Radians as ratio of arc length to radius

WEBVTT
Kind: captions
Language: en

00:00:00.870 --> 00:00:01.940
- [Instructor] What we're
going to do in this video

00:00:01.940 --> 00:00:05.040
is think about a way to measure angles.

00:00:05.040 --> 00:00:07.010
And there's several ways to do this.

00:00:07.010 --> 00:00:08.410
You might have seen this

00:00:08.410 --> 00:00:11.500
leveraging things like
degrees in other videos,

00:00:11.500 --> 00:00:13.440
but now we're going to
introduce a new concept.

00:00:13.440 --> 00:00:14.830
Or maybe you know this concept,

00:00:14.830 --> 00:00:17.190
another way of looking at this concept.

00:00:17.190 --> 00:00:20.510
So we have this angle ABC

00:00:20.510 --> 00:00:22.210
and we want to think about what is a way

00:00:22.210 --> 00:00:24.903
to figure out a measure of angle ABC.

00:00:26.010 --> 00:00:28.010
Now one way to think about it would be,

00:00:28.010 --> 00:00:31.920
well, this angle subtends some arc.

00:00:31.920 --> 00:00:36.920
In this case it subtends arc AC.

00:00:37.500 --> 00:00:40.670
And we could see if
this angle were smaller,

00:00:40.670 --> 00:00:45.280
if its measure were smaller,
it would subtend a smaller arc.

00:00:45.280 --> 00:00:47.500
The length of that arc would be smaller.

00:00:47.500 --> 00:00:51.530
And if the angle were wider
or had a larger measure,

00:00:51.530 --> 00:00:52.910
if it looked something like that,

00:00:52.910 --> 00:00:55.520
then the arc length would be larger.

00:00:55.520 --> 00:00:59.620
So should we define the
measure of an angle like this

00:00:59.620 --> 00:01:04.620
as being equal to the length
of the arc that it subtends?

00:01:07.030 --> 00:01:09.190
Is this a good measure?

00:01:09.190 --> 00:01:12.160
Well some of you might immediately
see a problem with that

00:01:12.160 --> 00:01:13.730
because this length,

00:01:13.730 --> 00:01:16.340
the length of the arc that is subtended,

00:01:16.340 --> 00:01:18.770
is not just dependent on the angle,

00:01:18.770 --> 00:01:20.000
the measure of the angle,

00:01:20.000 --> 00:01:22.680
it also depends on how big of
a circle you're dealing with.

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If the radius is larger

00:01:24.220 --> 00:01:26.480
then you're gonna have
a larger arc length.

00:01:26.480 --> 00:01:29.743
For example, let me introduce
another circle here.

00:01:30.900 --> 00:01:33.490
So we have the same angle measure,

00:01:33.490 --> 00:01:35.110
the central angle right over here,

00:01:35.110 --> 00:01:37.620
you could say angle ABC is still the same,

00:01:37.620 --> 00:01:40.280
but now it subtends a different arc

00:01:40.280 --> 00:01:42.070
in these two different circles.

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You have this arc right over here.

00:01:45.230 --> 00:01:48.283
Let's call this arc DE,

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and the length of arc DE

00:01:54.210 --> 00:01:58.670
is not equal to the length of AC.

00:01:58.670 --> 00:02:00.510
And so we can't measure an angle

00:02:00.510 --> 00:02:03.840
just by the length of
the arc that it subtends

00:02:03.840 --> 00:02:06.620
if that angle is a
central angle in a circle.

00:02:06.620 --> 00:02:08.950
So we can get rid of that equality here.

00:02:08.950 --> 00:02:11.040
But what could we do?

00:02:11.040 --> 00:02:14.020
Well you might realize that these two pis

00:02:14.020 --> 00:02:15.070
that I just created,

00:02:15.070 --> 00:02:19.760
you could kind of say pi ABC and pi DBE,

00:02:19.760 --> 00:02:21.930
these are similar pis.

00:02:21.930 --> 00:02:24.770
Now we're not used to talking
in terms of similar pis,

00:02:24.770 --> 00:02:26.450
but what does it mean to be similar?

00:02:26.450 --> 00:02:30.320
Well, you have similarity
if you can map one thing

00:02:30.320 --> 00:02:33.190
on to another, one shape on to another,

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through not just rigid transformations,

00:02:35.440 --> 00:02:37.550
but also through dilations.

00:02:37.550 --> 00:02:40.223
And in this situation, if
you were to take pi ABC

00:02:41.380 --> 00:02:44.880
and just dilate it by a
scale factor larger than one

00:02:44.880 --> 00:02:47.480
there's some scale factor
where you would dilate it out

00:02:47.480 --> 00:02:49.393
to pi DBE.

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And what's interesting about that is

00:02:52.800 --> 00:02:54.340
if two things are similar

00:02:54.340 --> 00:02:56.890
that means the ratio
between corresponding parts

00:02:56.890 --> 00:02:58.690
are going to be the same.

00:02:58.690 --> 00:03:03.203
So for example, the ratio
of the length of arc AC

00:03:05.960 --> 00:03:10.630
to segment, the length of segment BC

00:03:10.630 --> 00:03:15.630
is going to be equal to
the ratio of the length

00:03:15.830 --> 00:03:20.830
of arc DE to the length of segment BE.

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So maybe this is a good measure

00:03:29.760 --> 00:03:31.610
for an angle.

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And it is indeed a measure that we use

00:03:34.540 --> 00:03:38.130
in geometry and trigonometry
and throughout mathematics

00:03:38.130 --> 00:03:43.130
and we call it the radian
measure of an angle.

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And it equals the ratio

00:03:55.340 --> 00:04:00.340
of the arc length subtended

00:04:03.420 --> 00:04:06.020
by that angle to the radius.

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We just saw that in both
of these situations.

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So let's see if we can make
this a little bit more tangible.

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Let's say we had a circle here

00:04:22.480 --> 00:04:24.020
and it has a central point.

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Let's just call that
point, I don't know, F.

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And then let me create an angle here.

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And actually I could make a right angle.

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So let's call that F.

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And let's see, call this point G,

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and let's call this H.

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And let's say that the radius
over here is two meters.

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And now what would be the
length of the arc subtended

00:04:46.920 --> 00:04:48.683
by angle GFH?

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Well this could even be
one 1/4 the circumference

00:04:53.010 --> 00:04:55.480
of this entire circle, the
way that I've drawn it.

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So the entire circumference,

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you could write it here,

00:04:58.293 --> 00:04:59.200
the circumference is going to be equal

00:04:59.200 --> 00:05:03.040
to 2 pi times the radius,

00:05:03.040 --> 00:05:04.463
which is going to be
two pi times two meters

00:05:04.463 --> 00:05:08.050
so it's going to be four pi meters.

00:05:08.050 --> 00:05:12.310
And so if this arc length is 1/4 of that

00:05:12.310 --> 00:05:15.403
this is going to be pi meters.

00:05:16.450 --> 00:05:20.870
And so based on this arc
length and this radius,

00:05:20.870 --> 00:05:25.333
what is going to be the measure
of angle GFH in radians?

00:05:28.750 --> 00:05:33.750
Well we could say the measure
of angle GFH in radians

00:05:33.780 --> 00:05:35.250
is gonna be the ratio

00:05:35.250 --> 00:05:39.870
between the length of the
arc subtended and the radius.

00:05:39.870 --> 00:05:44.870
And so it's going to be
pi meters over two meters.

00:05:47.100 --> 00:05:50.130
The meters, you could view
those as canceling out.

00:05:50.130 --> 00:05:52.490
Which equals pi over two,

00:05:52.490 --> 00:05:54.120
and pi over two what?

00:05:54.120 --> 00:05:59.120
Well we would say this is
equal to pi over two radians!

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Now one thing to think about
is why do we call it radians.

00:06:03.870 --> 00:06:06.600
It seems close to the word radius.

00:06:06.600 --> 00:06:10.100
And one way to think about it
is when you divide this length

00:06:10.100 --> 00:06:12.310
by the length of the radius

00:06:12.310 --> 00:06:15.280
you're figuring out how many
of the radii is equivalent

00:06:15.280 --> 00:06:17.400
to the arc length in question.

00:06:17.400 --> 00:06:21.690
So, for example, in
this situation one radii

00:06:21.690 --> 00:06:22.930
would look something like this.

00:06:22.930 --> 00:06:24.380
If you took the same length

00:06:24.380 --> 00:06:26.160
and you just went around like this,

00:06:26.160 --> 00:06:29.840
so you can see it's going to
be one point something radii.

00:06:29.840 --> 00:06:31.170
And that's why you could also say

00:06:31.170 --> 00:06:33.150
it's one point something radians.

00:06:33.150 --> 00:06:34.880
If you took pi divided by two

00:06:34.880 --> 00:06:36.480
you're going to get a little bit over one.

00:06:36.480 --> 00:06:38.320
You're gonna get one point, I don't know,

00:06:38.320 --> 00:06:39.753
O, seven, something.


Dilating a triangle example

WEBVTT
Kind: captions
Language: en

00:00:00.340 --> 00:00:02.320
- [Instructor] We are
asked to draw the image

00:00:02.320 --> 00:00:05.240
of triangle ABC under a dilation

00:00:05.240 --> 00:00:10.240
whose center is P and scale factor is 1/4.

00:00:10.340 --> 00:00:11.810
So pause this video, and at least think

00:00:11.810 --> 00:00:13.010
about how you would do this.

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You don't have access
to the tool that I do

00:00:14.780 --> 00:00:16.040
where I can move this around.

00:00:16.040 --> 00:00:18.470
This is actually from the
Khan Academy exercise.

00:00:18.470 --> 00:00:20.950
But at least think about
how you would do this.

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Draw the image of triangle A, B, C

00:00:24.780 --> 00:00:26.980
under a dilation whose center is P

00:00:26.980 --> 00:00:29.113
and scale factor is 1/4.

00:00:30.560 --> 00:00:32.500
All right, now let's work
through this together.

00:00:32.500 --> 00:00:34.920
So one way to think about it is

00:00:34.920 --> 00:00:36.530
our center of dilation is P,

00:00:36.530 --> 00:00:38.270
and our scale factor is 1/4,

00:00:38.270 --> 00:00:40.120
so for each of these points,

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however far they were from P before,

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they're now going to be 1/4 as far.

00:00:45.190 --> 00:00:47.070
And one way to think about it is

00:00:47.070 --> 00:00:49.840
is to think about it in each
of the x and the y dimensions.

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So for example, point A right over here,

00:00:52.580 --> 00:00:54.700
to get from point P to point A,

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you have to go one, two,
three, four to the right

00:00:58.040 --> 00:01:02.630
and one, two, three, four down.

00:01:02.630 --> 00:01:05.090
So 1/4 of that in the
x and the y direction,

00:01:05.090 --> 00:01:07.200
instead of going four to
the right and four down,

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1/4 of that would be one
to the right and one down

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'cause one is 1/4 of four.

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So instead of four to the
right, we'd go one to the right,

00:01:16.230 --> 00:01:19.670
and instead of four down,
we would go one down.

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So this is what point
A would get mapped to,

00:01:22.430 --> 00:01:24.450
and now let's think about point B.

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In order to go from P to point B,

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you have to go in the Y
direction up one, two, three,

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four, five, six, seven, eight.

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Well, what's 1/4 of eight?

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It's two, so now we're gonna go up two,

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and to go from P to B,

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how much do we have to
go in the x direction?

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Well, we have to go to the
left one, two, three, four.

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So instead of going four to the left,

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we're now going to go 1/4 of that

00:01:52.460 --> 00:01:54.480
or just one to the left.

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So instead of eight up and four left,

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we're now going two up
and one to the left,

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1/4 in each direction.

00:02:01.740 --> 00:02:05.100
And then last but not
least, to go from P to C,

00:02:05.100 --> 00:02:09.240
it looks like we're going
one, two, three, four,

00:02:09.240 --> 00:02:12.120
five, six, seven, eight to the left,

00:02:12.120 --> 00:02:15.800
and one, two, three, four up.

00:02:15.800 --> 00:02:17.490
So if we take 1/4 of each of those,

00:02:17.490 --> 00:02:19.040
instead of eight to the left,

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we're now going to go two to the left.

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Instead of four up, we're
now going to go one up.

00:02:24.630 --> 00:02:25.650
And we're done.

00:02:25.650 --> 00:02:29.210
We have just created the
image of triangle ABC

00:02:29.210 --> 00:02:30.850
under a dilation whose
center is P (chuckling)

00:02:30.850 --> 00:02:32.803
and scale factor is 1/4.


Proving triangle congruence

WEBVTT
Kind: captions
Language: en

00:00:00.670 --> 00:00:02.270
- [Instructor] What I would
like to do in this video

00:00:02.270 --> 00:00:05.070
is to see if we can prove

00:00:05.070 --> 00:00:07.730
that triangle DCA

00:00:09.919 --> 00:00:13.107
is congruent to triangle BAC.

00:00:15.690 --> 00:00:16.560
Pause this video

00:00:16.560 --> 00:00:18.910
and see if you can figure
that out on your own.

00:00:20.050 --> 00:00:22.910
All right, now let's work
through this together.

00:00:22.910 --> 00:00:25.070
So let's see what we can figure out.

00:00:25.070 --> 00:00:29.460
We see that segment DC is
parallel to segment AB,

00:00:29.460 --> 00:00:31.420
that's what these little arrows tell us,

00:00:31.420 --> 00:00:35.240
and so you can view this segment AC

00:00:35.240 --> 00:00:38.570
as something of a transversal
across those parallel lines,

00:00:38.570 --> 00:00:41.500
and we know that alternate interior angles

00:00:41.500 --> 00:00:44.010
would be congruent, so we know for example

00:00:44.010 --> 00:00:45.270
that the measure of this angle

00:00:45.270 --> 00:00:47.620
is the same as the measure of this angle,

00:00:47.620 --> 00:00:50.690
or that those angles are congruent.

00:00:50.690 --> 00:00:53.120
We also know that both of these triangles,

00:00:53.120 --> 00:00:58.120
both triangle DCA and triangle
BAC, they share this side,

00:00:58.880 --> 00:01:02.680
which by reflexivity is going
to be congruent to itself,

00:01:02.680 --> 00:01:03.513
so in both triangles,

00:01:03.513 --> 00:01:07.910
we have an angle and a
side that are congruent,

00:01:07.910 --> 00:01:10.253
but can we figure out anything else?

00:01:11.450 --> 00:01:12.820
Well you might be tempted

00:01:12.820 --> 00:01:14.770
to make a similar argument thinking

00:01:14.770 --> 00:01:17.910
that this is parallel to that
'cause it looks parallel,

00:01:17.910 --> 00:01:20.040
but you can't make that
assumption just based

00:01:20.040 --> 00:01:20.873
on how it looks.

00:01:20.873 --> 00:01:22.080
If you did know that,

00:01:22.080 --> 00:01:24.330
then you would be able to
make some other assumptions

00:01:24.330 --> 00:01:27.580
about some other angles here
and maybe prove congruency.

00:01:27.580 --> 00:01:30.450
But it turns out, given the
information that we have,

00:01:30.450 --> 00:01:33.820
we can't just assume that
because something looks parallel,

00:01:33.820 --> 00:01:36.600
that, or because something
looks congruent that they are,

00:01:36.600 --> 00:01:38.610
and so based on just
the information given,

00:01:38.610 --> 00:01:41.680
we actually can't prove congruency.

00:01:41.680 --> 00:01:44.470
Now let me ask you a
slightly different question.

00:01:44.470 --> 00:01:45.580
Let's say

00:01:45.580 --> 00:01:49.210
that we did give you a
little bit more information.

00:01:49.210 --> 00:01:51.410
Let's say we told you that the measure

00:01:51.410 --> 00:01:54.780
of this angle right
over here is 31 degrees,

00:01:54.780 --> 00:01:58.110
and the measure of this angle
right over here is 31 degrees.

00:01:58.110 --> 00:02:02.070
Can you now prove that
triangle DCA is congruent

00:02:02.070 --> 00:02:03.173
to triangle BAC?

00:02:05.620 --> 00:02:08.340
So let's see what we can deduce now.

00:02:08.340 --> 00:02:12.040
Well we know that AC is in both triangles,

00:02:12.040 --> 00:02:14.540
so it's going to be congruent to itself,

00:02:14.540 --> 00:02:16.000
and let me write that down.

00:02:16.000 --> 00:02:19.610
We know that segment AC

00:02:19.610 --> 00:02:23.320
is congruent to segment AC,

00:02:23.320 --> 00:02:28.053
it sits in both triangles,
and this is by reflexivity,

00:02:29.430 --> 00:02:31.180
which is a fancy way of
saying that something

00:02:31.180 --> 00:02:33.750
is going to be congruent to itself.

00:02:33.750 --> 00:02:38.750
Now we also see that AB is
parallel to DC just like before,

00:02:39.000 --> 00:02:42.830
and AC can be viewed as
part of a transversal,

00:02:42.830 --> 00:02:45.867
so we can deduce that angle CAB,

00:02:47.435 --> 00:02:49.910
lemme write this down, I should
be doing different color,

00:02:49.910 --> 00:02:51.577
we can deduce that angle CAB,

00:02:53.832 --> 00:02:54.665
CAB,

00:02:56.280 --> 00:02:59.293
is congruent to angle ACD,

00:03:00.780 --> 00:03:03.730
angle ACD,

00:03:03.730 --> 00:03:08.297
because they are alternate,
alternate interior, interior,

00:03:09.970 --> 00:03:14.970
angles, where a transversal
intersects two parallel lines.

00:03:15.530 --> 00:03:17.453
So, just to be clear,

00:03:18.350 --> 00:03:21.050
this angle, which is CAB,

00:03:21.050 --> 00:03:25.290
is congruent to this angle, which is ACD.

00:03:25.290 --> 00:03:29.850
And so now, we have two angles and a side,

00:03:29.850 --> 00:03:33.520
two angles and a side, that are congruent,

00:03:33.520 --> 00:03:38.300
so we can now deduce by
angle-angle-side postulate

00:03:38.300 --> 00:03:40.860
that the triangles are indeed congruent.

00:03:40.860 --> 00:03:45.860
So we now know that triangle
DCA is indeed congruent

00:03:47.320 --> 00:03:48.720
to triangle BAC

00:03:50.470 --> 00:03:54.730
because of angle-angle-side congruency,

00:03:54.730 --> 00:03:57.020
which we've talked about
in previous videos,

00:03:57.020 --> 00:03:57.853
and just to be clear,

00:03:57.853 --> 00:03:59.940
sometimes people like
the two-column proofs,

00:03:59.940 --> 00:04:01.230
I can make this look a little bit more

00:04:01.230 --> 00:04:06.230
like a two column-proof by
saying these are my statements,

00:04:06.400 --> 00:04:11.400
statement, and this is my
rationale right over here.

00:04:11.940 --> 00:04:12.893
And we're done.


Applying volume of solids

WEBVTT
Kind: captions
Language: en

00:00:00.900 --> 00:00:03.600
- [Instructor] We're told that
a cone-shaped grain hopper,

00:00:03.600 --> 00:00:06.710
and they highlight hopper in
blue here, in case you want

00:00:06.710 --> 00:00:08.860
to know its definition on the exercise.

00:00:08.860 --> 00:00:10.450
It's something that would store grain,

00:00:10.450 --> 00:00:12.770
and then it can kind
of fall out the bottom,

00:00:12.770 --> 00:00:17.660
has a radius of 10 meters at
the top and is 8 meters tall.

00:00:17.660 --> 00:00:18.640
So let's draw that.

00:00:18.640 --> 00:00:22.430
So it's cone-shaped, and
it has a radius at the top,

00:00:22.430 --> 00:00:25.000
so the top must be where the base is.

00:00:25.000 --> 00:00:25.990
I guess one would think about it.

00:00:25.990 --> 00:00:28.040
It must be the wider part of the cone.

00:00:28.040 --> 00:00:32.400
So it looks like this,
something like that.

00:00:32.400 --> 00:00:34.470
That's what this first sentence tells us.

00:00:34.470 --> 00:00:37.170
It has a radius of 10
meters, so this distance

00:00:37.170 --> 00:00:42.170
right over here is 10 meters,
and the height is 8 meters.

00:00:43.690 --> 00:00:45.740
They say it's 8 meters tall,

00:00:45.740 --> 00:00:49.840
so this right over here is 8 meters.

00:00:49.840 --> 00:00:51.640
Then they tell us it is filled up

00:00:51.640 --> 00:00:54.727
to 2 meters from the top with grain.

00:00:54.727 --> 00:00:59.320
So one way to think about it,
it's filled about this high

00:00:59.320 --> 00:01:03.868
with grain, so it's filled
about that high with grain,

00:01:03.868 --> 00:01:08.868
so this distance is going
to be 8 minus these 2,

00:01:09.670 --> 00:01:12.319
so this is going to be 6 meters high.

00:01:12.319 --> 00:01:15.050
That's what that second sentence tells us.

00:01:15.050 --> 00:01:17.750
The hopper will pour the grain
into boxes with dimensions

00:01:17.750 --> 00:01:22.120
of 0.5 meters by 0.5 meters by 0.4 meters.

00:01:22.120 --> 00:01:24.010
The hopper pours grain at a rate

00:01:24.010 --> 00:01:26.552
of 8 cubic meters per minute.

00:01:26.552 --> 00:01:28.736
So, a lot of information there.

00:01:28.736 --> 00:01:30.830
The first question is what is the volume

00:01:30.830 --> 00:01:32.659
of grain in the hopper?

00:01:32.659 --> 00:01:34.570
Before we even get to
these other questions,

00:01:34.570 --> 00:01:35.560
let's see if we can answer that.

00:01:35.560 --> 00:01:38.360
So that's going to be this
volume right over here,

00:01:38.360 --> 00:01:41.310
of the red part, the cone
made up of the grain.

00:01:41.310 --> 00:01:44.120
Pause this video and try to figure it out.

00:01:44.120 --> 00:01:45.510
Well, from previous videos,

00:01:45.510 --> 00:01:47.840
we know that volume of
a cone is going to be

00:01:47.840 --> 00:01:52.320
1/3 times the area of the
base, times the height.

00:01:52.320 --> 00:01:55.980
Now we know the height is
6 meters, but what we need

00:01:55.980 --> 00:01:58.080
to do is figure out the area of the base.

00:01:58.080 --> 00:01:59.510
Well, how do we do that?

00:01:59.510 --> 00:02:03.270
Well, we'd have to figure
out the radius of the base.

00:02:03.270 --> 00:02:06.211
Let's call that r, right over here.

00:02:06.211 --> 00:02:08.310
And how do we figure that out?

00:02:08.310 --> 00:02:10.770
Well, we can look at these two triangles

00:02:10.770 --> 00:02:11.880
that you can see on my screen,

00:02:11.880 --> 00:02:14.570
and realize that they
are similar triangles.

00:02:14.570 --> 00:02:18.000
This line is parallel to that line.

00:02:18.000 --> 00:02:19.150
This is a right angle.

00:02:19.150 --> 00:02:21.410
This is a right angle,
because both of these cuts

00:02:21.410 --> 00:02:24.550
of these surfaces are going
to be parallel to the ground,

00:02:24.550 --> 00:02:27.470
and then this angle's going
to be converted to this angle,

00:02:27.470 --> 00:02:29.180
'cause you could view
this line as a transversal

00:02:29.180 --> 00:02:32.150
between parallel lines, and
these are corresponding angles.

00:02:32.150 --> 00:02:34.140
And then both triangles share this.

00:02:34.140 --> 00:02:35.580
So you have angle, angle, angle.

00:02:35.580 --> 00:02:36.960
These are similar triangles,

00:02:36.960 --> 00:02:40.400
and so we can set up a proportion here.

00:02:40.400 --> 00:02:43.500
We can say the ratio
between r and 10 meters,

00:02:43.500 --> 00:02:48.282
the ratio of r to 10, is
equal to the ratio of 6 to 8.

00:02:48.282 --> 00:02:51.410
Is equal to the ratio of 6 to 8,

00:02:51.410 --> 00:02:53.420
and then we could try to solve for r.

00:02:53.420 --> 00:02:58.100
R is going to be equal
to, r is equal to...

00:02:58.100 --> 00:03:00.131
Multiply both sides by 10.

00:03:00.131 --> 00:03:01.850
Multiply both sides by 10,

00:03:01.850 --> 00:03:05.160
and you're going to get 60 over 8.

00:03:05.160 --> 00:03:08.520
60 over 8, 8 goes into 60
seven times with 4 left over.

00:03:08.520 --> 00:03:13.520
So it's 7 4/8, or it's also 7.5,

00:03:13.610 --> 00:03:15.010
and so if you want to know

00:03:15.010 --> 00:03:16.790
the area of the base right over here,

00:03:16.790 --> 00:03:18.690
if you wanted to know this b,

00:03:18.690 --> 00:03:21.480
it would be pi times the radius squared,

00:03:21.480 --> 00:03:26.480
so b in this case, is
going to be pi times 7.5,

00:03:26.990 --> 00:03:28.900
we're dealing with meters squared,

00:03:28.900 --> 00:03:31.670
and so the volume, to
answer the first question,

00:03:31.670 --> 00:03:35.560
the volume's going to be 1/3
times the area of the base,

00:03:35.560 --> 00:03:40.560
this area up here, which is
pi times 7.5 meters squared,

00:03:43.320 --> 00:03:47.333
times the height, so times 6 meters.

00:03:47.333 --> 00:03:50.160
And let's see, we could
simplify this a little bit.

00:03:50.160 --> 00:03:53.330
6 divided by 3, or 6 times 1/3,

00:03:53.330 --> 00:03:55.520
is just going to be equal to 2,

00:03:55.520 --> 00:03:57.390
and so let me get my calculator.

00:03:57.390 --> 00:04:00.853
They say round to nearest
tenth of a cubic meter.

00:04:01.850 --> 00:04:06.170
So we have 7.5 squared

00:04:07.230 --> 00:04:12.230
times 2, times pi,

00:04:13.466 --> 00:04:18.120
is equal to, well if we
round to the nearest tenth,

00:04:18.120 --> 00:04:21.823
it's gonna be 353.4 cubic meters.

00:04:21.823 --> 00:04:26.823
So the volume is approximately
353.4 cubic meters.

00:04:29.410 --> 00:04:33.760
So that's the answer to the
first part right over there,

00:04:33.760 --> 00:04:36.130
and then they say how many complete boxes

00:04:36.130 --> 00:04:38.190
will the grain fill?

00:04:38.190 --> 00:04:41.490
Well, they talk about the
boxes right over here.

00:04:41.490 --> 00:04:43.430
The hopper will pour the grain into boxes

00:04:43.430 --> 00:04:48.360
with dimensions of 0.5 meters
by 0.5 meters by 0.4 meters,

00:04:48.360 --> 00:04:50.610
so we can imagine these boxes.

00:04:50.610 --> 00:04:52.163
They look like this,

00:04:53.460 --> 00:04:58.460
and they are 0.5 meters by
0.5 meters by 0.4 meters,

00:05:01.870 --> 00:05:04.260
so the volume of each
box is just going to be

00:05:04.260 --> 00:05:06.200
the product of these three numbers.

00:05:06.200 --> 00:05:08.190
So the volume of each box is going to be

00:05:08.190 --> 00:05:11.520
the width times the
depth times the height,

00:05:11.520 --> 00:05:16.520
so 0.5 meters times 0.5
meters times 0.4 meters,

00:05:21.700 --> 00:05:23.990
and we should be able
to do this in our head,

00:05:23.990 --> 00:05:26.720
because 5 times 5 is 25.

00:05:26.720 --> 00:05:31.410
25 times 4 is equal to 100,
but then we have to think

00:05:31.410 --> 00:05:34.500
we have one, two, three
digits to the right

00:05:34.500 --> 00:05:36.890
of the decimal point, so one, two, three.

00:05:36.890 --> 00:05:41.057
So this is going to be a
tenth, 0.100 cubic meters,

00:05:43.140 --> 00:05:45.230
so a tenth of a cubic meter.

00:05:45.230 --> 00:05:48.860
So how many tenths of
cubic meters can I fill up

00:05:48.860 --> 00:05:50.763
with this much grain?

00:05:50.763 --> 00:05:53.120
Well, it's just going to be this number

00:05:53.120 --> 00:05:54.687
divided by a tenth.

00:05:54.687 --> 00:05:57.178
Well, if you divide by a tenth,

00:05:57.178 --> 00:06:01.027
that's the same thing
as multiplying by 10,

00:06:01.027 --> 00:06:04.000
and so if you multiply this by 10,

00:06:04.000 --> 00:06:08.491
you're going to get 3,534 boxes.

00:06:08.491 --> 00:06:11.610
Now once again, let's just appreciate.

00:06:11.610 --> 00:06:15.130
Every cubic meter, you can
fill 10 of these boxes,

00:06:15.130 --> 00:06:17.480
and this is how many cubic meters we have,

00:06:17.480 --> 00:06:19.840
so if you multiply this by 10,

00:06:19.840 --> 00:06:22.200
it tells you how many boxes you fill up,

00:06:22.200 --> 00:06:23.270
and one way to think about it,

00:06:23.270 --> 00:06:24.690
we've seen this in other videos,

00:06:24.690 --> 00:06:27.121
we're shifting the decimal
one place over to the right

00:06:27.121 --> 00:06:31.940
to get this many boxes, and,
it's important to realize,

00:06:31.940 --> 00:06:35.756
complete boxes, because
when we got to 353.4,

00:06:35.756 --> 00:06:40.756
we did round down, so
we do have that amount,

00:06:40.930 --> 00:06:42.530
but we're not going to fill up another box

00:06:42.530 --> 00:06:44.772
with whatever this rounding error,

00:06:44.772 --> 00:06:46.072
that we rounded down from.

00:06:47.130 --> 00:06:49.810
So the last question is,
to the nearest minute,

00:06:49.810 --> 00:06:52.833
how long does it take to fill the boxes?

00:06:52.833 --> 00:06:55.050
Well, this is the total volume,

00:06:55.050 --> 00:06:59.330
and we're going to fill 8
cubic meters per minute,

00:06:59.330 --> 00:07:03.500
so the answer over here is
going to be our total volume,

00:07:03.500 --> 00:07:08.410
it's going to be 353.4 cubic meters,

00:07:08.410 --> 00:07:11.170
and we're going to
divide that by our rate,

00:07:11.170 --> 00:07:14.358
8 cubic meters per minute,

00:07:14.358 --> 00:07:19.358
and that is going to give
us 353.4 divided by 8,

00:07:21.010 --> 00:07:24.400
is equal to, and if we want to round

00:07:24.400 --> 00:07:28.237
to the nearest minute, 44 minutes.

00:07:28.237 --> 00:07:32.061
Is equal to approximately 44 minutes

00:07:32.061 --> 00:07:34.623
to fill all of the boxes, and we're done.


Proof: Parallel lines divide triangle sides proportionally

WEBVTT
Kind: captions
Language: en

00:00:00.320 --> 00:00:01.280
- [Instructor] We're asked to prove

00:00:01.280 --> 00:00:04.700
that if a line is parallel
to one side of a triangle,

00:00:04.700 --> 00:00:09.120
then it divides the other
two sides proportionally.

00:00:09.120 --> 00:00:11.040
So pause this video and
see if you can do that.

00:00:11.040 --> 00:00:13.223
And you might wanna leverage this diagram.

00:00:14.600 --> 00:00:16.810
All right, so let's work
through this together.

00:00:16.810 --> 00:00:18.780
So we can start with this diagram.

00:00:18.780 --> 00:00:19.940
And what we know

00:00:19.940 --> 00:00:24.300
is that segment ED is
parallel to segment CB.

00:00:24.300 --> 00:00:25.540
So we can write that down.

00:00:25.540 --> 00:00:30.540
Segment ED is parallel to segment CB.

00:00:33.190 --> 00:00:36.510
And so segment ED is what
they're talking about.

00:00:36.510 --> 00:00:38.150
That is a line or a line segment

00:00:38.150 --> 00:00:40.600
that is parallel to one
side of the triangle.

00:00:40.600 --> 00:00:42.360
So really given what we know,

00:00:42.360 --> 00:00:45.190
and what's already been written
over here on this triangle,

00:00:45.190 --> 00:00:47.897
we need to prove another
way of writing it,

00:00:47.897 --> 00:00:50.130
another way of saying it divides

00:00:50.130 --> 00:00:52.110
the other two sides proportionately,

00:00:52.110 --> 00:00:53.620
is that the ratio

00:00:53.620 --> 00:00:56.590
between the part of the
original triangle side

00:00:56.590 --> 00:00:58.710
that is on one side of the dividing line

00:00:58.710 --> 00:01:00.950
to the length on the other side

00:01:00.950 --> 00:01:03.310
is going to be the same on both sides

00:01:03.310 --> 00:01:04.400
that it is intersecting.

00:01:04.400 --> 00:01:05.880
So another way to say

00:01:05.880 --> 00:01:08.510
that it divides the other
two sides proportionately,

00:01:08.510 --> 00:01:10.340
if we look at this triangle over here,

00:01:10.340 --> 00:01:12.780
it would mean that the
length of segment AE

00:01:14.520 --> 00:01:16.590
over the length of segment EC

00:01:18.350 --> 00:01:20.830
is going to be equal to
the length of segment AD

00:01:22.820 --> 00:01:25.373
over the length of segment DB.

00:01:26.770 --> 00:01:27.960
This statement right over here,

00:01:27.960 --> 00:01:29.800
and what I underlined up here

00:01:29.800 --> 00:01:32.600
are equivalent given this triangle.

00:01:32.600 --> 00:01:34.640
So the way that we can try to do it

00:01:34.640 --> 00:01:36.830
is to establish a similarity

00:01:36.830 --> 00:01:41.830
between triangle AED and triangle ACB.

00:01:42.050 --> 00:01:43.850
So how do we do that?

00:01:43.850 --> 00:01:47.080
Well, because these
two lines are parallel,

00:01:47.080 --> 00:01:49.580
we can view segment AC

00:01:49.580 --> 00:01:52.440
as a transversal intersecting
two parallel lines.

00:01:52.440 --> 00:01:55.090
So that tells us that these
two corresponding angles

00:01:55.090 --> 00:01:57.040
are going to be congruent.

00:01:57.040 --> 00:02:02.040
So we could say that angle one
is congruent to angle three.

00:02:04.620 --> 00:02:05.970
And the reason why,

00:02:05.970 --> 00:02:10.893
is because they are corresponding,
corresponding angles.

00:02:12.190 --> 00:02:14.010
I'm just trying to write
a little bit of shorthand.

00:02:14.010 --> 00:02:16.370
This is short for corresponding angles.

00:02:16.370 --> 00:02:17.910
That's the rationale.

00:02:17.910 --> 00:02:19.820
And we also know that angle two

00:02:19.820 --> 00:02:22.650
is congruent to angle
four for the same reason.

00:02:22.650 --> 00:02:27.650
So angle two is congruent to angle four.

00:02:28.040 --> 00:02:31.450
Once again, because they
are corresponding angles.

00:02:31.450 --> 00:02:33.850
This time we have a different transversal,

00:02:33.850 --> 00:02:34.870
corresponding angles

00:02:34.870 --> 00:02:37.860
where a transversal
intersects two parallel lines.

00:02:37.860 --> 00:02:42.580
And so now, if you look at
triangle AED and triangle ACB,

00:02:42.580 --> 00:02:46.550
you see that they have two
sets of corresponding angles

00:02:46.550 --> 00:02:47.383
that are congruent.

00:02:47.383 --> 00:02:49.000
And if you have two sets
of corresponding angles,

00:02:49.000 --> 00:02:50.890
that means that all of
the angles are congruent.

00:02:50.890 --> 00:02:52.780
And you actually see that over
here, if you care about it,

00:02:52.780 --> 00:02:55.240
but two is enough, but
you actually have a third

00:02:55.240 --> 00:02:57.290
because angle, I guess you call it BAC

00:02:58.150 --> 00:03:00.000
is common to both triangles.

00:03:00.000 --> 00:03:02.710
And so we can say that triangle AED

00:03:05.683 --> 00:03:08.357
is similar to triangle ACB,

00:03:09.669 --> 00:03:14.669
ACB by angle similarity.

00:03:15.400 --> 00:03:16.233
Similarity.

00:03:17.460 --> 00:03:20.210
And then given that these two are similar,

00:03:20.210 --> 00:03:22.370
then we can set up a proportion.

00:03:22.370 --> 00:03:26.900
That tells us that the ratio
of the length of segment AE

00:03:28.320 --> 00:03:31.673
to this entire side to AC,

00:03:33.560 --> 00:03:38.560
is equal to the ratio of AD,
the length of that segment

00:03:39.650 --> 00:03:44.260
to the length of the entire thing, to AB.

00:03:44.260 --> 00:03:47.100
Now this implies, and I'm
just gonna start writing it

00:03:47.100 --> 00:03:48.990
to the right here to save space.

00:03:48.990 --> 00:03:52.750
This is the same thing
as the ratio of AE over,

00:03:52.750 --> 00:03:56.720
AC is AE plus EC's length.

00:03:56.720 --> 00:04:01.720
So AE's length plus EC's length,

00:04:01.860 --> 00:04:03.650
and then this is going to be equal

00:04:03.650 --> 00:04:05.600
to the length of segment AD

00:04:05.600 --> 00:04:10.503
over segment AB, its length
is the length of segment AD,

00:04:11.590 --> 00:04:16.590
AD plus segment DB, plus D B.

00:04:16.950 --> 00:04:18.170
Now, really what I need to do

00:04:18.170 --> 00:04:20.700
is figure out how do I
algebraically manipulate it

00:04:20.700 --> 00:04:23.840
so I get what I have up here.

00:04:23.840 --> 00:04:26.200
Let me scroll down a little bit.

00:04:26.200 --> 00:04:28.140
So one way I could try to simplify this

00:04:28.140 --> 00:04:30.490
is to essentially cross multiply,

00:04:30.490 --> 00:04:32.760
that's equivalent to
multiplying both sides

00:04:32.760 --> 00:04:34.590
by both of these denominators.

00:04:34.590 --> 00:04:36.080
And we've covered that in other videos.

00:04:36.080 --> 00:04:39.780
And so this is going to be equal
to the length of segment AE

00:04:39.780 --> 00:04:44.780
times AD plus DB, those segment lengths,

00:04:45.090 --> 00:04:49.290
that's gotta be equal
to length of AD times AE

00:04:52.090 --> 00:04:55.380
plus the length of segment EC.

00:04:55.380 --> 00:04:57.480
And I can distribute this over here.

00:04:57.480 --> 00:05:01.410
I have length of segment AE
times length of segment AD

00:05:02.298 --> 00:05:06.631
plus length of segment AE
times length of segment DB

00:05:08.751 --> 00:05:13.242
is equal to length of segment
AD times length of segment AE

00:05:13.242 --> 00:05:17.659
plus length of segment AD
times length of segment EC.

00:05:18.710 --> 00:05:21.390
And let's see, is there anything
that I can simplify here?

00:05:21.390 --> 00:05:25.200
We'll have AE times AD on both sides.

00:05:25.200 --> 00:05:29.550
So let me just subtract AE
times AD from both sides.

00:05:29.550 --> 00:05:33.340
And so then I'm just left
with this is equal to that.

00:05:33.340 --> 00:05:36.410
So scroll down a little bit more

00:05:36.410 --> 00:05:38.740
and let me actually just
rewrite this cleanly.

00:05:38.740 --> 00:05:43.740
So I have AE times DB
is equal to AD times EC.

00:05:46.470 --> 00:05:48.500
These are all the segment
lengths right over here.

00:05:48.500 --> 00:05:51.260
Now, if you divide both sides by EC,

00:05:51.260 --> 00:05:54.070
you're going to get an EC down here,

00:05:54.070 --> 00:05:55.520
and then this would cancel out.

00:05:55.520 --> 00:05:58.130
And then if you divide both sides by DB,

00:05:58.130 --> 00:06:01.660
this will cancel out and you'll
get a DB right over here.

00:06:01.660 --> 00:06:03.350
So if you just algebraically manipulate

00:06:03.350 --> 00:06:04.820
what we just had over there,

00:06:04.820 --> 00:06:07.020
you get that the length of segment AE

00:06:07.020 --> 00:06:08.700
over the length of segment EC,

00:06:08.700 --> 00:06:12.660
length of segment AE over
the length of segment EC

00:06:12.660 --> 00:06:15.043
is equal to the length of segment AD, AD

00:06:18.290 --> 00:06:22.750
over the length of segment DB,

00:06:22.750 --> 00:06:24.860
which is exactly what we wanted to prove.

00:06:24.860 --> 00:06:26.200
That this line right over here

00:06:26.200 --> 00:06:28.600
that is parallel to this side over here,

00:06:28.600 --> 00:06:31.483
divides the other two
sides proportionally.


Multi-step word problem with Pythagorean theorem

WEBVTT
Kind: captions
Language: en

00:00:00.220 --> 00:00:01.760
- [Instructor] We're told that Lainey runs

00:00:01.760 --> 00:00:04.160
a string of lights from
the ground straight up

00:00:04.160 --> 00:00:08.980
to a door frame that is 2.5 meters tall.

00:00:08.980 --> 00:00:11.200
Then they run the rest of the string

00:00:11.200 --> 00:00:13.870
in a straight line to
a point on the ground

00:00:13.870 --> 00:00:17.530
that is six meters from
the base of the door frame.

00:00:17.530 --> 00:00:22.410
There are 10 lights per
meter of the string.

00:00:22.410 --> 00:00:25.940
How many total lights are on the string?

00:00:25.940 --> 00:00:26.810
So I'll pause this video

00:00:26.810 --> 00:00:28.460
and see if you can work this out.

00:00:29.720 --> 00:00:31.330
All right, now let's work
through this together.

00:00:31.330 --> 00:00:34.080
I think this one warrants
some type of a diagram.

00:00:34.080 --> 00:00:38.740
So let me draw this door
frame that looks like this.

00:00:38.740 --> 00:00:42.700
And this door frame is 2.5 meters tall.

00:00:42.700 --> 00:00:44.600
So that's its height right over there.

00:00:44.600 --> 00:00:46.110
And what they're going to do,

00:00:46.110 --> 00:00:49.950
what Lainey's doing is she
is string up these lights,

00:00:49.950 --> 00:00:51.850
so that's this yellow right over here.

00:00:51.850 --> 00:00:53.950
So it goes up to the
top of that door frame

00:00:53.950 --> 00:00:56.960
and then they run the rest of the light

00:00:56.960 --> 00:00:58.960
in a straight line to
a point on the ground

00:00:58.960 --> 00:01:02.070
that is six meters from
the base of the door frame.

00:01:02.070 --> 00:01:03.930
So let me show a point that is six meters

00:01:03.930 --> 00:01:05.340
from the base of the door frame.

00:01:05.340 --> 00:01:09.930
So it looks something
like, maybe like that.

00:01:09.930 --> 00:01:12.740
So this distance right
over here is six meters.

00:01:12.740 --> 00:01:14.390
So they run the rest of the light

00:01:15.840 --> 00:01:17.440
from the top of the door frame

00:01:17.440 --> 00:01:20.570
to that point to that six meters away.

00:01:20.570 --> 00:01:21.900
So the yellow right over here,

00:01:21.900 --> 00:01:23.440
that is the light.

00:01:23.440 --> 00:01:25.130
And so we had to figure out

00:01:25.130 --> 00:01:26.840
how many total lights are on the string.

00:01:26.840 --> 00:01:29.060
So the way I would tackle
it is first of all,

00:01:29.060 --> 00:01:32.750
I wanna figure out how
long is the total string.

00:01:32.750 --> 00:01:33.980
And to figure that out,

00:01:33.980 --> 00:01:34.813
I just need to figure out,

00:01:34.813 --> 00:01:37.610
okay, it's gonna be 2.5 plus
whatever the hypothenuse

00:01:37.610 --> 00:01:39.380
is of this right triangle.

00:01:39.380 --> 00:01:41.980
I think it's safe to assume
that this is a standard house

00:01:41.980 --> 00:01:44.550
where door frames are at a
right angle to the floor.

00:01:44.550 --> 00:01:45.490
And so we have to figure out

00:01:45.490 --> 00:01:46.730
the length of this hypothenuse

00:01:46.730 --> 00:01:49.890
and if we know that, plus this 2.5 meters,

00:01:49.890 --> 00:01:53.200
then we know how long the
entire string of lights are.

00:01:53.200 --> 00:01:55.240
And then we just have to
really multiply it by 10

00:01:55.240 --> 00:01:58.370
because there's 10 lights
per meter of the string.

00:01:58.370 --> 00:01:59.750
So let's do that.

00:01:59.750 --> 00:02:01.510
So how do we figure out
the hypothenuse here?

00:02:01.510 --> 00:02:03.350
Well, of course, we would
use Pythagorean theorem.

00:02:03.350 --> 00:02:04.540
So let's call this,

00:02:04.540 --> 00:02:07.810
and also call this h for hypothenuse.

00:02:07.810 --> 00:02:09.830
We know that the hypothenuse squared

00:02:09.830 --> 00:02:14.830
is equal to 2.5 squared plus six squared.

00:02:17.680 --> 00:02:22.100
So this is going to be
equal to 6.25 plus 36,

00:02:26.280 --> 00:02:31.280
which is equal to 42.25 or we could say

00:02:31.440 --> 00:02:33.180
that the hypothenuse is going to be equal

00:02:33.180 --> 00:02:37.850
to the square root of 42.25.

00:02:37.850 --> 00:02:39.750
And I could get my
calculator out at this point,

00:02:39.750 --> 00:02:42.360
but I'll actually just
keep using this expression

00:02:42.360 --> 00:02:45.090
to figure out the total number of lights.

00:02:45.090 --> 00:02:47.040
So what's the total length of the string?

00:02:47.040 --> 00:02:48.200
We have to be careful here.

00:02:48.200 --> 00:02:49.033
A lot of folks would say,

00:02:49.033 --> 00:02:50.360
"Oh, I figure out the hypothenuse,

00:02:50.360 --> 00:02:52.350
let me just multiply it that by 10."

00:02:52.350 --> 00:02:54.820
In fact, my brain almost
did that just now.

00:02:54.820 --> 00:02:57.480
But we gotta realize
that the entire string

00:02:57.480 --> 00:02:59.313
is the hypothenuse plus this 2.5.

00:03:00.380 --> 00:03:02.250
So the whole string length,

00:03:02.250 --> 00:03:03.190
Write this way.

00:03:03.190 --> 00:03:08.190
String length is equal to 2.5

00:03:10.960 --> 00:03:14.453
plus the square root of 42.25.

00:03:18.050 --> 00:03:20.800
And then we would just
multiply it that time 10

00:03:20.800 --> 00:03:23.400
to get the total number of lights.

00:03:23.400 --> 00:03:26.650
So now let's actually
get the calculator out.

00:03:26.650 --> 00:03:31.610
So we have 42.25 and then we would've take

00:03:31.610 --> 00:03:34.430
the square root of that.

00:03:34.430 --> 00:03:37.483
Gets us to 6.5 and then
we add the other 2.5,

00:03:38.410 --> 00:03:41.860
plus 2.5 equals that.

00:03:41.860 --> 00:03:44.570
That's the total length of string.

00:03:44.570 --> 00:03:47.240
So the total length of
string is nine meters

00:03:47.240 --> 00:03:49.530
and there're 10 lights per meter.

00:03:49.530 --> 00:03:51.600
So the number of lights,

00:03:51.600 --> 00:03:56.600
number of lights is equal to
nine total meters of string

00:04:00.010 --> 00:04:05.010
times 10 lights per meter,

00:04:05.220 --> 00:04:09.420
which would give us 90 lights.

00:04:09.420 --> 00:04:10.960
Now some of you might debate,

00:04:10.960 --> 00:04:12.360
if you think really deeply about it,

00:04:12.360 --> 00:04:14.620
is if you have a light
right at the beginning,

00:04:14.620 --> 00:04:17.200
if these were kind of
set up like a fence post,

00:04:17.200 --> 00:04:20.680
then maybe you can argue
that there's one extra light

00:04:20.680 --> 00:04:22.990
in there, but for the sake of this,

00:04:22.990 --> 00:04:24.150
I kind of view this as,

00:04:24.150 --> 00:04:26.430
on average there're 10 lights per meter

00:04:26.430 --> 00:04:29.800
and so if it's a nine meter string,

00:04:29.800 --> 00:04:32.743
nine times 10 is 90 lights.


Proof: perpendicular radius bisects chord

WEBVTT
Kind: captions
Language: en

00:00:00.859 --> 00:00:02.940
- [Instructor] So we have this circle

00:00:02.940 --> 00:00:03.870
called circle O,

00:00:03.870 --> 00:00:05.660
based on the point at its center,

00:00:05.660 --> 00:00:07.860
and we have the segment OD,

00:00:07.860 --> 00:00:10.080
and we're told that segment OD,

00:00:10.080 --> 00:00:12.470
is a radius of circle O, fair enough.

00:00:12.470 --> 00:00:13.370
We're also told

00:00:13.370 --> 00:00:17.520
that segment OD is
perpendicular to this chord

00:00:17.520 --> 00:00:20.540
to chord AC, or two segment AC.

00:00:20.540 --> 00:00:25.023
And what we wanna prove is
that segment OD bisects AC.

00:00:26.080 --> 00:00:27.660
So another way to think about it,

00:00:27.660 --> 00:00:31.120
it intersects AC at AC's midpoint.

00:00:31.120 --> 00:00:34.710
So pause this video and see if
you can have a go with that.

00:00:34.710 --> 00:00:36.680
All right, now let's go
through this together.

00:00:36.680 --> 00:00:38.010
And the way that I'm going to do this,

00:00:38.010 --> 00:00:40.990
is by establishing two
congruent triangles.

00:00:40.990 --> 00:00:42.670
And let me draw these triangles.

00:00:42.670 --> 00:00:46.730
So I'm gonna draw one
radius going from O to C

00:00:46.730 --> 00:00:51.260
and another from A to O.

00:00:51.260 --> 00:00:56.200
Now we know that the
length AO is equal to OC

00:01:01.490 --> 00:01:06.490
because AO and OC, both radii.

00:01:12.420 --> 00:01:15.610
In a circle, the length of
the radius does not change.

00:01:15.610 --> 00:01:19.150
So I can put that right over there.

00:01:19.150 --> 00:01:21.910
And then we also know that OM

00:01:21.910 --> 00:01:23.810
is going to be congruent to itself,

00:01:23.810 --> 00:01:26.440
it's a side in both of these triangles.

00:01:26.440 --> 00:01:28.416
So let me just write it this way.

00:01:28.416 --> 00:01:33.416
OM is going to be congruent to OM

00:01:36.310 --> 00:01:38.105
and this is reflexivity.

00:01:38.105 --> 00:01:42.710
Reflexivity kind of obvious.

00:01:42.710 --> 00:01:44.320
It's going to be equal to itself,

00:01:44.320 --> 00:01:46.140
it's going to be congruent to itself.

00:01:46.140 --> 00:01:47.630
So you have it just like that.

00:01:47.630 --> 00:01:49.270
And now we have two right triangles.

00:01:49.270 --> 00:01:50.590
How do I know they're right triangles?

00:01:50.590 --> 00:01:51.780
Well, they told us

00:01:51.780 --> 00:01:55.520
that segment OD is
perpendicular to segment AC

00:01:55.520 --> 00:01:58.290
and our assumptions in our given.

00:01:58.290 --> 00:02:00.130
Now if you just had two triangles,

00:02:00.130 --> 00:02:03.310
that had two pairs of congruent sides

00:02:03.310 --> 00:02:06.960
that is not enough to establish
congruency of the triangles.

00:02:06.960 --> 00:02:09.090
But if you're dealing
with two right triangles,

00:02:09.090 --> 00:02:10.660
then it is enough.

00:02:10.660 --> 00:02:12.470
And there's two ways to think about it.

00:02:12.470 --> 00:02:17.180
We had thought about the RSH postulate

00:02:17.180 --> 00:02:19.070
where if you have a right triangle

00:02:19.070 --> 00:02:20.300
or two right triangles,

00:02:20.300 --> 00:02:21.880
you have a pair of sides are congruent,

00:02:21.880 --> 00:02:24.250
a pair and the hypothesis are congruent

00:02:24.250 --> 00:02:26.920
that means that the two
triangles are congruent.

00:02:26.920 --> 00:02:28.010
But another way to think about it,

00:02:28.010 --> 00:02:30.580
which is a little bit of common sense is

00:02:30.580 --> 00:02:32.150
using the Pythagorean theorem.

00:02:32.150 --> 00:02:34.100
If you know two sides of a right triangle,

00:02:34.100 --> 00:02:35.400
the Pythagorean theorem would tell us

00:02:35.400 --> 00:02:38.680
that you could determine
what the other side is.

00:02:38.680 --> 00:02:40.690
And so what we could say is

00:02:40.690 --> 00:02:42.130
and let's just use RSH for now,

00:02:42.130 --> 00:02:45.080
but you could also say we can
use the Pythagorean theorem

00:02:45.080 --> 00:02:50.080
to establish that AM is
going to be congruent to MC,

00:02:50.390 --> 00:02:51.950
but let me just write it this way.

00:02:51.950 --> 00:02:55.193
I will write that triangle,

00:02:56.079 --> 00:03:01.079
AMO is congruent to triangle CMO by RSH.

00:03:06.350 --> 00:03:07.870
And if the triangles are congruent

00:03:07.870 --> 00:03:10.640
then the corresponding
sides must be congruent.

00:03:10.640 --> 00:03:14.443
So, therefore, we know that AM,

00:03:15.894 --> 00:03:19.850
AM, segment AM is going to be,

00:03:19.850 --> 00:03:21.180
I'm having trouble writing congruent

00:03:21.180 --> 00:03:23.943
is going to be congruent to segment CM,

00:03:26.670 --> 00:03:31.590
that these are going to
have the same measure.

00:03:31.590 --> 00:03:33.160
And if they have the same measure,

00:03:33.160 --> 00:03:37.750
we have just shown that
M is the midpoint of AC

00:03:37.750 --> 00:03:40.210
or that OD bisects AC.

00:03:40.210 --> 00:03:41.210
So, let me just write it that way.

00:03:41.210 --> 00:03:43.550
Therefore, OD bisects AC.

00:03:48.075 --> 00:03:52.023
Segment OD bisects
segment AC and we're done.


Camp Khan Parent Webinar

WEBVTT
Kind: captions
Language: en

00:00:15.490 --> 00:00:17.020
- Hi everyone, good afternoon

00:00:17.020 --> 00:00:18.710
or good evening depending on

00:00:18.710 --> 00:00:21.790
where you're joining us in the country.

00:00:21.790 --> 00:00:23.660
My name is Roy, and I'm here to give you

00:00:23.660 --> 00:00:26.670
a quick overview of Camp Khan,

00:00:26.670 --> 00:00:29.283
our new summer camp.

00:00:30.560 --> 00:00:31.393
Quick agenda, here.

00:00:31.393 --> 00:00:33.460
We're gonna do intros real quickly

00:00:33.460 --> 00:00:35.350
talk about Camp Khan, the details

00:00:35.350 --> 00:00:37.640
Kind of from the 30,000 foot view

00:00:37.640 --> 00:00:40.040
all the way down to the ground level view.

00:00:40.040 --> 00:00:42.010
Talk a little bit about these new courses.

00:00:42.010 --> 00:00:44.150
Our Get ready for grade level courses,

00:00:44.150 --> 00:00:45.860
and then have some time for questions.

00:00:45.860 --> 00:00:48.243
We're gonna do all this
in about 30 minutes.

00:00:50.550 --> 00:00:52.020
First, some intros.

00:00:52.020 --> 00:00:53.600
As I mentioned, my name is Roy.

00:00:53.600 --> 00:00:57.730
I am on the district partnership
team at Khan Academy.

00:00:57.730 --> 00:01:00.610
I'm joined by my colleague
Patty Suquilanda.

00:01:00.610 --> 00:01:05.610
She is also my teammate on
the district partnership team.

00:01:05.650 --> 00:01:08.990
And Patty is going to be
moderating your questions.

00:01:08.990 --> 00:01:12.290
And we'll reference
them and go through them

00:01:12.290 --> 00:01:14.390
during the Q and A session.

00:01:14.390 --> 00:01:16.610
Lauren Quan is on our marketing team.

00:01:16.610 --> 00:01:18.490
She does a lot of our parent marketing.

00:01:18.490 --> 00:01:20.100
So it's great to have Lauren here.

00:01:20.100 --> 00:01:22.440
She's also going to be
monitoring questions.

00:01:22.440 --> 00:01:24.090
So feel free to type those in

00:01:24.090 --> 00:01:25.850
throughout the next 15 minutes.

00:01:25.850 --> 00:01:27.530
We'll get to them either in the chat

00:01:27.530 --> 00:01:31.490
or as we do the Q and
A a little bit later.

00:01:31.490 --> 00:01:35.120
And please note that this
webinar will be recorded

00:01:35.120 --> 00:01:38.100
and sent to you after this session.

00:01:38.100 --> 00:01:40.960
You'll also see that there is a handout,

00:01:40.960 --> 00:01:45.130
a one pager that just has
some details on Camp Khan

00:01:45.130 --> 00:01:49.740
right on your GoToWebinar dashboard there.

00:01:49.740 --> 00:01:52.263
It's titled, Camp Khan Article Webinar.

00:01:53.700 --> 00:01:54.743
That's who we are.

00:01:56.890 --> 00:01:59.820
And we don't have time to do intros

00:01:59.820 --> 00:02:01.870
for Every single person in here,

00:02:01.870 --> 00:02:03.580
but we have been talking with

00:02:03.580 --> 00:02:06.620
and hearing from parents
throughout the school year,

00:02:06.620 --> 00:02:08.030
particularly in the spring.

00:02:08.030 --> 00:02:09.160
And what we heard from them was

00:02:09.160 --> 00:02:12.920
this particular school
year was surprising.

00:02:12.920 --> 00:02:14.400
It was unexpected.

00:02:14.400 --> 00:02:15.650
It was overwhelming.

00:02:15.650 --> 00:02:16.880
It was hectic,

00:02:16.880 --> 00:02:18.453
it really it was just a lot.

00:02:19.330 --> 00:02:21.830
And recognizing all those things

00:02:21.830 --> 00:02:23.110
that the school year was,

00:02:23.110 --> 00:02:27.470
we wanna first thank you
parents for being a caregiver,

00:02:27.470 --> 00:02:31.440
and a teacher, a coach for your children.

00:02:31.440 --> 00:02:32.800
A juggler really, of all

00:02:32.800 --> 00:02:34.800
the different responsibilities you have.

00:02:34.800 --> 00:02:36.980
And really just for being there,

00:02:36.980 --> 00:02:39.293
for your family, for your children.

00:02:40.210 --> 00:02:43.810
And it is with that in mind
that we started Camp Khan

00:02:43.810 --> 00:02:47.570
which is our real first summer camp

00:02:47.570 --> 00:02:49.120
that we're doing virtually, of course.

00:02:49.120 --> 00:02:50.620
And we were trying to think of

00:02:50.620 --> 00:02:52.050
what could be a way that

00:02:52.050 --> 00:02:55.090
we could prepare students
for math next year.

00:02:55.090 --> 00:02:56.190
Do some things that might help

00:02:56.190 --> 00:02:57.380
to build their confidence.

00:02:57.380 --> 00:03:00.057
And also do it in a fun
way that recognizes,

00:03:00.057 --> 00:03:01.560
"Hey, it's still summer vacation,

00:03:01.560 --> 00:03:04.130
even though this past school year

00:03:04.130 --> 00:03:06.190
was all these different things

00:03:06.190 --> 00:03:08.317
that we didn't really expect."

00:03:09.240 --> 00:03:11.890
We wanna make sure that Camp Khan

00:03:11.890 --> 00:03:14.030
does prepare students for math

00:03:14.030 --> 00:03:15.850
and build a confidence
and also do it in a way

00:03:15.850 --> 00:03:20.160
that's kinda flexible for
parents and for children too.

00:03:20.160 --> 00:03:22.060
That's kind of like the 30,000 foot view

00:03:22.060 --> 00:03:23.030
of what Camp Khan is.

00:03:23.030 --> 00:03:24.760
I'm gonna just go a little bit lower

00:03:24.760 --> 00:03:27.423
to say like the 15,000 foot view.

00:03:28.410 --> 00:03:29.860
Give some details on Camp Khan.

00:03:29.860 --> 00:03:32.630
So Camp Khan runs from June 22nd.

00:03:32.630 --> 00:03:34.060
This Monday, we just launched.

00:03:34.060 --> 00:03:36.840
You might have received an email
from us about it, actually.

00:03:36.840 --> 00:03:38.980
And It'll go all the way to August 28th.

00:03:38.980 --> 00:03:41.720
So a total of 10 weeks.

00:03:41.720 --> 00:03:43.660
And it's intended for students

00:03:43.660 --> 00:03:47.730
entering grades three
through 12 this fall.

00:03:47.730 --> 00:03:49.900
And just like I mentioned before,

00:03:49.900 --> 00:03:51.900
we wanna make this flexible for folks

00:03:51.900 --> 00:03:54.840
so participants can join and stay whenever

00:03:54.840 --> 00:03:56.500
and for however long.

00:03:56.500 --> 00:03:59.150
And we also wanna make this
accessible for everyone.

00:03:59.150 --> 00:04:02.123
So we've made sure that
it's free for everyone to.

00:04:02.990 --> 00:04:05.760
Down below, you'll see
our four thinky pinkies.

00:04:05.760 --> 00:04:09.800
These are like our mascot for Camp Khan.

00:04:09.800 --> 00:04:12.480
And here are the ingredients of Camp Khan.

00:04:12.480 --> 00:04:16.900
So one is the Get ready for math courses.

00:04:16.900 --> 00:04:18.210
Get ready for grade level courses.

00:04:18.210 --> 00:04:20.040
These are our math
courses that we're gonna

00:04:20.040 --> 00:04:22.860
go into in a little bit more detail.

00:04:22.860 --> 00:04:25.730
In addition, Camp Khan is
gonna deliver some strategies

00:04:25.730 --> 00:04:27.190
for real self driven learning.

00:04:27.190 --> 00:04:29.410
So thinking about how children,

00:04:29.410 --> 00:04:33.330
students can really be
owners of their own learning.

00:04:33.330 --> 00:04:35.090
And really drive their own learning.

00:04:35.090 --> 00:04:37.360
And part we wanna make sure that

00:04:37.360 --> 00:04:40.010
the parents aren't being
asked to do too much,

00:04:40.010 --> 00:04:41.780
because we know you have done so much

00:04:41.780 --> 00:04:43.370
throughout this school year.

00:04:43.370 --> 00:04:45.050
And then also like I've mentioned,

00:04:45.050 --> 00:04:46.740
we wanna make sure that Camp Khan

00:04:46.740 --> 00:04:49.500
gives suggestions for fun

00:04:49.500 --> 00:04:52.450
and motivational things
that you and your children

00:04:52.450 --> 00:04:54.190
can do over the summer.

00:04:54.190 --> 00:04:57.220
And we think if we combine all
those three things together,

00:04:57.220 --> 00:04:59.040
that's gonna lead to sustained learning,

00:04:59.040 --> 00:05:02.423
not just this Summer, but in years ahead.

00:05:04.780 --> 00:05:05.870
All right, so how it works.

00:05:05.870 --> 00:05:08.830
I'm gonna go a little bit more detail now.

00:05:08.830 --> 00:05:10.500
I already mentioned this Monday,

00:05:10.500 --> 00:05:12.250
you all should have received an email

00:05:12.250 --> 00:05:14.210
just announcing Camp Khan.

00:05:14.210 --> 00:05:17.580
And we sent that email
to all parents in the US,

00:05:17.580 --> 00:05:20.350
all learners over the age of 13.

00:05:20.350 --> 00:05:22.173
And all the US math teachers too.

00:05:23.550 --> 00:05:25.600
From now until August 28

00:05:25.600 --> 00:05:27.980
over that period of the next nine weeks,

00:05:27.980 --> 00:05:30.470
we're gonna get weekly guidance

00:05:30.470 --> 00:05:34.010
where learners can progress
on those get ready courses

00:05:34.010 --> 00:05:35.600
that we're gonna go into

00:05:35.600 --> 00:05:40.410
and receive some weekly
recommendations via email too.

00:05:40.410 --> 00:05:43.470
And included in that weekly guidance

00:05:43.470 --> 00:05:45.940
is just some tips and opportunities

00:05:45.940 --> 00:05:49.370
to really recognize and
reflect on progress,

00:05:49.370 --> 00:05:52.530
giving some ideas for
how you might celebrate

00:05:52.530 --> 00:05:55.200
the effort your children are putting in

00:05:55.200 --> 00:05:57.870
the learnings that they might
have throughout the year.

00:05:57.870 --> 00:06:00.520
And again, making sure we
have some time for fun too.

00:06:02.290 --> 00:06:03.780
That's a real quick overview.

00:06:03.780 --> 00:06:05.800
If you have any additional questions,

00:06:05.800 --> 00:06:08.340
I'm gonna refer you back to that one pager

00:06:08.340 --> 00:06:09.820
that's in your handouts.

00:06:09.820 --> 00:06:14.820
And this website on the bottom
here, Khan.co/CampKhan2020.

00:06:15.930 --> 00:06:20.833
And we're also on social
under #CampKhan2020.

00:06:24.100 --> 00:06:25.260
All right, I mentioned

00:06:25.260 --> 00:06:28.540
the weekly recommendations and suggestions

00:06:28.540 --> 00:06:29.960
that we're sending out.

00:06:29.960 --> 00:06:33.530
Here's a rough outline
of what it looks like.

00:06:33.530 --> 00:06:36.790
Each of our weekly emails will have

00:06:36.790 --> 00:06:41.020
five suggestions along
three different topics.

00:06:41.020 --> 00:06:42.080
Before I get into that,

00:06:42.080 --> 00:06:43.940
I want to mention that all our messages

00:06:43.940 --> 00:06:46.130
are available in Spanish.

00:06:46.130 --> 00:06:48.470
And then those three topics are:

00:06:48.470 --> 00:06:50.090
one, learning goals for your

00:06:50.090 --> 00:06:52.350
Get ready for grade level courses;

00:06:52.350 --> 00:06:54.040
second topic is learning tips

00:06:54.040 --> 00:06:55.100
and they can be learning tips

00:06:55.100 --> 00:06:56.830
about how to use Khan Academy.

00:06:56.830 --> 00:06:58.740
How might you share progress

00:06:58.740 --> 00:07:02.520
with a teacher or with an adult?

00:07:02.520 --> 00:07:06.290
Or some reflection prompts
about how do you best learn.

00:07:06.290 --> 00:07:07.460
What are some things that

00:07:07.460 --> 00:07:12.410
you really like doing in a classroom;

00:07:12.410 --> 00:07:14.720
and then the third topic

00:07:14.720 --> 00:07:16.690
are these final motivational activities.

00:07:16.690 --> 00:07:18.270
And these are gonna be taken

00:07:18.270 --> 00:07:20.550
from our own content library.

00:07:20.550 --> 00:07:22.410
So for instance, one of the things

00:07:22.410 --> 00:07:24.490
that we're gonna suggest is our

00:07:24.490 --> 00:07:26.750
Pixar in a box content.

00:07:26.750 --> 00:07:30.390
Which is going to be a set
of courses and activities

00:07:30.390 --> 00:07:32.277
that students can really do

00:07:32.277 --> 00:07:35.250
to hone in on our imagination.

00:07:35.250 --> 00:07:36.290
And then we're also gonna take

00:07:36.290 --> 00:07:38.010
some fun and motivational activities

00:07:38.010 --> 00:07:40.410
from some of our partner
organizations too,

00:07:40.410 --> 00:07:42.470
who have great ideas for

00:07:42.470 --> 00:07:44.820
how do you spend the summer?

00:07:44.820 --> 00:07:45.810
And how do you spend a summer

00:07:45.810 --> 00:07:47.800
not just in front of a screen,

00:07:47.800 --> 00:07:51.293
but also outside and with
friends and with family.

00:07:52.710 --> 00:07:54.150
For each of these topics,

00:07:54.150 --> 00:07:58.030
we're gonna have clickable
videos on various weeks

00:07:58.030 --> 00:08:01.240
where you can just write
directly in the Email,

00:08:01.240 --> 00:08:04.773
view a video, or go to a partner resource.

00:08:06.000 --> 00:08:08.210
Now, to get these emails,
there's no signup.

00:08:08.210 --> 00:08:09.660
You don't need to do anything

00:08:09.660 --> 00:08:13.450
other than have a Khan Academy
account of your parent.

00:08:13.450 --> 00:08:14.970
And we'll also be sending

00:08:14.970 --> 00:08:17.900
a similar but slightly
differently worded email

00:08:17.900 --> 00:08:21.550
to learners who have spent any time

00:08:21.550 --> 00:08:23.723
on our get ready for math courses.

00:08:26.930 --> 00:08:28.690
All right, I feel like I've been talking

00:08:28.690 --> 00:08:31.850
up these Get ready for grade
level courses quite a bit.

00:08:31.850 --> 00:08:33.410
And wanna spend the next few minutes

00:08:33.410 --> 00:08:36.140
just highlighting what those are.

00:08:36.140 --> 00:08:39.190
So our get ready for math courses

00:08:39.190 --> 00:08:42.363
are newly created math courses.

00:08:43.410 --> 00:08:45.410
They were created or curated

00:08:45.410 --> 00:08:47.370
in part because we heard from parents,

00:08:47.370 --> 00:08:48.927
we heard from teachers who said,

00:08:48.927 --> 00:08:51.380
"Hey, what can we do,
or what can our students

00:08:51.380 --> 00:08:53.070
or children do between now

00:08:53.070 --> 00:08:54.680
and whenever school reopens

00:08:54.680 --> 00:08:56.490
that's gonna make sure that
they're ready to learn.

00:08:56.490 --> 00:08:58.250
That they're ready to
hit the ground running

00:08:58.250 --> 00:09:01.147
when school year 2021 begins."

00:09:02.060 --> 00:09:03.140
What we did was go back

00:09:03.140 --> 00:09:06.310
to all of our previous
or existing math courses,

00:09:06.310 --> 00:09:09.000
and we just pulled the content

00:09:09.000 --> 00:09:12.320
and the skills that we
think are most important

00:09:12.320 --> 00:09:14.770
for a student to be successful

00:09:14.770 --> 00:09:17.520
in the math class next year.

00:09:17.520 --> 00:09:19.150
So if you have a child

00:09:19.150 --> 00:09:22.260
going into fourth grade, for instance,

00:09:22.260 --> 00:09:23.093
you will take the

00:09:23.093 --> 00:09:25.480
get ready for fourth grade level course.

00:09:25.480 --> 00:09:28.020
And in that get ready for
fourth grade level course,

00:09:28.020 --> 00:09:29.230
you're gonna see skills

00:09:29.230 --> 00:09:31.910
that may be from third
grade, from second grade.

00:09:31.910 --> 00:09:33.940
The real foundational skills

00:09:33.940 --> 00:09:35.670
that we find to be important

00:09:35.670 --> 00:09:37.560
so that they can enter fourth grade

00:09:37.560 --> 00:09:40.370
really confident and knowledgeable

00:09:40.370 --> 00:09:43.573
to be successful in their
fourth grade math class.

00:09:47.130 --> 00:09:49.870
I'm gonna show you just a few screenshots

00:09:49.870 --> 00:09:54.210
of how you get to the get
ready for grade level courses.

00:09:54.210 --> 00:09:55.043
First thing you wanna do

00:09:55.043 --> 00:09:57.850
is get our newer website, Khanacademy.org.

00:09:57.850 --> 00:09:59.310
Here you can either log in

00:09:59.310 --> 00:10:01.470
or if you don't have khan
Academy accountant yet,

00:10:01.470 --> 00:10:03.480
you can sign up and it's pretty easy.

00:10:03.480 --> 00:10:06.130
You can do so with your
Google account, for instance.

00:10:06.130 --> 00:10:08.713
Or you can create a new
username and password.

00:10:11.250 --> 00:10:13.830
Once you're in the Khan Academy site,

00:10:13.830 --> 00:10:14.760
and we're looking at this

00:10:14.760 --> 00:10:16.400
from a student perspective.

00:10:16.400 --> 00:10:19.130
So this is what your child might see.

00:10:19.130 --> 00:10:23.730
They can on the top left
corner, go to Courses.

00:10:23.730 --> 00:10:27.020
And from there, click that drop down.

00:10:27.020 --> 00:10:30.380
And you can see on the bottom
right of my slide here,

00:10:30.380 --> 00:10:32.420
there's going to be a list

00:10:32.420 --> 00:10:34.730
of the entire Khan Academy library.

00:10:34.730 --> 00:10:37.420
And this math, get ready courses,

00:10:37.420 --> 00:10:40.740
they'll have a green new
button, to let you know.

00:10:40.740 --> 00:10:42.520
Will show up and then just pick

00:10:42.520 --> 00:10:43.780
the grade level that your child

00:10:43.780 --> 00:10:45.443
will be entering in the fall.

00:10:46.710 --> 00:10:48.290
Another way you can get to the

00:10:48.290 --> 00:10:50.050
Get ready for grade level courses

00:10:50.050 --> 00:10:54.230
is just by typing in or
clicking on this link directly.

00:10:54.230 --> 00:10:56.650
And we'll be making these
slides available too

00:10:56.650 --> 00:10:57.633
after the webinar.

00:11:01.110 --> 00:11:02.997
Once you click into a get ready course,

00:11:02.997 --> 00:11:05.547
you're gonna see a pop up that says,

00:11:05.547 --> 00:11:07.450
"Show what you know!"

00:11:07.450 --> 00:11:08.680
And there's gonna be an option

00:11:08.680 --> 00:11:10.280
to start a course challenge.

00:11:10.280 --> 00:11:12.960
Now, we recommend that
students or children

00:11:12.960 --> 00:11:15.480
start with the course challenge

00:11:15.480 --> 00:11:19.000
'cause it's gonna take them
through a set of skills

00:11:19.000 --> 00:11:21.040
where they can demonstrate what they know,

00:11:21.040 --> 00:11:24.300
and what they might just
brush up on a little bit.

00:11:24.300 --> 00:11:28.380
And that course challenge
can also guide students

00:11:28.380 --> 00:11:29.980
on what they should be doing

00:11:29.980 --> 00:11:32.207
or what they might wanna
focus their time on.

00:11:32.207 --> 00:11:34.530
Again, what they might wanna brush up on

00:11:34.530 --> 00:11:36.363
after taking the course challenge.

00:11:40.720 --> 00:11:42.100
And as your children are working to

00:11:42.100 --> 00:11:43.520
the Get ready course,

00:11:43.520 --> 00:11:45.640
you and they can track how they're doing

00:11:45.640 --> 00:11:47.610
by the number of mastery points

00:11:47.610 --> 00:11:51.000
that they earn, on the
top left hand corner.

00:11:51.000 --> 00:11:55.330
We suggest usage of increasing progress

00:11:55.330 --> 00:11:59.520
towards mastery by five to 10
percentage points each week.

00:11:59.520 --> 00:12:01.380
As you see right here in the screenshot,

00:12:01.380 --> 00:12:03.390
this student has made about 20%

00:12:03.390 --> 00:12:04.940
of progress through the entire

00:12:04.940 --> 00:12:07.420
Get ready for fifth grade course.

00:12:07.420 --> 00:12:10.730
Reimagined five to 10
percentage points each week.

00:12:10.730 --> 00:12:13.400
Camp Khan is 10 weeks.

00:12:13.400 --> 00:12:14.970
By the end of 10 weeks,

00:12:14.970 --> 00:12:19.030
if your child has followed
the weekly suggestion,

00:12:19.030 --> 00:12:21.910
they hopefully will be at 100% completion

00:12:21.910 --> 00:12:23.693
or getting pretty close to it.

00:12:29.000 --> 00:12:30.320
All right, delivered a lot of

00:12:30.320 --> 00:12:32.560
information pretty quickly here.

00:12:32.560 --> 00:12:34.980
And we'll just break down some FAQ's,

00:12:34.980 --> 00:12:38.600
some questions that we've
also heard from from parents.

00:12:38.600 --> 00:12:41.257
So when we hear a question,

00:12:41.257 --> 00:12:44.570
"Is Camp Khan right for my child?"

00:12:44.570 --> 00:12:45.750
As we mentioned before,

00:12:45.750 --> 00:12:47.340
Camp Khan is a free resource

00:12:47.340 --> 00:12:50.020
for students entering
grades three through 12.

00:12:50.020 --> 00:12:52.240
And it's a way to brush up on math

00:12:52.240 --> 00:12:54.880
and also a way to look for fun

00:12:54.880 --> 00:12:57.280
and motivational activities
throughout the summer.

00:12:57.280 --> 00:13:00.020
We're hoping it's a low (murmurs).

00:13:00.020 --> 00:13:01.830
And we're also hoping it's flexible.

00:13:01.830 --> 00:13:04.770
So if parents want to join us

00:13:04.770 --> 00:13:06.840
for the whole time, it's great.

00:13:06.840 --> 00:13:09.860
If they wanna join us for
five weeks or three weeks,

00:13:09.860 --> 00:13:12.297
that's totally fine too.

00:13:12.297 --> 00:13:14.960
"What age is Camp Khan for?"

00:13:14.960 --> 00:13:16.430
We are targeting Camp Khan

00:13:16.430 --> 00:13:18.810
for learners entering grades three to 12

00:13:18.810 --> 00:13:19.650
'cause that's where our

00:13:19.650 --> 00:13:23.100
Get ready for grade level
courses are at math.

00:13:23.100 --> 00:13:26.110
Now, younger students can also join us

00:13:26.110 --> 00:13:29.210
for Camp Khan kids beginning July sixth.

00:13:29.210 --> 00:13:31.270
These are for students

00:13:31.270 --> 00:13:32.820
who are ages two through seven.

00:13:32.820 --> 00:13:36.110
Again, younger kids who
might want to have that

00:13:36.110 --> 00:13:38.340
exposure to learning activities

00:13:38.340 --> 00:13:40.193
and fun activities this summer.

00:13:41.760 --> 00:13:43.257
Third question we've heard is,

00:13:43.257 --> 00:13:45.840
"What I have to do to
sign up and participate?"

00:13:45.840 --> 00:13:47.946
Really signing up for Khan Academy

00:13:47.946 --> 00:13:51.300
is most of what you
need to do as a parent.

00:13:51.300 --> 00:13:52.730
Now, your child will get

00:13:52.730 --> 00:13:55.040
these weekly notifications

00:13:55.040 --> 00:13:57.740
with suggestions and recommendations

00:13:57.740 --> 00:14:02.732
once they do any work on
our get ready courses.

00:14:02.732 --> 00:14:04.780
And speaking of get ready courses,

00:14:04.780 --> 00:14:05.687
our last question is,

00:14:05.687 --> 00:14:08.950
"Which get ready course
should my child sign up for?"

00:14:08.950 --> 00:14:12.170
I would suggest that children start

00:14:12.170 --> 00:14:14.950
with a grade level that they're entering.

00:14:14.950 --> 00:14:19.950
Now, if your child is exceptional at math

00:14:19.970 --> 00:14:23.010
or is really doing some advanced math,

00:14:23.010 --> 00:14:26.740
they might go to a
higher grade or assembly.

00:14:26.740 --> 00:14:28.900
If they are struggling a little bit math,

00:14:28.900 --> 00:14:31.410
we might recommend going
in it into a lower grade.

00:14:31.410 --> 00:14:34.150
But broadly, generally speaking,

00:14:34.150 --> 00:14:37.490
we would say the grade level course that

00:14:37.490 --> 00:14:39.150
they should start with on get ready

00:14:39.150 --> 00:14:41.450
is the one that we'll
be entering in the fall.

00:14:43.898 --> 00:14:46.273
All right, so we've done a few FAQ's.

00:14:47.570 --> 00:14:52.070
And so now we're gonna
turn it over to questions.

00:14:52.070 --> 00:14:54.810
And this is where I'm gonna
talk with Patty a little bit.

00:14:54.810 --> 00:14:57.330
And she's gonna share
some of the questions.

00:14:57.330 --> 00:14:59.780
Hopefully we'll be able
to answer them here.

00:15:02.810 --> 00:15:03.643
- Awesome.

00:15:03.643 --> 00:15:05.210
Thank you so much, Roy,

00:15:05.210 --> 00:15:07.850
for sharing that wonderful
information with us.

00:15:07.850 --> 00:15:10.550
And just again, my name is Patty, here.

00:15:10.550 --> 00:15:13.290
I get the pleasure to be on

00:15:13.290 --> 00:15:15.820
the district partnerships team with Roy.

00:15:15.820 --> 00:15:17.740
And so as part of the information

00:15:17.740 --> 00:15:19.150
that Roy just shared with us,

00:15:19.150 --> 00:15:20.750
we also wanna make sure we're grabbing

00:15:20.750 --> 00:15:23.010
any of the questions you might have.

00:15:23.010 --> 00:15:25.540
And so throughout the question area,

00:15:25.540 --> 00:15:27.977
I also saw people were asking,

00:15:27.977 --> 00:15:29.540
"Where can I get the slides?

00:15:29.540 --> 00:15:32.150
Where can I look at the handout?"

00:15:32.150 --> 00:15:34.910
And potentially, "Is this a webinar

00:15:34.910 --> 00:15:36.790
that's gonna be recorded
and shared with us?"

00:15:36.790 --> 00:15:39.570
So the answer to all those is, yes.

00:15:39.570 --> 00:15:42.470
You will receive both the deck.

00:15:42.470 --> 00:15:44.270
Slide deck or handout.

00:15:44.270 --> 00:15:46.480
And you'll also receive a
recording of the webinar

00:15:46.480 --> 00:15:49.300
via email after our session.

00:15:49.300 --> 00:15:53.270
And then if you are in
your GoToWebinar screen,

00:15:53.270 --> 00:15:56.290
there should be a little
tab that says handouts.

00:15:56.290 --> 00:15:58.500
And that tab will have a PDF

00:15:58.500 --> 00:16:00.820
called Camp Khan article webinar.

00:16:00.820 --> 00:16:01.800
So if you click on that,

00:16:01.800 --> 00:16:02.790
you'll then be able to see

00:16:02.790 --> 00:16:05.880
all the information
that Roy shared as well.

00:16:05.880 --> 00:16:07.730
So this would be a great time,

00:16:07.730 --> 00:16:10.080
if you wanna add some pressing questions

00:16:10.080 --> 00:16:11.450
that came up for you.

00:16:11.450 --> 00:16:14.010
I can see a lot of folks are
adding questions as well.

00:16:14.010 --> 00:16:15.340
And we're gonna start out with one

00:16:15.340 --> 00:16:18.920
that I also noticed
was pretty common, Roy.

00:16:18.920 --> 00:16:22.940
And it's specifically
coming to us from Carrie.

00:16:22.940 --> 00:16:25.650
And Carrie has actually already started

00:16:25.650 --> 00:16:27.890
using Camp Khan this week.

00:16:27.890 --> 00:16:31.220
And so she's using it with her two kiddos.

00:16:31.220 --> 00:16:33.400
One of them is in fifth
grade, and seventh grade.

00:16:33.400 --> 00:16:34.750
And they're enjoying it.

00:16:34.750 --> 00:16:36.850
And they're wondering a little bit about

00:16:36.850 --> 00:16:39.070
what the pace should be for a student

00:16:39.070 --> 00:16:40.840
to kind of move through the content.

00:16:40.840 --> 00:16:43.450
So she's saying she wasn't really sure

00:16:43.450 --> 00:16:44.777
what time to aim for.

00:16:44.777 --> 00:16:47.680
"Is there a recommendation or a time

00:16:47.680 --> 00:16:51.330
that students should spend
weekly on Camp Khan?"

00:16:51.330 --> 00:16:52.610
- Yeah, great question Carrie.

00:16:52.610 --> 00:16:53.870
And thanks for getting started

00:16:53.870 --> 00:16:55.480
on the Get ready courses.

00:16:55.480 --> 00:16:58.723
And hope your girls are
enjoying the courses.

00:16:58.723 --> 00:17:02.430
We recommend probably about
two or three hours per week

00:17:02.430 --> 00:17:05.883
on the Get ready for grade level courses.

00:17:05.883 --> 00:17:07.763
Now, you can split those out,

00:17:08.720 --> 00:17:10.820
an hour a day for two days.

00:17:10.820 --> 00:17:13.000
Or you can say, "I'm gonna do 30 minutes

00:17:13.000 --> 00:17:16.780
or 45 minutes a day
for four or five days."

00:17:16.780 --> 00:17:18.160
That's totally up to you.

00:17:18.160 --> 00:17:20.990
Again, we want this to be
as flexible as possible

00:17:20.990 --> 00:17:22.500
given your schedules.

00:17:22.500 --> 00:17:26.500
And then in addition to
the hours spent per week,

00:17:26.500 --> 00:17:28.640
we also recommend that students

00:17:28.640 --> 00:17:31.600
make about five to 10
percentage point increase

00:17:31.600 --> 00:17:33.563
in their mastery progress.

00:17:35.410 --> 00:17:36.500
- Awesome, thank you.

00:17:36.500 --> 00:17:38.500
I think that will be
really helpful for parents

00:17:38.500 --> 00:17:41.396
as they're nudging and
encouraging students

00:17:41.396 --> 00:17:45.330
to work through their Get
ready for grade level courses.

00:17:45.330 --> 00:17:47.540
So a little bit more
on the logistics, Roy,

00:17:47.540 --> 00:17:49.690
just to make sure
parents are really clear.

00:17:49.690 --> 00:17:52.469
And anyone who's joining us on the line.

00:17:52.469 --> 00:17:56.650
Stitcher wants to know, "Is
Camp Khan limited to math?"

00:17:56.650 --> 00:17:58.230
- Yeah, great question.

00:17:58.230 --> 00:18:02.290
So Camp Khan, the work that students

00:18:02.290 --> 00:18:04.700
will be going through is limited

00:18:04.700 --> 00:18:06.790
to the Get ready for grade level courses

00:18:06.790 --> 00:18:08.810
which are in math.

00:18:08.810 --> 00:18:10.225
At the same time,

00:18:10.225 --> 00:18:13.120
we're hoping that Camp Khan
is more than just math.

00:18:13.120 --> 00:18:14.550
We're hoping it's an opportunity

00:18:14.550 --> 00:18:16.100
for students to build confidence.

00:18:16.100 --> 00:18:17.370
It's an opportunity for students

00:18:17.370 --> 00:18:20.060
to have a little bit of
fun because it is summer.

00:18:20.060 --> 00:18:21.880
So we're going to be infusing

00:18:21.880 --> 00:18:24.350
those suggestions for progressing in math

00:18:24.350 --> 00:18:26.580
on those Get ready for
grade level courses.

00:18:26.580 --> 00:18:29.330
Along with say, some reflection prompts

00:18:29.330 --> 00:18:31.997
that asks students to really think about,

00:18:31.997 --> 00:18:33.560
"How do I learn best?

00:18:33.560 --> 00:18:36.540
What can I do when I
find myself struggling

00:18:36.540 --> 00:18:37.600
with learning something?

00:18:37.600 --> 00:18:41.417
How do I feel when I
finally do learn something

00:18:41.417 --> 00:18:43.120
that's really challenging."

00:18:43.120 --> 00:18:45.240
So some of those learning reflections

00:18:45.240 --> 00:18:47.090
and prompts that's gonna
build their confidence

00:18:47.090 --> 00:18:48.580
and awareness as a learner.

00:18:48.580 --> 00:18:50.180
And then also some fun activities,

00:18:50.180 --> 00:18:52.840
like getting outside and
going on nature walks.

00:18:52.840 --> 00:18:55.950
Or doing virtual tours through museums

00:18:55.950 --> 00:18:58.690
that are offering these
great opportunities.

00:18:58.690 --> 00:19:00.470
Or looking through some of our content

00:19:00.470 --> 00:19:03.173
like Pixar in a box or
Imagineering in a box.

00:19:03.173 --> 00:19:04.923
It's really about creativity.

00:19:06.570 --> 00:19:07.680
- Thank you for sharing that.

00:19:07.680 --> 00:19:08.790
Yeah, I think it's great

00:19:08.790 --> 00:19:12.410
to make sure there's a holistic set

00:19:12.410 --> 00:19:15.300
of opportunities for students.

00:19:15.300 --> 00:19:16.133
Awesome.

00:19:16.133 --> 00:19:18.750
So the next question
comes to us from Jeffrey.

00:19:18.750 --> 00:19:21.537
And Jeffrey wants to get super clear,

00:19:21.537 --> 00:19:25.180
"Do parents or students
pick the course level?

00:19:25.180 --> 00:19:27.877
And can they switch if needed?"

00:19:28.950 --> 00:19:30.830
- Great question, Jeffrey.

00:19:30.830 --> 00:19:33.490
Students will naturally
pick the course level.

00:19:33.490 --> 00:19:35.730
Though we went past that parents

00:19:35.730 --> 00:19:38.250
are just sitting alongside their child

00:19:38.250 --> 00:19:39.993
as they pick the course level.

00:19:41.040 --> 00:19:42.860
We do recommend that students

00:19:42.860 --> 00:19:45.050
at least start with the grade level

00:19:45.050 --> 00:19:46.740
that they're gonna be
entering in the fall.

00:19:46.740 --> 00:19:47.930
And your second question,

00:19:47.930 --> 00:19:49.890
they can always switch if they want.

00:19:49.890 --> 00:19:51.980
They can always click in the other classes

00:19:51.980 --> 00:19:54.090
in the other Get ready
for grade level courses.

00:19:54.090 --> 00:19:55.090
Depending on whether they find

00:19:55.090 --> 00:19:58.133
the material too challenging or too easy.

00:19:59.770 --> 00:20:02.900
- Great, I think that flexibility is key

00:20:02.900 --> 00:20:05.500
for students and for parents as well.

00:20:05.500 --> 00:20:07.960
So let's switch the view a little bit

00:20:07.960 --> 00:20:10.600
and think more about
the student themselves,

00:20:10.600 --> 00:20:12.560
who's gonna be working on this content.

00:20:12.560 --> 00:20:17.560
And so when we think about
the design of the courses,

00:20:19.480 --> 00:20:23.260
are they getting students to catch up

00:20:23.260 --> 00:20:24.350
on their current grade level?

00:20:24.350 --> 00:20:26.750
And this question is
specifically from (indistinct).

00:20:26.750 --> 00:20:28.050
So just wannabe clear, (indistinct).

00:20:28.050 --> 00:20:29.867
We're answering your question.

00:20:29.867 --> 00:20:31.530
"Are the Get ready classes designed

00:20:31.530 --> 00:20:34.000
to help students catch up to
their current grade level?

00:20:34.000 --> 00:20:37.580
Or can they also be used
for advanced learners,

00:20:37.580 --> 00:20:40.550
and how could they be used
for advanced learners?"

00:20:40.550 --> 00:20:41.383
- Yep.

00:20:41.383 --> 00:20:43.343
Again, another great question.

00:20:45.424 --> 00:20:47.190
The creation of the Get ready courses

00:20:47.190 --> 00:20:49.960
was more to get students caught up.

00:20:49.960 --> 00:20:52.150
So more to your first question.

00:20:52.150 --> 00:20:53.780
We wanna make sure again,

00:20:53.780 --> 00:20:56.990
that if you do the get
ready for let's say,

00:20:56.990 --> 00:20:59.870
fifth grade course, you're
gonna enter fifth grade

00:20:59.870 --> 00:21:02.213
ready to learn the fifth grade math.

00:21:03.220 --> 00:21:08.130
For advanced learners, will they be good?

00:21:08.130 --> 00:21:09.810
I think the get ready courses

00:21:09.810 --> 00:21:13.520
could potentially be good courses

00:21:13.520 --> 00:21:15.340
for advanced learners too.

00:21:15.340 --> 00:21:17.410
And I'm thinking particularly for,

00:21:17.410 --> 00:21:20.470
if we have some middle school students,

00:21:20.470 --> 00:21:23.880
middle school mathematician who

00:21:23.880 --> 00:21:25.560
are really kind of chomping at the bit

00:21:25.560 --> 00:21:28.450
to know a little bit
about high school math.

00:21:28.450 --> 00:21:31.880
Or to think, "I wonder how
well I would do in algebra?"

00:21:31.880 --> 00:21:35.130
They could take those
high school level courses,

00:21:35.130 --> 00:21:37.350
just to get a sense of
what they would need

00:21:37.350 --> 00:21:39.691
to be successful in those courses.

00:21:39.691 --> 00:21:42.260
So short answer is for advanced learners,

00:21:42.260 --> 00:21:45.020
I would recommend even
going on to grade levels

00:21:45.020 --> 00:21:48.193
above where a student is going
to be entering in the fall.

00:21:50.080 --> 00:21:50.913
- That's a great.

00:21:50.913 --> 00:21:51.770
That's a great suggestion.

00:21:51.770 --> 00:21:53.180
And as we're thinking about

00:21:53.180 --> 00:21:55.010
students potentially looking

00:21:55.010 --> 00:21:58.880
or reviewing content and
potentially getting stuck, right?

00:21:58.880 --> 00:22:00.050
We know that that happens.

00:22:00.050 --> 00:22:02.340
And that's okay when you're learning math.

00:22:02.340 --> 00:22:05.060
So how could kids seek help?

00:22:05.060 --> 00:22:07.440
And this is a question from Nepor,

00:22:07.440 --> 00:22:09.080
who wants to know...

00:22:09.080 --> 00:22:11.100
Or references that you mentioned, Roy

00:22:11.100 --> 00:22:13.960
that there's gonna be an
option to seek guidance.

00:22:13.960 --> 00:22:16.390
So how could students get help?

00:22:16.390 --> 00:22:17.954
- Yep, great question Nepor.

00:22:17.954 --> 00:22:21.510
In each of our exercises in Khan Academy,

00:22:21.510 --> 00:22:25.260
there are videos students can watch

00:22:25.260 --> 00:22:30.260
that gives them a teaching
of what the concept is.

00:22:30.640 --> 00:22:32.960
And in addition, there are hints

00:22:32.960 --> 00:22:35.210
that will give students
kind of step by step

00:22:35.210 --> 00:22:37.620
how you solve this problem.

00:22:37.620 --> 00:22:39.170
We always recommend that students

00:22:39.170 --> 00:22:40.400
watch the video first

00:22:40.400 --> 00:22:43.230
'cause that probably
just about the concept.

00:22:43.230 --> 00:22:44.540
And we've also seen some students

00:22:44.540 --> 00:22:46.210
just watch the videos before

00:22:46.210 --> 00:22:49.063
they even start on their problems.

00:22:50.350 --> 00:22:54.830
In addition to the videos,
if student is really stuck

00:22:54.830 --> 00:22:57.060
they can always just click the hint

00:22:57.060 --> 00:22:59.400
under each question and the hint will be

00:22:59.400 --> 00:23:00.680
a step by step solving

00:23:00.680 --> 00:23:04.020
of that particular question
the student is seeing.

00:23:04.020 --> 00:23:07.170
And we think this is a
great way for students to

00:23:07.170 --> 00:23:09.110
again, take a little bit of ownership

00:23:09.110 --> 00:23:11.720
or more ownership in their learning.

00:23:11.720 --> 00:23:13.610
And also, we hope this is a way

00:23:13.610 --> 00:23:15.980
where a student is constantly

00:23:15.980 --> 00:23:17.570
gonna be asking you the parent

00:23:17.570 --> 00:23:19.520
for help every time you might be stuck.

00:23:20.800 --> 00:23:22.410
- That's really helpful.

00:23:22.410 --> 00:23:25.870
And a similar question from Deanna,

00:23:25.870 --> 00:23:27.130
relate it to that, right?

00:23:27.130 --> 00:23:30.650
Like, "Do parents need
to be hands on helping?

00:23:30.650 --> 00:23:33.650
Or is it fairly simple for
kids to navigate on their own?"

00:23:33.650 --> 00:23:35.260
So maybe just sharing a little bit more

00:23:35.260 --> 00:23:38.000
about how kids can navigate on their own.

00:23:38.000 --> 00:23:39.967
- Yeah, great question.

00:23:39.967 --> 00:23:42.760
The question of whether or how much

00:23:42.760 --> 00:23:44.170
parents should be hands on,

00:23:44.170 --> 00:23:46.610
we leave it totally up to the parent.

00:23:46.610 --> 00:23:48.990
Again, we want Camp Khan and our courses

00:23:48.990 --> 00:23:51.150
to be pretty flexible and ready to promote

00:23:52.931 --> 00:23:55.360
self driven learning but from the student.

00:23:55.360 --> 00:23:59.620
So for a student when they
get on the Khan Academy,

00:23:59.620 --> 00:24:01.780
we do recommend starting
with that course challenge.

00:24:01.780 --> 00:24:03.230
And then the exercises,

00:24:03.230 --> 00:24:06.830
we always recommend that
follow a blue button.

00:24:06.830 --> 00:24:08.851
So there's a blue Start button,

00:24:08.851 --> 00:24:11.020
or a blue Continue button.

00:24:11.020 --> 00:24:12.162
And once you click on those

00:24:12.162 --> 00:24:15.520
then students will get
underway on their exercises.

00:24:15.520 --> 00:24:17.770
And then once in the exercises,

00:24:17.770 --> 00:24:19.726
they can start looking at those videos

00:24:19.726 --> 00:24:21.540
and viewing those hints.

00:24:21.540 --> 00:24:22.980
And then if they're stuck,

00:24:22.980 --> 00:24:24.890
we can recommend that they asked

00:24:24.890 --> 00:24:26.320
maybe an older sibling.

00:24:26.320 --> 00:24:30.330
Or they ask another adult
in the in their household,

00:24:30.330 --> 00:24:34.290
and then eventually we might ask that

00:24:34.290 --> 00:24:35.883
they reach out to the parent.

00:24:37.430 --> 00:24:39.080
- I think that's great scaffolding.

00:24:39.080 --> 00:24:40.940
I think very similar to the way teachers

00:24:40.940 --> 00:24:45.140
have the three before me rule
sometimes in the classroom.

00:24:45.140 --> 00:24:47.320
So maybe parents caregivers out there

00:24:47.320 --> 00:24:48.870
can do the three before me,

00:24:48.870 --> 00:24:51.490
and the first one can definitely be Khan

00:24:51.490 --> 00:24:53.870
and the resources that you mentioned, Roy.

00:24:53.870 --> 00:24:55.280
- Yeah.
- Similar to that,

00:24:55.280 --> 00:24:59.297
I think as part of being
a parent, Telacy asks,

00:24:59.297 --> 00:25:03.110
"How do we as parents see
the progress of our students

00:25:03.110 --> 00:25:04.730
and what they're learning?"

00:25:04.730 --> 00:25:06.930
- Yeah, then a great question.

00:25:06.930 --> 00:25:08.520
A couple ways you can do this.

00:25:08.520 --> 00:25:10.700
One is to just have the student

00:25:10.700 --> 00:25:13.760
have a child show you
what they're working on,

00:25:13.760 --> 00:25:17.080
and how much progress they're making.

00:25:17.080 --> 00:25:19.760
Another way, and we're gonna
send us an upcoming email

00:25:19.760 --> 00:25:24.760
is to join your student
account and watch...

00:25:25.520 --> 00:25:28.330
Not watch I guess, and see their progress

00:25:28.330 --> 00:25:31.000
on the Get ready for grade level course.

00:25:31.000 --> 00:25:34.440
So this is gonna require the parent

00:25:34.440 --> 00:25:36.860
to add the child's account

00:25:36.860 --> 00:25:39.400
and then for the child to
approve (murmurs) the parents.

00:25:39.400 --> 00:25:40.390
So there's gonna be a little bit

00:25:40.390 --> 00:25:44.700
of back and forth so
that the parent can see

00:25:44.700 --> 00:25:46.490
what the child is working on

00:25:46.490 --> 00:25:48.210
and how they're doing on it.

00:25:48.210 --> 00:25:50.140
And we're gonna send
those instructions out

00:25:50.140 --> 00:25:51.853
in an upcoming email.

00:25:53.520 --> 00:25:55.970
- Great, that'll be
really, really helpful.

00:25:55.970 --> 00:25:58.987
We have another question
from Kimberly asking,

00:25:58.987 --> 00:26:03.270
"Can my child use their
district Khan Academy account?

00:26:03.270 --> 00:26:06.840
Or do they have to create
a new student account?"

00:26:06.840 --> 00:26:09.740
- Yeah, students can use existing accounts

00:26:09.740 --> 00:26:11.850
and just go and start working

00:26:11.850 --> 00:26:12.890
on their get ready course.

00:26:12.890 --> 00:26:15.790
They don't need to create a
new account for our Camp Khan.

00:26:17.280 --> 00:26:18.113
- That's great.

00:26:18.113 --> 00:26:19.530
That's very helpful.

00:26:19.530 --> 00:26:22.350
We have now a question from April.

00:26:22.350 --> 00:26:24.940
And we probably have
room for a couple more.

00:26:24.940 --> 00:26:28.060
So for sure, please keep
asking your questions.

00:26:28.060 --> 00:26:30.557
This is from April, who says,

00:26:30.557 --> 00:26:32.000
"Do you have any example

00:26:32.000 --> 00:26:35.100
of the fun activities
that go in conjunction

00:26:35.100 --> 00:26:36.870
with the Get ready courses?

00:26:36.870 --> 00:26:38.927
Who makes the clickable videos?"

00:26:39.800 --> 00:26:41.520
- Yeah, great question.

00:26:41.520 --> 00:26:44.560
So like I mentioned, the fun activities

00:26:44.560 --> 00:26:47.670
will be coming some from
our content library.

00:26:47.670 --> 00:26:50.810
So I mentioned our Pixar in a box,

00:26:50.810 --> 00:26:52.390
our Imagineering and a box.

00:26:52.390 --> 00:26:54.750
And those are kind of
videos and activities

00:26:54.750 --> 00:26:58.060
that are meant to spark
children's imagination.

00:26:58.060 --> 00:26:59.040
We also have content

00:26:59.040 --> 00:27:01.110
from our growth mindset
library for instance.

00:27:01.110 --> 00:27:03.780
Which is really meant to explain

00:27:03.780 --> 00:27:07.130
the brain science behind getting smarter.

00:27:07.130 --> 00:27:10.430
So we see those as more kind
of motivational content.

00:27:10.430 --> 00:27:12.150
So that's one side of that,

00:27:12.150 --> 00:27:14.080
of the final motivation activities.

00:27:14.080 --> 00:27:15.950
They're gonna come from us.

00:27:15.950 --> 00:27:17.110
Another part of the answer

00:27:17.110 --> 00:27:20.190
is from our partner organizations.

00:27:20.190 --> 00:27:23.140
So we will be partnering with schools

00:27:25.040 --> 00:27:28.470
like wide open schools
that have great suggestions

00:27:28.470 --> 00:27:32.630
and activities on things
families can do outdoors

00:27:32.630 --> 00:27:33.560
during this summer.

00:27:33.560 --> 00:27:35.543
For instance, taking a nature walk.

00:27:36.980 --> 00:27:38.950
We'll work with other organizations

00:27:38.950 --> 00:27:42.410
about virtual tours that students

00:27:42.410 --> 00:27:43.870
can take during this summer.

00:27:43.870 --> 00:27:45.180
So those are just some examples

00:27:45.180 --> 00:27:46.680
of what we'll be including

00:27:46.680 --> 00:27:51.637
in the final activity
section of our weekly emails.

00:27:53.340 --> 00:27:55.370
- That's really helpful.

00:27:55.370 --> 00:27:56.203
Great.

00:27:56.203 --> 00:27:58.890
We have another question from Louise.

00:27:58.890 --> 00:28:02.370
Louise says, "I'm ready
Grandma helping my grandson.

00:28:02.370 --> 00:28:04.560
We're at different locations.

00:28:04.560 --> 00:28:06.137
Any suggestions?"

00:28:07.160 --> 00:28:07.993
- Thanks, Louise.

00:28:07.993 --> 00:28:09.500
And thanks for thinking
about your grand son

00:28:09.500 --> 00:28:13.120
even though he may not
be right there with you.

00:28:13.120 --> 00:28:17.060
Our suggestion is to
pass along the article

00:28:17.060 --> 00:28:20.160
that's in this webinar, that handout.

00:28:20.160 --> 00:28:23.180
And there'll be some directions
or for getting started.

00:28:23.180 --> 00:28:27.010
Or to have them get on Khan Academy.

00:28:27.010 --> 00:28:29.950
And there are links to sites,

00:28:29.950 --> 00:28:33.520
specifically the Camp Khan details

00:28:33.520 --> 00:28:36.720
that a student, any student who
wants to get on the website,

00:28:36.720 --> 00:28:38.260
they'll have directions there.

00:28:38.260 --> 00:28:39.450
And then they can get started

00:28:39.450 --> 00:28:41.563
just by following directions on our site.

00:28:43.230 --> 00:28:44.660
- Wonderful.

00:28:44.660 --> 00:28:48.110
And then I think this will
be our last question, Roy.

00:28:48.110 --> 00:28:51.710
Which came up a little bit
with some other participants.

00:28:51.710 --> 00:28:54.557
So this is specifically from
Lim and a couple others.

00:28:54.557 --> 00:28:56.840
"I would like to know
how the Get ready courses

00:28:56.840 --> 00:28:59.370
are different than the
other grade level courses

00:28:59.370 --> 00:29:01.460
you already have out there."

00:29:01.460 --> 00:29:02.600
- Yeah.

00:29:02.600 --> 00:29:04.140
Thanks for that question Lim.

00:29:04.140 --> 00:29:06.610
And I apologize for not
being clear about this

00:29:06.610 --> 00:29:07.557
during the webinar.

00:29:07.557 --> 00:29:09.320
The Get ready courses,

00:29:09.320 --> 00:29:13.730
let's say in our get ready
for fifth grade course level

00:29:13.730 --> 00:29:17.100
it's actually pulling
from our math courses.

00:29:17.100 --> 00:29:20.540
Our regular grade level
courses in fourth grade,

00:29:20.540 --> 00:29:22.750
in third grade, and second grade.

00:29:22.750 --> 00:29:24.910
So the get ready for fifth grade course

00:29:24.910 --> 00:29:28.590
is actually containing skills

00:29:28.590 --> 00:29:32.000
and content from grade
levels below fifth grade

00:29:33.486 --> 00:29:36.210
that have been identified
as the most crucial,

00:29:36.210 --> 00:29:41.030
most important things to know
before you start fifth grade.

00:29:41.030 --> 00:29:42.040
So in other words,

00:29:42.040 --> 00:29:42.873
the difference between

00:29:42.873 --> 00:29:45.700
the Get ready for fifth
grade course content

00:29:45.700 --> 00:29:48.280
and the fifth grade course content

00:29:48.280 --> 00:29:50.010
is the fifth grade course content

00:29:50.010 --> 00:29:53.070
is going to be what your
child learns in the fall.

00:29:53.070 --> 00:29:55.730
The Get ready for fifth
grade course content

00:29:55.730 --> 00:29:57.040
is gonna be the content

00:29:57.040 --> 00:29:58.028
that's gonna prepare your child

00:29:58.028 --> 00:30:01.293
to be successful to learn
fifth grade math in the fall.

00:30:02.340 --> 00:30:04.570
So I hope that distinction was helpful.

00:30:04.570 --> 00:30:06.010
- Yeah, I think that
will be really helpful

00:30:06.010 --> 00:30:06.843
to a lot of folks.

00:30:06.843 --> 00:30:09.570
And I think Roy, that'll
be it for our questions.

00:30:09.570 --> 00:30:11.820
So if you wanna wrap us up.

00:30:11.820 --> 00:30:12.740
- Great.

00:30:12.740 --> 00:30:15.583
Thanks very much again
for all of your time.

00:30:21.310 --> 00:30:23.820
We will send out these slides.

00:30:23.820 --> 00:30:27.300
And in addition, please visit our website

00:30:27.300 --> 00:30:30.527
and you will get an email
with the resources here

00:30:30.527 --> 00:30:32.350
and a survey link.

00:30:32.350 --> 00:30:33.960
So please fill out the survey link

00:30:33.960 --> 00:30:36.680
that'll help us to improve our webinars

00:30:36.680 --> 00:30:39.620
and also continue to hear from you all.

00:30:39.620 --> 00:30:40.553
Thanks very much.