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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.

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Algebra and Geometry - Great Together with Geogeb

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