Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
INTERPRETATION OF OBJECTIVE - G.GMD.B.4
This objective has students visualizing cross sections of solids. This is to help them understand volume from both a stacking and rotating perspective.
(1) The student will be able to determine the cross sections formed by a cut to a solid.
(2) The student will be able to determine all possible cross sections for a given solid.
(3) The student will be able to use cross sections to determine the shape after rotating it about an axis.
THE BIG IDEA
Visualizing - Do you see the Big Picture?... or Do you see the Little Pieces? This objective is all about being able to visualize geometric relationships between 3-D solids and 2-D figures. Thinking and understanding visual space is a powerful tool in many jobs.
TRAPS & PITFALLS
The only real pitfall here (and it is a big one) is that very few students have strong visualization skills. Because of that this objective must be done in a very hands-on approach. To deal with cross sections by just simply asking students to think about them and then do draw them would be very limiting. Only a few students will be able to do this. Use technology or hands on manipulatives to help students expand beyond their current visual limitations. In one of the worksheets I suggest using the SHODOR INTERACTIVE applet on the web to do this. It is really amazing.
There is no formally taught past connection, ultimately students who have strong spatial sense will greatly excel here.
In the future we look at cross sections of the double cone to analyze the conic sections. Also we use these cross sections to develop volumes and areas under curves.
MY REFLECTIONS (over line l)
Last year was my first time really doing something like this and it was fun. The Shodor Interactive applet was just amazing. It allowed students to have full control of the experience and it provided many views of the experience. It was probably one of the best lessons of the year.