Reflection: Discourse and Questioning The Pythagorean Identity - Section 1: The Ball is on the Tee!


It never fails, this is a fun portion of the lesson once the students get going with it!  "Proof by Example" (rather, lack there of) is a difficult thing for the students to understand until they begin to apply it to their own world.  I have an excellent light hearted relationship with many of my students, so here is an example of how I get things started with a specific example...

Claire, you think that Jimmy is really mean right?  Well does Jimmy being mean imply that EVERY boy is mean?  Usually there is a good deal of light-hearted humor that is going on right now.  After this has subsided, I ask the students if they can think of any other appropriate examples.  

One student told me the following:  My Chevrolet truck broke down on the way to school yesterday.  That doesn't mean that ALL chevy trucks are junk!

I allow my students time to think of other "proof by examples" and we also try to pick out instances in society where we improperly utilize this.  I conclude the conversation by noting that not only is it wrong in this setting, but it is also wrong in mathematics.  It is a nice little transition into the remainder of the lesson.


  When "Proof by Example" isn't really proof at all...
  Discourse and Questioning: When "Proof by Example" isn't really proof at all...
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The Pythagorean Identity

Unit 7: Trig Tidbits
Lesson 14 of 16

Objective: SWBAT prove and apply the Pythagorean Identity.

Big Idea: Making connections between the Pythagorean Theorem and The Pythagorean Identity.

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pythagorean identity
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