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# Focus on Justification: Interior and Exterior Angles

Lesson 4 of 9

## Objective: Students will be able to use angle relationships in polygons to solve problems and justify their reasoning.

*48 minutes*

#### Check for Understanding

*8 min*

I plan to begin this lesson with a Check for Understanding (CFU). I want to assess my students’ current knowledge of the how to reason about the **interior angle sum of polygons**. This CFU is an individual activity. After about 8 minutes, I will collect my students’ work and then go into the next activity. The goal for today is to help my students to get better at justifying their own reasoning.

#### Resources

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The Common Core calls students to construct viable arguments (**MP3**), which is why I think it is important to explicitly teach my students how to improve their skill at writing mathematical justifications.

Writing is a process. In order to situate my students within a process, I will now return their work for 3 Regular Hexagons Meet at Point B. Once I return their papers, I will have them consider the following guiding questions:

**Why did I choose the strategy I did?****Where do I see key parts of the problem in my work?****How can I convince the reader that my conclusion makes sense?**

In general, my students appreciate having a second chance to look at their math work. The idea of "improving my expression of ideas" takes some time to grow accustomed to, but once they see progress they appreciate it. From my perspective, giving students time to revise their justifications is an opportunity for them to see that they can improve how they write about their problem solving. I find that they demonstrate a deeper understanding as they come to recognize why the conclusions they have drawn make sense to them.

While students make revisions to yesterday's work, I will quickly scan the Checks for Understanding. I am looking to identify students with whom I might need to check in with about their understanding of the content in order to hep them make the revision process a successful learning opportunity.

#### Resources

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#### Group Quiz

*25 min*

To close this lesson I will give a Group Quiz. We worked in yesterday's lesson on group process, so it is important to follow this up with a relevant assessment. I also want to increase students’ accountability to each for understanding the interior angle sum of polygons.

On group quizzes, my students work with each other to come to an agreement about the answers to every problem. They also work together to write up their solutions. While I neither require nor encourage students to make all of their work identical, I have found that students evaluate each other’s work, checking to make sure that the work accurately represents the math ideas they must use and contains all necessary details for a reader to make sense of the work (**MP6**).

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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: Review Angle Relationships to Begin Conjecturing About Polygons
- LESSON 2: Interior and Exterior Angle Sum of Polygons
- LESSON 3: Going Deeper with Interior and Exterior Angles
- LESSON 4: Focus on Justification: Interior and Exterior Angles
- LESSON 5: Kite & Trapezoid Properties and Midsegments of Triangles & Trapezoids
- LESSON 6: Properties of Parallelograms and Special Parallelograms
- LESSON 7: Proofs: Properties of Parallelograms
- LESSON 8: Review: Polygon Properties
- LESSON 9: Discovering and Proving Polygon Properties Unit Assessment