Strategies for Decomposing 2-D Figures

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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.