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Algebra and Geometry - Great Together with Geogeb
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Algebra and Geometry - Great Together with Geogeb


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Shows how geogebra can be used to visualize algebraic concepts.

Shows how geogebra can be used to visualize algebraic concepts.

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  • 1. Great Together with GeoGebra and Geometry
  • 2. What comes to your mind at the mention of algebra?
  • 3.
  • 4.
    • Dynamic geometry – move it and see it
    • Visual and tactile
    What does the algebra problem look like in GeoGebra?
  • 5.
  • 6.
    • The ability to interact dynamically with a graph sets GeoGebra apart from many other graphing software and calculators
  • 7. What is GeoGebra?
    • Free and open source software created Markus Hohenwarter of Austria
    • A multi-platform dynamic mathematics software that joins geometry, algebra, tables, graphing, statistics and calculus in one easy-to-use package.
  • 8. What is GeoGebra?
    • Graphics, algebra and tables are connected and fully dynamic
    • Can easily create interactive learning materials as web pages
  • 9. Learning Materials
    • “ Crowdsource” – materials contributed by people all over the world
    • many materials are available in the GeoGebra Wiki
    • All materials created for GeoGebra must be non-commercial, unless prior permission is obtained
  • 10. Solution of Equations
    • Relate algebraic representation to graphical representation
    • Recast an equation as an intersection of the graphs of two functions
    • Explore nature of solutions
  • 11. Algebraic Problem
    • x 2 =2 x + k
    For what value(s) of k does this equation have no solutions? One solution? Two solutions?
  • 12. Solution of Inequalities
    • Relate algebraic representation to graphical representation
    • Recast solution of an inequality in terms of locations on a graph
    • Explore nature of solutions
  • 13.
    • Show graphically the solution of
    • |x| - k > 3
    • -5 < k <5
    Explore nature of solutions – absolute value inequality
  • 14. Enabling Guided Discovery
    • Parameters must be chosen carefully
    • Limit change of parameters to only one at a time
    • Students need guidance on what to observe
  • 15. Examine zeros by varying constant
  • 16. Geogebra Exploration: Trigonometric Functions
    • Quickly graph trig functions
    • Easily insert sliders to vary parameters
    • Explore effects of period and amplitude
  • 17. GeoGebra for web based demos
    • The GeoGebra web page at
    • has links to many online demos for a variety of topics
    • You can easily create your own web applets. You will need a web host to host your applet and related files. No programming required.
  • 18. Exemplary GeoGebra Sites
  • 19. More information