# A Tour of GeoGebra

## Award Winning Free Software for Visualizing Math

Calgary City Teachers' Convention

February 15,  2013

Glen Reesor

# A Tour of GeoGebra

• Sight-seeing tour with a little bit of hands-on
• GeoGebra features and constructions for typical high school math
• We'll just be scratching the surface of GeoGebra's capabilities

# What's This “GeoGebra” Thing?

## Part 1

### Classroom Example 1: Domain and Range

• So straight forward, yet...
• How about a graphical approach?

### Classroom Example 2: Sine Law

• Manipulate the equation
• Understand the geometric implications

### Classroom Example 3: Sine Law Ambiguous Case

• Show students dynamically that it's a result of specifying two sides and a non-contained angle

# What's This “GeoGebra” Thing?

## Part 2

• "GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus in one easy-to-use package."
• Created by Markus Hohenwarter as part of a Master's and then PhD in Math Education at University of Salzburg (2001), then continued at:
• Florida Atlantic University (2006 - 2008)
• Florida State University (2008 - 2009)
• Johannes Kepler University (Austria) (2009 - Present)
• Now developed by Hohenwarter and a team of open-source contributors around the world

• Some supporting institutions:
• Google Summer of Code  (2010 - 2012)
• Austrian Ministry of Education
• University of Luxembourg (2005 - 2010)
• Department of Math Sciences, Florida Atlantic University (2006 - 2009)
• Department of Math, University of Salzburg
• Free Software Foundation, Hungary

# Today's Plan

### What's This Geogebra Thing (Cont'd)

• Hands On: Points, angles, functions, sliders, and more

### Educational Scenarios

• Demos, activities, animated solutions, mathematical justifications, multi-step constructions, picture creation, upload to website

### Playtime!

• Play with GeoGebra
• Investigate others' constructions

# Hands On

### Inscribed Angles

• Points
• Line segments
• Angles
• Circles
• Arcs

• Functions
• Sliders
• Points
• Color
• Size

# Educational Scenarios

• Demonstrations
• Activities
• Animated problem solutions
• Mathematical justifications
• Multi-Step constructions
• Picture creation
• Upload to website / Learning Management System (Moodle, WebCT, etc)

## Multi-step Constructions

• GeoGebra isn't limited to the built-in commands.
• How would you create a parabola given the vertex and one point?
• Just do the math...

What a mess.  Does it work?

# Picture Creation

• Use GeoGebra to create beautiful, correct pictures in multiple formats (svg, png, emf, pdf, eps)

• Scenarios
• Shared drive in computer lab
• Learning Management System (Moodle, WebCT, Desire2Learn ...)
• School / Personal website
• www.geogebratube.org

# GeoGebra is Wonderful Because...

• It's a great tool for visualizing and exploring math concepts
• It's absolutely free
• You don't have to be a computer programmer to use it
• There are many GeoGebra constructions on the Internet--either use them directly or modify to your liking (just File/Open the web address)
• You can embed directly in webpages, thus students don't need to install any software
• It understands lots of other math like parametric curves, conics, derivatives, integrals, taylor polynomials, geometric transformations, statistics
• It has other powerful features such as a spreadsheet, CAS (computer algebra system), 3D (next version)
• iPad and Android versions are in the works