A brief collection of resources for starting to consider the idea of variable on Geogebra.
Geogebra is the free dynamic geometry and algebra software available either to download onto your computer or to run as a web app. Find out more at www.geogebra.org. Webstart installs it, and Applet start runs it in your browser. The main place for finding pre-made sketches on specific topics is the Geogebra Wiki.
As we consider the idea of a variable, there are two main uses in secondary algebra: to represent a changing quantity, and to represent an unknown. Both uses are an abstraction or generalization from arithmetic, and challenging concepts for learners.
One sketch that addresses the idea of the unknown asks students to identify an x on the numberline, where some other integers are located as clues. Give it a try. (More sketches from this group at realmath.)
One sketch that uses time as a variable in a 6 hour car race at constant speed explores linear functions in terms of slope and intercept. Give it a try. The sketch can be a little fussy, but has a lot of great features. (See their other sketches at Math 24-7.)
Guess My Rule sketch (webpage). It lets you get a new rule, and pick a variety of inputs, but is pretty clunky as you have to check and uncheck boxes. (Geogebra file.)
basic linear graphing in geogebra (webpage), give this sketch a try. It lets you adjust the y-intercept and another point on the line. You can also enter a line of your own using the input bar. (Geogebra file.)