When tutoring math online, the biggest challenge is student
engagement because you are not physically present with the
student. One solution to this is that you use some technology and
some tools which provide you this engagement. GeoGebra is one
of those tools, which has a lot of visualization capabilities,
and this tool is amazingly free. And you should take advantage of
this. In this video, I'm going to show you how you can use
GeoGebra in online math tutoring, to improve the
contents of your lectures, and to get high student engagement
and better learning outcomes. GeoGebra is very rich in
features. It has more than one applications, some applications
are focused on geometry, some are on calculations, I will show
you which version you should install. I will also show you
some of the powerful features to make geometry and algebra
concepts clear to your students. When teaching online. I will
also show you how to make animations. I will give you a
few examples. But as a math teacher, you should be able to
explore this tool further. There are many resources available,
created and made public by other math teachers and I will show
you how you can get those resources, you don't have to
reinvent the wheel. So after a short break, I will jump on my
computer and I will show you GeoGebra the visualization tool
for geometry and algebra. But before that, please subscribe to
my channel and hit the bell icon and then hit all notifications
so that you don't miss any video. So let's get started.
GeoGebra is a fantastic tool, which you can use to demonstrate
math concepts during online math tutoring. This provides you
great features for visualization of geometry and algebra
concepts, which your students will love. So first of all, in
order to download this tool in your browser, you type
geogebra.org slash download and you press enter. So there are
many applications available here as you can see, graphing
calculator 3d calculator, geometry, GeoGebra, classic six
and GeoGebra classic file. So I would recommend downloading and
installing GeoGebra classic file which I have done already. And I
would encourage you to create an account sign up with
geogebra.org as I have already signed up, and then you should
be able to get access to all these resources which are
available in this Resources tab. If I click on this resources,
there are a large number of resources which have been
developed and made public by other math teachers and we
should give them the credit while using their resources.
There are resources available for all type of students. For
example, as you can see 500 resources for middle school
math, then there are 1700 plus resources for high school
students. So these resources will give you the opportunity to
see what are other creative ways you can demonstrate mathematical
concepts to your students and they will enjoy it and they will
learn from your demonstrations you can make any missions you
you can plot graphs, you can plot, algebraic functions,
geometrical shapes, and a lot of other things. And no, I'm going
to show you some of the features of GeoGebra classic five and I'm
hoping that you should be able to explore this tool further by
looking into various resources or by based on your own
experience. So, what you are currently looking at, there are
a few windows here on the left hand side we have algebra view,
where we will be seeing our algebraic expressions which we
type in the input bar which is at the bottom and on the right
hand side we have this graphics window where we will be plotting
various shapes and lines and points these kind of things. So
in order to move these graphics window we use this move to move
graphics window tool because sometimes we draw some shape
which is going outside of our visible area so we can move this
window we can move individual objects by clicking on this
arrow. So first let us start drawing with a point so on the
second icon we have a point and there are some other functions
as well. For example points on object and intersect these kind
of things so I click on point and then I click on the graphics
window a point will be drawn a name will be assigned and this
is the coordinates of this point on the x axis it is 1.78 on the
y axis this point is at a location of 6.96. No, there is
this little arrow here set label style. If I click on this
triangle, I have few options currently name and value is
selected. So name of the point is a and value is these
coordinates. I can select only the name if I don't want to show
the coordinates but For now, I would like to show the name and
value. And know the next one is the line currently segment is
selected. But first, I would like to draw a line line is an
infinite thing and segment is a finite thing. So let's draw a
line. And I select one point. And now as you can see that I'm
free to select any other points. So if I select this point, a
line will be drawn in the input bar, if I write the equation of
a line, for example, y is equal to five x plus two, and press
enter, a line will be drawn here, it has an intercept of
two, as you can see that this two is a y intercept, and it has
a slope of five. So this line is drawn in this way as well. So
you can write the expression here. And now let us draw a
graph of x is quiet. So in the input bar, I type x hat hat is
four raised to the power, and then two, and no, I get a graph
of x squared. Similarly, if I want the graph of x cube, I can
do that as well. So this red color is the graph of x cube,
you can change the color from here, if you want, you can
change the color No, let us draw a circle first. And then I will
show you how to draw tangents. So this is the circle, click on
circle, click on the center, and then you start moving your mouse
outward, and it will draw the circle. And now if I click on
this tangents icon, I can draw tangents on this circle. So I
select the circle first, and then I select a point from where
I want to draw the tangent. So let me select this point. So as
you can see that this is one tangent and this is the second
tangent. Now you can move the window by using this move icon,
you can move here and there wherever you want, though, to
delete all this, I would click on Edit, select all, and press
Delete on my keyboard. Let me draw a polygon now. And I click
for first point, then I click for second point, then I click
for the third point and I want to draw triangles. So I close
this here. And now there is an angle icon here, if I click
here, there are various features available, I can find the area,
I can find the slope of any line, I can put the angle
measurement. So in this case, I want to pull the angle
measurement. So I click on angle, and then I click inside
this triangle. So it will show me all these angles. And because
this angle is not clear, so what I can do is click on Arrow, and
then I can move this to a very good location where I can see
this in particular this gamma value. So in this way, you can
draw very clear images. And you can demonstrate to your students
by using this tool. And there are more features to come. Let's
have a look at slider. This is a fantastic feature. So let me
erase this polygon First, select all and delete. Now this slider
is a very powerful feature, you click on slider, and then you
click inside this window. So you will get this slider dialog box.
In order to demonstrate slider I have to make a slider. So bear
with me, you will understand in a minute. So there is a variable
A, which is taking the values from minus five to five, this is
the minimum value and this is the maximum, you can change
these values. So let me change this minimum to zero and maximum
to five. So I click OK. So now this is having values zero to
five, you can do many things with this slider. So for
example, I want to have another variable, which is dependent on
a and as a math teacher, you know that if you want to draw a
point, you need two coordinates. So let us say that P is a point.
And you should take capital P and this p is equal to there are
two coordinates x and y assume that the x coordinate of P is
four, but the y coordinate of P is eight, which is changing. And
now if I press enter, this P will be drawn here based on the
current value of this a 2.5. So as you can see that the y value
of this P is the y coordinate of this P is 2.51 2.5. So the x
coordinate of this P is four. Now if I change the value of
this a, as you can see that this point is moving, because it is
taking the y coordinate from the value of a and you can read this
in the algebra window, the y coordinate of P is 4.7, which is
equal to the value of a at this point. So this is very good to
demonstrate few concepts. And you can also animate this whole
process. So if I right click on this slider, I can click on any
measure on and as you can see that it will move on and it will
demonstrate how the value of P is changing based on the value
of a and in order to stop this you either click on this button
Or you can also click on this animation on the second time and
it will stop. Now, let me give you a very quickly another
example, although it is not required. But, for example, you
want to demonstrate to your students the changes in the
value of sine of x when x is changing, so you can create an
angle slider. So click on the slider, and then click inside.
And instead of the number, no, I'm going to select the angle,
and it has assigned the value alpha here, and the angle is
changing from zero to 360 degree. So I click OK. And I
have this angle slider, the values changing from zero to
360. And I want to show to my students that when the angle is
changing from zero to 360, how the value of sine of this angle
will change. So this is the concept I want to demonstrate.
So what I will do in the input bar, I will take another
variable, let us say y equals sine of alpha. So when I type
sine, it shows me the way I should type sine of x, so it
should be in the brackets. And then I click on this alpha here,
and I can select any Greek letter, but I am interested in
alpha, so I select alpha here, so sine of alpha, and know I
have this y and when I hover over this y it shows me Why is
sine of alpha, which is sine of 356 degree at the moment,
because alpha is 356. So you can demonstrate to your student that
when alpha is zero, sine alpha is zero, when alpha is 360
degree, sine alpha is again zero, when alpha is 90 degree
sine alpha is one, when alpha is 180 degree, sine alpha is zero,
and when alpha is 270 degree sine alpha is minus one. So this
is another demonstration of the concept. Now let me delete all
this again. And now one last example, I would like to give
you with the geometric shapes. So let me draw a circle first.
So I click on the center, and then I move my mouse outward, a
circle is drawn. And now inside this point area, there is this
point on the object. So I draw one point here on the circle.
And now I have these three points, and I want to draw a
triangle. So I click here, and I click on the first point, then
the center of the circle, and then the second point on the
circle. And finally I close this know I have a triangle, which
has two sides equal and now I can demonstrate to my students
that this is a triangle on which two sides are equal side A, B is
the radius of the circle. And side AC is also the radius of
the circle, and radius is same, so a b equals AC. So I want to
demonstrate that if two sides of a triangle are equal, the
opposite angles are also equal. So first I draw angles. So I
click on angle, I click inside this and no angle values are
shown here. Then I move this to a clear position here, so that
my students can see that angle alpha and gamma have same
values, because alpha is opposite to a B and gamma is
opposite to a C. And because these two sides are equal, so
their opposite angles are equal. And not just this, what I can do
now here is I can move this point, so I see that this move
is selected, I click on this point, and I move this point,
and as I move
the angles are changing, but they are still the same, because
the sides are still same and points are on the circle. So
even if I move on the other side of the circle, and even if I am
changing the size of the circle, and know I can demonstrate that
even if the length of the size is changing, because the radius
of the circle is changing, but because both sides are same,
their opposite angle stay the same. So in this way, you can
clear the concept of your students in a very elegant and
professional manner. So this was the last example I wanted to
show you. And know I hope that you can explore this tool
further. And I wanted to show another very good tool for match
tutors, but this video will become very long. So therefore I
have decided to make a separate video for that tool. So stay
connected and I will bring another very important tool for
to train math online. I hope you like this video. If so please
give it a thumbs up and help me grow my channel by subscribing.
Because in that case, my resourcing and my contents will
reach to a larger audience. Thanks for watching and see you
next time.