What is GeoGebra?
GeoGebra is a dynamic mathematics software for all levels of education that brings together geometry, algebra, spreadsheets, graphing, statistics and calculus in one easy-to-use package (GeoGebra , 2018). GeoGebra can be used on a desktop or PC, and it’s available as an app that can be downloaded on your mobile device. The GeoGebra website offers the classic version of GeoGebra along with classroom resources with over 1 million free activities, simulations, exercises, lessons, and games for math & science. The app is more condensed, so it is just the classic version of GeoGebra.
When opening the classic version of GeoGebra, this is what the home screen looks like:
On the table of contents bracketed above, it lists graphing, Geometry, 3D graphics, CAS (Computer Algebra System), spreadsheet, probability, and exam mode.
Even though I cannot begin to cover everything that GeoGebra offers, I will give you what they call a “Crash Course” on the graphing and geometry capabilities. However, I highly encourage you to explore the other options available to fully understand what GeoGebra has to offer.
Graphing:
The graphing capabilities are similar to those of Desmos. You can graph various functions, find points of intersection, and observe how a function changes using sliders.
However, what I find most interesting about the graphing capabilities of GeoGebra is you can easily graph a circle, see its equation, and find its area. All you have to do is tap on the circle icon 
at the top of the screen, choose either of the first two options, and draw your circle where desired.
Once you have graphed the circle, you can find its area by tapping on the angle icon 
at the top of the page, selecting area, and then tapping on the perimeter of the circle.
If you wanted to find the x and y-intercepts, you can tap on the point icon 
, choose intersect, and tap in the general area of the x and y intercepts. This command with place a point at the intersection of either the x or y axis and the perimeter of the circle. At the bottom of the page, it will list the points at which the x and y intercepts occur.
Below I have found the two y-intercepts.
The graphing capabilities of GeoGebra can be easily implemented in the mathematics classroom. Whether you are showing students how the graph of a line changes depending on the slope value or showing how various amplitude values change the graph of trigonometric functions, students can visually see the graphs change and draw conclusions based on their observations. I recommend exploring the other options available with GeoGebra graphing because, again, there are so many options and so little time to discuss them all.
Geometry:
Geometry, like graphing, in Geogebra offers a multitude of options to choose from. You can work with circles, polygons, ellipses, parabolas, the list goes on. Using those shapes, you can then translate, reflect about a line, reflect about a point, rotate around a point, or all of the above. The possibilities are endless.
To appreciate the various capabilities with GeoGebra’s Geometry tool, I recommend exploring each icon. However, one of my favorite things to do with the Geometry tool is to reflect a polygon about a line.
You might be asking, how do you reflect a polygon about a line? You begin by tapping on the polygon icon 
at the top of the page. From here, you can mark the vertices of your polygon, but be sure to close your polygon by connecting the last line segment to your first vertex.
Now that the polygon has been created, you will select the line icon 
at the top of the page. Once you have that selected, you will create a line anywhere on the page by tapping and creating two points for the line to go through. Now that the line and the polygon are displayed on the page, you will tap on the reflect about a line icon
at the top of the page. Once you have that selected, tap on the polygon and then the line because this is how you select which polygon to reflect and which line you want to reflect about.
You can continue this process using new lines and either the original polygon or its reflection.
This Geometry tool would be useful in the classroom to show students how the orientation of a polygon changes depending on the transformation. It can be simplified by only focusing on one transformation or it can become more challenging when using multiple different transformations. There are also options to create parallel and perpendicular lines, so students can use their knowledge of geometric properties to create rectangles, square, trapezoids, rhombuses, etc.
Conclusion:
Once again, GeoGebra is a dynamic mathematics software for all levels of education that brings together geometry, algebra, spreadsheets, graphing, statistics and calculus in one easy-to-use package (GeoGebra , 2018). Since this mathematical tool brings together various subjects, it allows for more flexibility when implementing it in a classroom. Taking advantage of everything that GeoGebra has to offer can make learning in the classroom more interactive and visual which results in more of a relational understanding. I look forward to implementing GeoGebra in my classroom and discovering through exploration the various capabilities available.
References:
GeoGebra . (2018). GeoGebra. Retrieved from GeoGebra: https://www.geogebra.org/about
CTSE 5040 