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Come for:

  1. A better-than-expected investigation of the Pythagorean Theorem.

Stay for:

  1. Last day of Phobia Week!


Materials

  1. Lab packets.

Attachments

Slide Deck

  1. Fear of crowds, eating, kissing/love, rabies, words
  2. Discuss here a little about Pythagoras, the Pythagoreans, their code of silence, punishable by death.
  3. For the investigation you pass out lots of squares — 1×1, 2×2, 3×3, on up to 15×15 — and have them build triangles out of the sides. They write down the areas of the three squares and whether the triangle formed is obtuse, acute, or right. The conclusions follow pretty quickly from there.
  4. Translating words to symbols.
  5. Next year match this slide with one showing the accurately measured triangles for reference. (i.e. "Ohhh, it was acute.")

Notes & Revisions:

  1. See slide #10.

9 Responses to “Geometry – Day 65 – Pythagorean Theorem”

  1. on 23 Mar 2007 at 8:28 amIndependent George

    I love it.

    The pythagorean theorem was my first encounter with proofs (and, incidentally, Grover Cleveland, but I digress). I remember not being able to really grasp it at first, but nevertheless being aware that we were on the cusp of something huge.

  2. on 23 Mar 2007 at 8:49 amScott Elias

    I love that proof. Dang how I miss teaching whenever I read your site…

  3. on 24 Mar 2007 at 7:46 amdan

    George, I feel like every math class from Algebra through Precalculus exists (in part) to set up this awareness that we’re “on the cusp of something huge,” that some whisp of this concept transfers over to that one, that this can all be predicted somehow, and then calculus takes you over the cusp itself.

    There are certain kids, I’ve found, who are eager to find that waypoint, the kids who never ask “Why are we learning this?” even when they should. It’s easy to take them to the cusp. It’s the others who trouble me. I can only chip away at their resolve not to be impressed by any of this. Any ideas you have towards that end would be appreciated?

    And I’m happy to deal you a hit of nostalgia, Scott. First one’s free.

  4. on 25 Mar 2007 at 5:16 pmTony Lucchese

    I’m with George, proofs just don’t get much better than this. It’s one you can do without even understanding what constitutes a formal proof. It’s probably my second favorite, next to the proof of the existence of irrational numbers.

    I’ve been reading your work for some time and I love it, but if I had to put my finger on a favorite feature, it would be that you manage to work the concept of probability into almost every lesson. It’s a favorite topic of mine and I would argue the single most ubiquitous mathematical concept that we must face each and every day. Kudos!

  5. on 25 Mar 2007 at 7:05 pmdan

    Tony, I’m not sure I deserve any credit for pushing my uncontrollable gambling addiction onto my kids, but I’m glad you think it’s useful. You ever see a way to work a wager into a lesson, I hope you’ll toss me a comment.

  6. on 27 Mar 2007 at 12:17 pme

    Proof? Where is the proof? I must have missed something here, maybe the keynote –> powerpoint conversion swallowed it.

  7. on 03 Apr 2007 at 4:54 pmDee

    Dan, I don’t teach math – I do tech support, but I would like to ask your permission to share these with some teachers and I would like to make clear if it is okay to use these in there classes.

  8. on 03 Apr 2007 at 5:04 pmdan

    Oh, my word, yes. Everything here is re-usable, re-mixable, etc., without attribution. I’m tired of putting these hours in on lessons I only use once a year.

  9. on 03 Apr 2007 at 5:22 pmDee

    Thanks a lot – I’m not comfortable using things found on the internet without permission and these are wonderful. I find myself learning from them and and I am math challenged. I wish you had them up here at the beginning of the year when my daughter was having trouble with proofs LOL

    Again, thanks
    Dee