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Online Interactivities for Precalculus using GeoGebra and Wolfram|Alpha

Online Interactivities for Precalculus using GeoGebra and Wolfram|Alpha. Reva Narasimhan Kean University, Union, NJ. What comes to your mind at the mention of equations?. Dynamic geometry – move it and see it Visual and tactile.

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Online Interactivities for Precalculus using GeoGebra and Wolfram|Alpha

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  1. Online Interactivities for Precalculus using GeoGebra and Wolfram|Alpha Reva Narasimhan Kean University, Union, NJ www.mymathspace.net/geogebra

  2. What comes to your mindat the mention of equations? www.mymathspace.net/geogebra

  3. www.mymathspace.net/geogebra

  4. Dynamic geometry – move it and see it Visual and tactile What does the algebra problem look like in GeoGebra? www.mymathspace.net/geogebra

  5. www.mymathspace.net/geogebra

  6. What is GeoGebra? • Free and open source software created Markus Hohenwarter of Austria www.geogebra.org • A multi-platform dynamicmathematics software that joins geometry, algebra, tables, graphing, statistics and calculus in one easy-to-use package. www.mymathspace.net/geogebra

  7. What is GeoGebra? Graphics, algebra and tables are connected and fully dynamic Can easily create interactive learning materials as web pages www.mymathspace.net/geogebra

  8. 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 www.mymathspace.net/geogebra

  9. 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 www.mymathspace.net/geogebra

  10. Algebraic Problem x2=2x+ k For what value(s) of k does this equation have no solutions? One solution? Two solutions? www.mymathspace.net/geogebra

  11. 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 www.mymathspace.net/geogebra

  12. Explore nature of solutions – absolute value inequality Show graphically the solution of |x| - k > 3 -5 < k <5 www.mymathspace.net/geogebra

  13. 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 www.mymathspace.net/geogebra

  14. Examine zeros by varying constant www.mymathspace.net/geogebra

  15. GeoGebra for web based demos • The GeoGebra web page at www.geogebra.org 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. www.mymathspace.net/geogebra

  16. Exemplary GeoGebra Sites • http://math247.pbworks.com • http://webspace.ship.edu/msrenault/GeoGebraCalculus/GeoGebraCalculusApplets.html • http://www.slu.edu/classes/maymk/MathApplets-SLU.html www.mymathspace.net/geogebra

  17. Wolfram|Alpha (W|A) • W|A is a free online web-based computational engine www.wolframalpha.com • Advantage : can be accessed via smartphone http://blog.mymathspace.net Click on link for Wolfram|Alpha widgets • W|A widgets make it easy to visualize concepts www.mymathspace.net/geogebra

  18. W|A Exploration: Table of Values of a Function • Quickly generate a table of values for a function www.mymathspace.net/geogebra

  19. W|A Exploration: Trigonometric Functions • Quickly graph trig functions • Explore effects of period and amplitude www.mymathspace.net/geogebra

  20. Graphing Two Functions www.mymathspace.net/geogebra

  21. More widgets … • Polar Plotter www.mymathspace.net/geogebra

  22. Comparison www.mymathspace.net/geogebra

  23. More information Web: www.mymathspace.net Click on links for Geogebra or Wolfram|Alpha Email: RNARASIM@kean.edu www.mymathspace.net/geogebra

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