Counting American coins

WEBVTT
Kind: captions
Language: en

00:00:00.320 --> 00:00:03.524
- Let's get some practice counting money!

00:00:03.524 --> 00:00:07.378
So I have six coins right over here,

00:00:07.378 --> 00:00:10.304
and these are all United States coins,

00:00:10.304 --> 00:00:11.711
we're counting money in the United States

00:00:11.711 --> 00:00:16.285
for these examples, and
what is this first coin?

00:00:16.285 --> 00:00:18.862
Well, this is called a
quarter, or a quarter-dollar,

00:00:18.862 --> 00:00:22.577
so it represents 25 cents,
and we could write it out

00:00:22.577 --> 00:00:27.314
as 25 cents, but I'll just
keep that one like that.

00:00:27.314 --> 00:00:28.498
Now this one's another quarter,

00:00:28.498 --> 00:00:33.211
so it is also going to be 25 cents.

00:00:33.211 --> 00:00:34.581
Now this one looks different, but

00:00:34.581 --> 00:00:37.043
it's just the other side of these coins.

00:00:37.043 --> 00:00:38.923
This is what the other side looks like.

00:00:38.923 --> 00:00:43.010
So this is also going to be 25 cents.

00:00:43.010 --> 00:00:45.309
These are three quarters right over here.

00:00:45.309 --> 00:00:48.675
So how much money do these
three quarters represent?

00:00:48.675 --> 00:00:52.112
Well, it's going to be
25 plus 25, which is 50,

00:00:52.112 --> 00:00:54.852
plus 25, which is going to be 75,

00:00:54.852 --> 00:00:59.852
so these three quarters
are going to be 75 cents.

00:01:00.447 --> 00:01:02.955
And remember, 100 cents make a dollar,

00:01:02.955 --> 00:01:05.602
so this is still less than one dollar.

00:01:05.602 --> 00:01:07.576
But we're not done yet.

00:01:07.576 --> 00:01:11.012
We have this nickel, this
is a nickel right over here,

00:01:11.012 --> 00:01:13.427
that represents five
cents, and then we have

00:01:13.427 --> 00:01:15.331
another nickel here, it looks
different, but it's just

00:01:15.331 --> 00:01:18.790
the other side, this is the head
side, this is the tail side.

00:01:18.790 --> 00:01:21.066
So this is also another five cents,

00:01:21.066 --> 00:01:24.154
and so these two nickels,
if you add them together,

00:01:24.154 --> 00:01:28.496
they are going to represent 10 cents,

00:01:28.496 --> 00:01:30.864
and then finally, you
have a penny, and a penny,

00:01:30.864 --> 00:01:33.140
and it even says it right over
here, is one cent, in fact,

00:01:33.140 --> 00:01:37.226
they all say it here, this is
five cents, this is one cent.

00:01:37.226 --> 00:01:39.432
So this right over
here's gonna be one cent.

00:01:39.432 --> 00:01:42.822
So what is 75 plus 10 plus 1?

00:01:42.822 --> 00:01:47.822
Well 75 plus 10 is 85, plus 1 is 86,

00:01:48.255 --> 00:01:51.947
so this is equal to 86 cents.

00:01:51.947 --> 00:01:56.947
And if it felt a little bit
too fast to count up 25, 50, 75

00:01:57.195 --> 00:02:00.054
in your head, you could also add them up.

00:02:00.054 --> 00:02:05.054
25, 25, 25, plus 5, another 5, plus 1.

00:02:11.961 --> 00:02:13.655
You could add them up this way,

00:02:13.655 --> 00:02:15.619
and then what would you get?

00:02:15.619 --> 00:02:20.619
5 plus 5 is 10, plus 5 is 15,
plus 5 is 20, plus 5 is 25,

00:02:23.118 --> 00:02:26.926
plus 1 is 26, so that's
two tens and one six,

00:02:26.926 --> 00:02:28.668
put the two tens up here.

00:02:28.668 --> 00:02:33.668
2 plus 2 is 4, 4 plus
2 is 6, 6 plus 2 is 8.

00:02:34.101 --> 00:02:36.980
So you could get 86 cents, either way.

00:02:36.980 --> 00:02:39.859
Let's do one that has
even more coins in it.

00:02:39.859 --> 00:02:44.859
So here we go, we have, so what
is it, what's going on here?

00:02:45.107 --> 00:02:49.333
This right over here is a quarter,
that's going to be 25 cents.

00:02:49.333 --> 00:02:53.512
25 cents, and then, we
have one that we didn't see

00:02:53.512 --> 00:02:57.668
in the previous example,
we have two dimes.

00:02:57.668 --> 00:03:02.033
A dime represents 10 cents,
so we have two dimes,

00:03:02.033 --> 00:03:05.122
where we can have those
each represent 10 cents,

00:03:05.122 --> 00:03:07.792
then we have two nickels,
we've already seen

00:03:07.792 --> 00:03:12.792
those each represent
five cents, so 5 and 5,

00:03:13.132 --> 00:03:18.132
and then we have four pennies,
one, two, three, four.

00:03:19.215 --> 00:03:21.839
Now we could put each penny
separately, like that,

00:03:21.839 --> 00:03:24.231
or we could say, look, four
pennies, each of them represent

00:03:24.231 --> 00:03:27.110
one cent, so that's
going to be four cents.

00:03:27.110 --> 00:03:28.782
So let me do it that way.

00:03:28.782 --> 00:03:33.782
So, this one, two, three, four,

00:03:34.354 --> 00:03:36.305
that's going to be four cents.

00:03:36.305 --> 00:03:38.812
And then we could just add everything up,

00:03:38.812 --> 00:03:43.812
so 5 plus 0 plus 0 plus 5 is
10, plus 5 is 15, plus 4 is 19.

00:03:47.195 --> 00:03:49.334
19 is one ten and nine ones, so I could

00:03:49.334 --> 00:03:51.401
put the one ten in the tens place,

00:03:51.401 --> 00:03:56.401
1 plus 2 is 3, plus 1 is 4, plus 1 is 5.

00:03:56.857 --> 00:04:01.857
So it's five tens, five tens
and nine ones, so 59 cents.

00:04:02.467 --> 00:04:05.555
This right over here is 59 cents.

00:04:05.555 --> 00:04:07.784
And notice, we have more coins,

00:04:07.784 --> 00:04:11.058
but it represents less value
than the previous example.

00:04:11.058 --> 00:04:12.567
That's because we had a lot of coins

00:04:12.567 --> 00:04:13.960
that didn't represent a lot of values,

00:04:13.960 --> 00:04:16.096
like, we had these four pennies here,

00:04:16.096 --> 00:04:20.498
while the previous example,
we had three quarters!

00:04:20.498 --> 00:04:24.236
Each of these quarters is
equivalent to 25 pennies,

00:04:24.236 --> 00:04:26.071
so we're able to represent more money

00:04:26.071 --> 00:04:28.925
with fewer coins in the first example.


Comparison word problems

WEBVTT
Kind: captions
Language: en

00:00:00.186 --> 00:00:01.092
- [Voiceover] So they tell us

00:00:01.092 --> 00:00:04.284
that Alexander has nine marbles,

00:00:04.284 --> 00:00:07.412
Emily has five marbles.

00:00:07.412 --> 00:00:08.636
And then we're asked,

00:00:08.636 --> 00:00:12.271
how many more marbles does
Alexander have than Emily?

00:00:12.272 --> 00:00:13.433
So pause the video

00:00:13.433 --> 00:00:16.405
and try to see if you
could figure this out.

00:00:16.405 --> 00:00:19.842
Now let's work this out together.

00:00:19.842 --> 00:00:20.793
So let's just draw it out.

00:00:20.794 --> 00:00:22.675
Alexander has nine marbles.

00:00:22.675 --> 00:00:24.787
So we could draw his marbles.

00:00:24.787 --> 00:00:26.380
So one,

00:00:26.380 --> 00:00:27.840
two, three

00:00:27.840 --> 00:00:29.356
four, five

00:00:29.356 --> 00:00:30.855
six, seven

00:00:30.855 --> 00:00:33.091
eight, nine.

00:00:33.091 --> 00:00:35.259
And Emily has five marbles.

00:00:35.259 --> 00:00:37.746
One, two, three,

00:00:37.746 --> 00:00:39.357
four, five.

00:00:39.357 --> 00:00:40.507
So how many more marbles

00:00:40.507 --> 00:00:42.390
does Alexander have than Emily?

00:00:42.390 --> 00:00:44.640
Well we can see it in this
picture right over here.

00:00:44.640 --> 00:00:46.494
These are all the...

00:00:46.494 --> 00:00:51.281
So, up until this point

00:00:51.281 --> 00:00:54.437
this is the same number
that Alexander has as Emily.

00:00:54.437 --> 00:00:56.318
And then Alexander has...

00:00:56.319 --> 00:00:58.362
Alexander has...

00:00:58.362 --> 00:00:59.988
We see it right over here,

00:00:59.988 --> 00:01:02.162
he has one, two, three,

00:01:02.162 --> 00:01:04.843
four more marbles.

00:01:04.843 --> 00:01:06.312
Now what's another way

00:01:06.312 --> 00:01:08.231
that we could have thought about it?

00:01:08.231 --> 00:01:12.676
Well, Alexander has nine marbles

00:01:13.570 --> 00:01:16.752
and if you were to subtract the
number of marbles Emily has,

00:01:16.752 --> 00:01:19.515
that's how much more
marbles Alexander has.

00:01:19.515 --> 00:01:21.953
That's how much more nine is than five.

00:01:21.953 --> 00:01:26.031
So you could have said nine minus five

00:01:26.031 --> 00:01:28.051
is equal to...

00:01:28.051 --> 00:01:31.101
Is equal to the four...

00:01:31.101 --> 00:01:32.322
the four marbles.

00:01:32.322 --> 00:01:37.212
That's how much more marbles
Alexander has than Emily.

00:01:37.212 --> 00:01:39.541
Let's do another one of these.

00:01:41.987 --> 00:01:44.574
Noa was mailing two letters.

00:01:44.575 --> 00:01:46.732
The heavier letter...

00:01:46.732 --> 00:01:49.751
The heavier letter had eight stamps.

00:01:49.751 --> 00:01:54.186
The lighter letter had five fewer stamps.

00:01:54.186 --> 00:01:57.854
How many stamps did the
lighter letter have?

00:01:57.854 --> 00:01:59.062
So once again,

00:01:59.062 --> 00:02:00.548
try to pause this video

00:02:00.548 --> 00:02:03.427
and see if you can figure
it out on your own.

00:02:03.427 --> 00:02:04.332
So the heavier letter,

00:02:04.332 --> 00:02:05.470
it's always useful to just,

00:02:05.470 --> 00:02:06.392
well, what are they telling us?

00:02:06.392 --> 00:02:07.606
So they are saying,

00:02:07.606 --> 00:02:11.182
just write down whatever
information they give us.

00:02:11.182 --> 00:02:14.386
So the heavier letter has eight stamps,

00:02:14.386 --> 00:02:17.251
the lighter letter has five fewer stamps.

00:02:17.251 --> 00:02:19.286
So do we know how many
the lighter letter has?

00:02:19.286 --> 00:02:20.306
Well not immediately.

00:02:20.306 --> 00:02:21.631
That's what they're actually asking us.

00:02:21.631 --> 00:02:23.465
How many stamps did the
lighter letter have?

00:02:23.465 --> 00:02:24.905
But it's five fewer.

00:02:24.905 --> 00:02:26.275
Five fewer than what?

00:02:26.275 --> 00:02:28.828
Five fewer than eight stamps.

00:02:28.828 --> 00:02:30.290
And so we could write that.

00:02:30.290 --> 00:02:31.150
If we have eight stamps

00:02:31.151 --> 00:02:33.681
and we want to go five fewer than that...

00:02:33.681 --> 00:02:35.098
Five fewer...

00:02:35.098 --> 00:02:36.932
Well that's going to be eight minus five.

00:02:36.932 --> 00:02:38.999
This is five fewer than eight,

00:02:38.999 --> 00:02:43.503
which is going to be equal to three.

00:02:43.503 --> 00:02:45.500
The lighter letter has three stamps.

00:02:45.500 --> 00:02:47.032
Now another way you could
have thought about it,

00:02:47.032 --> 00:02:49.260
The heavier letter had eight stamps.

00:02:49.260 --> 00:02:50.887
Let's draw eight stamps.

00:02:50.887 --> 00:02:55.074
So one, two,

00:02:55.074 --> 00:02:58.214
three, four,

00:02:58.214 --> 00:03:00.914
five, six,

00:03:00.914 --> 00:03:03.274
seven, and eight.

00:03:03.275 --> 00:03:04.821
That's how much the heavier letter had.

00:03:04.821 --> 00:03:07.581
The lighter letter had five fewer stamps.

00:03:07.581 --> 00:03:08.694
Let's take away one,

00:03:08.709 --> 00:03:10.620
two, three

00:03:10.620 --> 00:03:12.061
four, five.

00:03:12.061 --> 00:03:14.244
And what are you going to be left with?

00:03:14.244 --> 00:03:15.786
Well you're going to be left with

00:03:15.786 --> 00:03:18.123
these three stamps right over here.

00:03:18.123 --> 00:03:22.036
This is how many stamps
the lighter letter had.


Comparing lengths

WEBVTT
Kind: captions
Language: en

00:00:00.357 --> 00:00:05.357
- Rectangle 1 is blank meters
blank than Rectangle 2.

00:00:06.432 --> 00:00:07.499
Let's look at this.

00:00:07.710 --> 00:00:11.690
Rectangle 1 has a width of 3 meters.

00:00:11.877 --> 00:00:15.835
Rectangle 2 has a width of 9 meters.

00:00:16.149 --> 00:00:20.434
Rectangle 1 is, if you compare 3 to 9,

00:00:20.434 --> 00:00:23.892
it's going to be 6 meters shorter.

00:00:24.195 --> 00:00:29.195
6 meters shorter than Rectangle 2.

00:00:29.534 --> 00:00:30.775
You see that right over here,

00:00:30.775 --> 00:00:34.152
because 3 meters is 6 less than 9 meters.

00:00:34.235 --> 00:00:35.315
It's 6 meters,

00:00:35.315 --> 00:00:36.825
and you know it's not going to be longer.

00:00:36.825 --> 00:00:38.416
Rectangle 1 is definitely ...

00:00:38.416 --> 00:00:40.041
it has less width.

00:00:40.041 --> 00:00:43.075
It's definitely shorter than Rectangle 2.

00:00:43.075 --> 00:00:45.715
It's 6 meters shorter than Rectangle 2.

00:00:45.906 --> 00:00:47.113
Let's do a few more of these.

00:00:47.440 --> 00:00:50.272
Line 1 is blank centimeters long.

00:00:50.272 --> 00:00:51.457
We can measure it.

00:00:51.857 --> 00:00:53.465
We could measure it right over here.

00:00:53.465 --> 00:00:56.717
Line 1 is 9 centimeters long.

00:00:57.547 --> 00:00:58.956
9 centimeters long.

00:00:58.956 --> 00:01:02.149
Line 2 is blank centimeters long.

00:01:02.149 --> 00:01:03.868
Let me actually zoom this in a little bit

00:01:03.868 --> 00:01:05.415
so that we can see it a little bit better.

00:01:05.415 --> 00:01:09.060
Line 2 is blank centimeters long.

00:01:09.060 --> 00:01:12.671
Line 2 is 5 centimeters long.

00:01:13.455 --> 00:01:15.606
Let me zoom in a little bit more even.

00:01:16.142 --> 00:01:20.344
Line 2 is 5 centimeters long.

00:01:20.344 --> 00:01:24.268
Line 1 is blank centimeters
blank than Line 2.

00:01:24.268 --> 00:01:26.927
Well, Line 1 is 9 verses 5,

00:01:26.927 --> 00:01:30.305
so it's 4 centimeters longer than Line 2.

00:01:30.305 --> 00:01:35.305
Line 1 is 4 centimeters
longer than Line 2.

00:01:36.081 --> 00:01:37.137
You can see it right over here.

00:01:37.137 --> 00:01:38.554
To go from Line 2 to Line 1,

00:01:38.554 --> 00:01:42.408
you'd have to add 1, 2, 3, 4 centimeters.

00:01:43.777 --> 00:01:46.329
Let's do a few more of these.

00:01:46.329 --> 00:01:48.904
Triangle 1 is blank centimeters long.

00:01:48.904 --> 00:01:50.250
We can just use a ruler to measure

00:01:50.250 --> 00:01:52.166
that it's 3 centimeters long.

00:01:53.089 --> 00:01:55.393
Triangle 2 is blank centimeters long.

00:01:55.393 --> 00:01:57.466
Let me scroll down to look at Triangle 2.

00:01:57.466 --> 00:02:01.622
Triangle 2 is 5 centimeters long.

00:02:02.575 --> 00:02:05.592
Triangle 2 is 5 centimeters long.

00:02:05.961 --> 00:02:10.271
Triangle 1 is blank centimeters
blank than Triangle 2.

00:02:10.655 --> 00:02:13.884
Well, Triangle 1 is 2 centimeters
shorter than Triangle 2.

00:02:13.884 --> 00:02:15.881
3 is 2 less than 5.

00:02:16.388 --> 00:02:18.587
It's going to be 2 centimeters shorter.

00:02:18.587 --> 00:02:21.071
Remember, Triangle 1, we see it's shorter

00:02:21.071 --> 00:02:22.468
it's smaller than Triangle 2,

00:02:22.468 --> 00:02:23.710
so it makes since that it's shorter.

00:02:23.710 --> 00:02:24.398
How much shorter?

00:02:24.398 --> 00:02:26.464
2 centimeters because 3 centimeters

00:02:26.464 --> 00:02:28.635
compared to 5 centimeters.

00:02:28.882 --> 00:02:30.346
Let's do one more of these.

00:02:30.522 --> 00:02:32.857
Rectangle 1 is blank centimeters long.

00:02:33.303 --> 00:02:34.649
We can just look right over here.

00:02:34.649 --> 00:02:36.286
It's 9 centimeters long.

00:02:36.870 --> 00:02:39.180
We have one end of the ruler
at one end of the rectangle,

00:02:39.180 --> 00:02:41.363
and then we just measure
off 9 centimeters.

00:02:41.778 --> 00:02:44.289
Rectangle 2 is, well,

00:02:44.289 --> 00:02:46.748
it looks like it's 6 centimeters long.

00:02:47.178 --> 00:02:49.370
6 centimeters long.

00:02:49.535 --> 00:02:51.705
Rectangle 1 is longer,

00:02:51.705 --> 00:02:55.490
and it's 3 centimeters
longer than Rectangle 2.

00:02:55.490 --> 00:02:58.428
9 centimeters is 3 centimeters
more than 6 centimeters.

00:02:58.428 --> 00:03:00.087
It's 3 centimeters longer.

00:03:00.087 --> 00:03:03.571
Rectangle 1 is the longer Rectangle.

00:03:04.124 --> 00:03:05.497
Then, we're done.


Measuring lengths 2

WEBVTT
Kind: captions
Language: en

00:00:00.853 --> 00:00:04.185
- [Voiceover] Which shows
the length of the rectangle

00:00:04.185 --> 00:00:06.054
measured correctly?

00:00:06.054 --> 00:00:07.192
Alright.

00:00:07.192 --> 00:00:10.454
So here, we have this green rectangle,

00:00:10.454 --> 00:00:12.083
and, let's see, how did we measure it?

00:00:12.083 --> 00:00:14.986
We have one centimeter, right over here,

00:00:14.986 --> 00:00:18.655
and then we put another
centimeter right over here.

00:00:18.655 --> 00:00:20.953
And they say, "Two rulers

00:00:20.953 --> 00:00:24.181
"measure the rectangle side-to-side."

00:00:24.181 --> 00:00:25.551
Well this makes sense, 'cause we can say,

00:00:25.551 --> 00:00:28.221
"Look, if from here to
here, from the beginning

00:00:28.221 --> 00:00:30.973
"of the rectangle to the
middle, is one centimeter,

00:00:30.973 --> 00:00:32.157
"and then it's another centimeter that

00:00:32.157 --> 00:00:34.885
"gets us to the other
side, to the right side,

00:00:34.885 --> 00:00:36.186
"then we know that this is going to be

00:00:36.186 --> 00:00:37.915
"two centimeters long."

00:00:37.915 --> 00:00:39.820
One, and two.

00:00:39.820 --> 00:00:41.758
So I'm pretty sure this
is measured correctly.

00:00:41.758 --> 00:00:43.523
But let's just make
sure that the other two

00:00:43.523 --> 00:00:46.925
don't really measure
the rectangle correctly.

00:00:46.925 --> 00:00:51.186
So this one right over here,
you have one centimeter

00:00:51.186 --> 00:00:53.020
and then another centimeter,
but you're leaving

00:00:53.020 --> 00:00:54.924
a gap right over here.

00:00:54.924 --> 00:00:57.258
And you can't leave a gap here, you wanna

00:00:57.258 --> 00:00:58.674
measure what this distance is.

00:00:58.674 --> 00:01:00.752
And you notice that this ends to the right

00:01:00.752 --> 00:01:02.761
of the right of the rectangle.

00:01:02.761 --> 00:01:04.955
So this isn't a good way of measuring it.

00:01:04.955 --> 00:01:06.952
And this way, you're
not going all the way,

00:01:06.952 --> 00:01:09.587
the entire length of the rectangle,

00:01:09.587 --> 00:01:11.178
so this, you're coming up short.

00:01:11.178 --> 00:01:12.351
You need to measure the entire length.

00:01:12.351 --> 00:01:14.452
You need to start on the
left side, which they did,

00:01:14.452 --> 00:01:16.484
but you need to go all
the way, without any gaps,

00:01:16.484 --> 00:01:19.189
and without overlapping
the rulers in any way

00:01:19.189 --> 00:01:20.095
to get to this side.

00:01:20.095 --> 00:01:21.917
So this isn't right either.

00:01:21.917 --> 00:01:23.717
So let's keep doing these.

00:01:23.717 --> 00:01:27.595
Which shows the length of the
eraser measured correctly?

00:01:27.595 --> 00:01:30.044
So, this one, well once
again, there's some

00:01:30.044 --> 00:01:32.087
weirdness over here, I don't
even know what's happening.

00:01:32.087 --> 00:01:34.653
But the entire ruler
isn't even getting to the

00:01:34.653 --> 00:01:37.126
entire length of this rectangle.

00:01:37.126 --> 00:01:38.995
So this isn't measured correctly.

00:01:38.995 --> 00:01:42.013
And they say, "Two rulers
measure the eraser and overlap."

00:01:42.013 --> 00:01:43.917
Oh, I see, this is kind of, the ruler's

00:01:43.917 --> 00:01:45.380
a little bit transparent, so this one is

00:01:45.380 --> 00:01:47.052
overlapping with the one underneath.

00:01:47.052 --> 00:01:48.420
So you definitely don't wanna do that.

00:01:48.420 --> 00:01:50.127
You wanna put them
right next to each other

00:01:50.127 --> 00:01:51.393
without a gap.

00:01:51.393 --> 00:01:53.123
And you wanna get all the way to the edge

00:01:53.123 --> 00:01:55.549
of this rectangle.

00:01:55.549 --> 00:01:56.954
So this one, you have a gap, and you're

00:01:56.954 --> 00:02:00.379
actually going beyond the
edge of the rectangle.

00:02:00.379 --> 00:02:01.528
So that's not good.

00:02:01.528 --> 00:02:04.152
Here, you have no overlap,
and no gap right over here.

00:02:04.152 --> 00:02:05.917
They're just right next to each other.

00:02:05.917 --> 00:02:08.808
And we're starting at the
left side of this rectangle.

00:02:08.808 --> 00:02:10.793
And we're going exactly to the right side.

00:02:10.793 --> 00:02:14.485
We're not overstepping it
or we're not under-doing it.

00:02:14.485 --> 00:02:17.190
So this is going to be right.

00:02:17.190 --> 00:02:18.618
This is a lot of fun.

00:02:18.618 --> 00:02:20.685
Let's do, okay this is interesting.

00:02:20.685 --> 00:02:24.191
What is the length of the
floor of the bank, in meters?

00:02:24.191 --> 00:02:25.085
This is a picture of a bank.

00:02:25.085 --> 00:02:27.082
I guess this is the big
money in the bank (laughs).

00:02:27.082 --> 00:02:29.520
Those are big dollar bills,
and those are big coins.

00:02:29.520 --> 00:02:31.157
Drag the ruler to make the measurement.

00:02:31.157 --> 00:02:34.280
And this is in meters,
so I can click on this,

00:02:34.280 --> 00:02:36.521
and then I can put it, remember I wanna,

00:02:36.521 --> 00:02:38.622
I don't wanna do this,
this would be wrong,

00:02:38.622 --> 00:02:42.024
because I wanna start
measuring right at the edge,

00:02:42.024 --> 00:02:43.893
right at the edge of the bank.

00:02:43.893 --> 00:02:45.890
So I wanna do it like that.

00:02:45.890 --> 00:02:48.456
And I see, okay, the length of the bank,

00:02:48.456 --> 00:02:49.454
well how much is that?

00:02:49.454 --> 00:02:51.126
Well you see this right
wall right over here,

00:02:51.126 --> 00:02:55.456
it's right at four, right at four meters.

00:02:55.456 --> 00:02:58.986
So this is going to be four meters long.

00:02:58.986 --> 00:03:00.855
Let's do another one.

00:03:00.855 --> 00:03:03.386
What is the length of
Maria's back yard in meters?

00:03:03.386 --> 00:03:05.418
Drag the ruler to make the measurement.

00:03:05.418 --> 00:03:07.357
So once again, you don't
wanna do something like this,

00:03:07.357 --> 00:03:10.027
where you're starting
to measure, before the

00:03:10.027 --> 00:03:11.594
garden even starts or you're starting to

00:03:11.594 --> 00:03:12.823
measure too late.

00:03:12.823 --> 00:03:16.422
You wanna measure right at
the edge, right over there.

00:03:16.422 --> 00:03:17.722
So that's where the
guard starts, so that's

00:03:17.722 --> 00:03:19.156
where your ruler should start, measuring

00:03:19.156 --> 00:03:23.521
one, two, three, four,
five, six, seven, eight,

00:03:23.521 --> 00:03:24.926
looks pretty close.

00:03:24.926 --> 00:03:29.350
Let's see, it looks pretty close to eight,

00:03:29.350 --> 00:03:32.554
eight meters right over here.

00:03:32.554 --> 00:03:36.257
So, yea, this length of
this is eight meters.

00:03:36.257 --> 00:03:38.821
Looks pretty close, I'll say eight.

00:03:38.821 --> 00:03:41.484
Alright, let's do one more of these.

00:03:41.486 --> 00:03:45.256
What is the length of the tray
of cookies in centimeters?

00:03:45.256 --> 00:03:47.018
Now when they say "length,"
they mean the longest,

00:03:47.018 --> 00:03:48.657
"length" actually means
the longest dimension.

00:03:48.657 --> 00:03:50.062
If you have a width and a length.

00:03:50.062 --> 00:03:51.593
And so the longest dimension of a tray

00:03:51.593 --> 00:03:54.020
of cookies is gonna be
this side right over here.

00:03:54.020 --> 00:03:56.284
You don't wanna measure,
you don't wanna measure

00:03:56.284 --> 00:03:59.453
that side up there, that
would not be the length.

00:03:59.453 --> 00:04:01.392
The length, if people
don't tell you otherwise,

00:04:01.392 --> 00:04:02.925
it's the longest dimension.

00:04:02.925 --> 00:04:06.025
So we wanna measure, so we wanna measure,

00:04:06.025 --> 00:04:07.882
let me make sure I don't lose my ruler.

00:04:07.882 --> 00:04:12.120
We wanna measure, we wanna
measure along the top

00:04:12.120 --> 00:04:13.594
or along the bottom.

00:04:13.594 --> 00:04:17.727
And we see that it is, once
again, we don't wanna do this,

00:04:17.727 --> 00:04:20.084
that would be starting the
ruler too far to the left,

00:04:20.084 --> 00:04:21.582
and you don't wanna do
this, starting the ruler

00:04:21.582 --> 00:04:22.906
too far to the right, you wanna put it

00:04:22.906 --> 00:04:25.820
right at the edge, right over there.

00:04:25.820 --> 00:04:27.654
My ruler isn't perfectly straight.

00:04:27.654 --> 00:04:30.591
And we see that this cookie tray is,

00:04:30.591 --> 00:04:34.318
it is right at about eight centimeters.

00:04:34.318 --> 00:04:36.385
Eight centimeters.

00:04:36.385 --> 00:04:38.144
And we're done.


Counting in pictures

WEBVTT
Kind: captions
Language: en

00:00:00.417 --> 00:00:04.117
- [Voiceover] How many people
do you see in this picture?

00:00:04.117 --> 00:00:09.117
Let's see, I see one,
two, three, four, five,

00:00:09.450 --> 00:00:11.717
six people in this picture.

00:00:11.717 --> 00:00:13.917
So, I'm gonna choose six.

00:00:13.917 --> 00:00:15.917
This is fun, lemme keep going.

00:00:15.917 --> 00:00:18.983
How many wheels do I see in the picture?

00:00:18.983 --> 00:00:23.867
One, two, three, four,
five, six, seven, eight.

00:00:24.684 --> 00:00:25.884
Wanna scroll down and make sure I don't

00:00:25.884 --> 00:00:29.350
miss these over here, nine, 10, 11, 12,

00:00:29.350 --> 00:00:32.750
13, 14, 15, 16 wheels.

00:00:32.750 --> 00:00:34.250
There are 16 wheels.

00:00:34.250 --> 00:00:36.983
These four cars have 16 wheels.

00:00:36.983 --> 00:00:39.834
So, 16 wheels, let's keep going.

00:00:40.750 --> 00:00:42.383
How many people are in the boat?

00:00:42.383 --> 00:00:44.184
I see one, two, and three.

00:00:44.184 --> 00:00:46.750
There's the guy rowing it,
there's I guess the mother,

00:00:46.750 --> 00:00:48.050
and then there's the baby.

00:00:48.050 --> 00:00:50.084
There's three people in this boat.

00:00:50.084 --> 00:00:52.084
Three people in the boat.

00:00:52.084 --> 00:00:54.450
This is too much fun,
how many faces do I see?

00:00:54.450 --> 00:00:56.317
One, two, three, four five,

00:00:56.317 --> 00:01:00.100
six, seven, eight, nine, 10 faces.

00:01:01.050 --> 00:01:02.763
Keep going.

00:01:02.763 --> 00:01:04.950
How many bottles do I see?

00:01:04.950 --> 00:01:08.000
One, two, three, four bottles.

00:01:09.254 --> 00:01:10.240
And we're done.


Addition and subtraction within 10

WEBVTT
Kind: captions
Language: en

00:00:00.267 --> 00:00:03.564
- [Voiceover] So we're given
four different equations here

00:00:03.564 --> 00:00:05.247
and each of them have a blank,

00:00:05.247 --> 00:00:06.908
and we need to fill in that blank

00:00:06.908 --> 00:00:08.231
with a missing number.

00:00:08.231 --> 00:00:09.949
So let's do each of these.

00:00:09.949 --> 00:00:11.794
So on the left hand side of this equation,

00:00:11.794 --> 00:00:14.597
we have one plus four,

00:00:15.277 --> 00:00:18.969
so one plus four is the same thing as...

00:00:18.969 --> 00:00:21.425
Well, one plus four is five.

00:00:21.425 --> 00:00:23.138
If we take four, and if you add one more,

00:00:23.138 --> 00:00:24.799
you're gonna have five.

00:00:24.799 --> 00:00:26.446
So now, we finished that one,

00:00:26.446 --> 00:00:29.244
because one plus four is the same thing

00:00:29.244 --> 00:00:30.846
as five.

00:00:30.846 --> 00:00:33.539
Now here, we're saying four plus something

00:00:33.539 --> 00:00:36.059
is the same thing as five.

00:00:36.059 --> 00:00:36.825
Well, we just figured out

00:00:36.825 --> 00:00:39.356
that one plus four, or four plus one

00:00:39.356 --> 00:00:41.259
is the same thing as five.

00:00:41.259 --> 00:00:43.279
So four plus one is five.

00:00:43.279 --> 00:00:44.719
So notice there, we have the equation,

00:00:44.719 --> 00:00:47.296
four plus one is the same thing as five.

00:00:47.296 --> 00:00:49.259
Equals means that what's on the left

00:00:49.259 --> 00:00:52.805
is the same thing as what
you have on the right.

00:00:52.805 --> 00:00:54.403
Now we have blank plus two

00:00:54.403 --> 00:00:55.994
is equal to five.

00:00:55.994 --> 00:01:00.266
So what plus two is
the same thing as five?

00:01:00.266 --> 00:01:03.691
Well, three plus two is equal to five,

00:01:03.691 --> 00:01:07.103
or five is equal to three plus two.

00:01:07.103 --> 00:01:08.404
Now you go here.

00:01:08.404 --> 00:01:09.948
Well now you have three plus blank

00:01:09.948 --> 00:01:10.911
is equal to five.

00:01:10.911 --> 00:01:11.667
Well, we already figured it out,

00:01:11.667 --> 00:01:15.125
because three plus two is equal to five.

00:01:15.125 --> 00:01:17.052
So we can write three plus two

00:01:17.052 --> 00:01:17.969
is equal to five,

00:01:17.969 --> 00:01:19.467
and then we can check ourselves.

00:01:19.467 --> 00:01:20.802
And then we can keep going.

00:01:20.802 --> 00:01:22.893
So now we have some subtraction.

00:01:22.893 --> 00:01:25.830
So what's the same thing
as nine minus three?

00:01:25.830 --> 00:01:27.141
So if I have nine things, and if I were

00:01:27.141 --> 00:01:28.686
to take away three of them,

00:01:28.686 --> 00:01:30.507
I'm going to have six left.

00:01:30.507 --> 00:01:33.686
Nine minus three is the same thing as six.

00:01:33.851 --> 00:01:35.654
10 minus blank

00:01:35.654 --> 00:01:38.474
is equal to six.

00:01:38.474 --> 00:01:39.462
So what do I have to take away

00:01:39.462 --> 00:01:43.322
from 10 in order to have six left over?

00:01:43.339 --> 00:01:45.451
Well, if I take four away from 10,

00:01:45.451 --> 00:01:48.291
I'm going to have six left over.

00:01:48.401 --> 00:01:49.920
Now something minus one

00:01:49.920 --> 00:01:52.470
is the same thing as six.

00:01:52.777 --> 00:01:54.332
Well, seven minus one

00:01:54.332 --> 00:01:56.857
is going to be equal to six.

00:01:56.857 --> 00:01:59.104
And then we get eight minus blank

00:01:59.104 --> 00:02:00.148
is equal to six.

00:02:00.148 --> 00:02:01.065
So how many do I have to take away

00:02:01.065 --> 00:02:04.780
from eight in order to get to six?

00:02:04.780 --> 00:02:05.802
Well, if I take away one,

00:02:05.802 --> 00:02:06.604
I'm going to get seven.

00:02:06.604 --> 00:02:09.457
If I take away two, I'm going to have six.

00:02:09.459 --> 00:02:13.929
So eight minus two is equal to six.


More word problems

WEBVTT
Kind: captions
Language: en

00:00:20.126 --> 00:00:23.825
Try to pause the video and figure it out
on your own.

00:00:24.082 --> 00:00:25.450
So what I like to do is

00:00:25.450 --> 00:00:27.710
I like to write down what they tell us

00:00:27.712 --> 00:00:31.802
and then think about what might make sense.

00:00:31.958 --> 00:00:33.718
So, first of all we have Emeka.

00:00:33.822 --> 00:00:41.712
They tell us that Emeka got a 17
when she spinned the wheel.

00:00:42.509 --> 00:00:47.009
So Emeka got a 17. This is Emeka's number
right over here, she got a 17.

00:00:47.009 --> 00:00:48.499
Now, what about Tom?

00:00:51.856 --> 00:00:54.121
They tell us Tom got a number

00:00:54.121 --> 00:00:58.871
that was 15 more than Emeka's number

00:00:58.892 --> 00:01:03.042
So, did Tom get a higher number or a
lower number than Emeka?

00:01:03.044 --> 00:01:06.173
Well, Tom's number is 15 more than Emeka's.

00:01:06.173 --> 00:01:08.507
So, it's going to be a larger number.

00:01:08.507 --> 00:01:11.683
So, it's going to be Emeka's number plus 15.

00:01:11.683 --> 00:01:13.743
So, 15 more than 17.

00:01:13.768 --> 00:01:18.770
So, it's Emeka's number,
and it's going to be 15 more than that.

00:01:18.770 --> 00:01:24.221
So, notice 15 more than Emeka's number

00:01:24.221 --> 00:01:26.976
Well, Emeka's number is 17.

00:01:26.976 --> 00:01:31.296
15 more than that is going to be 17 + 15.

00:01:31.300 --> 00:01:34.330
So what's 17 + 15 going to be?

00:01:34.341 --> 00:01:39.107
So, I can calculate it right over here.
So, I'll line them up.

00:01:39.107 --> 00:01:42.487
So, 17 is 1 ten and 7 ones

00:01:42.497 --> 00:01:46.617
and 15 is 1 ten and 5 ones

00:01:48.766 --> 00:01:50.306
and I'm going to add.

00:01:50.322 --> 00:01:52.762
So let's first look at the ones place.

00:01:52.772 --> 00:01:58.106
So, 7 ones + 5 ones, that's going to be
12 ones.

00:01:58.106 --> 00:02:03.016
But, 12 ones is the same thing as 1 ten
and 2 ones.

00:02:03.037 --> 00:02:07.817
So, I could write the 2 ones down here
and then I would write the 1 ten up here.

00:02:07.836 --> 00:02:11.720
Another way you could think about it is
I just carried the 1.

00:02:11.720 --> 00:02:14.713
7 + 5 is 12, I wrote the 2 down here
and I carried the 1.

00:02:14.713 --> 00:02:16.486
But what I'm really saying is

00:02:16.486 --> 00:02:21.486
look 7 + 5 is 12, 12 is 2 ones and 1 ten.

00:02:21.486 --> 00:02:25.926
And now I just add up the tens
1 ten + 1 ten + 1 ten is 3 tens

00:02:27.045 --> 00:02:29.235
So it's 32.

00:02:29.235 --> 00:02:31.065
So, Tom got a 32.

00:02:31.131 --> 00:02:34.601
And you should always check to see if
that makes sense.

00:02:35.080 --> 00:02:38.840
It says that Tom got a number that was 15
more than Emeka's number.

00:02:38.840 --> 00:02:42.813
Well, is 32, 15 more than Emeka's number?

00:02:42.813 --> 00:02:45.646
Is 32, 15 more than 17?

00:02:45.646 --> 00:02:49.362
Sure it is, because 17 + 15 is 32.

00:02:49.362 --> 00:02:52.012
That's how we figured it out.


Repeated addition example

WEBVTT
Kind: captions
Language: en

00:00:00.121 --> 00:00:03.661
- [Voiceover] There are
four seasons each year.

00:00:03.661 --> 00:00:07.944
Rafael gets a haircut
two times each season.

00:00:07.944 --> 00:00:12.763
One at Arlo's barber shop, and
the other at Awesome Snips.

00:00:12.763 --> 00:00:15.479
Which choices represent the number

00:00:15.479 --> 00:00:19.100
of haircuts Rafael will get this year?

00:00:19.100 --> 00:00:20.436
And they've even made a little

00:00:20.436 --> 00:00:22.640
diagram for us right over here.

00:00:22.640 --> 00:00:24.767
So they tell us there's
four seasons in the year,

00:00:24.767 --> 00:00:27.611
Spring, Summer, Autumn, Winter.

00:00:27.611 --> 00:00:31.535
And that each season
Rafael gets two haircuts.

00:00:31.535 --> 00:00:34.890
He gets one at Arlo's
and one at Awesome Snips.

00:00:34.890 --> 00:00:37.293
So in Spring this is
the one that he gets at

00:00:37.293 --> 00:00:39.974
Arlo's, this is the one that
he gets at Awesome Snips.

00:00:39.974 --> 00:00:42.134
And Summer, this is the
one he gets at Arlos',

00:00:42.134 --> 00:00:44.653
this is the one he gets at Awesome Snips.

00:00:44.653 --> 00:00:47.416
Autumn this is the he gets at Arlo's,

00:00:47.416 --> 00:00:49.412
this is the one at Awesome Snips.

00:00:49.412 --> 00:00:51.049
And Winter, this is the one at Arlo's,

00:00:51.049 --> 00:00:53.348
this is the one at Awesome Snips.

00:00:53.348 --> 00:00:56.691
So they ask us, which choices represent

00:00:56.691 --> 00:00:59.714
the number of haircuts
Rafael will get this year?

00:00:59.714 --> 00:01:01.974
Well one way to this about it is:

00:01:01.974 --> 00:01:05.608
In Spring he will get two haircuts then

00:01:05.608 --> 00:01:07.928
in Summer he is going to
get another 2 haircuts.

00:01:07.928 --> 00:01:10.581
In Autumn he is going to
get another two haircuts.

00:01:10.581 --> 00:01:13.138
And then in Winter he is going
to get another two haircuts.

00:01:13.138 --> 00:01:15.893
So he is going to get two in Spring,

00:01:15.893 --> 00:01:18.331
plus two in Summer, plus two in Autumn,

00:01:18.331 --> 00:01:19.967
plus two in Winter.

00:01:19.967 --> 00:01:23.404
Which is going to be
equal to eight haircuts.

00:01:23.404 --> 00:01:26.421
So which of these represent eight?

00:01:26.421 --> 00:01:29.104
Well let's see, two plus
two, that's not eight.

00:01:29.104 --> 00:01:31.611
Four plus four plus four plus four,

00:01:31.611 --> 00:01:34.049
that's not eight, that's 16.

00:01:34.049 --> 00:01:35.083
Two plus two is four.

00:01:35.083 --> 00:01:36.952
Four plus four is eight, plus four is 12

00:01:36.952 --> 00:01:39.401
plus four is 16, that's not eight.

00:01:39.401 --> 00:01:41.966
Four plus four, that is equal to eight.

00:01:41.966 --> 00:01:43.544
That is the number of haircuts

00:01:43.544 --> 00:01:45.206
Rafael is going to get this year.

00:01:45.206 --> 00:01:46.483
So we can check that one.

00:01:46.483 --> 00:01:48.526
Two plus two plus two plus two,

00:01:48.526 --> 00:01:51.428
that's exactly what we
wrote here, and it is eight.

00:01:51.428 --> 00:01:53.227
So that is equal to the number

00:01:53.227 --> 00:01:55.085
of haircuts he is going to get this year.

00:01:55.085 --> 00:01:57.348
And then two plus four, well that's not

00:01:57.348 --> 00:01:59.647
equal to eight, that's
six, so that's not right.

00:01:59.647 --> 00:02:02.770
So these are the two that represent

00:02:02.770 --> 00:02:07.770
the number of haircuts
Rafael will get this year.


Equal sign

WEBVTT
Kind: captions
Language: en

00:00:00.139 --> 00:00:02.522
- When you first learn
math, you see things like

00:00:02.523 --> 00:00:05.239
two plus three

00:00:05.239 --> 00:00:08.032
is equal to five,

00:00:08.032 --> 00:00:11.836
or you might see six plus one

00:00:11.836 --> 00:00:15.009
is equal to seven,

00:00:15.009 --> 00:00:19.026
or you might see eight minus two

00:00:19.026 --> 00:00:21.658
is equal to six.

00:00:21.658 --> 00:00:25.385
And all of these, you might
think that the equal sign

00:00:25.385 --> 00:00:26.718
just says, hey, give me the answer,

00:00:26.718 --> 00:00:28.569
figure out what two plus three is.

00:00:28.569 --> 00:00:30.124
Two plus three, well, the answer is five.

00:00:30.124 --> 00:00:31.817
Six plus one, the answer is seven.

00:00:31.817 --> 00:00:34.037
Eight minus two, the answer is six.

00:00:34.037 --> 00:00:36.476
That's not quite right.

00:00:36.476 --> 00:00:39.275
What the equal sign is saying is that

00:00:39.275 --> 00:00:43.683
what's on the left side
is the same amount,

00:00:43.683 --> 00:00:48.056
the same quantity, as what
is on the right-hand side.

00:00:48.056 --> 00:00:52.512
It's saying that two plus three
is the same thing as five.

00:00:52.512 --> 00:00:54.688
And you didn't have to write it this way.

00:00:54.688 --> 00:00:56.249
You could have written,

00:00:56.249 --> 00:01:00.740
you could have written five
is equal to two plus three.

00:01:00.740 --> 00:01:04.423
You could write that three plus two

00:01:04.423 --> 00:01:07.559
is equal to two plus three.

00:01:07.559 --> 00:01:10.390
Notice, here, we're not
figuring out the answer,

00:01:10.391 --> 00:01:13.015
we're just saying that
whatever three plus two is,

00:01:13.015 --> 00:01:14.494
that's going to be the same thing

00:01:14.494 --> 00:01:16.307
as whatever two plus three is.

00:01:16.307 --> 00:01:19.107
We know that they both equal five.

00:01:19.107 --> 00:01:21.801
You could even mix
addition and subtraction,

00:01:21.801 --> 00:01:24.047
you could write, you could write that

00:01:24.047 --> 00:01:27.594
six plus one is the same thing,

00:01:27.594 --> 00:01:31.914
is equal to, eight minus one.

00:01:31.915 --> 00:01:34.619
They are the same amount,
the same quantity.

00:01:34.619 --> 00:01:37.148
What is six plus one, well, that's seven.

00:01:37.148 --> 00:01:41.009
What's eight minus one,
well, that is seven.

00:01:41.009 --> 00:01:42.851
So the equal sign does not mean

00:01:42.851 --> 00:01:44.857
just give me the answer or just, you know,

00:01:44.857 --> 00:01:46.831
add the numbers or subtract the numbers.

00:01:46.831 --> 00:01:51.265
An equal sign is saying that
what's on the left-hand side

00:01:51.265 --> 00:01:55.429
is the same amount as what's
on the right-hand side.

00:01:55.429 --> 00:01:58.742
So with that in our brain,
let's write some statements

00:01:58.742 --> 00:02:02.434
using equal signs, some
equations, you could even say,

00:02:02.434 --> 00:02:04.207
using equal signs, and figure out

00:02:04.207 --> 00:02:07.237
which of them are actually true.

00:02:07.237 --> 00:02:11.918
So if I were to write down,
if I were to write down,

00:02:11.919 --> 00:02:13.899
I won't even read it out,
'cause it might give it away.

00:02:13.899 --> 00:02:18.041
If I were to write down
this, is this true?

00:02:19.348 --> 00:02:23.264
Well, the number on the left here is 18,

00:02:23.264 --> 00:02:26.032
the number on the left is
18, the number on the right

00:02:26.032 --> 00:02:29.848
is a different number, it is 81, it is 81.

00:02:29.848 --> 00:02:31.599
They swapped, or we swapped (chuckles),

00:02:31.599 --> 00:02:34.423
the one and the eight,
they're in different places.

00:02:34.423 --> 00:02:36.035
This is a different number, this is 81.

00:02:36.035 --> 00:02:38.077
These are not equal.

00:02:38.077 --> 00:02:41.693
These are not, not equal.

00:02:41.693 --> 00:02:43.781
So this statement is not true.

00:02:43.781 --> 00:02:45.709
And sometimes you might
even see someone do

00:02:45.709 --> 00:02:47.768
something like this, that means not equal.

00:02:47.768 --> 00:02:51.009
18 is not equal to 81.

00:02:51.009 --> 00:02:52.843
Let's keep going.

00:02:52.843 --> 00:02:54.531
What if I were to write,

00:02:54.532 --> 00:02:58.999
what if I were to write nine minus three

00:02:58.999 --> 00:03:02.671
plus two minus zero

00:03:02.671 --> 00:03:07.131
is equal to, is equal to...

00:03:07.131 --> 00:03:11.269
zero plus one minus one

00:03:11.269 --> 00:03:15.306
plus eight, is this true?

00:03:16.706 --> 00:03:19.997
Well, let's figure out
what the left-hand side is.

00:03:19.997 --> 00:03:21.861
See, nine minus three is six,

00:03:21.861 --> 00:03:25.688
plus two is eight, minus zero is eight.

00:03:25.688 --> 00:03:29.159
So this, this, if I were to, if I were

00:03:29.159 --> 00:03:31.843
to compute it, that's equal to eight.

00:03:31.843 --> 00:03:34.684
And then on the right-hand
side I have zero plus one

00:03:34.684 --> 00:03:37.593
minus one, well, one minus one is zero,

00:03:37.593 --> 00:03:40.122
so this is all going to be eight.

00:03:40.122 --> 00:03:44.228
So this is, this is
true, eight equals eight.

00:03:44.228 --> 00:03:46.223
This is another way of writing eight,

00:03:46.223 --> 00:03:50.172
nine minus three plus two
minus zero, this is eight.

00:03:50.172 --> 00:03:52.579
And this is also eight, so once again

00:03:52.580 --> 00:03:54.630
the equal sign is just saying that this,

00:03:54.630 --> 00:03:56.370
what we have on the left, is the same

00:03:56.370 --> 00:03:58.044
as what we have on the right.

00:03:58.044 --> 00:04:00.549
Let's do another example.

00:04:00.549 --> 00:04:03.291
Let's do another example,
let's do two more examples.

00:04:03.291 --> 00:04:07.101
If I were to write this,

00:04:07.101 --> 00:04:08.575
is this true?

00:04:10.020 --> 00:04:11.402
Well, you might be tempted, hey, if I put

00:04:11.402 --> 00:04:12.565
a one (chuckles) and a zero together,

00:04:12.566 --> 00:04:14.680
it's gonna look like a 10,
but that's not, this is not

00:04:14.680 --> 00:04:17.511
how we do mathematics, this
is not how we add things.

00:04:17.511 --> 00:04:21.180
One plus zero is just one, so
this would be the same thing

00:04:21.180 --> 00:04:24.059
as saying that 10 is equal
to one, which we know

00:04:24.059 --> 00:04:28.866
is not true, so this is not
equal, this is not equal.

00:04:28.866 --> 00:04:30.699
Let's do one more.

00:04:30.699 --> 00:04:34.090
Let's say I had seven plus one

00:04:34.090 --> 00:04:38.695
is equal to three plus four.

00:04:38.696 --> 00:04:41.690
Is this equation true?

00:04:41.690 --> 00:04:43.029
Well, what do we have on the left,

00:04:43.029 --> 00:04:46.171
seven plus one is eight,
three plus four is seven.

00:04:46.171 --> 00:04:48.480
These are not the same
quantity, they're not

00:04:48.480 --> 00:04:52.996
the same amount, so these are not equal.

00:04:52.996 --> 00:04:54.816
And we're done.


Telling time exercise example 2

WEBVTT
Kind: captions
Language: en

00:00:00.580 --> 00:00:02.514
We're asked, what time is it?

00:00:02.514 --> 00:00:05.180
So first, we want to look at the
hour hand, which is the shorter

00:00:05.180 --> 00:00:07.514
hand, and see where
it is pointing.

00:00:07.514 --> 00:00:08.930
So this right over
here would have

00:00:08.930 --> 00:00:14.800
been 12 o'clock, 1 o'clock, 2
o'clock, 3 o'clock, 4 o'clock.

00:00:14.800 --> 00:00:17.630
And it looks like it's a
little bit past 4 o'clock.

00:00:17.630 --> 00:00:19.780
So we are in the fourth hour.

00:00:19.780 --> 00:00:22.007
So the hour is 4.

00:00:22.007 --> 00:00:23.840
And then we have to
think about the minutes.

00:00:23.840 --> 00:00:27.390
The minutes are the longer hand,
and every one of these lines

00:00:27.390 --> 00:00:28.810
represent 5 minutes.

00:00:28.810 --> 00:00:29.600
We start here.

00:00:29.600 --> 00:00:33.700
This is 0 minutes past the hour,
then 5 minutes past the hour,

00:00:33.700 --> 00:00:35.750
then 10 minutes past the hour.

00:00:35.750 --> 00:00:40.230
So the time is-- the minutes are
10, 10 minutes past the hour,

00:00:40.230 --> 00:00:43.610
and the hour is 4, or it's 4:10.

00:00:43.610 --> 00:00:46.120
Let's do a few more.

00:00:46.120 --> 00:00:48.110
What time is it?

00:00:48.110 --> 00:00:50.110
So first, we want to
look at the hour hand.

00:00:50.110 --> 00:00:52.520
That's the shorter
hand right over here.

00:00:52.520 --> 00:00:53.430
It's at-- let's see.

00:00:53.430 --> 00:01:01.160
This is 12, 1, 2,
3, 4, 5, 6, 7, 8, 9.

00:01:01.160 --> 00:01:02.930
And it's between 9 and 10.

00:01:02.930 --> 00:01:04.720
It's just past 9.

00:01:04.720 --> 00:01:06.640
So it's still in the ninth hour.

00:01:06.640 --> 00:01:08.990
It hasn't gotten to
the 10th hour yet.

00:01:08.990 --> 00:01:12.360
The ninth hour's from starting
with 9 all the way until it's

00:01:12.360 --> 00:01:14.015
right almost before
it gets to 10,

00:01:14.015 --> 00:01:15.630
and then it gets
to the 10th hour.

00:01:15.630 --> 00:01:19.850
So the hour is 9, and
then we want the minutes.

00:01:19.850 --> 00:01:22.410
Well, we can just
count from 0 starting

00:01:22.410 --> 00:01:23.770
at the top of the clock.

00:01:23.770 --> 00:01:29.330
So 0, 5, 10, 15, 20, 25, 30.

00:01:29.330 --> 00:01:31.267
It's 9:30.

00:01:31.267 --> 00:01:32.850
And that also might
make sense to you,

00:01:32.850 --> 00:01:35.480
because we know there are
60 minutes in an hour.

00:01:35.480 --> 00:01:38.390
And this is exactly
halfway around the clock.

00:01:38.390 --> 00:01:41.080
And so half of 60 is 30.

00:01:41.080 --> 00:01:41.850
Let's do one more.

00:01:44.370 --> 00:01:46.170
What time is it?

00:01:46.170 --> 00:01:46.950
So let's count.

00:01:46.950 --> 00:01:50.160
This is 12, 1-- actually,
we can even count backwards.

00:01:50.160 --> 00:01:53.750
We can go 12, 11, 10.

00:01:53.750 --> 00:01:55.510
So right now we're
in the 10th hour.

00:01:55.510 --> 00:01:59.530
The hour hand has passed 10,
but it hasn't gotten to 11 yet.

00:01:59.530 --> 00:02:01.250
So we are in the 10th hour.

00:02:01.250 --> 00:02:03.970
And how many minutes
past the hour are we?

00:02:03.970 --> 00:02:09.340
So this would be 0, 5, 10,
15, 20 minutes past the hour.

00:02:09.340 --> 00:02:11.270
That's where the longer
hand is pointing.

00:02:11.270 --> 00:02:13.670
It is 10:20.


Introduction to addition

WEBVTT
Kind: captions
Language: en

00:00:00.833 --> 00:00:02.766
Voiceover:Let's think about what it means

00:00:02.766 --> 00:00:04.733
to add numbers.

00:00:05.434 --> 00:00:07.866
So let's start with 1.

00:00:08.567 --> 00:00:11.266
1 plus.

00:00:12.033 --> 00:00:14.267
1 plus 1.

00:00:14.900 --> 00:00:18.133
What is this going to be equal to?

00:00:19.366 --> 00:00:23.033
One way to think about this is we have

00:00:23.033 --> 00:00:28.800
1 thing, and that thing
will be a purple circle.

00:00:29.166 --> 00:00:31.533
So let me put that here.

00:00:31.633 --> 00:00:33.333
So that's this 1 thing.

00:00:33.566 --> 00:00:34.567
I'm just going to represent it with

00:00:34.567 --> 00:00:35.666
a purple circle.

00:00:35.700 --> 00:00:37.400
And I'm going to add another 1 thing.

00:00:37.700 --> 00:00:38.966
And since this is in blue, I'll make

00:00:38.966 --> 00:00:41.600
that other circle, I'll
make that in blue as well.

00:00:42.367 --> 00:00:44.667
So let me put that right over here.

00:00:45.500 --> 00:00:46.934
So 1 plus 1.

00:00:47.233 --> 00:00:48.266
1 plus 1.

00:00:48.633 --> 00:00:51.466
How many total circles do I now have?

00:00:52.100 --> 00:00:54.400
Well, I now have 2 circles.

00:00:54.966 --> 00:00:57.400
I now have 2 circles.

00:00:57.901 --> 00:01:04.266
1 plus 1 is equal to, is equal to 2.

00:01:04.701 --> 00:01:06.233
Okay, you're saying all
right Sal, all right,

00:01:06.233 --> 00:01:07.800
that makes sense.

00:01:08.033 --> 00:01:10.866
Let's do this with larger numbers.

00:01:11.499 --> 00:01:15.133
So let's say we want
to know what equals ...

00:01:15.300 --> 00:01:17.266
And I'll put a question mark over here.

00:01:17.566 --> 00:01:18.933
So, question mark.

00:01:19.500 --> 00:01:21.000
What equals ...

00:01:21.100 --> 00:01:26.334
So something is equal to, is equal to,

00:01:26.833 --> 00:01:33.667
let's say, 2, 2, 2 plus 3.

00:01:34.166 --> 00:01:38.066
Something is equal to 2 plus 3.

00:01:38.633 --> 00:01:41.400
What is this something going to be?

00:01:41.900 --> 00:01:44.100
I encourage you to pause
the video and think

00:01:44.100 --> 00:01:45.600
about it on your own.

00:01:46.366 --> 00:01:48.700
Well, you could view
this as, I have 2 objects

00:01:48.700 --> 00:01:51.066
and then we're going to
add another 3 objects.

00:01:51.366 --> 00:01:53.534
How many total objects would I have?

00:01:54.100 --> 00:01:58.300
So you have your 2 objects, which I'll use

00:01:58.300 --> 00:02:00.867
purple circles again.

00:02:01.300 --> 00:02:02.466
So let me ...

00:02:03.366 --> 00:02:09.200
Let me, so, we have 1
and 2 purple circles.

00:02:09.500 --> 00:02:11.066
This is the 2 right over here.

00:02:11.233 --> 00:02:13.800
And then to that we're
going to add 3 more.

00:02:14.233 --> 00:02:15.733
3 more circles.

00:02:15.900 --> 00:02:18.434
I'll represent those in blue because we

00:02:18.434 --> 00:02:20.066
wrote the 3, here, in blue.

00:02:20.766 --> 00:02:29.001
So that is 1, 2, and 3.

00:02:29.566 --> 00:02:33.066
So how many total circles do we now have?

00:02:33.833 --> 00:02:35.133
Well, we could count them.

00:02:35.433 --> 00:02:38.801
We have 1, 2, 3, 4, 5.

00:02:38.900 --> 00:02:40.000
In fact, let me count that.

00:02:40.034 --> 00:02:45.000
1, 2, 3, 4, 5 circles.

00:02:45.300 --> 00:02:47.033
So 2 plus 3.

00:02:47.033 --> 00:02:50.600
2 things plus another
3 things are 5 things.

00:02:50.966 --> 00:02:52.566
So our question mark, right over here,

00:02:52.566 --> 00:02:54.266
is equal to 5.

00:02:54.966 --> 00:02:56.833
So instead of writing the question mark

00:02:56.833 --> 00:02:59.469
right over here, let me clear that out.

00:02:59.766 --> 00:03:02.200
I could say 5 is equal to.

00:03:02.833 --> 00:03:10.000
I could write down that
5 is equal to 2 plus 3.


Sea monsters and superheroes

WEBVTT
Kind: captions
Language: en

00:00:00.720 --> 00:00:03.099
- Fourteen superheroes met on the moon

00:00:03.100 --> 00:00:05.457
for a top secret gathering.

00:00:05.457 --> 00:00:06.757
Fascinating.

00:00:06.757 --> 00:00:11.690
Three of them turned out to
be evil villains in disguise.

00:00:11.691 --> 00:00:12.573
Uh oh.

00:00:12.573 --> 00:00:15.150
How many were real superheroes?

00:00:15.150 --> 00:00:16.764
Real superheroes.

00:00:16.764 --> 00:00:19.921
So pause this video and see
if you can figure this out.

00:00:20.520 --> 00:00:23.737
Now you've had your try,
let's work on it together.

00:00:23.737 --> 00:00:26.302
So fourteen superheroes met on the moon.

00:00:26.303 --> 00:00:27.173
So let's write that down.

00:00:27.173 --> 00:00:29.412
Fourteen met on the moon.

00:00:29.413 --> 00:00:31.538
I'll put a little circle
around it like that.

00:00:31.538 --> 00:00:33.337
So fourteen met on the moon.

00:00:33.337 --> 00:00:36.320
Now of that fourteen, they
tell us that three of them

00:00:36.320 --> 00:00:39.292
turned out to be evil
villains in disguise.

00:00:39.292 --> 00:00:43.437
So three of them are evil villains.

00:00:43.437 --> 00:00:46.583
So of the fourteen,
we're either dealing with

00:00:46.583 --> 00:00:48.242
the three evil villains,

00:00:48.243 --> 00:00:51.203
or we're dealing with real superheroes.

00:00:51.203 --> 00:00:53.448
One way to think about it is
the fourteen are made up of

00:00:53.448 --> 00:00:56.153
evil villains or real superheroes.

00:00:56.153 --> 00:00:57.580
So this question mark right over here,

00:00:57.581 --> 00:00:59.694
this is the real superheroes.

00:00:59.694 --> 00:01:01.621
This is what we need to figure out.

00:01:01.621 --> 00:01:04.558
And so this relationship could
be written in different ways.

00:01:04.558 --> 00:01:06.102
You could write...

00:01:06.102 --> 00:01:08.853
You could write that the three villains

00:01:08.853 --> 00:01:12.393
plus the question mark, real superheroes,

00:01:12.394 --> 00:01:14.913
plus the question mark, real superheroes,

00:01:14.913 --> 00:01:18.535
is going to be equal to the
total number of characters

00:01:18.535 --> 00:01:20.416
that met on the moon.

00:01:20.416 --> 00:01:23.979
Or you could say, well if
three plus question mark

00:01:23.980 --> 00:01:28.036
is fourteen, well then
fourteen minus three,

00:01:28.036 --> 00:01:32.043
minus three, is going to
be equal to question mark.

00:01:32.043 --> 00:01:34.040
Is going to be equal to question mark.

00:01:34.040 --> 00:01:35.456
And you see it right over here.

00:01:35.456 --> 00:01:38.126
The fourteen is made up of
three and question mark.

00:01:38.126 --> 00:01:41.365
So if you take fourteen minus
three, you're just going to

00:01:41.365 --> 00:01:43.942
be left with the number
of real superheroes.

00:01:43.942 --> 00:01:46.651
So what's fourteen minus three?

00:01:46.651 --> 00:01:49.545
Well, there's several
ways you could do this.

00:01:49.546 --> 00:01:51.566
But one way is, let's
see, fourteen minus one

00:01:51.566 --> 00:01:53.052
is going to be thirteen.

00:01:53.052 --> 00:01:54.492
Fourteen minus two is twelve.

00:01:54.492 --> 00:01:56.384
Fourteen minus three is eleven.

00:01:56.384 --> 00:01:59.425
So we have eleven is equal...

00:01:59.425 --> 00:02:03.291
Eleven is equal to question mark.

00:02:03.291 --> 00:02:04.568
Or question mark is equal to eleven,

00:02:04.568 --> 00:02:06.565
or there are eleven real superheroes.

00:02:06.565 --> 00:02:08.770
Now let's do one more.

00:02:08.770 --> 00:02:10.733
Let's do one more.

00:02:11.580 --> 00:02:15.530
We found many sea monsters
in the nearby lake.

00:02:15.530 --> 00:02:18.178
Nine of them have stripes.

00:02:18.178 --> 00:02:21.526
Five of them have spots.

00:02:21.526 --> 00:02:24.945
How many sea monsters are in the lake?

00:02:25.253 --> 00:02:26.691
How many sea monsters are in the lake?

00:02:26.692 --> 00:02:28.046
So what are they telling us?

00:02:28.046 --> 00:02:29.868
So the total...

00:02:29.868 --> 00:02:31.064
How many sea monsters in the lake?

00:02:31.064 --> 00:02:32.747
This is the total number of sea monsters.

00:02:32.747 --> 00:02:34.198
This is what we're trying to figure out,

00:02:34.198 --> 00:02:36.404
the total number of sea monsters.

00:02:36.404 --> 00:02:38.261
That's how many sea
monsters are in the lake.

00:02:38.261 --> 00:02:39.422
And they tell us,

00:02:39.422 --> 00:02:42.638
they tell us that nine
of them have stripes.

00:02:42.638 --> 00:02:45.726
Nine of them have stripes.

00:02:45.726 --> 00:02:48.942
And five of them have spots.

00:02:48.942 --> 00:02:51.716
Five of them have spots.

00:02:51.716 --> 00:02:56.116
So all of the sea monsters are going to be

00:02:56.116 --> 00:02:59.935
the nine that have stripes,
plus the five that have spots.

00:02:59.935 --> 00:03:04.440
So we could write nine plus five.

00:03:04.440 --> 00:03:08.445
Nine plus five is equal to question mark.

00:03:08.445 --> 00:03:10.697
Is equal to question mark.

00:03:10.697 --> 00:03:13.123
And so what is nine plus five?

00:03:13.123 --> 00:03:15.283
Well you might have
that memorized already.

00:03:15.283 --> 00:03:16.803
That is fourteen.

00:03:16.803 --> 00:03:18.498
Or if you don't, you could
see say, well let's see.

00:03:18.498 --> 00:03:21.899
Nine plus one is going to be ten.

00:03:21.900 --> 00:03:24.221
Nine plus two is eleven,
nine plus three is twelve,

00:03:24.221 --> 00:03:27.623
nine plus four is thirteen,
nine plus five is fourteen.

00:03:27.623 --> 00:03:30.780
So you have fourteen is
equal to question mark.

00:03:30.781 --> 00:03:33.462
Or how many sea monsters are in the lake?

00:03:33.462 --> 00:03:34.981
Fourteen.


Understanding place value when subtracting tens

WEBVTT
Kind: captions
Language: en

00:00:00.511 --> 00:00:03.750
- [Voiceover] Right
here, we have 65 blocks.

00:00:03.750 --> 00:00:05.457
And you can count them if you like.

00:00:05.457 --> 00:00:09.973
But we can represent
them with the number 65.

00:00:09.973 --> 00:00:12.689
By writing a six in the tens place,

00:00:12.689 --> 00:00:15.858
we're literally saying
that we have six tens.

00:00:15.858 --> 00:00:19.689
And this is a 10, this is
a 10, this is another 10,

00:00:19.689 --> 00:00:22.931
this is another 10, this is a 10,

00:00:22.931 --> 00:00:24.914
and this is a 10.

00:00:24.914 --> 00:00:28.763
We have six groups of
ten and that makes 60.

00:00:28.763 --> 00:00:31.433
And then we have five ones.

00:00:31.723 --> 00:00:34.052
Five in that orange color.

00:00:34.514 --> 00:00:36.782
And then we have five ones.

00:00:36.782 --> 00:00:37.446
And you see them right here.

00:00:37.446 --> 00:00:39.791
One, two, three, four, five.

00:00:40.329 --> 00:00:41.195
Now let's do something inter...

00:00:41.195 --> 00:00:43.173
Well, actually, let me just
first write that down again.

00:00:43.173 --> 00:00:44.205
Just to emphasize it.

00:00:44.205 --> 00:00:46.806
We can write down that 65,

00:00:47.606 --> 00:00:50.838
65 is equal to six tens,

00:00:51.623 --> 00:00:55.485
six tens plus five ones.

00:00:56.301 --> 00:00:59.282
Plus five ones.

00:00:59.682 --> 00:01:01.804
Now, let's do something interesting.

00:01:01.804 --> 00:01:03.801
Let's start with 65,

00:01:03.801 --> 00:01:05.600
so let me write that down again,

00:01:05.600 --> 00:01:08.340
so we're gonna start with 65.

00:01:08.340 --> 00:01:10.128
I'm having trouble changing colors.

00:01:10.128 --> 00:01:12.020
We're gonna start with 65

00:01:12.020 --> 00:01:13.940
and I'm gonna subtract...

00:01:13.940 --> 00:01:16.470
I'm going to subtract 40.

00:01:16.994 --> 00:01:20.585
I'm going to subtract 40 from that.

00:01:20.585 --> 00:01:22.943
What am I really doing here?

00:01:22.943 --> 00:01:24.382
Well, I'm starting with 65,

00:01:24.382 --> 00:01:25.709
I'm starting with this,

00:01:25.709 --> 00:01:30.050
and I'm subtracting
four tens and zero ones.

00:01:30.050 --> 00:01:32.291
Let's subtract four tens from here.

00:01:32.767 --> 00:01:33.904
Let's subtract

00:01:33.904 --> 00:01:38.616
one, two, three, four.

00:01:39.186 --> 00:01:41.287
I took away four of the tens.

00:01:41.287 --> 00:01:43.992
How many tens do I have left over?

00:01:43.992 --> 00:01:46.326
Well, I have left over two tens.

00:01:46.326 --> 00:01:48.983
This is going to be equal to two tens.

00:01:49.983 --> 00:01:51.412
And how many ones do I have?

00:01:51.412 --> 00:01:53.883
Well, I still have five ones.

00:01:53.883 --> 00:01:55.729
So, I still...

00:01:55.729 --> 00:01:57.348
I still have five ones.

00:01:57.348 --> 00:01:58.446
And that makes sense.

00:01:58.446 --> 00:02:00.965
I had five ones, I took away zero ones,

00:02:00.965 --> 00:02:03.252
so I'm still going to have five ones.

00:02:03.252 --> 00:02:05.167
What is this going to be equal to?

00:02:05.167 --> 00:02:07.349
We can write 65.

00:02:08.011 --> 00:02:09.987
65.

00:02:10.449 --> 00:02:12.044
Minus 40.

00:02:12.552 --> 00:02:15.819
Minus 40 is...

00:02:15.819 --> 00:02:16.678
Let me do the...

00:02:16.678 --> 00:02:19.675
I want to do the ones
in that orange color.

00:02:19.675 --> 00:02:21.728
Minus 40 is equal to,

00:02:21.728 --> 00:02:23.102
another way of saying two tens

00:02:23.102 --> 00:02:26.201
is by putting a two in
the tens place, and a...

00:02:26.201 --> 00:02:27.619
And then we have five ones.

00:02:27.619 --> 00:02:30.125
A five in the ones place.

00:02:30.125 --> 00:02:34.639
Two tens plus five ones, or 25.


Measuring lengths with different units

WEBVTT
Kind: captions
Language: en

00:00:00.480 --> 00:00:02.442
- This is a rectangle.

00:00:02.442 --> 00:00:05.530
And yes, this is a rectangle.

00:00:05.530 --> 00:00:07.562
Let's measure the green line below

00:00:07.562 --> 00:00:10.848
using both rectangles
and a centimeter ruler.

00:00:10.848 --> 00:00:12.589
So, we have this green line

00:00:12.589 --> 00:00:14.901
and we're going to measure
it in terms of rectangles

00:00:14.901 --> 00:00:16.687
and we're going to
measure it on this ruler.

00:00:16.687 --> 00:00:17.720
And you immediately see

00:00:17.720 --> 00:00:21.040
the green line is equal
to one rectangle long,

00:00:21.040 --> 00:00:22.805
but if we measure it in centimeters

00:00:22.805 --> 00:00:25.579
it's equal to six centimeters long.

00:00:25.579 --> 00:00:29.340
So we can say the line
is one rectangle long,

00:00:29.340 --> 00:00:31.605
but it's six centimeters long

00:00:31.605 --> 00:00:32.405
and that makes sense

00:00:32.405 --> 00:00:34.924
because the rectangle is much more

00:00:34.924 --> 00:00:35.946
than a centimeter.

00:00:35.946 --> 00:00:38.663
Actually, the length of a
rectangle is six centimeters.

00:00:38.663 --> 00:00:41.042
So, the length of a rectangle is longer

00:00:41.042 --> 00:00:41.867
than a centimeter.

00:00:41.867 --> 00:00:42.505
You see that.

00:00:42.505 --> 00:00:44.119
This is the length of the rectangle,

00:00:44.119 --> 00:00:45.384
it's the same as the line,

00:00:45.384 --> 00:00:47.660
while centimeter is this length.

00:00:47.660 --> 00:00:50.039
The rectangle is actually
six centimeters long.

00:00:50.039 --> 00:00:52.559
So it takes blank rectangles,

00:00:52.559 --> 00:00:53.360
than centimeters,

00:00:53.360 --> 00:00:54.718
to measure the line.

00:00:54.718 --> 00:00:56.517
Well, since the rectangle is longer,

00:00:56.517 --> 00:00:58.456
it takes fewer rectangles than centimeters

00:00:58.456 --> 00:01:00.302
to measure the line.

00:01:00.302 --> 00:01:02.359
So it's fewer rectangles than centimeters

00:01:02.359 --> 00:01:03.345
and you see that.

00:01:03.345 --> 00:01:04.599
Fewer rectangles,

00:01:04.599 --> 00:01:06.807
one is fewer than six.

00:01:06.807 --> 00:01:07.861
It took one,

00:01:07.861 --> 00:01:08.989
it only took one rectangle

00:01:08.989 --> 00:01:09.732
to measure the line

00:01:09.732 --> 00:01:11.369
because a rectangle's so long

00:01:11.369 --> 00:01:13.249
and it took six centimeters
to measure the line.

00:01:13.249 --> 00:01:15.652
So it took fewer
rectangles than centimeters

00:01:15.652 --> 00:01:17.371
to measure the line.

00:01:17.371 --> 00:01:19.032
Let's keep going.

00:01:19.032 --> 00:01:21.968
Alright, so we have.

00:01:21.968 --> 00:01:23.268
This is a rectangle.

00:01:23.268 --> 00:01:25.033
Yes, that is a rectangle.

00:01:25.033 --> 00:01:26.716
Let's measure the blue line below

00:01:26.716 --> 00:01:29.293
using both a rectangle
and a centimeter ruler.

00:01:29.293 --> 00:01:30.849
So it's a similar idea.

00:01:30.849 --> 00:01:32.892
So, when we look at this blue line,

00:01:32.892 --> 00:01:36.955
the line is now two of
these green rectangles long.

00:01:36.955 --> 00:01:39.788
So it is two rectangles long.

00:01:39.788 --> 00:01:41.285
Now, in terms of centimeters,

00:01:41.285 --> 00:01:42.656
it is four,

00:01:42.656 --> 00:01:45.255
four centimeters long.

00:01:45.255 --> 00:01:46.869
Four centimeters long.

00:01:46.869 --> 00:01:50.375
The length of each rectangle is blank

00:01:50.375 --> 00:01:51.571
than a centimeter.

00:01:51.571 --> 00:01:53.765
Well, each rectangle is
more than a centimeter.

00:01:53.765 --> 00:01:54.589
It's longer.

00:01:54.589 --> 00:01:56.795
You see, each rectangle is
actually two centimeters.

00:01:56.795 --> 00:01:58.884
So, it's longer than a centimeter.

00:01:58.884 --> 00:02:01.724
So it takes blank
rectangles than centimeters

00:02:01.724 --> 00:02:03.273
to measure the line.

00:02:03.273 --> 00:02:04.991
Well, since each rectangle is longer,

00:02:04.991 --> 00:02:06.674
it's going to take fewer rectangles

00:02:06.674 --> 00:02:08.148
to measure the line.

00:02:08.148 --> 00:02:09.971
So we'll select fewer right over there

00:02:09.971 --> 00:02:11.109
and you see that over here.

00:02:11.109 --> 00:02:13.651
It only took two rectangles
to measure the line,

00:02:13.651 --> 00:02:15.184
but it took four centimeters.

00:02:15.184 --> 00:02:19.689
Two is fewer than four.

00:02:19.689 --> 00:02:20.802
Let's see.

00:02:20.802 --> 00:02:24.030
Let's do one more of these.

00:02:24.030 --> 00:02:25.423
These are a lot of fun.

00:02:25.423 --> 00:02:27.083
Alright, this is a rectangle.

00:02:27.083 --> 00:02:28.429
Let's measure the green line below.

00:02:28.429 --> 00:02:29.627
Same idea.

00:02:29.627 --> 00:02:33.224
The line is four rectangles long.

00:02:33.224 --> 00:02:36.869
The line is seven centimeters long.

00:02:36.869 --> 00:02:39.423
The length of each rectangle is shorter,

00:02:39.423 --> 00:02:41.188
sorry, longer than a centimeter.

00:02:41.188 --> 00:02:41.942
You see that right here.

00:02:41.942 --> 00:02:45.065
Each rectangle is more
than one centimeter.

00:02:45.065 --> 00:02:47.863
So it takes fewer
rectangles than centimeters

00:02:47.863 --> 00:02:48.745
to measure the line.

00:02:48.745 --> 00:02:49.860
So, we've seen this,

00:02:49.860 --> 00:02:52.652
we've seen this multiple times.


Comparing numbers of objects

WEBVTT
Kind: captions
Language: en

00:00:00.341 --> 00:00:02.861
Voiceover:Gavin has these horses.

00:00:02.861 --> 00:00:06.945
Is the number of horses
in each picture below

00:00:06.945 --> 00:00:11.410
more than, less than, or same as

00:00:11.410 --> 00:00:14.641
the number of horses Gavin has?

00:00:14.641 --> 00:00:19.137
Let's first look at how
many horses Gavin has.

00:00:19.137 --> 00:00:25.960
He has one, two, three,
four, five, six horses.

00:00:25.960 --> 00:00:27.300
Let's remember that

00:00:27.300 --> 00:00:30.090
and let's compare each of
these amounts of horses

00:00:30.090 --> 00:00:33.240
to the six horses that Gavin has.

00:00:33.240 --> 00:00:35.641
Let's look over here,

00:00:35.641 --> 00:00:39.296
over here we have one, two, three,

00:00:39.296 --> 00:00:41.861
four, five, six horses.

00:00:41.861 --> 00:00:44.866
This is the same number that Gavin has,

00:00:44.866 --> 00:00:46.792
they're just arranged differently.

00:00:46.792 --> 00:00:49.176
This is the same,

00:00:49.176 --> 00:00:52.884
we'll put in the Same as bucket.

00:00:52.884 --> 00:00:57.681
Now, here we have one, two,
three, four five horses.

00:00:57.681 --> 00:01:02.054
This is less than the six
horses that Gavin has,

00:01:02.054 --> 00:01:04.016
five is less than six.

00:01:04.016 --> 00:01:06.301
Here and I can just look at this

00:01:06.301 --> 00:01:08.046
and see that there's more than six

00:01:08.046 --> 00:01:09.279
but we can count them.

00:01:09.279 --> 00:01:11.618
We have one, two, three, four, five,

00:01:11.618 --> 00:01:13.986
and then another five
that's going to be 10.

00:01:13.986 --> 00:01:16.089
Or we can say one, two, three, four, five,

00:01:16.089 --> 00:01:18.746
six, seven, eight, nine, 10.

00:01:18.746 --> 00:01:20.910
Well 10 is more than six,

00:01:20.961 --> 00:01:23.183
10 is more than six,

00:01:23.183 --> 00:01:25.621
so we'll put it in the More than bucket.

00:01:25.621 --> 00:01:29.085
Now here we have four and four

00:01:29.085 --> 00:01:30.713
well that's going to be eight.

00:01:30.713 --> 00:01:32.235
One, two, three, four,

00:01:32.235 --> 00:01:33.764
five, six, seven, eight.

00:01:33.764 --> 00:01:38.290
It's again, that is more
than the six up here.

00:01:39.151 --> 00:01:40.588
That's more than six

00:01:40.588 --> 00:01:42.371
and then here we have one, two,

00:01:42.371 --> 00:01:43.775
three, four horses.

00:01:43.775 --> 00:01:46.818
Well four is less than six,

00:01:46.818 --> 00:01:48.760
so I will put that,

00:01:48.760 --> 00:01:52.485
I will put that in the less than,

00:01:52.485 --> 00:01:55.948
in the Less than bucket just like that.

00:01:55.948 --> 00:01:58.792
Let's check our answer to see how we did.

00:02:00.115 --> 00:02:01.379
We got it right.


Using crayons

WEBVTT
Kind: captions
Language: en

00:00:00.269 --> 00:00:04.229
- [Voiceover] Mrs. Henry's
class has 64 crayons.

00:00:04.230 --> 00:00:06.100
At the end of the year

00:00:06.100 --> 00:00:10.387
only 31 crayons remain.

00:00:10.387 --> 00:00:12.463
How many crayons have been used?

00:00:12.463 --> 00:00:13.479
And they give us a picture here.

00:00:13.480 --> 00:00:16.487
So, the beginning of the
year, this is 64 crayons.

00:00:16.487 --> 00:00:18.761
Six tens and four ones.

00:00:18.762 --> 00:00:21.582
One, two, three, four, five, six tens,

00:00:21.582 --> 00:00:24.353
and one, two, three, four ones.

00:00:24.353 --> 00:00:26.589
So this is 64 at the
beginning of the year,

00:00:26.589 --> 00:00:27.828
and at the end of the year

00:00:27.828 --> 00:00:29.799
only 31 crayons remain.

00:00:29.799 --> 00:00:32.500
Well, 31 is three tens and one one.

00:00:32.500 --> 00:00:33.658
Three tens.

00:00:33.658 --> 00:00:35.630
One ten, two tens, three tens,

00:00:35.630 --> 00:00:37.092
and one one.

00:00:37.092 --> 00:00:39.307
So how many have been used?

00:00:39.307 --> 00:00:43.025
And try to pause the video
and try it on your own.

00:00:43.025 --> 00:00:45.818
All right, I assume you have tried it.

00:00:45.818 --> 00:00:47.266
Let's do it together.

00:00:47.267 --> 00:00:48.912
So there's a couple of ways to do it.

00:00:48.912 --> 00:00:51.533
If we didn't have the picture here,

00:00:51.533 --> 00:00:52.590
we would say all right,

00:00:52.590 --> 00:00:57.283
she started, her class
started with 64 crayons,

00:00:57.283 --> 00:01:00.119
they used some, so if we are using crayons

00:01:00.119 --> 00:01:02.638
that would kind of
subtract the crayons away.

00:01:02.638 --> 00:01:04.791
So if you're using some crayons,

00:01:04.791 --> 00:01:07.535
you would subtract some number from 64,

00:01:07.535 --> 00:01:09.303
so I'm just gonna put a blank here.

00:01:09.303 --> 00:01:12.390
So 64 minus the number that are used

00:01:12.390 --> 00:01:15.195
is going to be equal to
the number that remain.

00:01:15.195 --> 00:01:17.348
So this is going to be
equal to what's left over,

00:01:17.348 --> 00:01:21.073
and they tell us that 31 crayons remain.

00:01:21.073 --> 00:01:22.556
31 crayons remain.

00:01:22.556 --> 00:01:25.318
So, we need to figure out what's here?

00:01:25.318 --> 00:01:26.112
What is this blank?

00:01:26.112 --> 00:01:28.448
64 minus blank is 31.

00:01:28.448 --> 00:01:31.211
Well, if 64 minus blank is 31,

00:01:31.211 --> 00:01:33.750
then I can swap the 31 and the blank.

00:01:33.750 --> 00:01:35.986
That means that 64 minus 31

00:01:38.205 --> 00:01:40.478
is going to be equal to blank.

00:01:40.478 --> 00:01:44.908
That means that 64 minus 31

00:01:47.909 --> 00:01:52.423
is going to be equal to blank.

00:01:52.423 --> 00:01:54.064
How did I do that?

00:01:54.064 --> 00:01:55.404
How do I think about that?

00:01:55.404 --> 00:01:57.213
Well, imagine 64 things.

00:01:57.213 --> 00:02:01.131
So if this block represents 64.

00:02:01.132 --> 00:02:02.976
So this is 64,

00:02:02.976 --> 00:02:04.785
just like that,

00:02:04.785 --> 00:02:07.948
and if this is 31,

00:02:11.282 --> 00:02:14.324
and then this is our blank.

00:02:14.324 --> 00:02:15.842
We know that the blank,

00:02:15.842 --> 00:02:18.483
so I could put a question
mark here if I like.

00:02:18.483 --> 00:02:19.784
I could put a question mark.

00:02:19.784 --> 00:02:21.388
So this is the question mark.

00:02:21.388 --> 00:02:24.172
So we know that 64 minus the question mark

00:02:24.172 --> 00:02:25.636
would be 31.

00:02:25.636 --> 00:02:29.319
Or that 31 plus question mark would be 64.

00:02:29.319 --> 00:02:33.259
Or that 64 minus 31 is going to get us

00:02:33.259 --> 00:02:35.460
the question mark right over here.

00:02:35.461 --> 00:02:36.619
So we just have to figure out

00:02:36.619 --> 00:02:39.158
what 64 minus 31 is.

00:02:39.158 --> 00:02:40.885
And let's do that.

00:02:40.885 --> 00:02:43.262
Let's do that right over here.

00:02:43.263 --> 00:02:46.676
So 64 minus 31,

00:02:50.721 --> 00:02:52.478
and it's going to be equal to,

00:02:52.478 --> 00:02:53.757
so let's look at that ones place.

00:02:53.757 --> 00:02:55.485
Four ones minus one one

00:02:55.485 --> 00:02:57.537
is going to be three ones.

00:02:57.537 --> 00:03:00.136
Six tens minus three tens

00:03:00.136 --> 00:03:02.677
is three tens.

00:03:02.677 --> 00:03:04.965
So the blank is 33.

00:03:04.965 --> 00:03:05.940
And you could check that,

00:03:05.940 --> 00:03:08.866
64 minus 33 is 31.

00:03:08.866 --> 00:03:12.543
Or 64 minus 31 is 33.

00:03:12.543 --> 00:03:15.611
So 33 crayons have been used.

00:03:15.611 --> 00:03:17.988
Now since they made this
neat picture for us,

00:03:17.988 --> 00:03:20.406
we actually could have
just used the picture.

00:03:20.406 --> 00:03:21.618
How would we have done that?

00:03:21.618 --> 00:03:23.427
Well, this is what they started with.

00:03:23.427 --> 00:03:24.523
This is the 64.

00:03:24.523 --> 00:03:25.924
Six tens.

00:03:25.925 --> 00:03:29.480
One, two, three, four, five, six tens,

00:03:29.480 --> 00:03:32.284
and one, two, three, four ones.

00:03:32.284 --> 00:03:33.382
So 64,

00:03:33.382 --> 00:03:35.548
and they end up with 31.

00:03:35.548 --> 00:03:37.205
So how many of the tens do we use up

00:03:37.205 --> 00:03:38.892
to go from what we started with

00:03:38.892 --> 00:03:40.273
to what we finish with?

00:03:40.273 --> 00:03:42.670
Well, we end up using, let's see,

00:03:42.670 --> 00:03:44.335
there's only three tens here.

00:03:44.336 --> 00:03:45.982
There were six tens here.

00:03:45.982 --> 00:03:49.863
So we used one, two, three tens.

00:03:49.863 --> 00:03:53.073
So we used up three tens.

00:03:53.073 --> 00:03:55.124
And how many ones do we use up?

00:03:55.124 --> 00:03:56.628
Well, we have four ones here,

00:03:56.628 --> 00:03:58.355
and we only have one right over here.

00:03:58.355 --> 00:04:00.631
So we use up three ones.

00:04:00.631 --> 00:04:03.457
We used up three ones.

00:04:03.457 --> 00:04:05.367
If you take away these three tens,

00:04:05.367 --> 00:04:06.546
and these three ones,

00:04:06.546 --> 00:04:08.495
you'll be left with the
same number of crayons

00:04:08.496 --> 00:04:10.175
that we have at the end of the year.

00:04:10.175 --> 00:04:12.085
So we use up three, I guess you could say,

00:04:12.085 --> 00:04:13.824
we used up three ten packs,

00:04:13.824 --> 00:04:16.099
and we used up three ones.

00:04:16.099 --> 00:04:17.236
So what's that going to be?

00:04:17.237 --> 00:04:19.065
Well, three tens plus three ones

00:04:19.065 --> 00:04:22.534
is 33.


Filling rectangles with squares

WEBVTT
Kind: captions
Language: en

00:00:00.654 --> 00:00:03.316
- [Voiceover] So I have
this yellow rectangle here,

00:00:03.316 --> 00:00:07.060
and I have begun to fill
it with green squares.

00:00:07.060 --> 00:00:09.678
And my question to you, and to me,

00:00:09.678 --> 00:00:11.913
is how many total green squares

00:00:11.913 --> 00:00:14.147
can I fit into this yellow rectangle

00:00:14.147 --> 00:00:15.956
if we don't make any of the green squares

00:00:15.956 --> 00:00:18.119
sit on top of each other?

00:00:18.119 --> 00:00:19.524
Well, let's see.

00:00:19.524 --> 00:00:20.283
We already have,

00:00:20.283 --> 00:00:23.835
One, two, three, four

00:00:23.835 --> 00:00:25.200
green squares.

00:00:25.200 --> 00:00:26.498
And let's add a few more.

00:00:26.498 --> 00:00:28.484
So I could put one right over here.

00:00:28.484 --> 00:00:30.801
So, that's one right over there.

00:00:30.801 --> 00:00:33.361
And then I could put
another one right over here.

00:00:33.361 --> 00:00:35.474
Put another one right over there.

00:00:35.474 --> 00:00:40.474
And so I'm gonna have, one,
two, three, four, five, six

00:00:40.508 --> 00:00:44.248
green squares can be
fit into this rectangle.

00:00:44.248 --> 00:00:46.666
Now let's look at this big yellow square.

00:00:46.666 --> 00:00:48.271
And we have the same thing going on.

00:00:48.271 --> 00:00:51.379
We've already started to
fill it with some squares,

00:00:51.379 --> 00:00:52.903
and my question to you is,

00:00:52.903 --> 00:00:56.052
how many total squares
could we fill this with?

00:00:56.052 --> 00:00:57.698
So let's start doing that.

00:00:57.698 --> 00:00:59.242
So in this space right over here,

00:00:59.242 --> 00:01:03.808
let's put more of these
squares of the same size.

00:01:04.280 --> 00:01:06.292
These squares of the same size.

00:01:06.292 --> 00:01:08.953
I'm gonna draw 'em first
and then we can count them.

00:01:08.953 --> 00:01:13.017
So there you go, and then
one more right over here.

00:01:13.079 --> 00:01:15.801
And so you could fit, now
we're ready to count them.

00:01:15.801 --> 00:01:19.824
One, two three, four, five,

00:01:19.824 --> 00:01:24.824
six, seven, eight, nine
of these smaller squares

00:01:25.188 --> 00:01:29.002
inside of this bigger yellow square.


Equal parts of circles and rectangles

WEBVTT
Kind: captions
Language: en

00:00:00.712 --> 00:00:04.034
- [Voiceover] Which circles
are divided into fourths?

00:00:04.034 --> 00:00:06.266
Select all that apply.

00:00:06.266 --> 00:00:08.033
Well to be divided into fourths,

00:00:08.033 --> 00:00:12.233
that means we have to be divided
into four equal sections.

00:00:12.233 --> 00:00:16.300
Cause a fourth is gonna be one
of the four equal sections.

00:00:16.300 --> 00:00:19.866
So all of these are
divided into four sections

00:00:19.866 --> 00:00:22.833
but not all of them are divided
into four equal sections.

00:00:22.833 --> 00:00:26.167
For example this one is
divided into four sections

00:00:26.167 --> 00:00:27.900
but this section right over here

00:00:27.900 --> 00:00:30.167
is bigger than this
section right over here.

00:00:30.167 --> 00:00:31.666
and its bigger than
this section over here.

00:00:31.666 --> 00:00:33.966
So this isn't four equal sections.

00:00:33.966 --> 00:00:36.565
But these top three, it looks
like four equal sections.

00:00:36.565 --> 00:00:38.809
It looks like each of these
four sections are equal.

00:00:38.809 --> 00:00:40.301
Each of these four sections are equal,

00:00:40.301 --> 00:00:42.308
each of these four sections are equal.

00:00:42.308 --> 00:00:46.733
So all of these up here
are divided into fourths

00:00:46.733 --> 00:00:49.334
and this one isn't so I
wont click on that one.

00:00:49.334 --> 00:00:51.130
Let's keep going, this is fun.

00:00:51.133 --> 00:00:53.533
Which squares are divided into fourths?

00:00:53.533 --> 00:00:55.066
Select all that apply.

00:00:55.066 --> 00:00:56.200
Well same idea.

00:00:56.200 --> 00:00:59.300
We have to be divided
into four equal sections.

00:00:59.300 --> 00:01:01.567
So all of these are
divided into four sections.

00:01:01.567 --> 00:01:02.966
One, two, three, four,

00:01:02.966 --> 00:01:04.834
one, two, three, four.

00:01:04.834 --> 00:01:08.233
But not all of them are divided
into four equal sections.

00:01:08.233 --> 00:01:12.243
For example, this one right
over here, this section,

00:01:12.243 --> 00:01:15.466
this little triangle is much
smaller than this section.

00:01:15.466 --> 00:01:17.840
So these aren't equal sections.

00:01:17.840 --> 00:01:20.548
But for the other three they
are four equal sections.

00:01:20.548 --> 00:01:23.600
Each of these triangles that
this squares divided into,

00:01:23.600 --> 00:01:25.034
these are all equal.

00:01:25.034 --> 00:01:27.367
They all have the same area.

00:01:27.367 --> 00:01:29.767
So that's four equal sections.

00:01:29.767 --> 00:01:32.000
Each of these smaller squares,
they all have the same area.

00:01:32.000 --> 00:01:34.033
So that's four equal sections.

00:01:34.033 --> 00:01:35.534
And then each of these four rectangles

00:01:35.534 --> 00:01:36.565
are all the same size.

00:01:36.565 --> 00:01:38.233
They all have the same area.

00:01:38.233 --> 00:01:40.366
So that's for equal sections.

00:01:40.366 --> 00:01:41.409
Let's keep going.

00:01:41.409 --> 00:01:42.813
I'm having a lot of fun.

00:01:42.838 --> 00:01:45.858
Alright, which circles
are divided into thirds?

00:01:45.858 --> 00:01:47.663
Well if your to divide to thirds,

00:01:47.663 --> 00:01:51.000
you have to be dividing
into three equal sections.

00:01:51.000 --> 00:01:53.400
So this one is divided
into four equal sections.

00:01:53.400 --> 00:01:55.533
So this is divided into fourths.

00:01:55.533 --> 00:01:56.848
So it's not thirds.

00:01:56.848 --> 00:01:59.497
This is divided into three
sections but they're not equal.

00:01:59.497 --> 00:02:00.715
This section right over here

00:02:00.715 --> 00:02:03.843
is smaller than this
section right over here.

00:02:03.843 --> 00:02:05.801
This one is divided into three sections

00:02:05.801 --> 00:02:06.866
and they're all equal.

00:02:06.866 --> 00:02:08.533
This section has the same
area as this section,

00:02:08.533 --> 00:02:10.666
has the same area as that section.

00:02:10.666 --> 00:02:12.231
So I'll check that one.

00:02:12.231 --> 00:02:13.934
This one is three sections

00:02:13.934 --> 00:02:15.968
but they're not equal just like this one.

00:02:15.968 --> 00:02:18.967
This section is much
smaller than this section.

00:02:18.967 --> 00:02:22.630
So this is the only one that
is really divided into thirds.

00:02:23.951 --> 00:02:25.650
Which circles are divided into thirds?

00:02:25.650 --> 00:02:27.176
Same idea.

00:02:27.176 --> 00:02:28.400
This is divided into fourths.

00:02:28.400 --> 00:02:29.566
These are aren't equal sections.

00:02:29.566 --> 00:02:30.884
Not equal sections.

00:02:30.884 --> 00:02:32.853
This one is divided into thirds.

00:02:32.853 --> 00:02:34.825
Let's do one more.

00:02:34.825 --> 00:02:37.168
Which rectangles are divided into fourths?

00:02:37.168 --> 00:02:39.548
Remember fourths, it needs
to be four equal sections.

00:02:39.573 --> 00:02:41.446
This looks like four equal sections.

00:02:41.471 --> 00:02:43.004
This is two equal sections.

00:02:43.004 --> 00:02:46.009
This is divided into halves not fourths.

00:02:46.009 --> 00:02:48.800
This is four equal sections.

00:02:48.800 --> 00:02:51.034
This is divided into six equal sections.

00:02:51.034 --> 00:02:52.733
So it's equal sections but not fourths.

00:02:52.733 --> 00:02:54.300
Six equal sections.

00:02:54.300 --> 00:02:57.166
So this right here is divided into sixths.

00:02:57.166 --> 00:02:59.907
So our two rectangles that
are divided into fourths,

00:02:59.907 --> 00:03:01.113
are this one and that one.

00:03:01.113 --> 00:03:03.758
Four equal sections.


Skip counting by 5 example

WEBVTT
Kind: captions
Language: en

00:00:00.442 --> 00:00:04.221
- When counting by 5s starting from 179,

00:00:04.854 --> 00:00:08.151
When counting by 5s starting from 179,

00:00:08.151 --> 00:00:10.281
which numbers will you say?

00:00:10.289 --> 00:00:11.118
So, let's do that.

00:00:11.118 --> 00:00:14.554
Let's start with 179,
and let's count by 5s.

00:00:14.885 --> 00:00:19.616
So, 179 + 5 is equal to what.

00:00:19.691 --> 00:00:21.082
Well, 179.

00:00:21.084 --> 00:00:23.545
One way I think about it, 179 + 5

00:00:23.545 --> 00:00:27.975
is the same thing as 179 + 1 + 4,

00:00:28.328 --> 00:00:31.016
and I've added 1 just so I get to 180.

00:00:31.161 --> 00:00:34.690
So, this part right here is equal to 180,

00:00:34.690 --> 00:00:37.082
so it's gonna be the
same thing as 180 + 4,

00:00:37.082 --> 00:00:39.886
so it's equal to 184.

00:00:40.635 --> 00:00:41.679
Now, let's keep going.

00:00:41.679 --> 00:00:46.504
So, we start at 179, then we go to 184.

00:00:46.973 --> 00:00:48.599
Then if we want to add 5 to that,

00:00:48.599 --> 00:00:53.010
well, 184 + 5, we add 5 in the ones place,

00:00:53.010 --> 00:00:55.791
we get 189.

00:00:56.586 --> 00:00:58.560
Now, if we add 5 again,

00:00:58.560 --> 00:01:00.092
we're gonna do just what we had over here.

00:01:00.092 --> 00:01:04.493
189 + 5,

00:01:04.493 --> 00:01:08.876
that's the same thing as 189 + 1 + 4.

00:01:09.601 --> 00:01:14.601
189 + 1 is 190, plus 4 is 194.

00:01:16.358 --> 00:01:19.046
So, this is gonna be 194.

00:01:19.748 --> 00:01:24.624
And then, if you add 5,
you're going to get 199.

00:01:24.624 --> 00:01:27.782
I just added the 5 to this
4 here in the ones place.

00:01:27.782 --> 00:01:29.453
Now, if you add 5 again.

00:01:30.373 --> 00:01:35.291
This would be 199 + 5 is the
same thing as 199 + 1 + 4.

00:01:35.807 --> 00:01:40.794
So, 199 + 1 is 200, plus 4 is 204.

00:01:41.449 --> 00:01:44.096
So, let's see which of
these numbers we see so far.

00:01:44.096 --> 00:01:46.599
So, we saw 184.

00:01:47.695 --> 00:01:49.664
We see 189.

00:01:49.971 --> 00:01:51.521
We didn't see 186.

00:01:51.898 --> 00:01:53.704
We saw 194.

00:01:54.893 --> 00:01:56.815
We saw 199.

00:01:58.237 --> 00:02:01.296
and we saw 204.

00:02:02.045 --> 00:02:03.781
And we are done.


Adding 5 + 3 + 6

WEBVTT
Kind: captions
Language: en

00:00:00.476 --> 00:00:02.229
- [Voiceover] So we have
three different shapes.

00:00:02.229 --> 00:00:06.351
We have stars, we have
squares and we have triangles.

00:00:06.351 --> 00:00:08.409
Now we have a different
number of each shape.

00:00:08.409 --> 00:00:12.039
So we have five stars,
we have three squares

00:00:12.039 --> 00:00:13.769
and we have six triangles.

00:00:13.769 --> 00:00:14.860
You don't see them all here.

00:00:14.860 --> 00:00:16.095
This is just telling us how many

00:00:16.095 --> 00:00:18.157
of each of these shapes that we have.

00:00:18.157 --> 00:00:21.976
So we have five stars, three
squares and six triangles,

00:00:21.976 --> 00:00:25.211
how many total shapes do we have?

00:00:25.211 --> 00:00:26.539
Well, you're probably saying,

00:00:26.539 --> 00:00:28.373
maybe I should add these numbers,

00:00:28.373 --> 00:00:30.787
because I'm trying to find
the total number of shapes.

00:00:30.787 --> 00:00:33.771
And if you said that I
would say you are right.

00:00:33.771 --> 00:00:35.536
So let's add those numbers.

00:00:35.536 --> 00:00:39.210
So we want to add five

00:00:39.210 --> 00:00:44.210
plus three plus six.

00:00:45.354 --> 00:00:47.200
So what is this going to be?

00:00:47.200 --> 00:00:49.394
Well what's five plus three,

00:00:49.394 --> 00:00:51.913
five triangles plus three squares.

00:00:51.913 --> 00:00:55.152
Well five plus three is eight,

00:00:55.152 --> 00:00:56.800
so this is going to be eight

00:00:56.800 --> 00:00:58.890
and then we still have to add six.

00:00:58.890 --> 00:01:02.175
So we're still going to add six.

00:01:02.175 --> 00:01:04.277
Now what's eight plus six?

00:01:04.277 --> 00:01:06.192
Well you may or may not know this,

00:01:06.192 --> 00:01:07.051
and if you don't this,

00:01:07.051 --> 00:01:09.779
well you could count
things out if you like,

00:01:09.779 --> 00:01:11.196
but it is a good thing to know

00:01:11.196 --> 00:01:12.612
just off of the top of your head.

00:01:12.612 --> 00:01:14.017
So if you don't know it yet,

00:01:14.017 --> 00:01:16.455
put this in your brain.

00:01:16.455 --> 00:01:19.612
Eight plus six is 14.

00:01:19.612 --> 00:01:23.315
Eight plus six is equal to 14.

00:01:23.315 --> 00:01:28.156
So five plus three plus
six is also equal to 14.

00:01:28.156 --> 00:01:30.397
Now one question you might have is,

00:01:30.397 --> 00:01:34.089
well does it matter the
order that I do this in?

00:01:34.089 --> 00:01:35.958
Well let's try it the other way around.

00:01:35.958 --> 00:01:37.327
Let's try it again.

00:01:37.327 --> 00:01:42.327
Let's try five plus three

00:01:44.847 --> 00:01:48.300
plus six.

00:01:48.300 --> 00:01:50.413
Instead of adding the
five and the three first,

00:01:50.413 --> 00:01:52.758
let's add the three and the six first.

00:01:52.758 --> 00:01:55.393
So what is three plus six?

00:01:55.393 --> 00:01:57.936
Well that's going to be nine.

00:01:57.936 --> 00:02:00.676
Then we're going to have five plus nine.

00:02:00.676 --> 00:02:03.450
Five plus nine.

00:02:03.450 --> 00:02:07.095
Well, once again, if you know
that, you'll know it's 14,

00:02:07.095 --> 00:02:08.779
If you don't know that,
that's another good thing

00:02:08.779 --> 00:02:11.228
to put in your brain and just to know.

00:02:11.228 --> 00:02:14.177
Five plus nine is equal to 14.

00:02:14.177 --> 00:02:15.013
If you don't know that,

00:02:15.013 --> 00:02:16.348
and you don't believe me

00:02:16.348 --> 00:02:18.368
take some pebbles out and five pebbles

00:02:18.368 --> 00:02:19.888
and then nine more, and you'll see

00:02:19.888 --> 00:02:21.595
that when you add them
together, you get to 14.

00:02:21.595 --> 00:02:24.648
But this is just a good thing
for you to know in your brain.

00:02:24.648 --> 00:02:26.111
And you could have done
it the other way around.

00:02:26.111 --> 00:02:28.189
You could have added five and six first,

00:02:28.189 --> 00:02:31.950
you get 11 plus three
would have also been 14.

00:02:31.950 --> 00:02:35.849
Either way, you have 14 total shapes.


Count by category

WEBVTT
Kind: captions
Language: en

00:00:00.721 --> 00:00:03.275
- [Voiceover] We count the most

00:00:03.275 --> 00:00:06.907
stars, numbers or letters?

00:00:07.274 --> 00:00:08.487
So let's see this.

00:00:08.487 --> 00:00:10.275
Let's count each of these.

00:00:10.275 --> 00:00:12.748
So, if we look at the number of stars.

00:00:12.748 --> 00:00:17.748
So we have one, two, three stars.

00:00:19.056 --> 00:00:21.280
How many numbers do we have?

00:00:21.280 --> 00:00:25.246
We have one, two numbers,

00:00:25.246 --> 00:00:26.567
two numbers

00:00:26.567 --> 00:00:28.873
How many letters do we have?

00:00:28.873 --> 00:00:32.377
We have one, two letters.

00:00:32.817 --> 00:00:34.588
So what do we have the most of?

00:00:34.588 --> 00:00:35.912
We have the most stars.

00:00:35.912 --> 00:00:38.473
Three stars, only two
numbers and two letters.

00:00:38.473 --> 00:00:42.407
We have the most number of stars.