# 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.

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.