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Friday, September 16, 2011

Geometry: Points, Lines and Planes

I was going to write up a description of this project we just wrapped up in Geometry, but luckily Allison already did it! (Maybe go read that post if the rest of this doesn't make any sense.) I liked it because it gave students an opportunity to get messy with points, lines and planes. There was a whole lot of productive struggle going on in my Geometry classes.

Here are some nice examples of student work:

Here are some examples that show misconceptions! I'm going to do something with these. Not sure what precisely yet.

Some kids really did seem to be enjoying themselves while learning, but there was also an awful lot of complaining going on. Managing all of their digital photos and getting them from their phones and cameras into their accounts was a bit of a hassle, so I can appreciate the frustration there. But it was good! There were lots of conversations, which if they were blog posts or magazine articles would have titles like:
  • Why You Are Making Us Do This
  • It Is No Fair Making Us Think
  • We Would Prefer to Just Fill Out Worksheets That Ask the Same Questions Over and Over
  • Why Miss Nowak or Anyone Would Like This Job
  • If You Give Miss Nowak Your Phone She Will Change Your Wallpaper to a Math Picture
However, there were also hopeful conversations like:
  • I Would Rather Be in This Class Where I Actually Learn Something Even Though It's Harder
  • My Friend is Jealous She Doesn't Get to Do This Project
  • Holy Crap, a Three-Legged Table Can Never Be Wobbly


  1. I love this idea- I just wished I had seen it earlier. I'll be testing on Chapter 1 this week. I'd love to try a modification as a sort of summary project. Would I lose much if I put them in groups for the discussion then had them pick 3 to illustrate? I could have a master list to make sure every statement was chosen by at least 2 groups

  2. Hm, I'm not sure it's reasonable to try to do anything like this in a short amount of time. Only because ramping up their facility with working with digital images will take longer than you think.

    But maybe you can do a misconception thing. Give them several printouts of images with prompts like, "Trish says that a plane and a line always intersect at one point. She tried to prove it using this picture/drawing. Come up with a way to get Trish to understand her misconception."

    Hope that helps!

  3. "If You Give Miss Nowak Your Phone She Will Change Your Wallpaper to a Math Picture"

    I think you've misclassified this. Surely it's one of the positive comments, right? right? >crickets<

  4. Perhaps I'm just being dumb and not seeing things correctly, but how exactly is the example for two planes intersecting in a line false? It looks to me like they have two planes that are overlapping, but wouldn't that just be the same plane? And if you are considering a finite plane, then why is the "3 points are coplanar is false" slide considered incorrect?

  5. The two planes intersecting at a line is false in the photograph because the index cards representing the planes are supposed to be parallel. The drawing is supposed to be of parallel planes, not overlapping planes. The students should have used dashed lines to indicate edges not in view behind something else.

    We define a plane to be infinite, so three points are always coplanar.

  6. That makes sense, so they are showing that two planes do not always intersect. I thought they were trying to show that the planes were intersecting, but not at a line.

  7. Any thoughts about how to do this if your school doesn't allow cell phones? It's a really cool concept, but the logistics look like a nightmare. Could do this with Google Presenter, and then it's easy to share as a class.

  8. I'm not familiar with Google Presenter.

    The logistics were indeed somewhat nightmarish.

    Do you have digital cameras available for use in class? I had to get permission for them to use cell phones, because I was only able to borrow three digital cameras.

  9. I'm confused about the intersection of two planes as well. You can get a plane (e.g. x = 0, x = 0), a line (e.g. x = 0, y = 0), or no intersection (e.g. x = 0, x = 1).

  10. It might help to read Allisons post outlining the project. For the sometimes statements, of which "two planes intersect in a line" is one, they had to provide two photographs: one example of the statement being true, and another of it being false.

  11. The art teacher has "a bunch", which may mean that I could scrounge a few more together and get one per group four, perhaps. And that's if everything works.

    Google Presenter is the free, bare-bones version of PowerPoint. If the kids have Google/Gmail accounts, they can create a presentation, upload pictures and edit them. They can then share it with other students (or yourself), and then you/they can edit. Y'all can go to file->revision history, and see who edited what.


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