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* *Reflection: Lesson Planning
The Pythagorean Theorem - Section 2: Launch the Pythagorean Theorem and Prove It!

Most students in my classroom have seen the Pythagorean Theorem before entering my classroom, which has several benefits and drawbacks. While exposure to the Pythagorean Theorem is good—most students recall that the theorem has to do with triangles—students often have misconceptions around the most important ideas and have little understanding of what “a,” “b,” and “c” even represent.

In creating a PowerPoint for today’s lesson, I realized I had created an organized structure through which I could keep my lesson moving forward while staying focused on the most important conceptual ideas. I did not get bogged down or distracted by students’ questions and confusions, nor did I give much time for students who had a strong grasp of this content to be bored; I was able to stay focused on reinforcing the most important ideas of the Pythagorean Theorem: that the theorem describes a relationship between the sides of a right triangle and that “c” must always represent the length of the triangle’s hypotenuse. I was also able to help students visually and kinesthetically understand that the converse of the Pythagorean Theorem was also true because of my PowerPoint’s clear directions and structure.

*Keep the Lesson Moving!*

*Lesson Planning: Keep the Lesson Moving!*

# 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