Tuesday, February 10, 2015

More Volumes in Calculus {Student Edition}

A couple summers ago, I made some really beautiful (I think) models to represent the kinds of figures we find the volumes of in calculus (post here).  The models worked well last year; I think it made the "formulas" make sense to the kids.  But, I thought it'd be even better if the kids actually got to create some of these in class.  I just couldn't quite figure out how I wanted to do it, without making it a project and without taking up too much class time.  And then, a year late, an idea finally came to me.

First, I bought a package of forty 5.5x8.5" foam sheets that were self-adhesive on one side ($5 at Wal-Mart).  I stacked three sheets together (so I have thirteen "boards") to produce the base of the desired solid.


Then, I graphed two functions (y=2cos(x/2) and y=e^(x/4)) on Desmos, printed them off, and used them as stencils.  So, each foam board has a graph on both sides:


I don't really know why I chose these two graphs other than the fact that I wanted one increasing and one decreasing function, both only in the first quadrant.

Next, I made and printed different kinds of cross sections for the kids to use on cardstock (see file below: squares, rectangles, semi-circles, equilateral triangles, and isosceles right triangles.

And after that, the students did the rest of the work.  They worked in groups of 2-3 to create a solid with either base f(x) or g(x) (I assigned).  Then, they calculated the volume of their solid and put their answer in this table:



Here are some examples of their finished products:


Here's how I told the kids to use the pins:



Finally, visit my Teachers Pay Teachers site HERE for everything you'll need if you want to do this with your calc kids, too!

The first two pages are the two graphs I used.  The next five pages are the cross sections that I printed off on cardstock.  The graphs/cross sections are sized to fit together.  All you'll need is some foam sheets, pins, and Sharpies. :)

6 comments:

  1. I absolutely love this! I can't wait to try this out with my students tomorrow. Thank you so much for the tips, visuals, directions, and the cut-outs!

    ReplyDelete
  2. super duper intutive and visual

    ReplyDelete
  3. I just came across your work. Your file that you have attached is no longer available

    ReplyDelete
  4. Students should download the DHSE Kerala Plus Two Model Paper 2022 for practise in order to achieve good results in the test. Candidates can get the Kerala Plus two question paper 2022 from the Kerala Higher Secondary Education Government's Education Portal. Kerala Plus-2 Model Paper 2022 Candidates must complete the syllabus for each topic before practising the practise papers. Aspirants can learn about the marking method and types of questions asked by looking at sample papers. The test for Kerala board Class 12th may be held between March 17 and March 30, 2022. To learn more about the DHSE Kerala 2022 Plus Two Model Paper, read the entire article.

    ReplyDelete

Tell me what you think!