Exercising gorillas

WEBVTT
Kind: captions
Language: en

00:00:00.560 --> 00:00:03.860
- There were some gorillas
lifting weights in the gym.

00:00:04.428 --> 00:00:08.312
Then, three more gorillas
came and started running.

00:00:08.821 --> 00:00:13.392
Now, 17 gorillas are in the gym.

00:00:13.392 --> 00:00:16.078
How many gorillas were lifting weights?

00:00:16.078 --> 00:00:17.359
So, that's the number of gorillas

00:00:17.359 --> 00:00:18.687
that were originally in the gym,

00:00:18.687 --> 00:00:20.322
the gorillas lifting weights.

00:00:20.322 --> 00:00:22.825
So, how many gorillas
were lifting weights?

00:00:22.825 --> 00:00:23.971
They have this diagram for us.

00:00:23.971 --> 00:00:25.180
Let's see, what is this
diagram telling us?

00:00:25.180 --> 00:00:26.673
How many squares are there?

00:00:26.673 --> 00:00:28.724
There's one, two, three, four, five,

00:00:28.725 --> 00:00:30.917
six, seven, eight, nine, ten,

00:00:30.917 --> 00:00:35.471
11, 12, 13, 14, 15, 16, 17 squares.

00:00:35.471 --> 00:00:37.555
So, this 17, this is how many gorillas

00:00:37.555 --> 00:00:39.617
there are now in the gym.

00:00:39.617 --> 00:00:42.364
So, this is the 17 right over here.

00:00:42.365 --> 00:00:43.848
How many gorillas,

00:00:44.094 --> 00:00:46.665
how many gorillas there
are now in the gym.

00:00:47.079 --> 00:00:49.402
How many gorillas there
are now in the gym,

00:00:49.402 --> 00:00:50.722
that's the 17.

00:00:51.076 --> 00:00:52.589
Now, there are some gorillas in the gym.

00:00:52.589 --> 00:00:54.682
Three more came and started running.

00:00:54.682 --> 00:00:56.629
So, maybe these are the three

00:00:56.629 --> 00:00:57.885
that came in and started running.

00:00:57.886 --> 00:01:02.422
So, one, two, three.

00:01:03.144 --> 00:01:05.003
So, how many were there to begin with?

00:01:05.003 --> 00:01:06.831
How many there were there lifting weights?

00:01:06.831 --> 00:01:08.338
So, all the rest of these must have

00:01:08.338 --> 00:01:09.613
been there lifting weights.

00:01:09.614 --> 00:01:11.220
So, that is

00:01:11.220 --> 00:01:15.718
one, two, three, four, five, six,

00:01:15.718 --> 00:01:18.018
seven, eight, nine,

00:01:18.018 --> 00:01:22.642
10, 11, 12, 13, 14.

00:01:22.642 --> 00:01:25.116
So, 14 gorillas were lifting weights.

00:01:25.116 --> 00:01:26.419
That's the ones where I wrote the numbers

00:01:26.419 --> 00:01:28.469
in this, in this purplish color.

00:01:28.469 --> 00:01:31.315
Then, three more came
in and started running

00:01:31.316 --> 00:01:32.575
and now, there are 17.

00:01:32.575 --> 00:01:33.698
You see the 17 blocks.

00:01:33.698 --> 00:01:35.830
So, how many gorillas were
lifting weights to begin with?

00:01:35.831 --> 00:01:37.414
Well, that's the 14.

00:01:38.075 --> 00:01:42.167
That is, that is the 14.

00:01:42.427 --> 00:01:44.075
Now, there's other ways that
you could have done this.

00:01:44.075 --> 00:01:45.753
You could have said, okay, there were

00:01:45.753 --> 00:01:47.400
some number of gorillas that were

00:01:47.400 --> 00:01:48.948
lifting weights in the gym.

00:01:48.948 --> 00:01:51.524
Now, three more gorillas walk in.

00:01:51.909 --> 00:01:55.042
Three more gorillas walk in
and now they're going to be,

00:01:55.241 --> 00:01:58.294
they are now going to be 17 gorillas.

00:01:58.294 --> 00:02:01.591
So, you could say okay,
something + 3 is 17

00:02:01.591 --> 00:02:05.169
or you could say 17 - 3,

00:02:05.523 --> 00:02:07.732
minus the three that walked in,

00:02:07.733 --> 00:02:10.991
well that's going to give you
how many you originally had.

00:02:10.991 --> 00:02:12.780
How many you originally had

00:02:12.780 --> 00:02:14.013
and either way you think about it,

00:02:14.013 --> 00:02:17.331
you're gonna get to, you
are going to get to 14.

00:02:17.331 --> 00:02:20.923
17 - 3, you can view that as well,

00:02:20.924 --> 00:02:23.674
this 17 is one 10 and seven ones.

00:02:23.674 --> 00:02:25.382
So, you take away three ones.

00:02:25.382 --> 00:02:30.275
7 - 3 is four. So, 17 - 3 is gonna be 14.

00:02:30.275 --> 00:02:31.573
Let's do another one of these.

00:02:31.573 --> 00:02:33.571
This is more of what you
might see on Khan Academy

00:02:33.571 --> 00:02:36.681
and it's good to just know
what they're asking for.

00:02:37.019 --> 00:02:39.261
So, this says, I bought a bag

00:02:39.613 --> 00:02:42.511
of 13 mini chocolate chip cookies.

00:02:42.957 --> 00:02:47.640
My sister ate some of them
and I was left with 8 cookies.

00:02:47.947 --> 00:02:50.773
And I was left with 8 cookies.

00:02:51.542 --> 00:02:53.775
How many cookies did my sister eat?

00:02:54.144 --> 00:02:56.338
So, I had a bag of 13 cookies.

00:02:56.338 --> 00:02:58.392
I had a bag of 13 cookies.

00:02:58.392 --> 00:02:59.769
My sister ate some of them.

00:02:59.770 --> 00:03:01.442
So, those cookies are going away.

00:03:01.442 --> 00:03:03.478
So, I'm gonna subtract those cookies.

00:03:03.478 --> 00:03:05.693
So, my sister ate some of them.

00:03:05.693 --> 00:03:07.190
So, that's the question mark.

00:03:07.190 --> 00:03:09.715
How many cookies did my sister eat?

00:03:09.715 --> 00:03:12.482
She ate some of them and then
I was left with 8 cookies.

00:03:12.774 --> 00:03:15.641
Then, I was left with 8 cookies.

00:03:15.641 --> 00:03:19.260
So, 13 - something is = 8.

00:03:19.260 --> 00:03:21.247
Or you could view this as,

00:03:21.247 --> 00:03:22.955
you wanna solve for the something,

00:03:22.955 --> 00:03:24.537
you could say that 13 and you,

00:03:24.537 --> 00:03:25.871
some of you might just say okay,

00:03:25.871 --> 00:03:28.319
I know 13 - 5 = 8, so you would know that

00:03:28.319 --> 00:03:30.370
the question mark is equal to five.

00:03:30.371 --> 00:03:33.138
Or you could say that 13,

00:03:34.029 --> 00:03:36.105
13 - 8,

00:03:37.197 --> 00:03:40.487
minus 8 is equal to ?.

00:03:40.994 --> 00:03:43.496
Is equal to ?

00:03:43.496 --> 00:03:47.434
Or, you could even say, well
if I was left with 8 cookies,

00:03:47.434 --> 00:03:49.997
you could say if I was left with 8 cookies

00:03:49.997 --> 00:03:52.125
and my sister ate some of them.

00:03:52.554 --> 00:03:53.959
So, this is what I'm left with

00:03:53.959 --> 00:03:55.855
plus the ones that my sister ate,

00:03:55.855 --> 00:03:58.814
that must be how many
cookies I originally had.

00:03:58.814 --> 00:04:02.001
That must be the number of
cookies I originally had.

00:04:02.002 --> 00:04:03.591
So, any way you do it, you get

00:04:03.591 --> 00:04:05.946
your question mark is equal to five.

00:04:05.946 --> 00:04:07.716
Sister ate 5 cookies.

00:04:07.716 --> 00:04:08.693
Now they ask us

00:04:08.693 --> 00:04:11.229
which choices can help
you solve the problem?

00:04:11.828 --> 00:04:14.296
Well, all of these, this is,

00:04:14.296 --> 00:04:16.365
now you know the question mark is five.

00:04:16.365 --> 00:04:20.188
We know that 13 - 5 is equal to 8.

00:04:20.188 --> 00:04:21.509
So, let me write that down.

00:04:21.509 --> 00:04:24.950
We know that, actually
let me just replace this.

00:04:24.950 --> 00:04:27.236
Let me just replace this with a 5.

00:04:27.237 --> 00:04:29.227
So, 13 - 5 = 8.

00:04:29.227 --> 00:04:30.328
Well, that's a true statement

00:04:30.328 --> 00:04:32.215
that's describing what just happened here.

00:04:32.216 --> 00:04:34.081
So, this could help me.

00:04:34.327 --> 00:04:36.359
Actually, not that one. That's 13 + 5.

00:04:36.359 --> 00:04:40.592
13 - 5 = 8, that's this right over here.

00:04:40.593 --> 00:04:42.684
And that is a useful thing
to know because look,

00:04:42.684 --> 00:04:45.873
if I started with 13 cookies,
my sister ate 5 of em,

00:04:45.873 --> 00:04:47.492
I'd be left with 8.

00:04:47.492 --> 00:04:49.381
Now, what about this one over here.

00:04:49.381 --> 00:04:52.801
13 - 8, well we know this
would be equal to 5 now.

00:04:52.802 --> 00:04:54.664
They don't have a 13 - 8 = 5,

00:04:54.664 --> 00:04:56.411
so we don't have to select that.

00:04:56.411 --> 00:04:58.373
Then here, we now know
the question mark is 5.

00:04:58.373 --> 00:05:01.325
So, 8 + 5 is 13.

00:05:01.325 --> 00:05:03.824
8 + 5 = 13, that's useful too.

00:05:03.824 --> 00:05:05.597
'Cause we know 8 + 5 is 13,

00:05:05.597 --> 00:05:07.019
then we know what I'm left with

00:05:07.019 --> 00:05:08.967
plus what my sister ate is 5,

00:05:08.967 --> 00:05:11.222
is going to be the 13 that I started with.

00:05:11.222 --> 00:05:14.429
13 + 5 = 18, not so useful.

00:05:14.429 --> 00:05:16.083
18 has nothing to do with the problem.

00:05:16.084 --> 00:05:17.561
There weren't, ya know, somehow,

00:05:17.561 --> 00:05:20.462
it's not like my sister
somehow baked five more cookies

00:05:20.463 --> 00:05:22.820
and added them and now
I'm left with 18 cookies.

00:05:22.820 --> 00:05:24.509
I'm left with eight cookies now

00:05:24.509 --> 00:05:27.269
and so I didn't add the
5. She ate those cookies.

00:05:27.545 --> 00:05:29.468
So, I would subtract them.


Order by length

WEBVTT
Kind: captions
Language: en

00:00:00.421 --> 00:00:03.327
- Drag the lines up or down.

00:00:03.327 --> 00:00:05.927
Order them from longest to shortest.

00:00:05.927 --> 00:00:08.589
Put the longest line on top.

00:00:08.589 --> 00:00:10.295
So, alright, out of these three lines,

00:00:10.295 --> 00:00:11.433
the longest one is this one.

00:00:11.433 --> 00:00:12.896
So, I click on this

00:00:12.896 --> 00:00:15.801
and I move it to the top.

00:00:15.801 --> 00:00:17.041
And they want us to order

00:00:17.041 --> 00:00:19.032
from longest to shortest.

00:00:19.032 --> 00:00:20.738
So, we want the longest on top,

00:00:20.738 --> 00:00:22.811
and the shortest on the bottom

00:00:22.811 --> 00:00:24.253
and the medium one in the middle.

00:00:24.253 --> 00:00:25.107
And, that's what we have.

00:00:25.107 --> 00:00:27.626
Longest, less long and the least long,

00:00:27.626 --> 00:00:29.521
or the shortest, right over there.

00:00:30.381 --> 00:00:31.344
Let's keep going.

00:00:32.314 --> 00:00:33.477
Alright.

00:00:33.477 --> 00:00:36.423
Is it taller or shorter?

00:00:36.423 --> 00:00:38.170
So, let's see this whale,

00:00:38.170 --> 00:00:39.694
even if we don't count the water

00:00:39.694 --> 00:00:41.320
that's coming out of its spout,

00:00:41.320 --> 00:00:44.448
is taller than these three blocks.

00:00:44.448 --> 00:00:45.220
So, I would say,

00:00:45.220 --> 00:00:49.873
the whale is taller than three blocks.

00:00:49.873 --> 00:00:53.063
If I said the whale is
shorter than three blocks

00:00:53.063 --> 00:00:54.261
it wouldn't make sense.

00:00:54.261 --> 00:00:57.817
'Cause a whale is more
than three blocks tall.

00:00:57.817 --> 00:01:00.418
So, it's taller than the three blocks.

00:01:00.418 --> 00:01:02.043
The squirrel is, well,

00:01:02.043 --> 00:01:04.522
the squirrel is clearly shorter

00:01:04.522 --> 00:01:05.476
than the three blocks.

00:01:05.476 --> 00:01:07.833
It looks like it's about two blocks tall.

00:01:07.833 --> 00:01:11.998
So, the squirrel is shorter
than the two blocks.

00:01:11.998 --> 00:01:14.233
You scroll down because
there's another question.

00:01:14.233 --> 00:01:17.728
So, the whale is blank the squirrel.

00:01:17.728 --> 00:01:18.926
Well, the whale's gonna be taller

00:01:18.926 --> 00:01:20.186
than the squirrel,

00:01:20.186 --> 00:01:22.705
and you can see that if
you just compare the whale

00:01:22.705 --> 00:01:23.721
straight to the squirrel,

00:01:23.721 --> 00:01:25.062
or you can say, "look,
if the whale is more

00:01:25.062 --> 00:01:26.484
"than three blocks,

00:01:26.484 --> 00:01:28.557
"the whale is taller than three blocks,

00:01:28.557 --> 00:01:30.893
"the squirrel is shorter
than three blocks,

00:01:30.893 --> 00:01:33.697
"so the whale must be
taller than the squirrel."

00:01:33.697 --> 00:01:35.464
Because the whale is
taller than the blocks

00:01:35.464 --> 00:01:37.029
which are taller than the squirrel.

00:01:37.029 --> 00:01:40.097
So, the whale is gonna be
taller than the squirrel.

00:01:40.097 --> 00:01:41.702
Let's keep going.

00:01:41.702 --> 00:01:43.693
Is it taller or shorter?

00:01:43.693 --> 00:01:47.655
The cookie is shorter
than these five blocks.

00:01:47.655 --> 00:01:49.849
The ice cream cone is, well it looks,

00:01:49.849 --> 00:01:52.002
it's taller than the five blocks.

00:01:52.002 --> 00:01:54.501
So, the cookie is, well,

00:01:54.501 --> 00:01:56.310
the cookie's shorter than the five blocks

00:01:56.310 --> 00:01:58.097
which is shorter than the ice cream cone.

00:01:58.097 --> 00:02:00.089
The ice cream cone is
taller than the blocks

00:02:00.089 --> 00:02:01.998
which are taller than the cookie.

00:02:01.998 --> 00:02:03.217
So, the cookie is, for sure,

00:02:03.217 --> 00:02:05.188
shorter than the ice cream cone.

00:02:05.188 --> 00:02:06.204
It's shorter than this

00:02:06.204 --> 00:02:07.707
which is shorter than the ice cream cone.

00:02:07.707 --> 00:02:10.390
So, it's definitely shorter
than the ice cream cone.

00:02:10.390 --> 00:02:12.116
Let's do one more.

00:02:12.116 --> 00:02:13.335
Is it taller or shorter?

00:02:13.335 --> 00:02:16.200
Well, the penguin is taller
than the four blocks.

00:02:16.200 --> 00:02:18.699
The turtle is shorter than the 10 blocks,

00:02:18.699 --> 00:02:20.487
sorry, the four blocks.

00:02:20.487 --> 00:02:22.417
The penguin is taller than four blocks.

00:02:22.417 --> 00:02:24.244
The turtle is shorter than four blocks.

00:02:24.244 --> 00:02:26.277
So, the penguin is, well,

00:02:26.277 --> 00:02:27.801
it's gonna be taller than a turtle.

00:02:27.801 --> 00:02:29.243
The penguin is taller than the blocks

00:02:29.243 --> 00:02:30.808
which are taller than the turtle.

00:02:30.808 --> 00:02:34.201
So, the penguin is taller than the turtle.

00:02:34.201 --> 00:02:35.324
Lots of fun.


Adding hundreds, tens, and ones

WEBVTT
Kind: captions
Language: en

00:00:00.305 --> 00:00:04.110
- [Voiceover] So I have
the number 163 and that is

00:00:04.110 --> 00:00:07.044
the same as, I have a
one in the 100s place,

00:00:07.044 --> 00:00:09.051
so that's one hundred.

00:00:11.206 --> 00:00:13.200
Plus six 10s

00:00:17.828 --> 00:00:21.549
Plus three ones, three in the ones place.

00:00:25.177 --> 00:00:30.177
Do that in the color blue which
I have for the ones place.

00:00:31.169 --> 00:00:32.592
And I've drawn that out here

00:00:32.592 --> 00:00:35.519
where I actually draw 163 squares.

00:00:35.519 --> 00:00:40.135
And you see it as one 100, six 10s.

00:00:40.135 --> 00:00:43.510
One, two, three, four, five, six 10s.

00:00:43.510 --> 00:00:45.879
And three ones.

00:00:45.879 --> 00:00:49.046
So this number right over here, 163,

00:00:49.046 --> 00:00:54.046
is the same thing as 100
plus six 10s plus three ones.

00:00:54.566 --> 00:00:56.606
And if you wanna think
about what it looks like,

00:00:56.606 --> 00:00:58.950
this is 163 things.

00:00:58.950 --> 00:01:02.496
You see the 100, you see the six 10s.

00:01:02.496 --> 00:01:05.262
And you see the three ones.

00:01:05.262 --> 00:01:09.701
Now I now wanna add the number 324 to 163.

00:01:09.701 --> 00:01:14.701
So 324 is, if we look at
the 100s place, it's 300s.

00:01:17.916 --> 00:01:20.276
It's two 10s,

00:01:20.276 --> 00:01:22.833
Three 100s plus two 10s,

00:01:24.172 --> 00:01:29.172
And four ones, so plus four ones.

00:01:29.466 --> 00:01:32.324
And we see that right over here drawn out,

00:01:32.324 --> 00:01:34.274
or I guess all the boxes.

00:01:34.275 --> 00:01:37.217
So 324 boxes, this is 324 boxes.

00:01:37.217 --> 00:01:40.740
You have three 100s, one two three 100s,

00:01:40.740 --> 00:01:43.866
Two 10s, one two 10s,

00:01:43.866 --> 00:01:45.227
And four ones.

00:01:45.227 --> 00:01:50.189
And so this number 324 is three 100s,

00:01:50.189 --> 00:01:53.068
two 10s, and four ones.

00:01:53.068 --> 00:01:55.634
And if you wanna think
about how many boxes it is,

00:01:55.635 --> 00:01:57.844
it's that many, and you see them.

00:01:57.844 --> 00:02:01.395
They are grouped into three groups of 100,

00:02:01.395 --> 00:02:02.512
that's the 300s,

00:02:02.513 --> 00:02:04.430
two groups of 10, that's the two 10s,

00:02:04.430 --> 00:02:07.334
and then four ones.

00:02:07.334 --> 00:02:09.445
So now let's add them together.

00:02:09.445 --> 00:02:11.533
So let's first look at the ones place.

00:02:11.533 --> 00:02:13.852
So the ones place you're
gonna have three ones

00:02:13.853 --> 00:02:15.620
plus four ones,

00:02:15.620 --> 00:02:19.124
well that's gonna be,
let me do this in blue.

00:02:19.124 --> 00:02:22.148
That's going to be seven ones.

00:02:22.148 --> 00:02:26.682
Three ones plus four
ones, that is seven ones.

00:02:26.682 --> 00:02:30.146
A seven in the ones place is seven ones.

00:02:30.146 --> 00:02:32.130
And we see that right over here.

00:02:32.130 --> 00:02:36.081
Three ones plus four
ones, that's seven ones.

00:02:36.081 --> 00:02:38.846
Now I have six 10s and two 10s,

00:02:38.847 --> 00:02:41.652
well if I add them together
I'm gonna have eight 10s.

00:02:43.882 --> 00:02:46.453
If I have six 10s and two 10s,

00:02:46.453 --> 00:02:48.536
the six and this two
they're in the 10s place.

00:02:48.536 --> 00:02:51.838
So this represents six 10s,

00:02:51.838 --> 00:02:53.037
this represents two 10s.

00:02:53.037 --> 00:02:56.109
Six 10s plus two 10s is eight 10s.

00:02:56.109 --> 00:02:57.373
And we also see it here,

00:02:57.373 --> 00:03:01.917
six 10s plus two 10s is eight 10s.

00:03:04.547 --> 00:03:09.547
And finally we have one 100
plus another three 100s.

00:03:10.257 --> 00:03:12.979
So that's going to be four 100s.

00:03:14.855 --> 00:03:15.781
And you see them right over here,

00:03:15.782 --> 00:03:17.765
one, two, three, four.

00:03:17.765 --> 00:03:21.100
Four hundreds, let me circle all of these.

00:03:22.640 --> 00:03:26.578
100 plus 300 is 400.

00:03:26.579 --> 00:03:30.035
So 163 plus 324 is 487.

00:03:30.035 --> 00:03:34.213
Four 100s, eight 10s, and seven ones.


Starfish rulers

WEBVTT
Kind: captions
Language: en

00:00:00.372 --> 00:00:01.789
- [Voiceover] Jacques took a submarine

00:00:01.789 --> 00:00:02.833
to the bottom of the ocean

00:00:02.834 --> 00:00:05.202
and discovered an underwater city.

00:00:05.202 --> 00:00:07.779
The starfish ruled the city.

00:00:07.779 --> 00:00:09.358
This is fascinating.

00:00:09.358 --> 00:00:12.632
There were 59 seahorses there,

00:00:12.632 --> 00:00:15.812
which was 28 fewer than

00:00:15.813 --> 00:00:17.559
the number of starfish.

00:00:17.559 --> 00:00:20.763
28 fewer than the number--

00:00:20.763 --> 00:00:22.365
I already used that color.

00:00:22.365 --> 00:00:25.644
Than the number

00:00:25.644 --> 00:00:27.734
of starfish.

00:00:27.734 --> 00:00:32.213
How many starfish, how
many starfish were there?

00:00:32.401 --> 00:00:34.560
So let's think about this
second sentence, here.

00:00:34.560 --> 00:00:37.230
So, number of seahorses is 28 fewer

00:00:37.230 --> 00:00:39.483
than the number of starfish.

00:00:39.483 --> 00:00:42.552
So we could write, we could write,

00:00:42.552 --> 00:00:45.417
number of seahorses,

00:00:45.999 --> 00:00:50.525
seahorses, is 28 fewer than
the number of starfish.

00:00:50.767 --> 00:00:51.812
So that means that this is going

00:00:51.812 --> 00:00:54.457
to be equal to then number of starfish.

00:00:54.691 --> 00:00:56.849
Number of starfish,

00:00:57.919 --> 00:01:01.401
starfish minus 28.

00:01:01.402 --> 00:01:03.722
28 fewer than the number of starfish.

00:01:03.956 --> 00:01:06.531
So, let me write that in blue.

00:01:07.740 --> 00:01:09.041
So, if I have the number of starfish,

00:01:09.041 --> 00:01:11.686
and I go 28 fewer than that,

00:01:11.711 --> 00:01:13.263
that's going to be the
number of seahorses.

00:01:13.263 --> 00:01:14.025
That's what they tell us.

00:01:14.025 --> 00:01:14.950
The number of seahorses.

00:01:14.950 --> 00:01:16.645
"There were 59 seahorses there,

00:01:16.645 --> 00:01:19.500
"which was 28 fewer than
the number of starfish."

00:01:19.501 --> 00:01:20.639
And, they actually tell us what the number

00:01:20.639 --> 00:01:21.378
of seahorses is.

00:01:21.378 --> 00:01:23.838
It's 59, so we could write this as--

00:01:24.188 --> 00:01:27.694
We could write this as, 59

00:01:27.694 --> 00:01:30.339
is equal to the number of starfish.

00:01:31.154 --> 00:01:33.545
Number, actually maybe I'll just draw--

00:01:33.545 --> 00:01:36.005
well I'll write it out, starfish.

00:01:36.378 --> 00:01:39.464
The number of starfish minus 28.

00:01:40.000 --> 00:01:42.483
Minus 28.

00:01:42.833 --> 00:01:44.621
Or, another way to think about it is

00:01:44.621 --> 00:01:48.289
there's 28 more starfish than seahorses.

00:01:48.289 --> 00:01:50.402
So we could rewrite this as saying,

00:01:50.402 --> 00:01:53.047
well whatever the number of seahorses are,

00:01:53.421 --> 00:01:54.555
whatever the number of seahorses are,

00:01:54.555 --> 00:01:57.155
they tell us, there's 59 seahorses.

00:01:57.155 --> 00:01:59.296
There's going to be 28 more.

00:01:59.296 --> 00:02:02.268
There's going to be 28 more starfish.

00:02:02.268 --> 00:02:03.963
Whenever you do a problem like this,

00:02:03.963 --> 00:02:06.308
it's always a good idea
just to do a check.

00:02:06.308 --> 00:02:07.423
Just to say, "Okay, are
there going to be more

00:02:07.423 --> 00:02:09.696
"starfish or more seahorses?"

00:02:09.838 --> 00:02:12.647
And when you look at the
information they give us,

00:02:12.647 --> 00:02:14.505
they say they there are 59 seahorses

00:02:14.505 --> 00:02:17.335
which was 28 fewer than
the number of starfish.

00:02:17.477 --> 00:02:19.381
So, if there are fewer
seahorses than starfish,

00:02:19.381 --> 00:02:21.586
that tells you there's
going to be more starfish.

00:02:21.586 --> 00:02:22.326
So it makes sense.

00:02:22.326 --> 00:02:23.951
If you want to go from the seahorses,

00:02:23.951 --> 00:02:25.808
the number of seahorses
to the number of starfish,

00:02:25.808 --> 00:02:27.828
you would add 28 because there is more

00:02:27.829 --> 00:02:30.218
starfish than seahorses.

00:02:30.383 --> 00:02:31.497
So now we just have to figure out

00:02:31.497 --> 00:02:34.560
what 59 plus 28 is, so let's do that.

00:02:35.212 --> 00:02:39.089
So, 59 is five 10s, and nine, ones.

00:02:39.090 --> 00:02:42.399
28, let's write the two
10s in the 10s place,

00:02:42.399 --> 00:02:44.535
and the eight ones, in the one's place.

00:02:44.535 --> 00:02:46.298
We're adding.

00:02:46.416 --> 00:02:47.414
We're going to go from the number

00:02:47.414 --> 00:02:49.364
of seahorses add 28 more than that

00:02:49.365 --> 00:02:51.244
to get to the number of starfish.

00:02:51.919 --> 00:02:53.800
So let's first go to the one's place.

00:02:53.800 --> 00:02:57.815
Nine ones, plus eight ones is 17 ones.

00:02:57.991 --> 00:03:00.383
Write the seven ones, and one 10,

00:03:00.383 --> 00:03:02.047
or you could think of
it as I carried the one.

00:03:02.047 --> 00:03:05.108
But all I did was I
wrote the one 10 in 17,

00:03:05.108 --> 00:03:06.966
I wrote that in the ten's place.

00:03:06.966 --> 00:03:09.125
And now I could add one 10, plus five 10,

00:03:09.125 --> 00:03:10.492
plus two 10s. So let's see.

00:03:10.492 --> 00:03:12.697
One, plus five, plus two is eight.

00:03:12.697 --> 00:03:14.228
Eight tens.

00:03:14.346 --> 00:03:18.477
So the number of starfish is 87.

00:03:18.502 --> 00:03:20.012
And you should always
see if that makes sense.

00:03:20.012 --> 00:03:22.194
The number of starfish is,

00:03:22.194 --> 00:03:24.539
this right over here, is 87.

00:03:24.539 --> 00:03:26.118
So, if there are 59 seahorses,

00:03:26.118 --> 00:03:29.019
is that 28 fewer than 87?

00:03:29.020 --> 00:03:29.879
Sure, it is.

00:03:29.879 --> 00:03:31.528
It's exactly 28 fewer.

00:03:31.528 --> 00:03:35.357
Like, that's what we used
to solve this question.


Addition using groups of 10 intro

WEBVTT
Kind: captions
Language: en

00:00:00.848 --> 00:00:03.274
- What I want to calculate in this video

00:00:03.274 --> 00:00:08.231
is 53 plus 17,

00:00:08.800 --> 00:00:10.864
plus 17.

00:00:10.864 --> 00:00:12.903
And the way that I want to do it is

00:00:12.903 --> 00:00:16.567
by breaking up the 53 and
then rearranging the numbers,

00:00:16.567 --> 00:00:18.628
and you'll see what I'm
talking about in a second.

00:00:19.187 --> 00:00:23.164
So 53 plus 17, that's going
to be the same thing as,

00:00:23.425 --> 00:00:25.641
I'm gonna break up 53, essentially

00:00:25.641 --> 00:00:27.517
into the tens and the ones.

00:00:27.517 --> 00:00:32.516
So 53 can be rewritten as 50 plus 3.

00:00:34.543 --> 00:00:36.195
That's 53 right?

00:00:36.195 --> 00:00:38.842
And I could put parentheses
around it like this.

00:00:38.842 --> 00:00:41.914
So these curvy things, so
this is an open parenthesis

00:00:41.914 --> 00:00:43.897
and this is a close parenthesis.

00:00:43.980 --> 00:00:48.492
This just means to do whats
inside the parentheses first.

00:00:48.661 --> 00:00:52.195
So 53 is the same thing as 50 plus 3

00:00:52.195 --> 00:00:57.195
and we still have the plus,
we still have the plus 17.

00:00:57.732 --> 00:01:01.454
Now, I could just add the 50 plus 3 first

00:01:01.454 --> 00:01:02.913
and then add the 17 and that would just

00:01:02.913 --> 00:01:04.405
get back there, but we want to

00:01:04.406 --> 00:01:06.484
figure out what this whole thing is.

00:01:06.484 --> 00:01:11.324
So I could rewrite this,
this is the same thing as

00:01:11.817 --> 00:01:16.817
50 plus 3 plus 17,

00:01:17.959 --> 00:01:20.184
plus 17,

00:01:20.184 --> 00:01:23.939
and I could do the 3 plus 17 first.

00:01:24.022 --> 00:01:26.011
So here I'm doing the 50 plus 3 first,

00:01:26.011 --> 00:01:27.829
I have those in the parentheses.

00:01:27.829 --> 00:01:31.722
Here I'm doing the 3 plus
17 first, and this is just

00:01:31.722 --> 00:01:34.128
a property of addition
that I could do this.

00:01:34.129 --> 00:01:37.282
I could change the order
in which I'm adding.

00:01:37.282 --> 00:01:39.321
So here I'm adding 50 plus 3 first.

00:01:39.321 --> 00:01:41.920
Here I'm going to add 3 plus 17 first.

00:01:42.119 --> 00:01:44.202
And so what's this going to be equal to?

00:01:44.540 --> 00:01:46.188
Well this is going to be equal to

00:01:46.188 --> 00:01:51.188
I have my 50 here, I have my 50 plus,

00:01:51.362 --> 00:01:56.324
now whats 3 plus 17? What's 3 plus 17?

00:01:57.102 --> 00:02:02.102
Well 3 plus 7 would be 10, so
3 plus 17 is going to be 20.

00:02:03.253 --> 00:02:06.683
So it's going to be 50 plus 20.

00:02:06.737 --> 00:02:08.232
Now what's that going to be?

00:02:08.232 --> 00:02:12.560
Well it's 5 tens plus 2 tens,
which is going to be equal to

00:02:12.713 --> 00:02:17.676
this is just going to be
equal to 7 tens, or 70.

00:02:18.107 --> 00:02:20.120
Let's do another example,
and this is going to be

00:02:20.120 --> 00:02:21.926
one like the type of exercise that

00:02:21.926 --> 00:02:23.589
you might see on Khan Academy.

00:02:23.589 --> 00:02:26.006
So let's, let me take, open that up.

00:02:26.313 --> 00:02:29.935
So they'll say "Complete
to solve 41 plus 9"

00:02:30.298 --> 00:02:31.455
so once again we can look at,

00:02:31.455 --> 00:02:36.455
we can look at the 41
and we can break it up.

00:02:36.763 --> 00:02:40.727
41 is the same thing as 40 plus what?

00:02:41.158 --> 00:02:44.334
Well, it's 40 plus 1, and of course

00:02:44.596 --> 00:02:48.011
then you have the plus 9
there and I can do the 9

00:02:48.011 --> 00:02:51.127
see this plus 9 is this plus 9 there.

00:02:51.268 --> 00:02:52.939
Now they change the order
in which we're adding.

00:02:52.939 --> 00:02:55.418
So 40 plus 1, that's in the parentheses

00:02:55.419 --> 00:02:58.826
and then you add 9, well that's
the same thing as 40 plus

00:02:59.385 --> 00:03:03.231
well, that's the same
thing as 40 plus 1 plus 9.

00:03:03.231 --> 00:03:05.247
So here we're doing the 1 plus 9 first,

00:03:05.508 --> 00:03:08.615
and if we do the 1 plus
9 first what do we get?

00:03:08.706 --> 00:03:12.902
Well, 1 plus 9, 1 plus 9 is what?

00:03:13.043 --> 00:03:15.324
Well, that's just going to be equal to 10.

00:03:15.431 --> 00:03:18.988
Notice what this, this box is replacing

00:03:19.083 --> 00:03:21.418
what was in the parentheses before,

00:03:21.443 --> 00:03:25.148
so in the parentheses you
had 1 plus 9, well that's 10.

00:03:25.475 --> 00:03:27.802
And what's 40 plus 10?

00:03:27.882 --> 00:03:31.065
Well it's 4 tens plus
1 ten so that's 5 tens.

00:03:31.065 --> 00:03:35.040
Or, 50, and we're done.


Counting in order

WEBVTT
Kind: captions
Language: en

00:00:00.051 --> 00:00:03.150
- [Voiceover] How do we count the flowers?

00:00:03.150 --> 00:00:08.150
So, this first choice,
they go one, two, three,

00:00:08.683 --> 00:00:11.117
and then they don't count
this one and then they skip it

00:00:11.117 --> 00:00:14.017
and they go four, five, six,

00:00:14.017 --> 00:00:15.617
and then they skip this one again,

00:00:15.617 --> 00:00:17.317
and then they say seven, eight.

00:00:17.317 --> 00:00:18.883
That's not how you count flowers!

00:00:18.883 --> 00:00:21.283
You'd say this is four, this is five, six,

00:00:21.283 --> 00:00:23.884
seven, eight, nine, 10.

00:00:23.884 --> 00:00:26.217
So, this first choice is not right.

00:00:26.217 --> 00:00:27.850
Now, the second one looks better.

00:00:27.850 --> 00:00:31.783
One, two, three, four,
they didn't skip this one,

00:00:31.783 --> 00:00:35.450
five, six, seven, eight, nine, 10.

00:00:35.450 --> 00:00:38.497
That one looks good so
I'll click right over here

00:00:38.497 --> 00:00:40.367
and check my answer.

00:00:41.350 --> 00:00:43.484
How do we count the mice?

00:00:43.484 --> 00:00:47.484
Let's see, one, two, this
isn't the third mouse!

00:00:47.484 --> 00:00:49.050
This is the second mouse!

00:00:49.050 --> 00:00:51.020
This is crazy, this isn't right.

00:00:51.020 --> 00:00:52.417
All right, this one over here.

00:00:52.417 --> 00:00:56.050
One, two, three, four, five,

00:00:56.050 --> 00:00:58.550
six, seven, this is right.

00:00:58.550 --> 00:01:00.117
Up here they skipped the number two,

00:01:00.117 --> 00:01:03.050
this should be the second
mouse, not the third mouse!

00:01:03.050 --> 00:01:04.060
All right.

00:01:04.684 --> 00:01:06.150
Let's keep going.

00:01:06.150 --> 00:01:07.517
Type the missing numbers.

00:01:07.517 --> 00:01:09.250
It says count the ladybugs.

00:01:09.250 --> 00:01:12.617
Type the missing numbers in the boxes.

00:01:12.617 --> 00:01:15.550
All right, this is ladybug number one.

00:01:15.550 --> 00:01:20.550
Two, then let me type three,
then let me type four.

00:01:21.984 --> 00:01:23.423
It's a lot of fun.

00:01:23.423 --> 00:01:25.217
Count the flowers.

00:01:25.217 --> 00:01:27.583
Type the missing numbers in the boxes.

00:01:27.583 --> 00:01:31.184
This is flower number
one, flower number two.

00:01:31.184 --> 00:01:33.150
Just gonna type that right in there.

00:01:33.150 --> 00:01:35.217
Check it, lemme do one more.

00:01:35.217 --> 00:01:37.283
How do we count the flowers?

00:01:37.283 --> 00:01:39.883
So, we saw one like this
a few questions ago.

00:01:39.883 --> 00:01:43.684
One, two, three, four, five, six,

00:01:43.684 --> 00:01:46.450
seven, eight, nine, 10.

00:01:46.450 --> 00:01:48.084
That one looks good.

00:01:48.084 --> 00:01:50.350
This one, just like the
last time, they skipped,

00:01:50.350 --> 00:01:51.850
actually they skipped the same ones.

00:01:51.850 --> 00:01:53.017
This wouldn't be the right way to do it.

00:01:53.017 --> 00:01:56.100
So, we select this one right
here, and then we're done.


Reading bar graph examples

WEBVTT
Kind: captions
Language: en

00:00:00.369 --> 00:00:02.666
- [Voiceover] Some
students traveled by train,

00:00:02.666 --> 00:00:05.615
airplane, or boat during the summer.

00:00:05.615 --> 00:00:07.751
This bar graph shows how many students

00:00:07.751 --> 00:00:09.748
used each type of travel.

00:00:09.748 --> 00:00:11.896
All right, let's look at this thing.

00:00:11.896 --> 00:00:13.753
All right, so it tells us

00:00:13.753 --> 00:00:17.665
that five students traveled by train.

00:00:17.665 --> 00:00:22.110
It tells us that 10 students
traveled by airplane.

00:00:22.110 --> 00:00:25.111
Two students traveled by boat.

00:00:25.111 --> 00:00:28.454
Then we're asked how many
more students traveled

00:00:28.454 --> 00:00:30.686
by airplane than boat?

00:00:30.686 --> 00:00:34.715
Well let's see, 10 students
traveled by airplane,

00:00:34.715 --> 00:00:36.827
two traveled by boat.

00:00:36.827 --> 00:00:40.147
So how many more is 10 than two?

00:00:40.147 --> 00:00:42.248
Well we could figure that out by saying,

00:00:42.248 --> 00:00:44.605
well what's 10 minus two?

00:00:44.605 --> 00:00:49.028
So 10 minus two is going
to be equal to eight.

00:00:49.028 --> 00:00:52.122
Eight more students traveled by airplane

00:00:52.122 --> 00:00:53.466
than by boat.

00:00:53.466 --> 00:00:55.881
And you could even see it in the bar graph

00:00:55.881 --> 00:00:57.204
that if you wanted to go from the two

00:00:57.204 --> 00:01:00.002
who traveled by boat to the 10

00:01:00.002 --> 00:01:02.232
who traveled by airplane, you would have

00:01:02.232 --> 00:01:06.762
to add one, two, three, four,

00:01:06.762 --> 00:01:09.212
five, six, seven, eight.

00:01:09.212 --> 00:01:13.530
So eight more traveled
by airplane than by boat.

00:01:13.530 --> 00:01:15.142
Let's keep going.

00:01:16.282 --> 00:01:18.987
Sunny, Rover, and Buster buried,

00:01:18.987 --> 00:01:21.123
Sunny, Rover, and Buster buried bones

00:01:21.123 --> 00:01:23.723
in the backyard, or in the yard.

00:01:23.723 --> 00:01:25.963
This bar graph shows how many bones

00:01:25.963 --> 00:01:27.809
each dog buried.

00:01:27.809 --> 00:01:31.524
All right, so Sunny buried 10 bones.

00:01:31.524 --> 00:01:34.600
Rover buried three bones.

00:01:34.600 --> 00:01:38.141
Buster buried seven bones.

00:01:38.141 --> 00:01:42.321
How many fewer bones did
Rover bury than Sunny?

00:01:42.321 --> 00:01:45.281
Let's see, Rover buried three bones,

00:01:45.281 --> 00:01:47.185
Sunny buried 10 bones.

00:01:47.185 --> 00:01:49.974
So how many fewer is three than 10?

00:01:49.974 --> 00:01:51.542
Well to go from 10 to three

00:01:51.542 --> 00:01:53.262
you have to take away seven.

00:01:53.262 --> 00:01:54.482
10 minus seven is three,

00:01:54.482 --> 00:01:56.328
or 10 minus three is seven.

00:01:56.328 --> 00:02:00.932
One, two, three, four, five, six, seven.

00:02:00.932 --> 00:02:05.564
So Rover buried seven
fewer bones than Sunny.

00:02:05.564 --> 00:02:08.247
10 minus three is seven.

00:02:08.247 --> 00:02:11.639
The difference here is seven.

00:02:11.639 --> 00:02:13.056
Seven.

00:02:13.056 --> 00:02:15.270
Let's do one more of these.

00:02:15.270 --> 00:02:17.228
Let's do one more.

00:02:18.426 --> 00:02:19.540
The weather in November

00:02:19.540 --> 00:02:22.105
was sunny, cloudy, or rainy.

00:02:22.105 --> 00:02:24.230
This bar graph shows the number of days

00:02:24.230 --> 00:02:25.925
of each kind of weather.

00:02:25.925 --> 00:02:27.032
All right.

00:02:27.032 --> 00:02:31.292
So we have 18 sunny days in November.

00:02:31.292 --> 00:02:35.390
We have seven cloudy days in November.

00:02:35.390 --> 00:02:39.431
We have five rainy days in November.

00:02:39.431 --> 00:02:41.949
How many rainy days
were there in November?

00:02:41.949 --> 00:02:43.097
Well I just said it.

00:02:43.097 --> 00:02:44.910
Look at the rainy category,

00:02:44.910 --> 00:02:46.175
and this bar graph shows us

00:02:46.175 --> 00:02:48.532
it goes all the way up to five.

00:02:48.532 --> 00:02:53.532
There were five rainy days in November.

00:02:54.456 --> 00:02:55.887
We got it right.


Telling time exercise example 1

WEBVTT
Kind: captions
Language: en

00:00:00.530 --> 00:00:06.420
We are asked, what time is it?

00:00:06.420 --> 00:00:09.730
So we first want to look at the
hour hand, which is a shorter

00:00:09.730 --> 00:00:11.680
hand here and see
where it is pointing.

00:00:11.680 --> 00:00:13.980
And it is pointing
right at seven.

00:00:13.980 --> 00:00:17.730
So we've just crossed
the seventh hour.

00:00:17.730 --> 00:00:19.440
So the hour is seven.

00:00:19.440 --> 00:00:22.250
And then we look at the minute
hand, which is the longer hand.

00:00:22.250 --> 00:00:26.470
And this minute hand is pointing
straight up, right at the 12.

00:00:26.470 --> 00:00:28.150
So this means the
12, when you think

00:00:28.150 --> 00:00:31.850
of minutes, that's zero
minutes past the hour.

00:00:31.850 --> 00:00:34.810
And then each number
represents five more minutes.

00:00:34.810 --> 00:00:36.420
So this is right at 7:00.

00:00:40.480 --> 00:00:41.680
Let's check our answer.

00:00:41.680 --> 00:00:43.850
Let's do a few more of these.

00:00:43.850 --> 00:00:45.980
Where is the hour hand?

00:00:45.980 --> 00:00:48.150
So this hour hand,
you might say,

00:00:48.150 --> 00:00:51.480
hey, this looks closer to
eight than it is to seven,

00:00:51.480 --> 00:00:54.720
but the key is to realize
that it has passed seven

00:00:54.720 --> 00:00:57.300
and it hasn't gotten
quite to eight yet.

00:00:57.300 --> 00:00:59.910
So we're still in
the seventh hour.

00:00:59.910 --> 00:01:01.830
So the hour is seven.

00:01:01.830 --> 00:01:05.060
Notice, these hands go
in a clockwise direction.

00:01:05.060 --> 00:01:08.440
So just past seven hasn't
gotten to eight yet.

00:01:08.440 --> 00:01:10.350
So the hour is seven.

00:01:10.350 --> 00:01:12.610
And when we want to think
about the minutes, remember,

00:01:12.610 --> 00:01:15.250
we start at the top
of the clock, that's

00:01:15.250 --> 00:01:17.210
zero minutes past the hour.

00:01:17.210 --> 00:01:19.500
And then we can count
by fives all the way

00:01:19.500 --> 00:01:21.210
to where the minute hand is.

00:01:21.210 --> 00:01:30.040
So 0, 5, 10, 15, 20,
25, 30, 35, 40, 45.

00:01:30.040 --> 00:01:32.690
We're 45 minutes past the hour.

00:01:32.690 --> 00:01:33.380
So it's 7:45.

00:01:36.300 --> 00:01:38.210
Let's do a couple more.

00:01:38.210 --> 00:01:40.010
So where's the hour hand?

00:01:40.010 --> 00:01:42.340
Well it's between
the one and the two,

00:01:42.340 --> 00:01:45.300
but the key is to realize
that it's going clockwise,

00:01:45.300 --> 00:01:48.140
it's passed the one, and
it's about to get to two.

00:01:48.140 --> 00:01:50.340
So it's still in the first hour.

00:01:50.340 --> 00:01:52.140
So the hour is still one.

00:01:52.140 --> 00:01:57.900
And then the minutes, we just
have to count from 0 by fives.

00:01:57.900 --> 00:02:05.780
So 0, 5, 10, 15, 20,
25, 30, 35, 40, 45.

00:02:05.780 --> 00:02:07.880
It's 1:45 PM.

00:02:07.880 --> 00:02:08.699
Let's do one more.

00:02:11.240 --> 00:02:14.200
So here, once again, hour
hand is between 1 and 2.

00:02:14.200 --> 00:02:17.050
So it's past one, it
hasn't gotten to two yet.

00:02:17.050 --> 00:02:19.470
So we're still in
the first hour.

00:02:19.470 --> 00:02:22.070
And then the minutes,
well, we start at 12.

00:02:22.070 --> 00:02:24.720
That's zero minutes
past the hour.

00:02:24.720 --> 00:02:28.750
0, 5, 10, 15.

00:02:28.750 --> 00:02:31.010
So it is 1:15.

00:02:31.010 --> 00:02:34.430
Let's do even one more.

00:02:34.430 --> 00:02:40.120
So this one the hour
hand is exactly at two.

00:02:40.120 --> 00:02:43.010
And the minute hand
is exactly at 12.

00:02:43.010 --> 00:02:46.250
So that means we're zero
minutes past the hour.

00:02:46.250 --> 00:02:50.320
So it's zero minutes
past the hour.


Adding two-digit numbers without regrouping

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:05.060
So above this dotted line, I have a certain number of boxes.

00:00:05.070 --> 00:00:10.198
And we could see each of these gold bars, they have 10 boxes in them. 1, 2, 3...

00:00:10.198 --> 00:00:13.438
4, 5, 6, 7, 8, 9, 10

00:00:13.438 --> 00:00:17.776
And I have two groups of these tens. So I have two tens.

00:00:17.776 --> 00:00:20.380
I have two tens and I have 1, 2, 3 ones.

00:00:20.380 --> 00:00:25.750
That's how many boxes I have above that line and below that line...

00:00:25.972 --> 00:00:28.722
I have 1, 2, 3, 4 tens.

00:00:28.722 --> 00:00:31.132
Four tens.

00:00:31.132 --> 00:00:33.543
And I have 1,2,3,4,5...

00:00:33.761 --> 00:00:37.398
I have five ones.

00:00:37.398 --> 00:00:40.595
So, this first number is two tens and three ones or 23.

00:00:40.595 --> 00:00:45.753
Two tens, three ones. The second number is four tens and five ones.

00:00:46.050 --> 00:00:50.676
Four tens and five ones...45, now, what I want to do is add the numbers.

00:00:50.676 --> 00:00:54.039
So let's do that. So let's add, so let's

00:00:54.913 --> 00:00:59.442
add that amount. This amount to this amount.

00:00:59.442 --> 00:01:01.300
23 to 45.

00:01:01.462 --> 00:01:07.114
Well, I have three ones here, I have five ones here, so if you add those to those you're going to end up with

00:01:07.114 --> 00:01:08.040
eight ones.

00:01:08.040 --> 00:01:10.491
So let me do that in that blue color.

00:01:10.491 --> 00:01:12.422
So you're gonna have: 1,

00:01:12.422 --> 00:01:15.394
2, 3, 4, ...

00:01:15.551 --> 00:01:19.951
5, 6, 7, 8 and if we look at it...

00:01:19.951 --> 00:01:24.155
look at it over here where we write down the numbers with digits,

00:01:24.155 --> 00:01:28.678
or with numerals. Then here you're gonna have three ones plus five ones

00:01:28.678 --> 00:01:31.317
is eight ones. Eight ones... eight ones.

00:01:31.585 --> 00:01:36.187
Now you have two tens plus four tens.

00:01:36.187 --> 00:01:40.282
Well, that's going to be six tens. So let me actually copy and paste this.

00:01:42.044 --> 00:01:45.249
So I have two tens.

00:01:46.139 --> 00:01:51.251
So two plus four is six. So two,

00:01:51.251 --> 00:01:54.028
four and...

00:01:54.518 --> 00:01:57.687
two, four and six.

00:01:57.721 --> 00:02:01.661
So I have... I have.

00:02:02.176 --> 00:02:04.194
Let me change my tools. So

00:02:04.194 --> 00:02:05.862
I have

00:02:05.862 --> 00:02:08.231
1, 2, 3, 4, 5, 6 tens

00:02:10.231 --> 00:02:12.844
Woops, using the wrong thing. I have...

00:02:12.844 --> 00:02:15.457
I have

00:02:15.457 --> 00:02:17.602
six tens. So just like that,

00:02:17.602 --> 00:02:22.392
you can see when I had 23 to 45, I just added the ones place. Three plus five was eight.

00:02:22.392 --> 00:02:25.377
Three plus five is eight. Three ones plus five ones is eight ones.

00:02:25.377 --> 00:02:28.042
And I added the tens place.

00:02:26.693 --> 00:02:29.740
Two tens plus four tens is equal to 6 tens.

00:02:29.740 --> 00:02:33.080
So I got 68.


Compose shapes

WEBVTT
Kind: captions
Language: en

00:00:00.740 --> 00:00:03.511
Use these semicircles, a semicircle

00:00:03.511 --> 00:00:06.567
semi means half

00:00:06.567 --> 00:00:10.018
So use these half circles to make a circle

00:00:10.018 --> 00:00:11.818
so if you take two halfs of a circle

00:00:11.818 --> 00:00:13.715
and if you put them together just right

00:00:13.715 --> 00:00:15.355
You're going to make a circle

00:00:15.355 --> 00:00:17.548
So how do we do that?

00:00:17.548 --> 00:00:19.371
Well this first choice right over here,

00:00:19.371 --> 00:00:20.933
these are no longer the semicircles

00:00:20.938 --> 00:00:22.723
These are each a third of a circle

00:00:22.723 --> 00:00:23.697
So we're not gonna,

00:00:23.697 --> 00:00:26.431
and this isn't even complete the entire circle

00:00:26.431 --> 00:00:27.623
so that didn't make a circle

00:00:28.065 --> 00:00:29.748
This one, they took the two semicircles

00:00:29.748 --> 00:00:30.954
but they didn't make them

00:00:30.954 --> 00:00:33.904
so that their outsides
completely line up with each other.

00:00:33.904 --> 00:00:36.002
so this isn't a circle

00:00:36.002 --> 00:00:37.980
But this one they took the two semicircles

00:00:37.980 --> 00:00:39.937
and they put them together just right

00:00:39.937 --> 00:00:42.003
so now their outsides line up

00:00:42.003 --> 00:00:44.261
and we have a full circle

00:00:44.261 --> 00:00:46.496
So that's our choice

00:00:46.496 --> 00:00:48.538
and we got it right

00:00:48.538 --> 00:00:49.392
Let's keep doing this

00:00:49.392 --> 00:00:53.816
Use these small triangles
to make a big triangle

00:00:53.816 --> 00:00:55.249
All right, well here, they used them

00:00:55.249 --> 00:00:56.810
to make not a triangle

00:00:56.810 --> 00:00:59.764
but this looks like a parallelogram, a quadrilateral

00:01:00.445 --> 00:01:02.125
Here, they've used the two triangles

00:01:02.125 --> 00:01:03.157
and made a triangle

00:01:03.157 --> 00:01:05.519
because this whole thing has three sides

00:01:05.519 --> 00:01:08.532
one, two, three

00:01:08.532 --> 00:01:11.537
Here they used those two triangles
to make a square

00:01:11.537 --> 00:01:13.224
but we wanna make a big triangle

00:01:13.224 --> 00:01:15.155
so this is our choice

00:01:15.155 --> 00:01:16.428
Let's do a few more of these

00:01:16.785 --> 00:01:19.975
Use these semicircles to make a circle

00:01:19.975 --> 00:01:22.824
Well here, they're not meeting on the flat side

00:01:22.824 --> 00:01:24.395
so this isn't a circle

00:01:24.395 --> 00:01:25.800
This looks like something else

00:01:25.800 --> 00:01:27.347
like two smiles or something

00:01:27.347 --> 00:01:29.068
Two pieces of a blue watermelon

00:01:29.068 --> 00:01:31.560
which is sliced on top of a purple one

00:01:31.560 --> 00:01:33.138
This is a circle

00:01:33.138 --> 00:01:35.912
So that, they put the two semicircles
in the right way

00:01:35.912 --> 00:01:37.983
Here they didn't even make the meet

00:01:37.983 --> 00:01:41.134
so this would be our choice

00:01:41.134 --> 00:01:44.293
Use these small rectangles
to make a big rectangle

00:01:44.982 --> 00:01:48.336
Well here they didn't line them up right
to make a big rectangle

00:01:48.336 --> 00:01:49.093
Here they did

00:01:49.093 --> 00:01:54.177
This whole thing has one, two, three, four sides

00:01:54.177 --> 00:01:55.307
so I'll click that one

00:01:55.307 --> 00:01:56.364
This one doesn't look like a rectangle

00:01:56.364 --> 00:01:58.524
It looks like some type of an L or something

00:01:58.524 --> 00:02:01.286
So I'm not going to select that one

00:02:01.286 --> 00:02:03.015
We got it right


Solving problems with bar graphs 2

WEBVTT
Kind: captions
Language: en

00:00:00.628 --> 00:00:02.636
- [Voiceover] How many more bikes does

00:00:02.636 --> 00:00:06.049
Bike World have than Bikes R Us?

00:00:06.049 --> 00:00:09.973
So let's compare Bike World to Bikes R Us.

00:00:09.973 --> 00:00:12.539
So Bike World is right over here

00:00:12.539 --> 00:00:14.837
and we see that Bike World,

00:00:14.837 --> 00:00:18.378
if we just look at this right over here,

00:00:18.378 --> 00:00:21.280
Bike World has 19 bikes,

00:00:21.280 --> 00:00:23.463
has 19 bikes.

00:00:23.463 --> 00:00:27.425
And they wanted us to compare
Bike World to Bikes R Us

00:00:27.425 --> 00:00:30.150
and say how many more
bikes does Bike World have

00:00:30.150 --> 00:00:31.968
than Bikes R Us?

00:00:31.968 --> 00:00:33.761
So Bike World has 19,

00:00:33.761 --> 00:00:35.893
how many does Bikes R Us have?

00:00:35.893 --> 00:00:38.346
This is Bikes R Us right over here,

00:00:38.346 --> 00:00:40.818
Bikes R Us has,

00:00:40.818 --> 00:00:43.721
Bikes R Us has 12 bicycles.

00:00:43.721 --> 00:00:47.389
So how many more does Bike
World have than Bikes R Us?

00:00:47.389 --> 00:00:50.082
Well we can just subtract
Bikes R Us's number

00:00:50.082 --> 00:00:53.321
of bikes from Bike World's, 19 minus 12.

00:00:53.321 --> 00:00:55.492
What is that going to be?

00:00:55.492 --> 00:00:56.943
Well if we look at the ones place,

00:00:56.943 --> 00:00:59.509
nine ones minus two ones is seven ones,

00:00:59.509 --> 00:01:02.028
and then one ten minus one ten is no tens.

00:01:02.028 --> 00:01:04.501
I could write no tens there
but I don't have to write that.

00:01:04.501 --> 00:01:08.088
So there's seven more bikes
at Bike World than Bikes R Us.

00:01:08.088 --> 00:01:09.492
And you can also see it here.

00:01:09.492 --> 00:01:12.012
If you start at Bikes R Us,

00:01:12.012 --> 00:01:13.416
If you were to start at Bikes R Us

00:01:13.416 --> 00:01:14.968
and you wanted to go

00:01:14.968 --> 00:01:15.978
and you wanted to see how many more bikes

00:01:15.978 --> 00:01:18.327
would I have to get to the same number

00:01:18.327 --> 00:01:20.324
of bikes as Bike World,

00:01:20.324 --> 00:01:23.656
you would see that you would
have to go from 12 to 19,

00:01:23.656 --> 00:01:26.082
or you would have to add seven bikes,

00:01:26.082 --> 00:01:29.843
or that Bike World has seven
more bicycles than Bikes R Us,

00:01:29.843 --> 00:01:34.278
one, two, three, four, five, six, seven.

00:01:34.278 --> 00:01:37.737
So how many more bikes does
Bike World have than Bikes R Us?

00:01:37.737 --> 00:01:40.765
It has seven more bikes.


Counting whales, sheep, and flowers

WEBVTT
Kind: captions
Language: en

00:00:00.494 --> 00:00:03.930
- [Voiceover] Which box has 12 whales?

00:00:03.930 --> 00:00:06.577
All right, so this green box, here,

00:00:06.577 --> 00:00:09.665
let's see, it has one,
two, three, four, five,

00:00:09.665 --> 00:00:12.637
six, seven, eight, nine, 10,

00:00:12.637 --> 00:00:14.936
11, 12, 13, 14.

00:00:14.936 --> 00:00:16.863
Well, that's not 12 whales.

00:00:16.863 --> 00:00:18.070
This one right over here,

00:00:18.070 --> 00:00:19.417
you see has one, two, three,

00:00:19.417 --> 00:00:21.089
four, five, six whales,

00:00:21.089 --> 00:00:22.761
so that's not 12.

00:00:22.761 --> 00:00:24.711
So it's gotta be this one,
but let's just make sure.

00:00:24.711 --> 00:00:25.942
One, two, three, four,

00:00:25.942 --> 00:00:27.854
five, six, seven, eight,

00:00:27.854 --> 00:00:29.517
nine, ten, eleven, twelve.

00:00:29.517 --> 00:00:33.395
All right, this one has 12 whales in it.

00:00:33.395 --> 00:00:34.788
Let's check our answer.

00:00:34.788 --> 00:00:36.181
Let's do a few more of these.

00:00:36.181 --> 00:00:38.735
How many sheep are there?

00:00:38.735 --> 00:00:40.918
One, two, three, four, five,

00:00:40.918 --> 00:00:43.101
six, seven, eight, nine, 10,

00:00:43.101 --> 00:00:45.353
11, 12, 13, 14, 15,

00:00:45.353 --> 00:00:47.953
16, 17 sheep.

00:00:47.953 --> 00:00:52.527
There are 17, 17 sheep.

00:00:52.527 --> 00:00:54.176
Let's do one more.

00:00:54.176 --> 00:00:55.987
How many flowers are there?

00:00:55.987 --> 00:00:58.170
One, two, three, four, five.

00:00:58.170 --> 00:01:00.765
There are five flowers.


Making line plots

WEBVTT
Kind: captions
Language: en

00:00:00.476 --> 00:00:02.310
- Create a picture graph to show

00:00:02.310 --> 00:00:04.818
how many wands each fairy owns.

00:00:04.818 --> 00:00:08.649
So Glenda owns two wands,
Tink owns three wands,

00:00:08.649 --> 00:00:12.979
Merry owns four wands, and
Gracie owns five wands.

00:00:12.979 --> 00:00:16.253
And in our picture graph,
each picture of a wand

00:00:16.253 --> 00:00:19.990
represents one wand, it
is equal to one wand,

00:00:19.990 --> 00:00:22.208
it means one wand.

00:00:22.208 --> 00:00:24.657
All right, so Glenda has two wands.

00:00:24.657 --> 00:00:28.210
So let's see, I'll click
one, two wands for Glenda.

00:00:28.210 --> 00:00:31.229
Tink has three wands.

00:00:31.229 --> 00:00:34.932
So I'm gonna have one,
two, three wands for Tink.

00:00:34.932 --> 00:00:38.275
Merry has four wands, so I'll have

00:00:38.275 --> 00:00:41.956
one, two, three, four wands for Merry.

00:00:41.956 --> 00:00:45.809
And then Gracie has five wands.

00:00:45.809 --> 00:00:49.455
So I'm gonna have one, two, three, four,

00:00:49.455 --> 00:00:52.287
five wands for Gracie.

00:00:52.287 --> 00:00:55.248
Let me check my answer, let's keep going,

00:00:55.248 --> 00:00:58.011
this is actually a lot of fun.

00:00:59.857 --> 00:01:02.564
The zookeeper measured four penguins.

00:01:02.564 --> 00:01:07.384
Their heights were 40, 44,
48, and 48 centimeters.

00:01:07.384 --> 00:01:10.335
Make a line plot of their heights.

00:01:10.335 --> 00:01:13.713
So a line plot, we have
a number line here,

00:01:13.713 --> 00:01:16.894
and we wanna put a dot,
as many dots as we have,

00:01:16.894 --> 00:01:19.552
at a certain measurement.

00:01:19.552 --> 00:01:22.873
So we have one penguin
that it was 40 centimeters,

00:01:22.873 --> 00:01:25.379
so at 40 we have one
penguin right over there.

00:01:25.379 --> 00:01:28.538
We have another penguin
that's at 44 centimeters.

00:01:28.538 --> 00:01:30.952
So we put 44 right over there.

00:01:30.952 --> 00:01:34.610
And then we have two
penguins at 48 centimeters.

00:01:34.610 --> 00:01:37.744
So we could put two dots right over there.

00:01:37.744 --> 00:01:40.831
Two penguins at 48 centimeters.

00:01:40.831 --> 00:01:42.166
So there you go.

00:01:42.166 --> 00:01:44.652
That is our line plot.

00:01:44.652 --> 00:01:46.730
Let's keep going, this is a lot of fun.

00:01:46.730 --> 00:01:48.888
There are five books on the shelf.

00:01:48.888 --> 00:01:51.965
The heights of the books are 32, 36, 38,

00:01:51.965 --> 00:01:54.461
32, and 35 centimeters.

00:01:54.461 --> 00:01:57.050
Make a line plot of the heights.

00:01:57.050 --> 00:02:01.241
So let's see, there is one
book that is 32 centimeters.

00:02:01.241 --> 00:02:04.480
Then there is a book
that is 36 centimeters.

00:02:04.480 --> 00:02:08.485
Then there is a book
that is 38 centimeters.

00:02:10.700 --> 00:02:13.570
Then there is another book
that is 32 centimeters.

00:02:13.570 --> 00:02:15.532
So we actually have two books,

00:02:15.532 --> 00:02:18.596
one, two books that are at 32 centimeters.

00:02:18.596 --> 00:02:21.174
And then one book that is at 35.

00:02:21.174 --> 00:02:23.437
So there you go, I made the line plot.

00:02:23.437 --> 00:02:26.340
And remember, all a line
plot is is it's essentially

00:02:26.340 --> 00:02:28.859
counting how many of each height we have.

00:02:28.859 --> 00:02:30.740
We have two at 32 centimeters,

00:02:30.740 --> 00:02:34.160
one at 35 centimeters,
one at 36, and one at 38.

00:02:34.160 --> 00:02:36.517
Let's do one more of these.

00:02:37.732 --> 00:02:39.919
Robin Hood measured four arrows.

00:02:39.919 --> 00:02:43.877
The lengths were 26, 26,
23, and 25 centimeters.

00:02:43.877 --> 00:02:47.000
Make a line plot of the lengths.

00:02:47.000 --> 00:02:49.971
So we have two arrows that were 26,

00:02:49.971 --> 00:02:52.619
that were 26 centimeters.

00:02:52.619 --> 00:02:54.929
So on 26 on our number line here

00:02:54.929 --> 00:02:56.717
I'm gonna put two dots.

00:02:56.717 --> 00:02:58.888
We have an arrow that's 23 centimeters,

00:02:58.888 --> 00:03:00.815
so I'll put one dot there.

00:03:00.815 --> 00:03:03.588
And then I have one arrow
that is 25 centimeters.

00:03:03.588 --> 00:03:05.110
So I'll put a dot there.

00:03:05.110 --> 00:03:06.873
And we're done.


Understanding place value while subtracting ones

WEBVTT
Kind: captions
Language: en

00:00:00.366 --> 00:00:03.266
- So, right here, we have the number 46,

00:00:03.266 --> 00:00:05.633
we have a four in the tens place,

00:00:05.633 --> 00:00:08.000
so it literally represents four tens,

00:00:08.000 --> 00:00:10.733
and we see them here, one,
two, three, four tens.

00:00:10.733 --> 00:00:15.533
That's a ten, that's a ten,
that's a ten, and that's a ten.

00:00:15.533 --> 00:00:17.433
Each of these are ten squares,

00:00:17.433 --> 00:00:22.433
so all together we have four
tens or 40 squares in purple

00:00:22.601 --> 00:00:25.667
and then we have a six in the ones place.

00:00:25.667 --> 00:00:30.667
We have a six in the ones
place, we have six ones,

00:00:31.633 --> 00:00:33.866
and we see that right over
here, one, two, three, four,

00:00:33.866 --> 00:00:38.866
five, six, so we can write
that 46, use the same colors,

00:00:40.733 --> 00:00:45.733
46 is equal to four tens, four tens

00:00:47.256 --> 00:00:52.256
and six ones, or I could
write plus six ones.

00:00:55.033 --> 00:00:58.066
Now, let's do something interesting.

00:00:58.066 --> 00:01:03.066
Let's subtract, let's subtract
four ones from the 46,

00:01:04.634 --> 00:01:07.567
so, let's think about
what it means to take,

00:01:07.567 --> 00:01:11.800
let's take 46, so I'm
going to start with 46,

00:01:11.800 --> 00:01:14.033
just the number that
we have in front of us,

00:01:14.033 --> 00:01:17.000
and we are going to subtract four.

00:01:17.000 --> 00:01:19.000
We are going to subtract four.

00:01:19.000 --> 00:01:22.466
What is this going to be
equal to, how many tens?

00:01:22.466 --> 00:01:24.633
So it's going to be a
certain number of tens,

00:01:24.633 --> 00:01:28.166
and it's going to be plus
a certain number of ones,

00:01:28.166 --> 00:01:30.200
plus a certain number of ones,

00:01:30.200 --> 00:01:32.266
so I've left blanks right over here,

00:01:32.266 --> 00:01:35.133
so how many tens are we going to have?

00:01:35.133 --> 00:01:37.300
So, 46, that's what we started with,

00:01:37.300 --> 00:01:40.700
we're subtracting four ones,
so we're going to subtract

00:01:40.700 --> 00:01:45.166
one, two, three, four, we're
going to take away four ones.

00:01:45.166 --> 00:01:47.166
So how many tens do we have?

00:01:47.166 --> 00:01:51.933
Well, we still have four tens,
so let's write that down,

00:01:51.933 --> 00:01:55.833
we still have four tens, but
now how many ones do we have?

00:01:55.833 --> 00:01:59.900
Well, now we only have two
ones, we only have two ones,

00:01:59.900 --> 00:02:02.633
and so you see when you
have four tens and six ones

00:02:02.633 --> 00:02:05.666
and you subtracted four ones,
well, six ones minus four ones

00:02:05.666 --> 00:02:10.666
is two ones, and so we
get 46, let me do that

00:02:11.333 --> 00:02:16.333
in the same color, we get
40, I'm having issues here,

00:02:16.833 --> 00:02:20.700
(laughs) So, it's going
to be, this is going to be

00:02:20.700 --> 00:02:25.700
46 minus four is equal to four tens,

00:02:27.633 --> 00:02:30.800
well that's just a four in the tens place,

00:02:30.800 --> 00:02:32.694
so write a four in the tens place,

00:02:32.694 --> 00:02:36.933
and then two ones, put a
two in the ones place, 42.

00:02:36.933 --> 00:02:39.266
46 minus four is 42, and
you can see that right there

00:02:39.266 --> 00:02:43.266
in the ones place, we just
took four from this six.


Length word problems

WEBVTT
Kind: captions
Language: en

00:00:00.789 --> 00:00:05.596
- Dominique drew a 72 centimeter
line on the playground

00:00:05.596 --> 00:00:07.535
with blue chalk.

00:00:07.535 --> 00:00:09.729
So the line that she drew,

00:00:09.729 --> 00:00:11.610
maybe it looks something like that.

00:00:11.610 --> 00:00:14.233
And that is 72 centimeters,

00:00:14.233 --> 00:00:15.788
72 centimeters long.

00:00:15.788 --> 00:00:19.539
So from there to there is 72 centimeters.

00:00:19.539 --> 00:00:22.509
And another line with pink chalk that is,

00:00:22.509 --> 00:00:24.252
so let's do this with pink chalk,

00:00:24.252 --> 00:00:27.397
another line with pink
chalk that is 14 centimeters

00:00:27.397 --> 00:00:29.672
longer than the blue line.

00:00:29.672 --> 00:00:31.113
So let me draw the other line.

00:00:31.113 --> 00:00:33.794
So the other line, whoops.

00:00:33.794 --> 00:00:37.416
The other line is going to
be 14 centimeters longer.

00:00:37.416 --> 00:00:40.213
So maybe it looks something like that.

00:00:40.213 --> 00:00:41.735
So it's definitely going to be longer.

00:00:41.735 --> 00:00:43.593
And it's 14 centimeters longer,

00:00:43.593 --> 00:00:48.457
so if we go from here to here,
that's going to be the same,

00:00:48.457 --> 00:00:50.740
should maybe make it the same length,

00:00:50.740 --> 00:00:53.472
this is going to be the 72 centimeters.

00:00:53.472 --> 00:00:55.154
That's 72 centimeters.

00:00:55.154 --> 00:00:57.615
But it's also another 14 centimeters.

00:00:57.615 --> 00:01:00.773
So it's gonna be 14 centimeters longer.

00:01:00.773 --> 00:01:04.336
So how long is a pink chalk
line that Dominique drew?

00:01:04.336 --> 00:01:07.516
Well you would just add the 72 plus 14.

00:01:07.516 --> 00:01:11.313
So 72 plus 14 is equal to,

00:01:11.313 --> 00:01:13.414
two ones plus four ones is six ones,

00:01:13.414 --> 00:01:16.538
seven 10s plus one 10 is eight 10s.

00:01:16.538 --> 00:01:19.938
So this longer line
here is going to be 86,

00:01:19.938 --> 00:01:22.934
86 centimeters.

00:01:22.934 --> 00:01:24.047
Let's do another one.

00:01:25.418 --> 00:01:29.295
So we're told a cable on
the Golden Gate Bridge

00:01:29.295 --> 00:01:31.756
is 33 meters long.

00:01:31.756 --> 00:01:36.389
Another cable is 13 meters
longer than the first cable.

00:01:36.389 --> 00:01:37.712
Let me do this in a different color.

00:01:37.712 --> 00:01:41.055
Is 13 meters longer than the first cable.

00:01:41.055 --> 00:01:44.516
How long would the cables
be if lined up end to end?

00:01:44.516 --> 00:01:46.372
So they're not just saying,
"How long is the longer one?"

00:01:46.372 --> 00:01:47.916
Like they did in the last example.

00:01:47.916 --> 00:01:50.087
They want to know how long are the cables

00:01:50.087 --> 00:01:52.293
if you line them up end to end?

00:01:52.293 --> 00:01:55.009
So this first cable is 33 meters.

00:01:55.009 --> 00:01:56.670
Let me draw it this way.

00:01:56.670 --> 00:02:00.431
So the first cable is 33 meters long.

00:02:00.431 --> 00:02:03.752
33, and actually why
don't I draw it this way,

00:02:03.752 --> 00:02:06.908
because this is what the cables
would actually look like.

00:02:06.908 --> 00:02:09.940
So this cable is 33...

00:02:09.940 --> 00:02:13.828
33 meters long.

00:02:13.828 --> 00:02:17.728
Another cable is 13 meters
longer than the first cable.

00:02:17.728 --> 00:02:19.272
So this other cable right over here

00:02:19.272 --> 00:02:21.710
is 13 meters longer.

00:02:21.710 --> 00:02:23.707
So this cable right here
is 13 meters longer.

00:02:23.707 --> 00:02:25.693
So what's the length of this cable?

00:02:25.693 --> 00:02:27.004
Well it's going to be the
length of the first one,

00:02:27.004 --> 00:02:29.384
33, plus 13.

00:02:29.384 --> 00:02:31.370
It's 13 meters longer.

00:02:31.370 --> 00:02:33.412
Plus 13, that gets us...

00:02:33.412 --> 00:02:34.713
three plus three is six,

00:02:34.713 --> 00:02:36.024
three plus one is four.

00:02:36.024 --> 00:02:38.903
This one over here is gonna be 46 meters.

00:02:38.903 --> 00:02:41.782
Now they didn't just ask, "How
long is the second cable,"

00:02:41.782 --> 00:02:43.152
which is 46 meters.

00:02:43.152 --> 00:02:46.360
They're asking, "How
long would the cables be

00:02:46.360 --> 00:02:49.004
"if we lined them up end to end?"

00:02:49.004 --> 00:02:51.464
So if we lined the 33 meter one,

00:02:51.464 --> 00:02:53.624
so if we lined up the 33 meter one,

00:02:53.624 --> 00:02:55.342
and then right next to that,

00:02:55.342 --> 00:02:59.544
we, right next to that,
put the 46 meter one.

00:02:59.544 --> 00:03:01.448
So if we did something like that.

00:03:01.448 --> 00:03:04.189
Well we know that this one
over here is 33 meters,

00:03:04.189 --> 00:03:07.509
and the next one is 46 meters,

00:03:07.509 --> 00:03:10.608
so we would have to add
33 plus 46 to figure out

00:03:10.608 --> 00:03:14.184
how long they would be end to end.

00:03:14.184 --> 00:03:15.845
And what is that gonna be?

00:03:15.845 --> 00:03:19.888
So if we say 33 plus 46,

00:03:19.888 --> 00:03:22.241
plus 46,

00:03:22.241 --> 00:03:24.980
three ones plus six ones is nine ones,

00:03:24.980 --> 00:03:28.047
three 10s plus four 10s is 70, sorry...

00:03:28.047 --> 00:03:30.806
three 10s plus four 10s is seven 10s.

00:03:30.806 --> 00:03:35.392
So it's going to be 79
meters if we line them up

00:03:35.392 --> 00:03:37.642
end to end.

00:03:37.642 --> 00:03:41.062
Let's do one more.

00:03:41.062 --> 00:03:45.519
Reynaldo has a 36 centimeter scarf.

00:03:45.519 --> 00:03:48.258
So he has a 36 centimeter scarf.

00:03:48.258 --> 00:03:50.314
He decides to cut out part of the scarf

00:03:50.314 --> 00:03:53.192
so it is now only 19 centimeters.

00:03:53.192 --> 00:03:56.920
How many centimeters did
Reynaldo cut off of his scarf?

00:03:56.920 --> 00:03:58.753
So let's draw his scarf.

00:03:58.753 --> 00:04:00.986
So it was a 36 centimeter scarf,

00:04:00.986 --> 00:04:03.431
so it might've looked something like this.

00:04:03.431 --> 00:04:06.218
So this was his scarf before,
if I stretch it all out,

00:04:06.218 --> 00:04:08.598
and it is 36 centimeters,

00:04:08.598 --> 00:04:12.012
36 centimeters long.

00:04:12.012 --> 00:04:13.741
But he cuts part of his scarf

00:04:13.741 --> 00:04:15.958
so it's only 19 centimeters long.

00:04:15.958 --> 00:04:18.807
So now it is only 19 centimeters.

00:04:18.807 --> 00:04:22.737
So after he cut it, it's gonna
look something like this.

00:04:22.737 --> 00:04:24.163
Actually maybe I'll...

00:04:24.164 --> 00:04:26.418
actually, I'll draw it in green again.

00:04:26.418 --> 00:04:27.451
So after he cuts it,

00:04:27.451 --> 00:04:30.109
his scarf is gonna look
something like this.

00:04:30.109 --> 00:04:31.978
It's gonna look something like this,

00:04:31.978 --> 00:04:34.358
where now it's only 19 centimeters.

00:04:34.358 --> 00:04:36.390
19 centimeters.

00:04:36.390 --> 00:04:38.352
So how much did he cut off?

00:04:38.352 --> 00:04:39.990
Well what he cut off is
going to be the difference

00:04:39.990 --> 00:04:41.696
between 36 and 19.

00:04:41.696 --> 00:04:44.168
He would have had to cut off,

00:04:44.168 --> 00:04:45.347
he would have had to cut off

00:04:45.347 --> 00:04:49.531
all of this right over here
in order to get it down to 19.

00:04:49.531 --> 00:04:51.075
So much would he have to cut off?

00:04:51.075 --> 00:04:54.348
Well this right over here
is going to be 36 minus 19.

00:04:54.348 --> 00:04:57.145
It's the difference between 36 and 19.

00:04:57.145 --> 00:04:59.093
So let's figure out what that is.

00:04:59.093 --> 00:05:03.732
It's going to be 36 minus 19.

00:05:03.732 --> 00:05:05.643
So let's see, if we...

00:05:05.643 --> 00:05:07.698
we have six ones, we want
to take away nine ones.

00:05:07.698 --> 00:05:08.964
So let's do a little bit of regrouping.

00:05:08.964 --> 00:05:10.125
Let's take one of our 10s here,

00:05:10.125 --> 00:05:13.364
so instead of three 10s, we have two 10s.

00:05:13.364 --> 00:05:15.303
And then if we add that
10 to the ones place,

00:05:15.303 --> 00:05:18.262
instead of six ones,
we're gonna have 16 ones.

00:05:18.262 --> 00:05:21.617
16 minus nine is seven.

00:05:21.617 --> 00:05:24.937
Two 10s minus one 10 is one 10.

00:05:24.937 --> 00:05:26.958
So he would have had to cut off

00:05:26.958 --> 00:05:29.721
17 centimeters of his scarf.

00:05:29.721 --> 00:05:31.695
If he started with 36 centimeters,

00:05:31.695 --> 00:05:34.063
he cuts off 17 centimeters,

00:05:34.063 --> 00:05:38.090
he's going to be left with 19 centimeters.

00:05:38.090 --> 00:05:39.740
And you could do that
the other way around.

00:05:39.740 --> 00:05:43.697
You could start with 36, you could cut 17,

00:05:43.697 --> 00:05:44.941
and see what you end up with.

00:05:44.941 --> 00:05:48.259
You're going to see
that you end up with 19.


Counting dogs, mice, and cookies

WEBVTT
Kind: captions
Language: en

00:00:00.448 --> 00:00:03.699
- [Voiceover] How many dogs do you see?

00:00:03.699 --> 00:00:05.370
And I have the dogs down here,

00:00:05.370 --> 00:00:06.926
we just need to count them.

00:00:06.926 --> 00:00:08.691
So, if I'm starting with this dog,

00:00:08.691 --> 00:00:10.593
and I wanna make sure that
I don't count him again,

00:00:10.593 --> 00:00:13.356
so I wanna remember, I'm
starting with this top dog.

00:00:13.356 --> 00:00:16.769
One, two, three, four,

00:00:16.769 --> 00:00:19.881
five, six, seven, eight.

00:00:19.881 --> 00:00:20.995
I see eight dogs.

00:00:20.995 --> 00:00:22.737
You might be tempted to go, nine.

00:00:22.737 --> 00:00:24.385
But I already counted this dog.

00:00:24.385 --> 00:00:26.893
So there's only eight dogs.

00:00:26.893 --> 00:00:29.075
So I see eight dogs.

00:00:29.075 --> 00:00:30.677
So let's check our answer.

00:00:30.677 --> 00:00:31.862
Got it right.

00:00:31.862 --> 00:00:33.510
How many mice do you see?

00:00:33.510 --> 00:00:36.111
Same thing, I like to
start with the top mouse,

00:00:36.111 --> 00:00:36.900
but we have to remember,

00:00:36.900 --> 00:00:38.827
if I'm gonna start counting
with the top mouse,

00:00:38.827 --> 00:00:41.103
I don't wanna keep counting the top mouse.

00:00:41.103 --> 00:00:43.982
So one, two, three,

00:00:43.982 --> 00:00:47.674
four, five, six, seven.

00:00:47.674 --> 00:00:49.565
Now, you might be tempted to go

00:00:49.565 --> 00:00:52.109
eight, but we already
counted this top mouse.

00:00:52.109 --> 00:00:54.082
So there's only seven mice here.

00:00:54.082 --> 00:00:55.290
Seven mice.

00:00:55.290 --> 00:00:56.404
You gotta be careful not to keep going

00:00:56.404 --> 00:00:57.751
in circles and counting the mice

00:00:57.751 --> 00:00:59.051
over and over and over again.

00:00:59.051 --> 00:01:01.930
You only wanna count
each of the mice once.

00:01:01.930 --> 00:01:02.720
Let's do another one.

00:01:02.720 --> 00:01:03.973
This is too much fun.

00:01:03.973 --> 00:01:05.227
How many cookies do you see?

00:01:05.227 --> 00:01:07.224
All right, they're all jumbled up here,

00:01:07.224 --> 00:01:08.617
and we just have to be careful

00:01:08.617 --> 00:01:10.612
not to count the cookie twice.

00:01:10.612 --> 00:01:13.724
So let's see, one, two, three,

00:01:13.724 --> 00:01:16.696
four, five, six, seven,

00:01:16.696 --> 00:01:18.669
eight, nine.

00:01:18.669 --> 00:01:20.434
There are nine cookies.

00:01:20.434 --> 00:01:23.290
I see nine cookies.

00:01:23.290 --> 00:01:24.683
How many mice are there?

00:01:24.683 --> 00:01:26.703
Okay, now, here there are a lot of mice.

00:01:26.703 --> 00:01:28.050
So there's one, two, three,

00:01:28.050 --> 00:01:30.281
four, five, six, seven,

00:01:30.281 --> 00:01:32.669
eight, nine, 10, 11,

00:01:32.669 --> 00:01:35.236
12, 13, 14, 15, 16,

00:01:35.236 --> 00:01:38.742
17, 18 19 mice.

00:01:38.742 --> 00:01:40.855
There are 19 mice there.

00:01:40.855 --> 00:01:42.916
That's a lot of mice.


Adding and subtracting on number line word problems

WEBVTT
Kind: captions
Language: en

00:00:00.696 --> 00:00:02.768
- All right, so we have Ying Ying

00:00:02.768 --> 00:00:06.912
had run a total of 30
laps for Running Class,

00:00:06.913 --> 00:00:08.554
or Running Club, I should say.

00:00:08.579 --> 00:00:11.114
So Ying Ying ran a total of 30 laps.

00:00:11.586 --> 00:00:15.826
Then, Ying Ying ran four
more laps before school.

00:00:16.401 --> 00:00:19.301
So she ran four more laps before school.

00:00:19.428 --> 00:00:21.541
Three more laps at lunch,

00:00:21.541 --> 00:00:24.320
three more laps at lunch.

00:00:24.386 --> 00:00:26.436
And two more laps at recess.

00:00:26.437 --> 00:00:27.794
Ying Ying's doing a lot of running.

00:00:28.226 --> 00:00:30.151
Two more laps at recess.

00:00:30.379 --> 00:00:31.334
So what I want to do is,

00:00:31.334 --> 00:00:33.894
I want to figure out
the total number of laps

00:00:33.894 --> 00:00:36.129
that Ying Ying ran, and I'm going to do it

00:00:36.129 --> 00:00:37.425
using a number line.

00:00:37.425 --> 00:00:39.046
So let's draw a number line here.

00:00:39.681 --> 00:00:41.706
Let's draw a number line.

00:00:44.922 --> 00:00:47.461
And Ying Ying starts at 30 laps.

00:00:47.462 --> 00:00:48.417
She had run 30 laps,

00:00:48.417 --> 00:00:51.886
and then she keeps running
more laps than that.

00:00:52.135 --> 00:00:52.988
So my number line,

00:00:52.988 --> 00:00:54.309
I could start it wherever I want,

00:00:54.309 --> 00:00:56.991
but it might be convenient
to start it at 30.

00:00:56.991 --> 00:00:59.185
And obviously I could do it at 29,

00:00:59.185 --> 00:01:00.668
and then I could go 30,

00:01:00.668 --> 00:01:02.333
actually let me just
keep going up from there.

00:01:02.334 --> 00:01:07.334
31, 32, 33, 34, 35, a few more left.

00:01:11.497 --> 00:01:16.497
36, 37, 38, 39, and let's say 40.

00:01:22.792 --> 00:01:23.890
And I could go all the way to 41.

00:01:23.890 --> 00:01:25.327
That's how much space I have.

00:01:25.658 --> 00:01:26.369
So let's see.

00:01:26.369 --> 00:01:28.681
Ying Ying started at 30 laps.

00:01:29.031 --> 00:01:30.956
So she started at 30 laps

00:01:31.652 --> 00:01:33.053
for Running Club.

00:01:33.053 --> 00:01:36.628
Then she ran, Ying Ying ran four more laps

00:01:36.629 --> 00:01:37.554
before school.

00:01:37.554 --> 00:01:39.809
So on the number line, if I go four more,

00:01:39.809 --> 00:01:41.110
that's going to be to the right.

00:01:41.110 --> 00:01:43.036
I'm going to be increasing by four.

00:01:43.122 --> 00:01:46.855
So I'm going to be increasing
by one, two, three, four.

00:01:47.022 --> 00:01:48.891
So those four laps before school

00:01:48.891 --> 00:01:51.995
take us from 30 to 34.

00:01:52.650 --> 00:01:55.834
Then she runs three more laps at lunch.

00:01:56.348 --> 00:02:01.118
So then from 34, she's gonna
go one, two, three to 37.

00:02:01.630 --> 00:02:03.250
She's gonna go to 37.

00:02:03.682 --> 00:02:05.531
So that's what those
three more laps at lunch

00:02:05.531 --> 00:02:06.522
do for us.

00:02:06.669 --> 00:02:08.945
And then two more laps at recess.

00:02:08.945 --> 00:02:11.398
So she was at 37,

00:02:11.686 --> 00:02:14.974
and now we're gonna go one, two, to 39.

00:02:15.954 --> 00:02:19.464
So how many total laps does Ying Ying run?

00:02:19.753 --> 00:02:24.156
Well, Ying Ying runs a total of 39 laps.

00:02:24.710 --> 00:02:27.311
39 laps, and we were able to figure it out

00:02:27.311 --> 00:02:28.851
using this number line.

00:02:29.180 --> 00:02:31.800
Now let's do an exercise
very similar to this

00:02:31.800 --> 00:02:33.970
that you might see on Khan Academy.

00:02:35.316 --> 00:02:37.037
So this one right over here.

00:02:37.490 --> 00:02:38.912
Let me get rid of the
stuff about Ying Ying

00:02:38.912 --> 00:02:40.167
so we don't get confused.

00:02:40.558 --> 00:02:42.101
So this says, and it's
a little bit smaller

00:02:42.101 --> 00:02:43.783
but hopefully you can see what it says.

00:02:43.870 --> 00:02:48.870
A red ant army started
with 100 marching ants.

00:02:50.818 --> 00:02:53.007
So we're gonna start with 100.

00:02:53.093 --> 00:02:54.108
And actually they tell us,

00:02:54.109 --> 00:02:55.385
well let me just read the whole thing.

00:02:55.572 --> 00:02:57.599
They started with 100 marching ants.

00:02:57.786 --> 00:03:02.252
Then the red army lost
three ants down a hole.

00:03:02.521 --> 00:03:06.903
So actually let me, so lost
three ants down a hole.

00:03:07.417 --> 00:03:09.789
Three ants were eaten by a bird.

00:03:10.018 --> 00:03:11.049
That's unfortunate.

00:03:12.070 --> 00:03:13.756
And one ant just blew away.

00:03:13.756 --> 00:03:15.442
I guess ants are fairly light creatures,

00:03:15.442 --> 00:03:16.555
so that makes sense.

00:03:16.843 --> 00:03:17.976
One ant blew away.

00:03:18.083 --> 00:03:20.318
Which number line shows how to find

00:03:20.318 --> 00:03:22.812
how many ants the red army has left?

00:03:23.630 --> 00:03:27.180
Well, the army started
with 100 marching ants.

00:03:27.205 --> 00:03:28.342
We underlined that over here,

00:03:28.342 --> 00:03:29.903
so we need to start with 100.

00:03:30.253 --> 00:03:32.137
We need to start with 100.

00:03:32.590 --> 00:03:34.027
This one starts with 10.

00:03:34.032 --> 00:03:35.978
So I can immediately rule this one out.

00:03:36.511 --> 00:03:39.863
And so we could just select that one,

00:03:39.863 --> 00:03:41.260
but let's just make sure it makes sense.

00:03:41.590 --> 00:03:42.987
So we start with 100,

00:03:43.561 --> 00:03:46.649
and then we lose three ants down a hole.

00:03:46.649 --> 00:03:47.867
So we're gonna go down.

00:03:47.867 --> 00:03:49.351
Remember, we're losing ants,

00:03:49.351 --> 00:03:50.794
so we're gonna go to the
left of the number line.

00:03:50.794 --> 00:03:51.809
We're gonna go to lower values.

00:03:51.809 --> 00:03:53.450
We're gonna go down one, two, three.

00:03:53.780 --> 00:03:56.964
So these are the three
ants we lose down a hole.

00:03:57.173 --> 00:03:58.591
So three down the hole.

00:03:59.022 --> 00:04:01.495
Then we have three that
were eaten by a bird,

00:04:01.623 --> 00:04:03.203
so you're gonna lose three more.

00:04:03.329 --> 00:04:04.954
That's those three right over there.

00:04:04.954 --> 00:04:06.758
It goes to 94 ants left.

00:04:06.965 --> 00:04:09.155
And then we have the one
ant that gets blown away.

00:04:09.424 --> 00:04:13.035
So that gets us down to 93 ants left.

00:04:13.141 --> 00:04:15.702
So the red army, or the red ant army,

00:04:15.702 --> 00:04:18.846
has 93 ants left.

00:04:19.338 --> 00:04:23.824
93 ants left.

00:04:24.072 --> 00:04:25.531
And we are done.


Adding by getting to group of 10 first

WEBVTT
Kind: captions
Language: en

00:00:00.342 --> 00:00:01.426
- [Voiceover] What I wanna show you now

00:00:01.426 --> 00:00:02.416
is a way to add numbers,

00:00:02.416 --> 00:00:04.102
or a way that I sometimes add numbers,

00:00:04.102 --> 00:00:05.981
when I'm doing it in my head.

00:00:05.981 --> 00:00:09.303
So let's say I wanna add five to 68.

00:00:09.303 --> 00:00:11.549
And we've already seen
other ways of doing it,

00:00:11.549 --> 00:00:12.725
so what I'm showing in this video

00:00:12.725 --> 00:00:13.748
isn't the only way to do it

00:00:13.749 --> 00:00:16.686
but it might be helpful when
you're doing it in your head.

00:00:16.686 --> 00:00:20.004
Well when I look at a number
like 68 I think well gee,

00:00:20.004 --> 00:00:24.036
If I added just two to
that I would get to 70.

00:00:24.036 --> 00:00:28.949
So why don't I break up
five into three and two,

00:00:28.949 --> 00:00:33.293
add the two to 68 and then
I have to add the three.

00:00:33.293 --> 00:00:34.924
So what's that going to get me?

00:00:34.924 --> 00:00:39.688
Well if I break up the
five into three plus two,

00:00:39.688 --> 00:00:42.508
and the whole reason why I
broke it up into three and two

00:00:42.508 --> 00:00:45.051
is so I have this two here to add to 68.

00:00:45.051 --> 00:00:47.924
So five is three plus two,

00:00:47.924 --> 00:00:52.525
and to that I'm going to add 68, 68.

00:00:52.587 --> 00:00:55.794
And once again the reason
why I took this two out

00:00:55.794 --> 00:00:56.858
is because I said hey,

00:00:56.859 --> 00:00:59.882
what do I have to add to 68 to get to 70?

00:00:59.882 --> 00:01:03.489
So now I could just rewrite this as,

00:01:03.490 --> 00:01:08.490
Three plus two plus 68, 68.

00:01:10.290 --> 00:01:13.924
But now I can add the two to the 68.

00:01:13.924 --> 00:01:17.873
So two plus 68 is going to be

00:01:17.873 --> 00:01:20.344
Two plus 68 is 70.

00:01:21.559 --> 00:01:24.048
70 and I still have this three here,

00:01:24.049 --> 00:01:28.757
so I have three plus 70
which is equal to 73.

00:01:29.865 --> 00:01:31.261
73.

00:01:31.261 --> 00:01:34.848
Now it might seem like this
really long way of doing it,

00:01:34.849 --> 00:01:37.262
but this is just a way to think about it.

00:01:37.262 --> 00:01:39.689
In your head you'd say okay five plus 68,

00:01:39.689 --> 00:01:43.160
let's see if I add two
to 68 I'll get to 70

00:01:43.160 --> 00:01:46.271
and so let's see, five is three plus two,

00:01:46.272 --> 00:01:48.825
I add the two to 68, I get to 70,

00:01:48.825 --> 00:01:50.360
and I have three left over.

00:01:50.360 --> 00:01:52.392
So it's going to be 73.

00:01:52.392 --> 00:01:55.905
Another way you could think
about it is on a number line.

00:01:55.905 --> 00:01:58.512
So let's draw ourselves
a number line here.

00:01:58.512 --> 00:02:02.544
Let's draw a number line
and let me draw some

00:02:02.544 --> 00:02:06.328
let me draw some tick marks here.

00:02:06.328 --> 00:02:09.136
And let's say that this right over here,

00:02:09.136 --> 00:02:13.511
this right over here is 68,

00:02:13.511 --> 00:02:17.272
and so this is going to be 70,

00:02:17.272 --> 00:02:19.791
this is going to be 70,

00:02:19.791 --> 00:02:21.710
and we're gonna add five.

00:02:21.711 --> 00:02:23.567
We're gonna add five.

00:02:23.567 --> 00:02:26.335
So if you add five you say
well let me add two first.

00:02:26.335 --> 00:02:29.607
So if I add two first I get to 70.

00:02:29.607 --> 00:02:31.026
So plus two,

00:02:31.026 --> 00:02:33.159
that's what I did right
over here to get to 70,

00:02:33.159 --> 00:02:37.007
and then if I wanna add five
then I have to add three more.

00:02:37.007 --> 00:02:39.374
Then I have to add three more.

00:02:40.575 --> 00:02:43.182
And so it's going to be 70 plus three.

00:02:43.182 --> 00:02:46.720
Which of course is 73.

00:02:46.720 --> 00:02:49.087
Hopefully you found that interesting.


Understanding place value while adding tens

WEBVTT
Kind: captions
Language: en

00:00:00.533 --> 00:00:02.567
- [Voiceover] So in the number 23,

00:00:02.567 --> 00:00:05.370
we have a two in the 10's place.

00:00:05.370 --> 00:00:08.567
So, that two literally represents two 10s.

00:00:08.567 --> 00:00:10.062
And we see it right over here.

00:00:10.062 --> 00:00:12.971
We have two groups of 10 blocks.

00:00:12.971 --> 00:00:15.951
This is a 10 and this is a 10.

00:00:15.951 --> 00:00:19.696
So this two literally represents two 10s.

00:00:19.696 --> 00:00:22.762
One 10 and two 10s.

00:00:22.762 --> 00:00:25.475
Now this three is in the one's place,

00:00:25.475 --> 00:00:27.167
and it represents three ones.

00:00:27.167 --> 00:00:28.634
We can see them right over here.

00:00:28.634 --> 00:00:30.820
One, two, three blocks.

00:00:30.820 --> 00:00:34.128
And of course, if you had three
ones together with two 10s.

00:00:34.128 --> 00:00:36.716
These two 10s, represent 20,

00:00:36.716 --> 00:00:40.722
and these three ones represent
three, so you get 23.

00:00:40.722 --> 00:00:42.165
So, let's write that down.

00:00:42.165 --> 00:00:45.318
So we can write down the 23.

00:00:45.318 --> 00:00:50.050
23 is equal to two 10s,

00:00:50.050 --> 00:00:54.534
two 10s plus three ones,

00:00:54.782 --> 00:00:59.433
plus three, three ones.

00:00:59.516 --> 00:01:03.905
Now what would happen if I added 20 to 23.

00:01:03.905 --> 00:01:06.057
Let me do that, so let's say...

00:01:06.057 --> 00:01:08.122
Actually let me do
something more interesting.

00:01:08.122 --> 00:01:12.148
Let's say we take 23,

00:01:12.148 --> 00:01:15.100
and to that we add 30.

00:01:15.100 --> 00:01:19.967
So, let's add, let's add 30.

00:01:20.202 --> 00:01:24.567
Three zero, three zero.

00:01:24.567 --> 00:01:26.680
So, what is this going to be?

00:01:26.680 --> 00:01:29.672
Well, I start with 23, which
I have represented here,

00:01:29.672 --> 00:01:31.061
and I'm going to add 30.

00:01:31.061 --> 00:01:33.502
30 has a three in the 10's place,

00:01:33.502 --> 00:01:36.145
so it literally means I'm
going to add three 10s

00:01:36.145 --> 00:01:37.895
and I'm going to add zero ones.

00:01:37.895 --> 00:01:39.886
So, let me add those three 10s.

00:01:39.886 --> 00:01:44.228
So, that's one 10...

00:01:44.228 --> 00:01:48.734
this is two 10s...

00:01:48.883 --> 00:01:53.883
and then that is three 10s.

00:01:53.979 --> 00:01:58.800
So I've added one, two and three 10s here.

00:01:58.884 --> 00:02:02.467
So now, now,

00:02:02.467 --> 00:02:05.333
how many 10s do I have?

00:02:05.366 --> 00:02:10.366
Well, I now have one, two,
three, four, five 10s.

00:02:10.840 --> 00:02:15.531
Now notice, two 10s plus three
10s is equal to five 10s.

00:02:15.531 --> 00:02:19.300
So now I have five 10s.

00:02:19.550 --> 00:02:21.371
And how many ones do I have?

00:02:21.371 --> 00:02:23.023
Well, I still have those three ones,

00:02:23.023 --> 00:02:24.252
and you can think of it this way,

00:02:24.252 --> 00:02:29.036
three ones plus zero ones is
still going to be three ones.

00:02:29.157 --> 00:02:30.979
Three ones.

00:02:30.979 --> 00:02:34.640
So, what's 23, what's
23 plus 30 going to be?

00:02:34.640 --> 00:02:39.640
Let me rewrite it, 23 plus 30,

00:02:45.340 --> 00:02:48.571
is going to be equal to, well, five 10s,

00:02:48.571 --> 00:02:51.875
we can just write that as
a five in the 10's place,

00:02:51.875 --> 00:02:53.723
represents five 10s, or 50,

00:02:53.723 --> 00:02:56.405
and then we're going to have three ones.

00:02:56.405 --> 00:02:57.721
Whoops, let me do that in a different,

00:02:57.721 --> 00:03:00.205
in the ones color, in that orange color.

00:03:00.205 --> 00:03:02.359
Is the three ones.

00:03:02.359 --> 00:03:05.559
So, 23 plus 30 is 53.

00:03:05.559 --> 00:03:08.907
You have two 10s plus three
10s, give you five 10s,

00:03:08.907 --> 00:03:13.907
three ones plus zero ones
is equal to three ones.


Getting to 10 by filling boxes

WEBVTT
Kind: captions
Language: en

00:00:00.732 --> 00:00:04.537
- [Voiceover] We have three
plus blank is equal to 10.

00:00:04.772 --> 00:00:06.896
So pause the video and try to figure out

00:00:06.896 --> 00:00:08.371
what the blank is.

00:00:08.371 --> 00:00:12.049
What do I have to add
to three to get to 10?

00:00:13.119 --> 00:00:15.148
So you've had a go at it.

00:00:15.151 --> 00:00:17.679
Now let's see if we can do this together.

00:00:17.993 --> 00:00:21.608
So over here, I have three of these,

00:00:22.070 --> 00:00:26.267
I guess you could say purple,
these purple pinkish circles

00:00:26.605 --> 00:00:27.954
and I have 10 boxes.

00:00:27.954 --> 00:00:30.370
One, two, three, four, five, six, seven,

00:00:30.370 --> 00:00:31.877
eight, nine, ten.

00:00:32.355 --> 00:00:33.748
So one way to think about it is,

00:00:33.748 --> 00:00:37.010
how many more circles do
I need to add to fill up

00:00:37.010 --> 00:00:38.366
all of the boxes?

00:00:38.450 --> 00:00:39.817
Well, let's just count that together.

00:00:40.156 --> 00:00:45.156
I need to add one, two, three, four,

00:00:45.229 --> 00:00:50.229
five, six, seven to fill up all 10 boxes.

00:00:51.114 --> 00:00:53.646
So three plus what is equal 10?

00:00:53.646 --> 00:00:56.847
Well, three plus one, two,
three, four, five, six, seven.

00:00:56.847 --> 00:00:59.390
is equal to 10.

00:00:59.508 --> 00:01:00.924
Let's do one more of these.

00:01:02.086 --> 00:01:07.086
So now I have six plus
blank is equal to 10.

00:01:09.109 --> 00:01:11.234
So again, try to pause the video

00:01:11.234 --> 00:01:13.730
and see if you can figure
out what the blank is.

00:01:13.730 --> 00:01:16.608
What do I need to add to six to get to 10?

00:01:17.115 --> 00:01:18.592
Let's do it together.

00:01:18.663 --> 00:01:23.663
So we now have one, two,
three, four, five, six circles.

00:01:24.363 --> 00:01:26.151
We have 10 boxes here.

00:01:26.151 --> 00:01:29.551
One, two, three, four, five,
six, seven, eight, nine, ten.

00:01:30.005 --> 00:01:31.863
So we just have to think
about how many more circles

00:01:31.863 --> 00:01:34.707
do we need to fill up all
the boxes to get to 10

00:01:34.707 --> 00:01:36.969
because we already have six filled in.

00:01:37.006 --> 00:01:42.006
Well, we need one, two,
three, four to get to 10.

00:01:43.030 --> 00:01:44.561
So let's just fill that in.

00:01:44.726 --> 00:01:47.790
Six plus four is equal to 10,

00:01:47.790 --> 00:01:48.684
or we could say even that

00:01:48.684 --> 00:01:52.270
four plus six is equal to 10, either way.


Introduction to subtraction

WEBVTT
Kind: captions
Language: en

00:00:00.633 --> 00:00:02.434
Voiceover:Let's explore what it means

00:00:02.434 --> 00:00:04.333
to subtract numbers.

00:00:04.700 --> 00:00:08.700
So let's say that I want to figure out

00:00:08.700 --> 00:00:13.933
what 4, what 4 minus 3 is.

00:00:14.500 --> 00:00:17.000
4 minus 3.

00:00:17.833 --> 00:00:20.367
So one way to think
about this, is you start

00:00:20.367 --> 00:00:21.933
with 4 objects.

00:00:22.433 --> 00:00:24.600
And so let me just draw 4 objects.

00:00:25.433 --> 00:00:35.600
So there I have 1, 2, 3, and 4.

00:00:36.633 --> 00:00:37.300
And when I ...

00:00:37.300 --> 00:00:39.133
So this is the 4 objects right over here.

00:00:39.500 --> 00:00:41.966
And when I say minus 3, or if I'm going

00:00:41.966 --> 00:00:45.366
to subtract 3 from the 4, one way to think

00:00:45.366 --> 00:00:46.833
about it is, I'm going to take 3

00:00:46.833 --> 00:00:48.733
of these 4 objects away.

00:00:48.766 --> 00:00:49.867
So let's do that.

00:00:50.034 --> 00:00:52.833
So I'm going to take away 1, I'm going to

00:00:52.833 --> 00:00:56.400
take away 2, and I'm going to take away 3.

00:00:56.633 --> 00:01:01.666
Notice, I took away 1, 2, 3 objects.

00:01:01.833 --> 00:01:04.133
So how many do I have leftover?

00:01:04.900 --> 00:01:08.001
Well, if I start with 4 and I take away 3,

00:01:08.100 --> 00:01:12.033
I subtract 3, 4 minus 3, I am left

00:01:12.033 --> 00:01:16.533
with, I am left with, 1
object, right over here.

00:01:16.633 --> 00:01:22.333
So 4 minus 3 is equal to, is equal to 1.

00:01:22.833 --> 00:01:23.767
Fascinating.

00:01:23.767 --> 00:01:25.066
Let's do another one of these.

00:01:25.233 --> 00:01:34.733
Let's figure out what 5,
what 5, what 5 minus 2 is.

00:01:35.033 --> 00:01:36.334
And let's write it this way.

00:01:36.433 --> 00:01:38.900
Let's say we want to figure out something,

00:01:38.900 --> 00:01:41.766
some question mark, some question mark ...

00:01:41.766 --> 00:01:43.200
Actually, let me just clear this out.

00:01:44.833 --> 00:01:46.733
I'll just do it right over here, actually.

00:01:47.233 --> 00:01:49.200
So let's say we have some question mark.

00:01:50.033 --> 00:01:52.333
So there's some unknown
number right over here.

00:01:52.767 --> 00:01:54.400
So I'll just put a
question mark over here.

00:01:54.633 --> 00:01:58.100
And we say that unknown
number is equal to,

00:01:58.100 --> 00:02:05.633
is equal to 5, 5 minus 2.

00:02:05.633 --> 00:02:07.600
Minus 2.

00:02:08.501 --> 00:02:09.866
Minus 2.

00:02:09.901 --> 00:02:11.200
So what is this going to be?

00:02:11.901 --> 00:02:13.233
Well let's visualize it.

00:02:13.233 --> 00:02:15.033
This means I have 5 things and I'm going

00:02:15.033 --> 00:02:17.766
to take away 2 of them
and this is going to be

00:02:17.766 --> 00:02:20.366
what I have leftover after I start with 5

00:02:20.366 --> 00:02:22.333
and take away 2.

00:02:22.834 --> 00:02:33.400
So I have 1, 2, 3, 4, 5 things.

00:02:33.566 --> 00:02:36.734
Now I am going to take away 2 of them.

00:02:37.101 --> 00:02:40.668
So I'm going to take away 1 and 2.

00:02:40.766 --> 00:02:43.467
So I took away 1, 2 objects.

00:02:43.766 --> 00:02:45.600
So how many do I have leftover?

00:02:45.900 --> 00:02:49.234
Well, I have leftover these, these ...

00:02:49.234 --> 00:02:50.666
Let me do this in a different color.

00:02:50.901 --> 00:02:57.466
I have leftover these purple
things right over here.

00:02:58.034 --> 00:02:59.266
So how many is that?

00:02:59.433 --> 00:03:00.933
How many do I have leftover?

00:03:01.234 --> 00:03:07.466
Well, I have leftover 1,
2, 3 of my original 5.

00:03:07.900 --> 00:03:10.400
So something is equal is 5 minus 2.

00:03:10.433 --> 00:03:12.333
That something is 3.

00:03:12.500 --> 00:03:15.334
3 is equal to 5 minus 2.

00:03:15.633 --> 00:03:21.000
Let me just replace this with a 3.

00:03:21.900 --> 00:03:23.600
So we see that 3 ...

00:03:24.300 --> 00:03:25.735
Actually, let me do
the 3 in the same color

00:03:25.735 --> 00:03:26.800
as this green.

00:03:26.833 --> 00:03:32.500
So we see that 3, 3 is equal to 5 minus 2

00:03:32.500 --> 00:03:36.133
or we could say that 5
minus 2 is equal to 3.

00:03:36.233 --> 00:03:37.400
Either way.


Making 5

WEBVTT
Kind: captions
Language: en

00:00:00.306 --> 00:00:02.046
Voiceover: What I want to do in this video

00:00:02.046 --> 00:00:05.924
is think about the
different ways to make five.

00:00:05.924 --> 00:00:08.328
What do I mean about that?

00:00:08.328 --> 00:00:12.504
Right over here we have
three plus something,

00:00:12.504 --> 00:00:16.218
so there's some unknown
number right over here.

00:00:16.218 --> 00:00:19.507
Three plus something is
going to be equal to five.

00:00:19.507 --> 00:00:23.061
In this diagram we have three circles here

00:00:23.061 --> 00:00:24.499
that represents the three

00:00:24.499 --> 00:00:27.359
and then we have five boxes.

00:00:27.359 --> 00:00:30.217
One, two, three, four, five.

00:00:30.217 --> 00:00:34.403
How many more circles do
we need in order to fill up

00:00:34.403 --> 00:00:36.265
all the five boxes?

00:00:36.265 --> 00:00:38.335
We've clearly already filled three.

00:00:39.565 --> 00:00:41.319
Well, let's think about it.

00:00:41.319 --> 00:00:47.078
We just have to add one and two circles.

00:00:47.078 --> 00:00:49.392
Now we have a total of five.

00:00:49.392 --> 00:00:53.835
Three blue ones and two
of this purple color

00:00:53.835 --> 00:00:55.310
or I guess this pink color.

00:00:55.310 --> 00:01:03.535
We see that three plus
two is equal to five.

00:01:03.535 --> 00:01:06.495
That mystery number
here, that blank is two.

00:01:06.495 --> 00:01:09.582
Three plus two is equal to five.

00:01:09.582 --> 00:01:11.993
Now over here we have two

00:01:11.993 --> 00:01:16.133
plus a mystery number
is equal to five again.

00:01:16.133 --> 00:01:20.237
Once again, we have five spaces

00:01:20.237 --> 00:01:22.998
and two of them are filled in with this

00:01:22.998 --> 00:01:25.428
kind of purple, pink stars.

00:01:25.428 --> 00:01:27.344
How many more do we have to fill in

00:01:27.344 --> 00:01:30.189
in order to fill in all five boxes,

00:01:30.189 --> 00:01:33.409
two plus what is equal to five.

00:01:33.409 --> 00:01:34.777
I encourage you to pause the video

00:01:34.777 --> 00:01:35.697
and think about it.

00:01:35.697 --> 00:01:39.232
I'm assuming you've had a go at it.

00:01:39.232 --> 00:01:42.175
Let's think about how
many more of this boxes

00:01:42.175 --> 00:01:45.431
we need to fill in, in order
to fill in all five of them.

00:01:45.431 --> 00:01:53.243
We need to fill in one,
two, and three of the boxes

00:01:53.243 --> 00:01:55.342
in order to fill out all five.

00:01:55.342 --> 00:01:57.049
Now we have five stars.

00:01:57.049 --> 00:01:58.958
We have two of the pink ones

00:01:58.958 --> 00:02:00.893
and we have three of the blue ones.

00:02:00.893 --> 00:02:03.856
We can say that two plus three,

00:02:03.856 --> 00:02:06.406
the mystery number here is three.

00:02:06.406 --> 00:02:10.917
Two plus three is equal to five.

00:02:10.917 --> 00:02:12.402
Let's do a few more of this.

00:02:13.755 --> 00:02:17.648
Here I have four plus some mystery number

00:02:17.648 --> 00:02:18.978
is equal to five.

00:02:18.978 --> 00:02:22.730
I filled out four of the five boxes,

00:02:22.730 --> 00:02:24.584
how many more do I need to fill in

00:02:24.584 --> 00:02:26.689
in order to have five things,

00:02:26.689 --> 00:02:29.235
in order to have all
five boxes filled out.

00:02:29.742 --> 00:02:32.106
Well we see very clearly here

00:02:32.106 --> 00:02:35.147
that there is exactly one box

00:02:35.147 --> 00:02:37.038
that we need to fill in

00:02:37.038 --> 00:02:40.708
or one box that we need
to add to the other four.

00:02:40.708 --> 00:02:49.086
We see that four plus
one is equal to five.

00:02:49.086 --> 00:02:50.967
Now let's go the other way.

00:02:50.967 --> 00:02:55.727
We have the five boxes, only
one of them is filled in.

00:02:55.727 --> 00:02:58.184
How many more of these smiley faces

00:02:58.184 --> 00:03:01.144
do we need to add, in order
to fill in all the boxes?

00:03:01.144 --> 00:03:02.520
Or another way of thinking about it,

00:03:02.520 --> 00:03:03.463
we have one,

00:03:03.463 --> 00:03:06.399
how many more do we need to add to one

00:03:06.399 --> 00:03:08.037
to get to five?

00:03:08.037 --> 00:03:11.160
Like always, I encourage
you to pause the video

00:03:11.160 --> 00:03:12.705
and think about it on your own.

00:03:12.705 --> 00:03:16.256
Well, let's see, we can add one,

00:03:16.256 --> 00:03:21.294
we can add two, we can add three,

00:03:21.294 --> 00:03:26.209
and four yellow smiley faces.

00:03:26.209 --> 00:03:30.257
We could say one, one we
have one white smiley face

00:03:30.257 --> 00:03:34.658
plus one, two, three,
four yellow smiley faces

00:03:34.658 --> 00:03:37.400
is equal to five.

00:03:37.400 --> 00:03:39.301
You see a pattern here.

00:03:39.301 --> 00:03:41.298
Let's start at the beginning.

00:03:41.298 --> 00:03:44.314
Three plus two is equal to five,

00:03:44.314 --> 00:03:47.265
and two plus three is equal to five.

00:03:47.265 --> 00:03:49.030
When you had three filled in,

00:03:49.030 --> 00:03:50.744
you needed two more to get to five.

00:03:50.769 --> 00:03:52.433
When you had two filled in,

00:03:52.433 --> 00:03:54.945
you needed three more to get to five.

00:03:54.945 --> 00:03:57.427
Notice three plus two, two plus three.

00:03:57.427 --> 00:03:58.992
Same thing over here,

00:03:58.992 --> 00:04:01.476
four plus one is equal to five,

00:04:01.476 --> 00:04:05.041
one plus four is equal to five.