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Sunday, December 7, 2008

Change of Plans

So there's been a change of plans since the last post. My mentor teacher decided that my lesson on proofs was going to be way over the students heads. I am inclined to disagree, but it's her class, so I'm happy to comply with her wishes. I'm going to teach a lesson on the Pythagorean Theorem instead. As an activity, I made some of those knotted ropes the ancient Egytians used to survey land. We're going to scout out the foundation of a pyramid and hopefully find some Pythagorean triples in the process. After that, I'm going to introduce the actual equation and do the following informal proof.





Each of the four right triangles are of equal size with area equal to

½AB

The A-side angle and B-side angle of each of these triangles are complementary angles, so each of the angles of the blue area in the middle is a right angle, making this area a square with side length C. The area of this square is C2. Thus the area of everything together is given by:

However, as the large square has sides of length A + B, we can calculate its area as (A + B)2. We can expand this to A2 + 2AB + B2. So

4(½AB) + C2 = A2 + 2AB + B2

2AB + C2 = A2 + 2AB + B2

C2 = A2 + B2

Q.E.D.

So that's the plan for now. I teach the lesson this coming Friday. I'll let you know how it goes. Right now, I'm off to take the Praxis I. Wish me luck.



1 comment:

vlorbik said...

i love this one.
i'm pretty consistent about
including the other diagram
(next to "similarity proof"
and labelled "proof by area
subtraction" in the (what else?)
wikipedia page on the p'an thm:
as clear an example as i know
of a "proof from the book".