Debugging Pythagorean Theorem

We have been asked at what time or another in our educational experiences to memorize certain formulas and facts.  Of course, Google makes memorization pretty much a waste of time.  If I want to  know what the Pythagorean Theorem is, all I need to do is Google it.  And, because I am well-versed in algebraic equations, I can easily just plug in numbers to the formula.

But, students get more out of discovering the theorem for themselves.  Plus, a great body of research demonstrates the benefit for students in accessing information in multiple ways such as visually and kinesthetically.  So, when it was time to work on the pythagorean theorem we got creative.

First, I cut out several perfect squares of different sizes from graph paper.  The more the better so that students can work with discover different pythagorean triangles.  Students used the squares to make right triangles.  They were asked to write an equation for each set of triangles they made.  Then, we started to debug the patterns.  What were we seeing?  What were different ways we could write the equations to find a pattern?  For example 9 + 16 = 25 can also be written as 32 + 42 = 52.  We "played" around with this quite a bit until the students eventually could come up with a pattern in a formula.  We then we talked about how variables can be substituted for the numbers.  The students retained the formula but also had a good understanding of why it works.  It's also much more fun than just using pen and pencil to work on a new formula.

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