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

2. What comes to your mind at the mention of equations? 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

6. What is GeoGebra? Free and open source software created Markus Hohenwarter of Austria www.geogebra.org A multi-platform dynamic mathematics 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 x 2 =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/GeoGebraCalcul us/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 GeogebraWolfram|Alpha DynamicYesNo InteractiveYes Easy to UseYes, but a learning curve exists Yes SyntaxSpecificNatural language Mobile Device useOnly IpadsTablets and smartphones Makes math interesting Yes!! 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