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# The Pythagorean Theorem

Lesson 1 of 6

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

*50 minutes*

#### Warm-Up: Estimating Radicals

*15 min*

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.

#### Resources

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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**).

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#### Debrief and Notes

*10 min*

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.

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- UNIT 1: Creating Classroom Culture to Develop the Math Practices
- UNIT 2: Introducing Geometry
- UNIT 3: Transformations
- UNIT 4: Discovering and Proving Angle Relationships
- UNIT 5: Constructions
- UNIT 6: Midterm Exam Review
- UNIT 7: Discovering and Proving Triangle Properties
- UNIT 8: Discovering and Proving Polygon Properties
- UNIT 9: Discovering and Proving Circles Properties
- UNIT 10: Geometric Measurement and Dimension
- UNIT 11: The Pythagorean Theorem
- UNIT 12: Triangle Similarity and Trigonometric Ratios
- UNIT 13: Final Exam Review

- LESSON 1: The Pythagorean Theorem
- LESSON 2: Converse of the Pythagorean Theorem and Special Right Triangles Investigation
- LESSON 3: Pythagorean Triples and Special Right Triangles
- LESSON 4: Distance in Geometry
- LESSON 5: The Pythagorean Theorem in Circles
- LESSON 6: Pythagorean Theorem Unit Assessment