3-D and Graphing Technologies

For the past week we have been focusing on the 2D/3D graphing functionality of the TI-Nspire CAS CX and the 3D graphing of Geogebra.  One thing that I didn’t know before that I learned this week was that Geogebra is able to not only graph 3 dimensional shapes, but also calculate the surface area and volume.  The immediate subject I could see these graphing tools being used for is geometry.  This technology could aid in lessons surrounding proving surface area and volume equations, calculating the volume of irregular objects, and plotting points using (x,y,z) coordinates.  The lesson idea I used for my quiz involved starting with a rectangular prism and fitting in as many pyramids with the same base and height into that prism.  After placing 3 pyramids inside the prism, students could see in the calculator tab that all three pyramids totaled the volume of the prism, thus proving that the volume of a pyramid is 1/3Bh.  Another lesson I could see this being used for is finding the volume of irregular 3D objects.  For example, students could place a sphere inside a cube and calculate the volume of the shape created by the cube’s volume minus the sphere.  The functionality of graphing and calculating is much easier using these technologies, because graphing is as simple as clicking points and typing in values.  This method is vastly superior than trying to draw out a 3D graph by hand, plus it allows students to experiment with greater ease and with less time erasing errors due to a lack of artistic ability (which I was very familiar with in geometry).