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Laura Veuve, Leadership High School, San Francisco: I put several teachers' ideas and worksheets together for a "C Topics" project where students in pairs or small teams choose a topic from a list of "C topics" (as opposed to AB topics) and then teach it to the class, with a homework assignment and 3 test questions. I'd be happy to share the assignment explanation, expectations, and rubric with you all - I can only take credit for writing a little of it, but I like the way it all came together and I think it's useful. You'll need to adjust it if you have larger classes or a different end-of-year schedule, of course. And the page numbers are from FDWK.
How Sweet It Is: Volumes of Revolution with Candy [doc] [pdf]
Dixie Ross, Pflugerville HS, Texas: The idea is to have the kids sketch each region and then ask them “what does this look like?” They will say various things and when they finally hit Egg! for the first one you pull out the chocolate Easter eggs and pass them out along with plastic knives. Have them hold egg horizontally and think about slicing it with the knife. Should we slice with respect to x or y? They will decide with respect to x and you set up the problem showing how the thickness of the slice is dx. Tell them they can “dispose of their volume model” once they have worked the problem correctly. Materials: Chocolate eggs, Hershey’s kisses, Reese’s peanut butter cups, gumdrops, Vanilla Wafer cookies, golf tees
Video Analysis of Speed Scenarios: projects
Using VideoPoint software, students analyze the position, velocity, acceleration and speed of a hovercraft under different scenarios.
Volumes of Known Cross Sections
Here's a worksheet and directions for making models of volumes with cross sections of
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Calculating the Volume of a Vase
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| http://www.edfac.usyd.edu.au/staff/leadbeam/Woodturning.html |
Volumes of Revolution
My students have always had difficulty visualizing volumes formed by revolving a bounded area around an axis. I made some plywood areas, attached them to dowels and spun them with an electric drill. The radius of the disk or washer is represented as a white rectangle.
| Disks: These are the most basic forms used. |  |
| These are rotated about the y or the x-axis by changing the orientation of the drill. |  |
| The same area is a disk or a washer depending on the axis of rotation. |  |
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Washer method: the same area is rotated around the y or the x-axis.
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