'Using Geogebra to Discover and Explore Mathematics '
The following is a series of brief mathematical activities to introduce participants to geogebra. It's a great piece of software for getting students to investigate and discover some mathematics for themselves.
Watch the very first "overview" video of this activity: Equation Reflections
and try and reproduce the geogebra files shown in the video for yourself. This will introduce you to functions, trace to spreadsheet, dragging functions, hide/show and the reflection options in geogebra.
Try the Equable Shapes activity from Richard Wade's Lisbon 2011 conference
page. This provides a mathematically interesting introduction to the regular polygon, measure and slider tools in geogebra.
The Paper Baubles
activity can be used with all year groups from Y7 to 12SL (as a bit of mathematical fun before Christmas!). For older year groups, get them to produce the nets for the two Archimedes' Baubles at the bottom of the page (Hexagons and Triangles and Triangles and Squares). I've tried this activity with bright Y9, Y11 and Y12SL classes - all of whom had fun with it and completed the task (at different speeds)! A good introduction for students to the regular polygon tool (the regular polygon tool continues the shape in the same direction, clockwise or anti-clockwise, as the user chooses to select the points!) in the mathematical context of producing nets from a 3D image.
Get students to discover the construct, and then discover, the circle theorems for themselves Circle Theorems
Geogebra 4.2 beta (download here) has a CAS perspective for students to check their algebraic manipulations or Finding Factors
The Lisbon 2011 conference
page "Why Geogebra" has some nice links to some applets showing the far reaching potential of Geogebra for investigating, discovering and creating with mathematics.