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# Strategies for Decomposing 2-D Figures

Lesson 4 of 14

## Objective: Students will be able to decompose 2-D figures to strategically calculate area.

## Big Idea: Through small group and whole class discussion, students will be able to make connections between multiple ways of viewing composite areas and shaded areas of circles.

*60 minutes*

#### Warm-Up: Area Decomposition

*20 min*

I want students to focus on sense making, particularly as students consider sector area and ratios of similarity in 2-D and 3-D figures later in this unit. I give this warm-up so students can develop a variety of strategies and make connections between the strategies.

When I debrief the warm-up with students, I call on the Recorder/Reporter from each group to share out a method that emerged from his/her group. After the Recorder/Reporter shares, I open up the problem to student volunteers who want to add another strategy (which I record in a different color) or connect the strategies that have been shared, which requires them to construct viable arguments and critique the reasoning of others (**MP3**). I have found that having the expectation that the Recorder/Reporter will share out encourages a smooth and lively discussion.

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#### Notes: Sector Area

*10 min*

I give brief notes on sector area, encouraging students to first consider how much of the circle we must deal with, then writing out a formula. Since proportional reasoning is sometimes confusing for students, I make sure we try out at least a couple of practice problems as a whole class to model how to think about and apply the formula when solving problems.

#### Resources

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#### Homework Review

*15 min*

Since the Area Application homework featured complex problems, I want to make sure we have time to make sense of our work. In small groups, students compare their work, with the goal of making sure everyone understands. As a whole class, I facilitate a discussion around Problem #3, which requires students to think about how changing the side length of similar figures changes their areas—this is often a difficult concept for students to grasp, which is why I encourage students to come to the board to write out their work, draw models, explain their thinking, and get feedback from their peers.

#### Resources

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#### Check for Understanding

*10 min*

At this point in the unit, I want to assess my students’ understanding of regular polygon area and circle area. I collect students' work, which they do on scratch paper, as students exit the classroom.

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#### Homework: More Circles

*5 min*

In the More Circles homework assignment, students must strategically decompose figures so that they can find the area of shaded regions of circles.

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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: Sectors of Circles
- LESSON 2: Making Sense of Area Formulas for Triangles, Parallelograms, Trapezoids, and Kites
- LESSON 3: Making Sense of Area Formulas for Regular Polygons and Circles
- LESSON 4: Strategies for Decomposing 2-D Figures
- LESSON 5: Sector Area Application: The Grazing Goat
- LESSON 6: Surface Area and Area Differentiation
- LESSON 7: Extreme Couponing: Pizza Edition
- LESSON 8: Area "Quest"
- LESSON 9: Introduction to Volume: Origami Boxes
- LESSON 10: Origami Boxes Gallery Walk
- LESSON 11: Volume Formulas, Cavalieri's Principle, and 2-D Cross-Sections
- LESSON 12: Real World Volume Context Problems
- LESSON 13: Ratios of Similarity and 3D Solids Generated by Revolving 2D Figures
- LESSON 14: Volume "Quest"