.581 --> 00:01:11.895
$9.00 for each of the six hours he worked,

00:01:11.895 --> 00:01:13.228
which is a total

00:01:14.341 --> 00:01:15.174
of $54.00.

00:01:18.278 --> 00:01:22.445
Jacob charged a total of $54.00
to paint the living room.


Interpreting picture graphs (notebook)

WEBVTT
Kind: captions
Language: en

00:00:01.115 --> 00:00:04.077
- [Voiceover] Maria has
70 pages in her notebook.

00:00:04.077 --> 00:00:06.099
She made a graph of the kinds of writing

00:00:06.099 --> 00:00:08.858
on all the pages she has used so far.

00:00:08.858 --> 00:00:12.190
How many pages are left
in Maria's notebook?

00:00:12.190 --> 00:00:15.760
Down here we have a picture
graph, or pictograph,

00:00:15.760 --> 00:00:19.292
showing all the pages Maria's
used so far in her notebook,

00:00:19.292 --> 00:00:23.174
but we're asked how many pages are left

00:00:23.174 --> 00:00:25.400
in Maria's notebook.

00:00:25.400 --> 00:00:27.151
To find that out, we need to know how many

00:00:27.151 --> 00:00:31.235
she started with, which
it tells us right here.

00:00:31.235 --> 00:00:34.858
Her notebook started with 70 pages,

00:00:34.858 --> 00:00:38.594
and then if we take away
the ones she's used so far.

00:00:38.594 --> 00:00:42.092
If we take away however
many pages she's used so far

00:00:42.092 --> 00:00:44.906
that will tell us how many

00:00:44.906 --> 00:00:46.989
are left in her notebook.

00:00:48.474 --> 00:00:51.235
The question here is how
many has she used so far?

00:00:51.235 --> 00:00:54.785
We don't know exactly, but
we have this picture graph

00:00:54.785 --> 00:00:57.783
that will help us find that answer.

00:00:57.783 --> 00:01:00.623
Super important on the
picture graph first,

00:01:00.623 --> 00:01:03.546
is right here, it tells
us that each of these

00:01:03.546 --> 00:01:07.713
pieces of paper represents
two pages in Maria's notebook.

00:01:08.807 --> 00:01:12.727
For poems, she wrote on two
pages and another two pages,

00:01:12.727 --> 00:01:15.810
or she wrote on a total of four pages

00:01:16.684 --> 00:01:17.684
about poems.

00:01:18.853 --> 00:01:23.020
She did reports on two,
four, six, eight, ten pages.

00:01:25.951 --> 00:01:27.992
She wrote stories, she
wrote a lot of stories.

00:01:27.992 --> 00:01:30.625
She wrote stories on
two, four, six, eight,

00:01:30.625 --> 00:01:32.958
10, 12, 14 pages of stories.

00:01:35.794 --> 00:01:39.865
She wrote letters on two,
four, six, eight pages.

00:01:39.865 --> 00:01:42.239
And finally, she journaled on two, four,

00:01:42.239 --> 00:01:44.322
six, eight, 10, 12 pages.

00:01:48.648 --> 00:01:53.268
This here, this is the total
pages she's used so far.

00:01:53.268 --> 00:01:55.805
If we combine all of
these, the four for poems,

00:01:55.805 --> 00:01:58.034
the 10 for reports, and so on,

00:01:58.034 --> 00:02:02.522
this will tell us how many
pages she's used so far.

00:02:02.522 --> 00:02:05.468
Then we can substitute that in right here,

00:02:05.468 --> 00:02:07.895
and we can say 70 she started with,

00:02:07.895 --> 00:02:09.715
take away what she used so far,

00:02:09.715 --> 00:02:11.371
and we'll get our final solution

00:02:11.371 --> 00:02:14.535
for the pages left in her notebook.

00:02:14.535 --> 00:02:19.173
Let's find this total,
there's four pages for poems,

00:02:19.173 --> 00:02:22.152
plus 10 pages for reports,

00:02:22.152 --> 00:02:23.319
14 on stories,

00:02:24.310 --> 00:02:26.276
eight more pages to write letters,

00:02:26.276 --> 00:02:28.276
and 12 pages to journal.

00:02:29.977 --> 00:02:32.993
If we add these, I'll start with the ones,

00:02:32.993 --> 00:02:35.993
two ones plus eight ones is 10 ones.

00:02:36.894 --> 00:02:39.311
10 ones plus four ones is 14.

00:02:40.481 --> 00:02:43.625
Plus zero more is still 14 ones.

00:02:43.625 --> 00:02:45.792
Plus four more is 18 ones.

00:02:47.214 --> 00:02:49.716
Plus, now let's add our 10s.

00:02:49.716 --> 00:02:53.133
One 10 plus another 10 is two 10s, or 20.

00:02:54.245 --> 00:02:57.315
Plus one more 10 is three 10s, or 30.

00:02:57.315 --> 00:03:00.131
She's 18 ones plus three 10s,

00:03:00.131 --> 00:03:01.842
so 18 plus 30 pages,

00:03:01.842 --> 00:03:04.259
which is a total of 48 pages.

00:03:06.332 --> 00:03:08.582
She's used 48 pages so far.

00:03:10.547 --> 00:03:13.802
If we take those 48 away from 70,

00:03:13.802 --> 00:03:17.389
we'll know how many pages are left.

00:03:17.389 --> 00:03:18.346
One way we could do this,

00:03:18.346 --> 00:03:20.667
is we can think of it as counting up.

00:03:20.667 --> 00:03:23.995
We can say there's 48 pages
used, let's count up to 70

00:03:23.995 --> 00:03:27.606
to see how many more pages
there still are in the notebook.

00:03:27.606 --> 00:03:31.890
If we count up from 48 to 50,
that's two more pages she has,

00:03:31.890 --> 00:03:36.057
and then from 50 to 70 is 20,
that's 20 more pages she has,

00:03:36.967 --> 00:03:38.717
so she has a total of

00:03:39.594 --> 00:03:42.511
22 more pages left in her notebook.


Interpreting bar graphs (colors)

WEBVTT
Kind: captions
Language: en

00:00:01.033 --> 00:00:02.764
- [Voiceover] Chelsea asked 600 people

00:00:02.764 --> 00:00:04.770
at her school their favorite color

00:00:04.770 --> 00:00:06.182
and graphed the results.

00:00:06.182 --> 00:00:08.746
Some colors are not on Chelsea's graph.

00:00:08.746 --> 00:00:10.545
How many people chose colors

00:00:10.545 --> 00:00:13.334
other than those on Chelsea's graph?

00:00:13.334 --> 00:00:16.204
So, here's Chelsea's graph,
she made a bar graph,

00:00:16.204 --> 00:00:18.347
and she listed some favorite colors,

00:00:18.347 --> 00:00:20.990
blue, green, red, yellow, pink,

00:00:20.990 --> 00:00:23.650
and graphed people who
had those favorite colors.

00:00:23.650 --> 00:00:26.205
But, some of these 600 people, like me,

00:00:26.205 --> 00:00:28.093
had a different favorite color.

00:00:28.093 --> 00:00:30.255
My favorite color, orange,
isn't on the graph.

00:00:30.255 --> 00:00:32.692
So, we're asked how many people like me

00:00:32.692 --> 00:00:34.250
were not graphed.

00:00:34.250 --> 00:00:35.827
How many people picked a
different color besides

00:00:35.827 --> 00:00:39.345
blue, green, red, yellow, and pink?

00:00:39.345 --> 00:00:41.076
So, the way we can figure this out

00:00:41.076 --> 00:00:43.444
is if we look at the graph
and find out how many

00:00:43.444 --> 00:00:46.361
of the 600 people are on the graph,

00:00:47.440 --> 00:00:51.039
then we can take that away
from the total 600 people

00:00:51.039 --> 00:00:54.552
to find out how many are not on the graph.

00:00:54.552 --> 00:00:57.168
So, we'll start by looking at the graph.

00:00:57.168 --> 00:01:01.379
First one, blue, this bar lines up to 90.

00:01:01.379 --> 00:01:03.546
So, 90 people picked blue.

00:01:04.753 --> 00:01:08.003
Plus, next one, green, lines up to 135,

00:01:09.594 --> 00:01:11.594
135 people picked green.

00:01:13.681 --> 00:01:16.961
Moving over to red,
this bar lines up to 75,

00:01:16.961 --> 00:01:18.544
75 more picked red.

00:01:20.095 --> 00:01:22.385
Yellow and pink, the bars
are the same heights,

00:01:22.385 --> 00:01:25.452
that means the same amount of
people picked yellow and red,

00:01:25.452 --> 00:01:28.761
and we can move over and
see that that was 120,

00:01:28.761 --> 00:01:32.844
so 120 picked yellow, and
another 120 picked red.

00:01:35.433 --> 00:01:38.335
So, if we combine all of these numbers,

00:01:38.335 --> 00:01:40.965
combine all of the people
that are on the graph,

00:01:40.965 --> 00:01:42.274
that will help us to figure out

00:01:42.274 --> 00:01:45.142
how many are not on the graph.

00:01:45.142 --> 00:01:47.082
So, let's start, let's
start with the ones.

00:01:47.082 --> 00:01:50.332
Zero ones, plus five ones is five ones,

00:01:51.769 --> 00:01:55.201
plus five more ones is
10, plus zero is still 10,

00:01:55.201 --> 00:01:59.158
plus zero is still 10, so we have 10 ones,

00:01:59.158 --> 00:02:02.178
plus, let's look at our tens,

00:02:02.178 --> 00:02:05.261
nine tens plus three tens is 12 tens,

00:02:06.418 --> 00:02:09.335
12 tens plus seven tens is 19 tens,

00:02:11.293 --> 00:02:13.626
19 tens plus two is 21 tens,

00:02:16.086 --> 00:02:20.253
and two more tens 21 tens
plus two more tens is 23 tens,

00:02:21.507 --> 00:02:23.840
so we have 230 tens, or 230,

00:02:25.432 --> 00:02:28.226
that zero because we're
talking about tens,

00:02:28.226 --> 00:02:30.976
plus, we can now do our hundreds,

00:02:32.271 --> 00:02:33.421
only a few of these had hundreds,

00:02:33.421 --> 00:02:34.836
we had one hundred,

00:02:34.836 --> 00:02:37.485
plus another one hundred is two hundreds,

00:02:37.485 --> 00:02:42.155
plus another is three
hundreds, so three hundreds,

00:02:42.155 --> 00:02:43.972
we have two zeros now because
we're talking about hundreds,

00:02:43.972 --> 00:02:45.222
three hundreds.

00:02:46.429 --> 00:02:49.465
And, if we add all of these,

00:02:49.465 --> 00:02:51.465
10 plus 230, 230 is 240,

00:02:54.305 --> 00:02:55.722
and 240 plus 300,

00:02:57.547 --> 00:02:59.873
well, let's see, that will still be 40

00:02:59.873 --> 00:03:02.803
but 200 plus another 300 is 500.

00:03:02.803 --> 00:03:05.470
So, 540 people are on the graph,

00:03:07.193 --> 00:03:11.430
but we're asked how many
are not on the graph.

00:03:11.430 --> 00:03:16.368
So, up here, we see there are
600 total people were asked,

00:03:16.368 --> 00:03:17.785
600 total people,

00:03:19.343 --> 00:03:23.510
and we want to take away the
540 who were on the graph,

00:03:24.601 --> 00:03:28.252
and that will tell us how
many were not on the graph.

00:03:28.252 --> 00:03:30.740
If we take these people away,

00:03:30.740 --> 00:03:32.887
everybody who's left is like me,

00:03:32.887 --> 00:03:35.823
who's favorite color is not on the graph.

00:03:35.823 --> 00:03:37.298
So, let's do that.

00:03:37.298 --> 00:03:40.966
If we started with 600
and we're subtracting 540,

00:03:40.966 --> 00:03:43.482
let's first subtract the 500.

00:03:43.482 --> 00:03:45.232
600 minus 500 is 100.

00:03:46.536 --> 00:03:49.392
But we still need to subtract the 40.

00:03:49.392 --> 00:03:53.924
100 is like 10 tens, minus
40 which is four tens,

00:03:53.924 --> 00:03:57.036
10 tens minus four tens is six tens,

00:03:57.036 --> 00:03:57.869
or 60.

00:04:00.002 --> 00:04:02.824
So, there were 60 people who chose colors

00:04:02.824 --> 00:04:04.758
other than those on Chelsea's graph.


Interpreting bar graphs (alligators)

WEBVTT
Kind: captions
Language: en

00:00:00.839 --> 00:00:03.105
- [Voiceover] James counted
the number of alligators

00:00:03.105 --> 00:00:05.185
in various local bodies of water

00:00:05.185 --> 00:00:06.633
and graphed the results.

00:00:06.633 --> 00:00:10.047
How many fewer alligators
are in Bite Swamp

00:00:10.047 --> 00:00:13.543
than Chomp Lake and
Reptile Creek combined?

00:00:13.543 --> 00:00:15.801
So, down here, we have this bar graph

00:00:15.801 --> 00:00:18.301
that James somehow survived to create

00:00:18.301 --> 00:00:20.864
after going to all these bodies of water

00:00:20.864 --> 00:00:23.114
and counting the alligators.

00:00:23.114 --> 00:00:25.725
We'll hope he was behind
a fence or something.

00:00:25.725 --> 00:00:29.793
So then, we're asked how
many fewer alligators are

00:00:29.793 --> 00:00:33.960
in Bite Swamp than in Chomp
Lake and Reptile Creek combined?

00:00:36.525 --> 00:00:39.627
So, we need to know first
how many are in Chomp Lake

00:00:39.627 --> 00:00:42.592
and Reptile Creek combined

00:00:42.592 --> 00:00:45.823
before we can figure out how
many fewer are in Bite Swamp.

00:00:45.823 --> 00:00:46.948
So, let's look down here.

00:00:46.948 --> 00:00:50.089
Here's Chomp Lake sounding super scary,

00:00:50.089 --> 00:00:52.862
and it's bar lines up to six,

00:00:52.862 --> 00:00:55.980
so there's six alligators in Chomp Lake.

00:00:55.980 --> 00:01:00.147
Plus, in Reptile Creek, if we
go over here to Reptile Creek

00:01:01.365 --> 00:01:03.070
this bar lines up to nine,

00:01:03.070 --> 00:01:07.225
so there's nine alligators
hanging out in Reptile Creek.

00:01:07.225 --> 00:01:10.975
Six plus nine, let's
see nine plus one is 10,

00:01:12.679 --> 00:01:15.805
so we can make our six
into a a five and a one,

00:01:15.805 --> 00:01:19.555
nine plus one is 10 plus
five more equals 15.

00:01:21.365 --> 00:01:24.830
So, there's total of 15 alligators

00:01:24.830 --> 00:01:28.421
in Chomp Lake and Reptile Creek combined.

00:01:28.421 --> 00:01:32.588
Now, we can answer how many
fewer than 15 are in Bite Swamp.

00:01:33.741 --> 00:01:35.544
So, Bite Swamp down here,

00:01:35.544 --> 00:01:38.193
sounding the most dangerous of them all,

00:01:38.193 --> 00:01:40.693
has a bar that lines up to 12.

00:01:42.858 --> 00:01:46.554
So, 12, there's 12
alligators in Bite Swamp,

00:01:46.554 --> 00:01:49.804
so how many fewer is 12 than the amount

00:01:50.679 --> 00:01:53.645
in Chomp Lake and Reptile
Creek combined, 15,

00:01:53.645 --> 00:01:57.085
so how much fewer is 12 than 15?

00:01:57.085 --> 00:02:00.573
Well, if we have 15 and we take 12 away,

00:02:00.573 --> 00:02:02.740
that leaves us with three.

00:02:04.423 --> 00:02:07.423
Three fewer alligators in Bite Swamp

00:02:08.264 --> 00:02:11.978
than there are in Chomp Lake
and Reptile Creek combined.


Time word problem (puzzle)

WEBVTT
Kind: captions
Language: en

00:00:02.476 --> 00:00:06.323
- [Voiceover] Amelia
started a puzzle at 12:56 pm

00:00:06.323 --> 00:00:08.406
and solved it at 1:33 pm.

00:00:09.598 --> 00:00:13.922
How long did it take
Amelia to solve the puzzle?

00:00:13.922 --> 00:00:17.834
So we can see she started at 12:56 pm

00:00:17.834 --> 00:00:20.370
and ended at 1:33 pm.

00:00:20.370 --> 00:00:23.722
These are both pm and we'll
assume on the same day,

00:00:23.722 --> 00:00:25.199
so that means it didn't take all the way

00:00:25.199 --> 00:00:26.307
from morning to night.

00:00:26.307 --> 00:00:28.379
They're both afternoon.

00:00:28.379 --> 00:00:30.296
So she started at 12:56

00:00:34.739 --> 00:00:36.583
and we want to know how long it takes

00:00:36.583 --> 00:00:40.250
to get to 1:33 when she
finished the puzzle.

00:00:42.261 --> 00:00:44.594
Well, from 12:56 to 1:00 pm,

00:00:47.372 --> 00:00:49.222
we can figure out how long that is.

00:00:49.222 --> 00:00:53.973
That's only four minutes,
there's only four minutes

00:00:53.973 --> 00:00:55.890
between 12:56 and 1:00,

00:00:57.258 --> 00:01:01.341
and then to get from 1:00
all the way to 1:33 pm,

00:01:03.441 --> 00:01:06.691
is another 33 minutes, so Amelia worked

00:01:11.440 --> 00:01:14.857
for four minutes, plus another 33 minutes

00:01:15.906 --> 00:01:16.912
after one o'clock.

00:01:16.912 --> 00:01:19.227
She worked for four minutes before 1:00,

00:01:19.227 --> 00:01:23.264
33 minutes after one, so
she worked for a total

00:01:23.264 --> 00:01:27.097
of 37 minutes on her
puzzle before solving it.


Identifying unit fractions word problem

WEBVTT
Kind: captions
Language: en

00:00:01.644 --> 00:00:04.367
- [Voiceover] This question
says, Vera's dinner plate

00:00:04.367 --> 00:00:07.950
is divided into three
equal-sized sections.

00:00:08.877 --> 00:00:12.170
Vera puts all her broccoli in one section.

00:00:12.170 --> 00:00:15.000
And then we're asked, what fraction

00:00:15.000 --> 00:00:18.140
of Vera's plate has broccoli?

00:00:18.140 --> 00:00:18.973
Okay.

00:00:18.973 --> 00:00:23.879
So we have we plate with
three equal-sized sections,

00:00:23.879 --> 00:00:27.938
and we know that Vera puts
broccoli in one section,

00:00:27.938 --> 00:00:30.168
and we're asked to
figure out what fraction

00:00:30.168 --> 00:00:32.490
of the plate that is.

00:00:32.490 --> 00:00:34.030
So we can draw Vera's plate,

00:00:34.030 --> 00:00:36.712
try to represent this with a picture.

00:00:36.712 --> 00:00:39.525
Maybe Vera's plate is a rectangle.

00:00:39.525 --> 00:00:43.733
We don't really know,
but a rectangle will work

00:00:43.733 --> 00:00:46.313
as long as it has three
equal-sized sections.

00:00:46.313 --> 00:00:48.480
So let's try to draw that.

00:00:50.125 --> 00:00:51.406
This may not be perfect.

00:00:51.406 --> 00:00:54.450
We can probably do that
second one a little better,

00:00:54.450 --> 00:00:57.712
but this should represent
three equal-sized sections

00:00:57.712 --> 00:00:59.106
on a plate.

00:00:59.106 --> 00:01:01.130
And then we know she puts broccoli in one

00:01:01.130 --> 00:01:04.876
of those sections, so let's
use green, draw some broccoli.

00:01:04.876 --> 00:01:07.260
Broccoli, broccoli, broccoli.

00:01:07.260 --> 00:01:11.427
And then, look at this
picture, and ask ourselves,

00:01:12.578 --> 00:01:16.571
what fraction of Vera's
plate has broccoli?

00:01:16.571 --> 00:01:19.919
Well, our fraction's
gonna have a numerator.

00:01:19.919 --> 00:01:23.085
On top will be how many
sections have broccoli,

00:01:23.085 --> 00:01:27.090
which is one, and then,
our denominator will be

00:01:27.090 --> 00:01:30.348
out of the total number of equal sections,

00:01:30.348 --> 00:01:34.777
and we know there are
three equal-sized sections.

00:01:34.777 --> 00:01:38.944
So 1/3 or one of the three
sections has broccoli.


Comparing fractions with same numerator

WEBVTT
Kind: captions
Language: en

00:00:00.661 --> 00:00:03.831
- [Voiceover] Let's compare 5/6 and 5/8.

00:00:03.831 --> 00:00:05.369
Let's think about what they mean.

00:00:05.369 --> 00:00:09.036
5/6 means five out of six pieces.

00:00:10.085 --> 00:00:12.307
If you have a whole,
let's say a whole cake

00:00:12.307 --> 00:00:14.357
and you cut it into six pieces,

00:00:14.357 --> 00:00:18.722
5/6 is five of those six pieces.

00:00:18.722 --> 00:00:21.548
5/8 again is five pieces.

00:00:21.548 --> 00:00:22.797
That's something that's the same.

00:00:22.797 --> 00:00:24.900
We're both talking about five pieces,

00:00:24.900 --> 00:00:26.716
but this time, we've split our cake

00:00:26.716 --> 00:00:31.323
into eight pieces, so it's
five out of eight pieces.

00:00:31.323 --> 00:00:33.900
We can represent that by drawing it.

00:00:33.900 --> 00:00:37.746
Maybe we can draw, here is one whole.

00:00:37.746 --> 00:00:39.496
And then another one.

00:00:42.127 --> 00:00:44.047
So these are two equal wholes,

00:00:44.047 --> 00:00:46.330
and on one of them, we can shade 5/6

00:00:46.330 --> 00:00:47.646
and the other 5/8.

00:00:47.646 --> 00:00:50.335
That way we can look and compare them.

00:00:50.335 --> 00:00:53.657
So for 5/6, if we divide this whole,

00:00:53.657 --> 00:00:55.610
and we were using the example of cake,

00:00:55.610 --> 00:00:57.860
into six equal-size pieces,

00:01:00.440 --> 00:01:01.729
not sure if those are perfect,

00:01:01.729 --> 00:01:04.619
but let's say those are
six equal-size pieces,

00:01:04.619 --> 00:01:08.786
5/6 is talking about five of those pieces.

00:01:10.054 --> 00:01:11.637
So one, two, three,

00:01:15.316 --> 00:01:16.233
four, five.

00:01:18.488 --> 00:01:21.572
This image represents 5/6.

00:01:21.572 --> 00:01:25.659
Now for 5/8, let's think
about it for a second.

00:01:25.659 --> 00:01:29.185
Will the pieces in 5/8 be bigger

00:01:29.185 --> 00:01:31.461
or smaller than 5/6?

00:01:31.461 --> 00:01:34.961
Are eighths bigger or smaller than sixths?

00:01:35.940 --> 00:01:37.813
Well, we can draw and see.

00:01:37.813 --> 00:01:39.578
If we have the same size whole,

00:01:39.578 --> 00:01:41.712
which we need to have the same size whole,

00:01:41.712 --> 00:01:45.879
and we draw and we split it
into eight pieces this time,

00:01:47.468 --> 00:01:50.468
so now we have fourths, and eighths,

00:01:52.948 --> 00:01:55.263
these pieces, these eighths,

00:01:55.263 --> 00:01:57.851
1/8 is smaller than a sixth

00:01:57.851 --> 00:01:59.482
'cause this time we had to split the cake

00:01:59.482 --> 00:02:03.054
between eight people, so
we got smaller pieces.

00:02:03.054 --> 00:02:05.823
Now again we can shade five of them.

00:02:05.823 --> 00:02:07.561
Seems like five pieces might be equal

00:02:07.561 --> 00:02:10.721
to five pieces, but we can look and see.

00:02:10.721 --> 00:02:13.971
Four, five, and now we can look and see

00:02:15.705 --> 00:02:19.379
the 5/6 takes up more
space, takes up more area,

00:02:19.379 --> 00:02:24.051
this is a larger amount,
and the reason is because

00:02:24.051 --> 00:02:27.432
each sixth, each piece is larger.

00:02:27.432 --> 00:02:31.599
So five larger pieces is more
than five smaller pieces,

00:02:32.723 --> 00:02:37.520
or is greater than, and
remember with our symbol,

00:02:37.520 --> 00:02:40.265
the open side, the larger side,

00:02:40.265 --> 00:02:43.009
should be facing our larger number.

00:02:43.009 --> 00:02:47.092
So 5/6 is greater than 5/8.

00:02:47.967 --> 00:02:49.947
Here's one more, but this time,

00:02:49.947 --> 00:02:51.801
let's try to compare them without drawing,

00:02:51.801 --> 00:02:54.818
let's just think about what these mean.

00:02:54.818 --> 00:02:58.485
2/5 means two pieces out of five.

00:02:59.345 --> 00:03:02.050
So one whole was split five ways

00:03:02.050 --> 00:03:04.467
and we got two of the pieces.

00:03:05.716 --> 00:03:09.755
2/3 means that same whole
was split three ways

00:03:09.755 --> 00:03:12.679
and we got two of the pieces.

00:03:12.679 --> 00:03:15.429
Well which two pieces are larger?

00:03:17.115 --> 00:03:19.921
The 2/3 are larger, 'cause if we only

00:03:19.921 --> 00:03:22.405
have to split our pieces three ways,

00:03:22.405 --> 00:03:24.423
we can have larger pieces.

00:03:24.423 --> 00:03:27.347
So the 2/5 are smaller.

00:03:27.347 --> 00:03:30.347
These two smaller pieces are less...

00:03:31.873 --> 00:03:34.620
These two smaller pieces are less

00:03:34.620 --> 00:03:37.303
than the two larger pieces, and again,

00:03:37.303 --> 00:03:40.260
the open end of our
symbol should be facing

00:03:40.260 --> 00:03:41.607
the larger number.

00:03:41.607 --> 00:03:45.440
So 2/5 is less than 2/3.


Comparing fractions with the same denominator

WEBVTT
Kind: captions
Language: en

00:00:00.908 --> 00:00:03.943
- [Voiceover] Let's compare 2/4 and 3/4.

00:00:03.943 --> 00:00:07.306
First let's think about
what these fractions mean.

00:00:07.306 --> 00:00:11.447
2/4 means we have some
whole, and we've split it

00:00:11.447 --> 00:00:15.936
into four equal size pieces,
and we get two of those pieces.

00:00:15.936 --> 00:00:17.836
Maybe we can think about
pizza for an example.

00:00:17.836 --> 00:00:20.092
We split a pizza into
four equal size pieces,

00:00:20.092 --> 00:00:22.788
and we ate two of them.

00:00:22.788 --> 00:00:26.792
3/4 means that same whole, that same pizza

00:00:26.792 --> 00:00:29.837
was again split into
four equal size pieces,

00:00:29.837 --> 00:00:32.069
but this time, what's
different is we got three

00:00:32.069 --> 00:00:33.236
of the pieces.

00:00:34.086 --> 00:00:36.454
So maybe from that description,
we can start to think

00:00:36.454 --> 00:00:40.927
about which one is larger,
but let's draw them also

00:00:40.927 --> 00:00:45.094
just to be sure that we can
decide which one is larger.

00:00:46.768 --> 00:00:50.510
So for 2/4, we're gonna have a fraction,

00:00:50.510 --> 00:00:54.028
maybe it's a pizza, and
it's gonna be divided, split

00:00:54.028 --> 00:00:56.361
into four equal size pieces.

00:00:57.946 --> 00:01:00.192
These may not be perfect lines,

00:01:00.192 --> 00:01:04.032
but should represent
four equal size pieces.

00:01:04.032 --> 00:01:06.615
And we get two of those pieces.

00:01:09.924 --> 00:01:14.289
So this represents 2/4, two out of four.

00:01:14.289 --> 00:01:18.456
3/4, again, will be the same
as the four equal size pieces,

00:01:20.732 --> 00:01:23.703
but this time, we get three of the four.

00:01:23.703 --> 00:01:26.953
So, one, two, three of the four pieces.

00:01:30.612 --> 00:01:33.536
And this will represent 3/4.

00:01:33.536 --> 00:01:37.764
Now we can look at it
visually and see very clearly

00:01:37.764 --> 00:01:41.715
that 3/4 is greater,
or takes up more space,

00:01:41.715 --> 00:01:45.882
or we can say that 2/4 is less than 3/4.

00:01:47.220 --> 00:01:49.669
Remember this is the less than symbol

00:01:49.669 --> 00:01:52.018
'cause we always want
this open, bigger side

00:01:52.018 --> 00:01:54.566
facing our larger number.

00:01:54.566 --> 00:01:57.893
In this case, it's
facing the second number.

00:01:57.893 --> 00:02:02.060
So we'll say 2/4 is less than 3/4.

00:02:03.705 --> 00:02:07.080
Each of these fourths is the same size,

00:02:07.080 --> 00:02:11.163
so two of them is less
than three of the fourths.

00:02:13.082 --> 00:02:15.009
Here we can try one more, but this time,

00:02:15.009 --> 00:02:16.097
let's don't draw the picture.

00:02:16.097 --> 00:02:17.544
Lets' just think about what they mean

00:02:17.544 --> 00:02:20.083
and see if we can figure it out.

00:02:20.083 --> 00:02:22.943
So for 5/8, we have a whole,

00:02:22.943 --> 00:02:26.075
and it's been divided
into eight equal pieces.

00:02:26.075 --> 00:02:29.872
For 3/8, same thing, eight equal pieces.

00:02:29.872 --> 00:02:32.976
But here in 5/8, we get
five of those pieces,

00:02:32.976 --> 00:02:36.657
and in 3/8, we get three of the pieces.

00:02:36.657 --> 00:02:38.602
So the pieces are the same size.

00:02:38.602 --> 00:02:40.770
They're eighths on both side.

00:02:40.770 --> 00:02:42.740
These are eighths, and these are eighths,

00:02:42.740 --> 00:02:46.835
but here we have five of the
eights, and here we have three.

00:02:46.835 --> 00:02:49.110
So if the pieces are the same size,

00:02:49.110 --> 00:02:53.034
five pieces is greater than three pieces

00:02:53.034 --> 00:02:57.272
or 5/8 is greater than 3/8.

00:02:57.272 --> 00:02:59.818
And here our open end, our bigger side

00:02:59.818 --> 00:03:01.331
is still facing our bigger number,

00:03:01.331 --> 00:03:03.804
but our bigger number is first this time,

00:03:03.804 --> 00:03:05.642
so this is the greater than symbol.

00:03:05.642 --> 00:03:09.475
5/8 is greater than 3/8.


Recognizing fractions greater than 1

WEBVTT
Kind: captions
Language: en

00:00:01.053 --> 00:00:03.491
- [Voiceover] This circle
represents one whole.

00:00:03.491 --> 00:00:05.660
This circle right here
represents one whole.

00:00:05.660 --> 00:00:08.828
If we know that, we can
answer what fraction

00:00:08.828 --> 00:00:11.153
of the circle is shaded in blue below?

00:00:11.153 --> 00:00:12.233
So down here.

00:00:12.233 --> 00:00:14.277
What fraction is in blue?

00:00:14.277 --> 00:00:16.579
Let's start back up here with the whole.

00:00:16.579 --> 00:00:20.079
This whole is divided into one, two, three

00:00:21.394 --> 00:00:26.083
equal size pieces, so
it's divided into thirds,

00:00:26.083 --> 00:00:27.786
three equal size pieces.

00:00:27.786 --> 00:00:31.334
And each of those pieces,
each of those pie pieces,

00:00:31.334 --> 00:00:34.667
is 1/3, is one of the thirds.

00:00:35.560 --> 00:00:39.410
So knowing that, let's go
down here to these ones

00:00:39.410 --> 00:00:42.193
and lets see how many of these 1/3 pieces.

00:00:42.193 --> 00:00:46.360
Here's 1/3, another 1/3,
another 1/3 shaded in blue,

00:00:48.412 --> 00:00:50.805
another one and another one.

00:00:50.805 --> 00:00:54.638
So we have one, two,
three, four, five thirds.

00:00:57.094 --> 00:01:00.761
We have 5/3 shaded in blue below.


Perimeter word problem (skating rink)

WEBVTT
Kind: captions
Language: en

00:00:01.324 --> 00:00:03.267
- [Voiceover] Gus plans
to install a handrail

00:00:03.267 --> 00:00:05.101
around a skating rink.

00:00:05.101 --> 00:00:09.424
The rink forms a 40 meter
by 20 meter rectangle.

00:00:09.424 --> 00:00:13.004
How many meters of handrail does Gus need?

00:00:13.004 --> 00:00:15.510
So here's what we know
about the skating rink.

00:00:15.510 --> 00:00:18.677
It's a 40 meter by 20 meter rectangle.

00:00:20.387 --> 00:00:22.724
So let's draw the skating rink.

00:00:22.724 --> 00:00:25.391
That might help us to visualize,

00:00:27.940 --> 00:00:31.690
and we know that one
side length is 40 meters

00:00:34.422 --> 00:00:37.505
and another side length is 20 meters.

00:00:38.931 --> 00:00:42.232
So Gus definitely needs to put
some handrails 40 meters here

00:00:42.232 --> 00:00:45.104
and 20 meters here,
but that is not enough.

00:00:45.104 --> 00:00:46.831
As somebody who doesn't know how to skate,

00:00:46.831 --> 00:00:50.067
I very much hope Gus puts
handrail on this length

00:00:50.067 --> 00:00:51.874
and this length also.

00:00:51.874 --> 00:00:55.473
He needs to put the handrails
all the way around the outside

00:00:55.473 --> 00:00:58.473
where what we could call
the perimeter of the shape,

00:00:58.473 --> 00:01:01.908
the entire distance around the outside.

00:01:01.908 --> 00:01:04.471
Because the skating rink is a rectangle,

00:01:04.471 --> 00:01:06.685
we know that opposite sides are equal.

00:01:06.685 --> 00:01:09.818
So if this length is 40 meters up here,

00:01:09.818 --> 00:01:14.201
then this length down here
must also be 40 meters.

00:01:14.201 --> 00:01:16.549
And we can do the same thing with 20.

00:01:16.549 --> 00:01:19.718
If we have 20 over here,
then the length across

00:01:19.718 --> 00:01:21.635
must also be 20 meters.

00:01:22.524 --> 00:01:24.813
So now we can figure out the entire amount

00:01:24.813 --> 00:01:28.526
of handrail Gus needs, the
amount of meters he needs to buy

00:01:28.526 --> 00:01:30.334
to put around the skating rink.

00:01:30.334 --> 00:01:34.417
For this first side here,
he needs 40 meters plus

00:01:36.333 --> 00:01:37.593
to go down this side,

00:01:37.593 --> 00:01:41.187
he'll need another 20 meters of handrail.

00:01:41.187 --> 00:01:42.855
Going across the bottom of the rink,

00:01:42.855 --> 00:01:45.994
he'll need another 40 meters of handrail,

00:01:45.994 --> 00:01:47.418
and then, going up the side,

00:01:47.418 --> 00:01:50.835
he'll need another 20 meters of handrail.

00:01:51.934 --> 00:01:54.948
So we can add these to find
the total amount he needs.

00:01:54.948 --> 00:01:56.365
40 plus 20 is 60.

00:01:58.196 --> 00:02:00.779
Then 60 plus 40 plus 40 is 100,

00:02:05.062 --> 00:02:07.979
and 100 plus 20 more is 120 meters.

00:02:12.456 --> 00:02:16.117
So to go the entire
distance around the outside

00:02:16.117 --> 00:02:19.941
of the skating rink, or the
perimeter of the skating rink

00:02:19.941 --> 00:02:24.108
with handrail, Gus will
need 120 meters of handrail.


Perimeter word problem (tables)

WEBVTT
Kind: captions
Language: en

00:00:01.270 --> 00:00:04.407
- [Voiceover] Lea and Pedro
push two tables together.

00:00:04.407 --> 00:00:07.083
The figure below shows
the new arrangement.

00:00:07.083 --> 00:00:10.533
We have table number
one and table number two

00:00:10.533 --> 00:00:12.657
that Lea and Pedro have pushed together.

00:00:12.657 --> 00:00:14.570
Maybe they're having a
bunch of people over for a

00:00:14.570 --> 00:00:17.835
fancy breakfast and so
they've pushed one, two tables

00:00:17.835 --> 00:00:21.457
together to have a lot of
room for people to sit.

00:00:21.457 --> 00:00:25.624
We're asked, what is the
perimeter of the new figure?

00:00:26.673 --> 00:00:29.982
Perimeter is the distance
around the outside,

00:00:29.982 --> 00:00:34.149
so all of this space around
the outside is the perimeter

00:00:36.073 --> 00:00:38.375
and we need to figure that out.

00:00:38.375 --> 00:00:40.160
What we could do we could
say, "Here we know there is

00:00:40.160 --> 00:00:43.064
three meters around the
outside, here is another meter,

00:00:43.064 --> 00:00:46.363
so that's four meters around the outside."

00:00:46.363 --> 00:00:50.442
Then we get to here and oh,
oh we don't have this one

00:00:50.442 --> 00:00:52.265
and we don't have this side
length, through this length,

00:00:52.265 --> 00:00:55.645
through this length, so we
can't know the entire distance

00:00:55.645 --> 00:00:57.766
around the outside until we figure out

00:00:57.766 --> 00:00:59.966
what those missing side lengths are.

00:00:59.966 --> 00:01:02.460
Let's fill in some of those first.

00:01:02.460 --> 00:01:06.811
These tables are rectangles,
opposite sides are equal.

00:01:06.811 --> 00:01:09.508
If this side down here is one meter,

00:01:09.508 --> 00:01:12.660
then the side up here has to be one meter.

00:01:12.660 --> 00:01:15.165
Same here if this is three meters,

00:01:15.165 --> 00:01:18.795
the opposite side is also three meters.

00:01:18.795 --> 00:01:22.056
We have one meter on the end of this table

00:01:22.056 --> 00:01:23.769
so that inside this length from

00:01:23.769 --> 00:01:26.352
here to here is also one meter.

00:01:28.031 --> 00:01:31.528
That's an interesting
one, this one meter here

00:01:31.528 --> 00:01:33.867
because this part now right here,

00:01:33.867 --> 00:01:35.980
that's on the inside of the arrangement.

00:01:35.980 --> 00:01:37.682
That's not the outside,

00:01:37.682 --> 00:01:40.765
so that is not part of the perimeter.

00:01:42.514 --> 00:01:45.427
This one meter will not be
included in our perimeter

00:01:45.427 --> 00:01:49.670
but it is still important
to us and here is why.

00:01:49.670 --> 00:01:53.653
This length and this length
are part of the outside

00:01:53.653 --> 00:01:55.674
and we need to know how long those are.

00:01:55.674 --> 00:02:00.488
What we can say is, if this
entire length is three meters,

00:02:00.488 --> 00:02:03.739
then this entire length is three meters,

00:02:03.739 --> 00:02:08.122
but one of those meters
was moved to the inside,

00:02:08.122 --> 00:02:12.289
so how many meters are still
left here on the outside?

00:02:14.298 --> 00:02:18.465
We had three meters over here,
we moved one to the inside,

00:02:20.500 --> 00:02:24.724
so we have two meters left on the outside.

00:02:24.724 --> 00:02:29.048
This length and this length
are a total of two meters.

00:02:29.048 --> 00:02:31.538
We can't know for sure, they
look pretty evenly divided,

00:02:31.538 --> 00:02:33.453
we can't know for sure
that they're both one meter

00:02:33.453 --> 00:02:36.462
but we do know for sure that it's a total

00:02:36.462 --> 00:02:39.403
of two meters when we combine them.

00:02:39.403 --> 00:02:42.922
Again this one meter
is not on the outside,

00:02:42.922 --> 00:02:45.522
it's not part of our
perimeter but it did help us

00:02:45.522 --> 00:02:47.689
to find the other lengths.

00:02:49.165 --> 00:02:51.540
Now everything is labelled,
so we can get back to

00:02:51.540 --> 00:02:54.778
finding the perimeter, the
distance around the outside

00:02:54.778 --> 00:02:59.008
will be all of these lengths put together.

00:02:59.008 --> 00:03:03.175
Here we have one meter plus
moving down the outside three

00:03:05.701 --> 00:03:09.868
more meters, plus one more,
plus one here on that side

00:03:11.131 --> 00:03:15.298
we just figured out, plus
another three, one on the end,

00:03:19.362 --> 00:03:23.309
another alongside of three and finally

00:03:23.309 --> 00:03:26.059
one more meter going up the side.

00:03:28.277 --> 00:03:29.760
We can add these lengths.

00:03:29.760 --> 00:03:32.171
When we combine these
lengths they'll tell us

00:03:32.171 --> 00:03:35.470
the total distance around the outside.

00:03:35.470 --> 00:03:39.541
One plus three is four,
plus one more is five,

00:03:39.541 --> 00:03:43.331
plus one more is six,
six plus three is nine,

00:03:43.331 --> 00:03:47.262
nine plus one is 10, 10 plus three is 13

00:03:47.262 --> 00:03:49.512
and 13 plus one more is 14.

00:03:50.395 --> 00:03:52.655
The perimeter of the new figure,

00:03:52.655 --> 00:03:56.238
of this new table
arrangement is 14 meters.


Finding perimeter when a side length is missing

WEBVTT
Kind: captions
Language: en

00:00:00.740 --> 00:00:04.055
- [Voiceover] What is the
perimeter of the figure below?

00:00:04.055 --> 00:00:06.214
So down here, we have this figure,

00:00:06.214 --> 00:00:09.381
and we are asked to find the perimeter

00:00:10.225 --> 00:00:12.125
of this figure.

00:00:12.125 --> 00:00:14.423
Perimeter is the distance

00:00:14.423 --> 00:00:18.550
all the way around the outside of a shape.

00:00:18.550 --> 00:00:19.425
So in this case,

00:00:19.425 --> 00:00:21.239
if I were to walk around the outside,

00:00:21.239 --> 00:00:23.160
or maybe a human's too big,

00:00:23.160 --> 00:00:25.104
if an awesome little ant was to walk

00:00:25.104 --> 00:00:28.160
all the way around the
outside of this figure,

00:00:28.160 --> 00:00:31.660
how far she walked would be the perimeter.

00:00:32.590 --> 00:00:35.981
So to find that, what we can do is

00:00:35.981 --> 00:00:37.680
figure out how long is this side,

00:00:37.680 --> 00:00:39.783
and then combine it with
the length of this side,

00:00:39.783 --> 00:00:42.064
and combine it with the
length of this side,

00:00:42.064 --> 00:00:45.306
and once we combine all
of the side lengths,

00:00:45.306 --> 00:00:46.698
we'll have the perimeter,

00:00:46.698 --> 00:00:51.167
or the distance around
the outside of the figure.

00:00:51.167 --> 00:00:53.107
So let's start, we can start up here.

00:00:53.107 --> 00:00:54.587
We can see that this side length

00:00:54.587 --> 00:00:56.254
is five centimeters.

00:00:57.477 --> 00:00:59.614
So we have five centimeters,

00:00:59.614 --> 00:01:02.195
plus, moving down the side here,

00:01:02.195 --> 00:01:05.860
we have another three centimeters,

00:01:05.860 --> 00:01:08.209
and then going across,

00:01:08.209 --> 00:01:11.042
next distance is four centimeters.

00:01:12.705 --> 00:01:16.372
After that, we go down
this side right here,

00:01:17.513 --> 00:01:20.346
which is another four centimeters,

00:01:21.475 --> 00:01:23.225
and as we keep going,

00:01:24.135 --> 00:01:25.635
across the bottom,

00:01:26.702 --> 00:01:29.277
we have another nine centimeters.

00:01:29.277 --> 00:01:32.779
And then, we head up this side, and uh oh,

00:01:32.779 --> 00:01:33.753
we don't have a label.

00:01:33.753 --> 00:01:35.882
We don't know how far this is.

00:01:35.882 --> 00:01:37.361
But to find perimeter,

00:01:37.361 --> 00:01:40.633
we need the distance
around the entire outside.

00:01:40.633 --> 00:01:41.565
If this little ant,

00:01:41.565 --> 00:01:43.123
she walked the whole way,

00:01:43.123 --> 00:01:46.966
we've gotta know the
entire distance she walked.

00:01:46.966 --> 00:01:49.139
So what we can do is,

00:01:49.139 --> 00:01:50.363
we can look over here and say,

00:01:50.363 --> 00:01:53.763
this length right here
is three centimeters.

00:01:53.763 --> 00:01:56.662
Well then, that same length over here

00:01:56.662 --> 00:01:58.829
is also three centimeters.

00:01:59.889 --> 00:02:03.282
And where that three centimeters left off,

00:02:03.282 --> 00:02:05.194
this four centimeters,

00:02:05.194 --> 00:02:07.147
this length, picked up.

00:02:07.147 --> 00:02:08.814
So from here to here

00:02:09.847 --> 00:02:12.180
is another four centimeters.

00:02:13.479 --> 00:02:15.948
So if we have four centimeters

00:02:15.948 --> 00:02:18.299
plus another three centimeters,

00:02:18.299 --> 00:02:21.716
that's a total of seven more centimeters.

00:02:23.254 --> 00:02:25.531
So now we know the entire,

00:02:25.531 --> 00:02:29.096
all of the lengths, around the outside.

00:02:29.096 --> 00:02:31.358
So if we combine them or add them,

00:02:31.358 --> 00:02:33.820
we'll know the perimeter.

00:02:33.820 --> 00:02:37.320
So we can start, five plus three is eight.

00:02:38.597 --> 00:02:42.009
Four plus four is another eight.

00:02:42.009 --> 00:02:44.409
Nine plus seven, let's
see, instead of seven,

00:02:44.409 --> 00:02:46.815
I could do nine plus one and six,

00:02:46.815 --> 00:02:47.823
'cause that's the same as seven.

00:02:47.823 --> 00:02:49.586
Nine plus one is 10,

00:02:49.586 --> 00:02:51.419
and 10 plus six is 16.

00:02:53.377 --> 00:02:55.300
Eight plus eight is another 16,

00:02:55.300 --> 00:02:57.383
so we have a 16 and a 16.

00:02:58.715 --> 00:03:00.348
16, let's see, six ones

00:03:00.348 --> 00:03:02.848
plus six more ones is 12 ones,

00:03:04.233 --> 00:03:06.169
and one 10 plus another 10,

00:03:06.169 --> 00:03:07.836
or 10 plus 10 is 20.

00:03:08.855 --> 00:03:09.943
So another way we could add this

00:03:09.943 --> 00:03:13.331
is 20 plus 12, which is a total

00:03:13.331 --> 00:03:14.164
of 32.

00:03:15.982 --> 00:03:18.219
And we're talking about centimeters here,

00:03:18.219 --> 00:03:19.719
so 32 centimeters.

00:03:21.419 --> 00:03:23.748
The distance all the way around

00:03:23.748 --> 00:03:25.697
the outside of this figure,

00:03:25.697 --> 00:03:28.560
or the perimeter of the figure,

00:03:28.560 --> 00:03:30.060
is 32 centimeters.


Finding missing side length when given perimeter

WEBVTT
Kind: captions
Language: en

00:00:01.317 --> 00:00:02.649
- [Voiceover] The perimeter of the figure

00:00:02.649 --> 00:00:04.868
is 24 centimeters.

00:00:04.868 --> 00:00:07.812
What is the length of the missing side?

00:00:07.812 --> 00:00:09.798
So we're told this figure down here

00:00:09.798 --> 00:00:13.139
has a perimeter of 24 centimeters.

00:00:13.139 --> 00:00:15.806
The perimeter is 24 centimeters.

00:00:16.948 --> 00:00:19.215
So what that tells us is that the distance

00:00:19.215 --> 00:00:22.882
around the entire outside
is 24 centimeters.

00:00:25.009 --> 00:00:28.023
But what we want to know
is what is the length

00:00:28.023 --> 00:00:29.589
of the missing side?

00:00:29.589 --> 00:00:31.272
Well, the missing side
is going to be the side

00:00:31.272 --> 00:00:34.326
we're not told, so it
will be this one here.

00:00:34.326 --> 00:00:36.317
Because we have this question mark.

00:00:36.317 --> 00:00:38.584
It's missing, it is not labeled.

00:00:38.584 --> 00:00:40.430
So we've got to figure out

00:00:40.430 --> 00:00:44.542
what number should go on this missing side

00:00:44.542 --> 00:00:48.209
so that the entire
length is 24 centimeters.

00:00:49.589 --> 00:00:51.738
So let's start with what we do know.

00:00:51.738 --> 00:00:54.706
We know that this top length,

00:00:54.706 --> 00:00:58.257
this top side, has a
length of six centimeters,

00:00:58.257 --> 00:01:00.290
plus, going down the left,

00:01:00.290 --> 00:01:03.982
has a length of five more centimeters.

00:01:03.982 --> 00:01:08.117
Plus across the bottom
is four more centimeters.

00:01:08.117 --> 00:01:12.284
And the last known side is
another four centimeters.

00:01:14.402 --> 00:01:18.069
So when we add those
plus this mystery side,

00:01:20.548 --> 00:01:24.006
we should get a perimeter of 24.

00:01:24.006 --> 00:01:26.756
The entire distance, all of this,

00:01:27.861 --> 00:01:30.354
the six, plus the five, plus
the four, plus the four,

00:01:30.354 --> 00:01:33.392
plus this mystery number should get us

00:01:33.392 --> 00:01:35.142
to a perimeter of 24.

00:01:36.640 --> 00:01:39.023
So let's add over here and try
to make it a little simpler

00:01:39.023 --> 00:01:40.799
to find our missing side.

00:01:40.799 --> 00:01:43.415
I can add in any order,
and I love making tens,

00:01:43.415 --> 00:01:46.507
so I'm gonna say six and four is 10.

00:01:46.507 --> 00:01:48.470
10 plus five is 15.

00:01:48.470 --> 00:01:50.479
And 15 plus four more is 19.

00:01:50.479 --> 00:01:54.731
So we know where 19 centimeters
come from on this shape.

00:01:54.731 --> 00:01:58.540
Here's the 19 centimeters
are here outlined in blue.

00:01:58.540 --> 00:02:00.526
So how many more centimeters,

00:02:00.526 --> 00:02:03.609
what length must this missing side be

00:02:04.895 --> 00:02:07.442
to get us a total distance

00:02:07.442 --> 00:02:10.853
around the outside of 24 centimeters.

00:02:10.853 --> 00:02:14.171
We can do that math,
19 plus one more is 20.

00:02:14.171 --> 00:02:17.840
And then plus four more
to 24, so one more to 20,

00:02:17.840 --> 00:02:21.423
and four more, that's
a total of five more.

00:02:22.839 --> 00:02:26.756
So the missing side length
is five centimeters.

00:02:27.816 --> 00:02:31.532
This side right here
must be five centimeters

00:02:31.532 --> 00:02:35.032
in order for the total perimeter to be 24.

00:02:36.531 --> 00:02:38.401
Okay, let's look at one more.

00:02:38.401 --> 00:02:42.373
This time it says that the
perimeter of a rectangle

00:02:42.373 --> 00:02:43.456
is 32 meters.

00:02:44.593 --> 00:02:47.373
And one side is 11 meters.

00:02:47.373 --> 00:02:49.382
What is the length of the missing side?

00:02:49.382 --> 00:02:52.233
So again, we have a missing side.

00:02:52.233 --> 00:02:53.588
So let's visualize this.

00:02:53.588 --> 00:02:56.755
Let's draw ourselves a rectangle here.

00:02:57.817 --> 00:02:59.897
This is what a rectangle looks like.

00:02:59.897 --> 00:03:03.868
And we know that one
side is 11 centimeters,

00:03:03.868 --> 00:03:07.201
so one side is 11, or meters, excuse me.

00:03:08.822 --> 00:03:11.696
And because we know that
this side is 11 meters,

00:03:11.696 --> 00:03:14.570
we also know that this side is 11 meters,

00:03:14.570 --> 00:03:17.023
on a rectangle, opposite sides are equal.

00:03:17.023 --> 00:03:19.313
So those two we know.

00:03:19.313 --> 00:03:22.911
But what we don't know are
this top and the bottom.

00:03:22.911 --> 00:03:24.289
Those are the missing sides.

00:03:24.289 --> 00:03:26.510
So what are those side lengths?

00:03:26.510 --> 00:03:30.528
Well, again, we know we have
a perimeter of 32 meters,

00:03:30.528 --> 00:03:34.337
we're told right here
perimeter is 32 meters.

00:03:34.337 --> 00:03:36.837
So, the question is 11 plus 11

00:03:39.828 --> 00:03:42.411
for these two sides, 11 and 11.

00:03:45.972 --> 00:03:47.972
Plus some mystery number

00:03:48.847 --> 00:03:52.071
and then plus that same mystery number

00:03:52.071 --> 00:03:55.249
because these two sides are equal.

00:03:55.249 --> 00:03:58.999
And that has to give us
a total of equals 32.

00:04:04.922 --> 00:04:08.987
Because 32 is the total
distance around the outside.

00:04:08.987 --> 00:04:10.786
So let's add the 11s.

00:04:10.786 --> 00:04:12.203
11 plus 11 is 22.

00:04:13.473 --> 00:04:16.723
So 22 plus how many more gets us to 32?

00:04:20.366 --> 00:04:22.699
Well, 22 plus 10 more is 32,

00:04:25.529 --> 00:04:28.683
but if we label one of these sides as 10,

00:04:28.683 --> 00:04:30.483
then the other one would have to be zero.

00:04:30.483 --> 00:04:33.263
So they have to be equal,
so how can we equally split

00:04:33.263 --> 00:04:36.044
those 10 meters between the two sides?

00:04:36.044 --> 00:04:37.627
Half of 10 is five.

00:04:39.175 --> 00:04:42.175
So these sides are each five meters.

00:04:44.222 --> 00:04:46.348
22, five plus five is ten.

00:04:46.348 --> 00:04:47.765
22 plus 10 is 32.

00:04:49.783 --> 00:04:53.283
So the missing side length is five meters.


Measuring area with partial unit squares

WEBVTT
Kind: captions
Language: en

00:00:00.838 --> 00:00:03.212
- [Voiceover] Each square
on the a grid is unit square

00:00:03.212 --> 00:00:05.875
with an area of one square centimeter.

00:00:05.875 --> 00:00:10.042
So each of these squares
is one square centimeter.

00:00:11.014 --> 00:00:13.093
This is one square centimeter,

00:00:13.093 --> 00:00:16.494
and this is one square
centimeter, and so on.

00:00:16.494 --> 00:00:21.086
And now we're asked, what
is the area of the figure?

00:00:21.086 --> 00:00:23.218
By figure I'm sue they mean this bluish,

00:00:23.218 --> 00:00:27.666
purplish quadrilateral,
and we wanna know its area.

00:00:27.666 --> 00:00:31.833
And area is talking about how
much space the shape covers.

00:00:34.340 --> 00:00:36.983
How much space does this
quadrilateral cover?

00:00:36.983 --> 00:00:41.150
How many square centimeters
does the quadrilateral cover?

00:00:42.572 --> 00:00:44.885
To figure it out, we
could start by counting.

00:00:44.885 --> 00:00:45.921
Here's one.

00:00:45.921 --> 00:00:49.418
Here's one square centimeter
the quadrilateral covers,

00:00:49.418 --> 00:00:51.409
and I can keep counting like that,

00:00:51.409 --> 00:00:53.919
all of the square
centimeters that I can see.

00:00:53.919 --> 00:00:55.419
Here's two, three.

00:00:56.519 --> 00:00:59.047
Another row's got some here.

00:00:59.047 --> 00:01:00.380
Four, five, six.

00:01:02.638 --> 00:01:04.638
Down here, here's seven.

00:01:07.166 --> 00:01:08.166
Eight, nine.

00:01:09.863 --> 00:01:13.196
So there's nine full square centimeters.

00:01:14.705 --> 00:01:17.007
Nine square centimeters,

00:01:17.007 --> 00:01:18.638
but that's not the entire area.

00:01:18.638 --> 00:01:20.889
That's not everything it covers.

00:01:20.889 --> 00:01:22.948
It also covers these small parts,

00:01:22.948 --> 00:01:26.615
these triangle-shaped
little spaces of area,

00:01:28.392 --> 00:01:31.185
and so we need to count those too.

00:01:31.185 --> 00:01:32.224
Let's look over here.

00:01:32.224 --> 00:01:35.932
Let's look, if we drew
one of these triangles

00:01:35.932 --> 00:01:39.932
into a unit square, and
then we drew another one

00:01:41.151 --> 00:01:43.870
on the other half of this unit square,

00:01:43.870 --> 00:01:48.590
we would see that combined
they make one full unit square.

00:01:48.590 --> 00:01:49.573
So we can do that.

00:01:49.573 --> 00:01:51.527
We can take this triangle up here,

00:01:51.527 --> 00:01:55.048
which is half of a unit
square and combine it

00:01:55.048 --> 00:01:58.273
with this half of a unit square.

00:01:58.273 --> 00:02:00.657
So if we combine these two together,

00:02:00.657 --> 00:02:02.654
that's one more unit square.

00:02:02.654 --> 00:02:06.737
Now we have nine full unit
squares plus one more.

00:02:07.608 --> 00:02:11.969
But there's still more of
them, so we can keep combining.

00:02:11.969 --> 00:02:15.058
This half unit square
combined with the other one

00:02:15.058 --> 00:02:18.475
on the bottom makes a second unit square,

00:02:20.943 --> 00:02:25.110
and finally, there's two
more halves here, one, two,

00:02:27.746 --> 00:02:29.536
which combine to make another whole.

00:02:29.536 --> 00:02:32.786
So we have nine full unit squares plus,

00:02:35.623 --> 00:02:40.338
plus three more unit squares
that we made by combining.

00:02:40.338 --> 00:02:43.408
We made one by combining these
two, a second unit square

00:02:43.408 --> 00:02:46.502
with these two, and a
third unit square here.

00:02:46.502 --> 00:02:48.824
So we have nine full unit squares

00:02:48.824 --> 00:02:52.396
and then three more unit
squares we put together,

00:02:52.396 --> 00:02:56.479
which is a total of 12
square units or 12 square,

00:03:00.691 --> 00:03:04.858
in this case our unit is
centimeters, 12 square centimeters.

00:03:06.353 --> 00:03:10.520
Our figure, our quadrilateral
covers 12 square centimeters,

00:03:11.508 --> 00:03:15.091
so it has an area of
12 square centimeters.


Transitioning from counting to multiplying to find area

WEBVTT
Kind: captions
Language: en

00:00:01.536 --> 00:00:03.921
- [Voiceover] This
square is 1 square unit,

00:00:03.921 --> 00:00:07.385
so what is the area of Rectangle A?

00:00:07.385 --> 00:00:08.739
The first thing we're told is that

00:00:08.739 --> 00:00:13.264
each of these little
squares equal 1 square unit,

00:00:13.264 --> 00:00:17.431
and then, we're asked to
find the area of Rectangle A.

00:00:18.755 --> 00:00:22.922
Here's Rectangle A, and area
is the space that it covers.

00:00:24.608 --> 00:00:28.025
So how much space does Rectangle A cover?

00:00:29.446 --> 00:00:33.196
How many square units
does Rectangle A cover?

00:00:34.910 --> 00:00:36.369
One way to answer that would be count

00:00:36.369 --> 00:00:38.159
how many square units it covers,

00:00:38.159 --> 00:00:41.242
except they've covered
up our square units.

00:00:41.242 --> 00:00:44.026
So, one idea's we could draw them back.

00:00:44.026 --> 00:00:47.551
Say you cover'em up,
we'll draw them back in.

00:00:47.551 --> 00:00:50.931
So goin' like this, connect all these,

00:00:50.931 --> 00:00:54.465
and then, we should be able
to count our square units.

00:00:54.465 --> 00:00:58.048
So we have one, two,
three, four, five six,

00:01:00.449 --> 00:01:03.032
seven, eight, nine, 10, 11, 12.

00:01:04.694 --> 00:01:06.027
12 square units.

00:01:10.190 --> 00:01:12.182
Rectangle A covers 12 square units,

00:01:12.182 --> 00:01:15.126
so it has an area of 12 square units.

00:01:15.126 --> 00:01:18.575
But this isn't the only way
that we could've solved this.

00:01:18.575 --> 00:01:21.173
We could've also said, we
could've also looked at this

00:01:21.173 --> 00:01:25.340
and said, okay, this top row
is four square units long.

00:01:26.979 --> 00:01:31.146
One, two, three, four, has
a length of four units.

00:01:34.161 --> 00:01:36.973
So that means the top row will have

00:01:36.973 --> 00:01:41.407
one, two, three, four
square units inside of it.

00:01:41.407 --> 00:01:45.137
And then we coulda looked
over on the side, over here,

00:01:45.137 --> 00:01:49.142
and said, well, how many
rows of four will they'll be?

00:01:49.142 --> 00:01:52.309
It'll be one, two, three rows of four.

00:01:53.419 --> 00:01:56.171
So we'll have this row of four,

00:01:56.171 --> 00:01:58.989
and then a second row
of four, and a third.

00:01:58.989 --> 00:02:02.906
So three times, we will
have four square units.

00:02:04.435 --> 00:02:05.925
There's four square units at the top,

00:02:05.925 --> 00:02:07.869
another in the middle,
and another at the bottom.

00:02:07.869 --> 00:02:11.393
Three times, we will
have four square units.

00:02:11.393 --> 00:02:15.461
Or, we could go even farther than that.

00:02:15.461 --> 00:02:20.343
So we coulda done three times
four, or we could look at this

00:02:20.343 --> 00:02:23.093
and say, okay, here's one column.

00:02:26.199 --> 00:02:29.116
This column has three square units.

00:02:30.529 --> 00:02:31.460
It has a length of three.

00:02:31.460 --> 00:02:32.793
One, two, three.

00:02:33.795 --> 00:02:37.901
How many of these columns
like this will there be?

00:02:37.901 --> 00:02:40.734
There'll be one, two, three, four,

00:02:43.061 --> 00:02:45.615
'cause our length here at the top is four.

00:02:45.615 --> 00:02:50.348
So, this time, four times, we
will see three square units.

00:02:50.348 --> 00:02:53.628
One, two, three, and we'll see that

00:02:53.628 --> 00:02:55.961
one, two, three, four times.

00:02:59.628 --> 00:03:02.257
So, no matter which of these we solved,

00:03:02.257 --> 00:03:05.778
whether we counted the square
units like in the beginning,

00:03:05.778 --> 00:03:09.524
or we multiplied the side
lengths, the three and the four,

00:03:09.524 --> 00:03:11.882
in every case, we're gonna find

00:03:11.882 --> 00:03:15.219
that this equals 12 square units.

00:03:15.219 --> 00:03:18.680
The area of Rectangle A is 12 square units

00:03:18.680 --> 00:03:21.174
because it covers 12 square units.


Decomposing shapes to find area (subtract)

WEBVTT
Kind: captions
Language: en

00:00:01.040 --> 00:00:04.004
- [Voiceover] What is the
area of the shaded figure?

00:00:04.004 --> 00:00:07.581
So down here we have
this green shaded figure,

00:00:07.581 --> 00:00:11.818
and it looks like a rectangle
except it has a square

00:00:11.818 --> 00:00:14.133
cut out in the middle.

00:00:14.133 --> 00:00:16.490
So when we find its
area, we can think of it

00:00:16.490 --> 00:00:17.802
exactly like that.

00:00:17.802 --> 00:00:19.916
We want to know how much space it covers.

00:00:19.916 --> 00:00:22.888
It covers this rectangle's amount of area

00:00:22.888 --> 00:00:24.958
with this square cut out.

00:00:24.958 --> 00:00:29.029
So what we can do is find the
area of the larger rectangle

00:00:29.029 --> 00:00:33.661
and then cut out or subtract
the area of the square

00:00:33.661 --> 00:00:37.162
to see what's left in this shaded area.

00:00:37.162 --> 00:00:39.995
So let's start by finding the area

00:00:42.177 --> 00:00:44.260
of this larger rectangle.

00:00:46.324 --> 00:00:49.173
And to do that, we can
look at the side lengths.

00:00:49.173 --> 00:00:52.281
It has side lengths of nine and eight.

00:00:52.281 --> 00:00:54.765
To find the area of a
rectangle, we can multiple

00:00:54.765 --> 00:00:56.757
the side lengths.

00:00:56.757 --> 00:00:58.924
So nine times eight is 72.

00:00:59.933 --> 00:01:01.970
So that means that this rectangle

00:01:01.970 --> 00:01:04.387
covers 72 square centimeters.

00:01:05.962 --> 00:01:10.129
This entire rectangular area
covers 72 square centimeters.

00:01:12.588 --> 00:01:15.755
But now we need to cut out or subtract

00:01:17.344 --> 00:01:20.148
the area of this square
'cause that's not part

00:01:20.148 --> 00:01:21.260
of our shaded figure.

00:01:21.260 --> 00:01:24.315
We need to cut that part out.

00:01:24.315 --> 00:01:27.001
So to do that, we know
the side lengths are four

00:01:27.001 --> 00:01:30.296
on the square so we can think of this as

00:01:30.296 --> 00:01:32.817
this is four centimeters
across so we can divide it

00:01:32.817 --> 00:01:35.380
into four equal sections,

00:01:35.380 --> 00:01:37.380
and same going this way,

00:01:38.295 --> 00:01:41.212
and then if we connect these lines,

00:01:42.160 --> 00:01:45.243
what it will show us is that we have,

00:01:46.479 --> 00:01:50.993
it's not drawn perfect,
but we have four rows

00:01:50.993 --> 00:01:52.701
of four square centimeters.

00:01:52.701 --> 00:01:55.999
Four times we see four square centimeters.

00:01:55.999 --> 00:01:58.805
This top row, one, two,
three, four, and so on.

00:01:58.805 --> 00:02:02.993
Four rows, so there's
16 square centimeters

00:02:02.993 --> 00:02:05.326
we need to cut out of the 72

00:02:06.245 --> 00:02:09.090
of this entire rectangular area,

00:02:09.090 --> 00:02:11.533
we need to cut out or subtract

00:02:11.533 --> 00:02:14.421
16 of these square centimeters.

00:02:14.421 --> 00:02:16.047
So let's do that.

00:02:16.047 --> 00:02:19.178
We have 72 as the entire area,

00:02:19.178 --> 00:02:20.741
and then let's start subtracting out.

00:02:20.741 --> 00:02:23.015
We subtract out 10 of them,

00:02:23.015 --> 00:02:26.223
just for me like subtracting
10s 'cause they're simpler.

00:02:26.223 --> 00:02:29.973
So four, eight, 10 of
the square centimeters.

00:02:31.298 --> 00:02:34.131
Now we're down an area of 62 left.

00:02:35.606 --> 00:02:38.455
And then let's subtract those two more.

00:02:38.455 --> 00:02:43.071
We'll get us to subtract
two more, will get us to 60.

00:02:43.071 --> 00:02:45.306
And then there's four
left to subtract in order

00:02:45.306 --> 00:02:48.306
to subtract all 16, so 60 minus four

00:02:50.208 --> 00:02:51.375
gets us to 56.

00:02:54.359 --> 00:02:56.442
So the entire area of 72,

00:02:57.647 --> 00:03:01.385
we subtracted out these
16 square centimeters,

00:03:01.385 --> 00:03:04.135
leaves us with a final area of 56

00:03:06.309 --> 00:03:07.892
square centimeters.