The Pythagorean Theorem

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Objective

Students will be able to prove the Pythagorean Theorem and solve problems using the Pythagorean Theorem.

Big Idea

Students will apply their understanding of area to prove the Pythagorean Theorem.

Warm-Up: Estimating Radicals

15 minutes

While students work on the Estimating Radicals Warm-Up, which requires them to estimate radicals by identifying the two integers between which they fall, I quickly scan students’ pre-assessments.  The pre-assessments for this unit give me an idea of the extent to which I will need to review the skills used to simplify radicals and radical expressions; it may also uncover some misconceptions that I will need to address during the unit.

Launch the Pythagorean Theorem and Prove It!

25 minutes

Today I use a powerpoint to launch a discussion around the Pythagorean Theorem.  Most of my students have seen this important theorem before, perhaps several times. Today, as a whole class, we prove the Theorem.  In this class, students have just finished a unit on measurement and dimensionality. Building on what they learned, we will decompose a given diagram and determine each area in terms of the parameters a, b, and c, using the resulting expressions to prove the Pythagorean Theorem (MP3, MP4).  

Debrief and Notes

10 minutes

Like most lessons, I debrief the big ideas of the lesson by having students take notes in their notetakers.  I circulate the room as students take notes, checking to see if students want (or need) more examples to try. In general, this part of the lesson goes smoothly, but I am prepared to provide more practice if it is necessary.