# Strategies for Decomposing 2-D Figures

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## 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.

## Warm-Up: Area Decomposition

20 minutes

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.

## Notes: Sector Area

10 minutes

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.

## Homework Review

15 minutes

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.

## Check for Understanding

10 minutes

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.

## Homework: More Circles

5 minutes

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