#### What is Geogebra?

GeoGebra is a free dynamic mathematics software for all levels of education that brings together geometry, algebra, spreadsheets, graphing, statistics, and calculus. This technology tools allows developing and/or using materials/applications for mathematics taught from elementary school through college level.

This technology tool is available to use on a number of platforms, including PC, Mac operating systems, Linux, and tablet apps (Ipad, Android, Windows). GeoGebra is also a great tool for using with EOL (English as Other Language) students, as it is available in more than 60 different languages.

Many tutorials are available for the beginners and for advanced GeoGebra users who wish to develop their own material. Teachers have complete freedom to create their own applications for a specific mathematics topic or download an existing application on the topic developed by other educators. GeoGebra allows teachers to develop materials with the potential to challenge learners to think at a higher level. One of the features, GeoGebra Books, is very useful, as it provides teachers with a collection of materials about the same topic, similar to traditional book chapters.

Due to the success of GeoGebra it has a large library of materials developed by many educators. These materials can be sorted by topic, target age, and language. Teachers' discretion is advised when selecting already posted applications as the quality of the applets ranges widely. Also, when developing applications that require precision it is easier to do so on a computer than on a tablet. When looking through highest rated materials, teachers might want to consider searching by date as well, because some of the newer applications could be high-quality but not rated.

## Intuitive Notion of the Limit

 `f(x)` = `f(x)` = Examples 1. Jump discontinuities 1 2. Jump discontinuities 2 3. Continuous 4. One jump 5. Hole at x = 1 6. Exploding 1 7. Exploding 2 8. Infinitely wiggly 9. Shifted square root
In this applet, we see a function `f` graphed in the `xy`-plane. You can move the blue point on the `x`-axis and you can change `delta`, the "radius" of an interval centered about that point. The point has `x`-value `c`, and you can see the values of `c` and `f(c)`. You can type in your own functions in the left input box, or you can use the pre-loaded examples in the right drop down box.

## Pythagorean Theorem

In this applet, we can slide both the green and blue sliders. We notice that the area of the of the orange square is equal to the sum of the area of the blue square and the green square.

#### Resources

1. Geogebra Tutorials
GeoGebra apps for iOS, Android, Windows, Mac, Chromebook and Linux

#### What is the GeoGebra Augmented Reality app?

The Geogebra Augmented Reality App was created to explore the potential of augmented reality for learning and teaching mathematics.

The user can place math objects on a table, floor, or any flat surface, walk around them, and take screenshots from different angles.
The app can display several examples of 3D math objects (Basic solids, Penrose triangle, Sierpinski pyramid, Football, 3D Function, Kleinâ€™s bottle, Ruled Surface, Spiral Staircase).

Guided activities lead you to discover math in the real world by taking screenshots from different perspectives.
The app allows the user/student to enter his/her own functions. Two functions can be shown at the same time and be modified at any time.
The app is currently available for installation on iPhone and on newer versions of iPad. The iPad must have support for augmented reality.