Going Deeper with Interior and Exterior Angles

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SWBAT justify their reasoning when solving a diagram for missing angle measures.

Big Idea

By working on a Hands-On Activity in groups students develop collaboration skills and practice justifying their conjectures.

Group Warm-Up: The Hands-On Task

20 minutes

This group Warm-Up requires students to use angle relationships to solve problems and justify their reasoning. I am also expecting that my students will exhibit the positive group work behaviors that we value in our classroom (MP1). 

To get them started, I will read the directions for the warm-up out loud to the whole class. As I do so I call attention to our class poster listing positive group work behaviors. For today's task, I emphasize the importance of all members of the group having their hands on the group's poster paper. Hands-on is a big step towards ensuring participation. I will also ask them to color code their work today. Students should write their names in their color, and continue to use that color for all of their contributions. My students like to work in color and this helps to ensure individual accountability.

While students work in groups on the problems, I actively circulate the room. I am looking to praisegroups who exhibit positive group work behaviors. I will point out posters that show an equal distribution of colors. I will highlight examples of strategic thinking. I will call attention to groups who justify their reasoning with academic and geometry vocabulary (MP6). I have found that I can motivate effective group work by forcing students to recognize their own great mathematical practices and group habits. Sometimes, catching students doing the right thing works really well. 

Teacher's Note: A colleague in my math department, David Heinke, is the creator of the "hands on" activity structure used in this lesson.



Homework Review

10 minutes

In this Homework, I use the document camera to project an answer key for students.  When students ask questions about the problems, I avoid answering directly and, instead, turn the questions back to the whole class so students have the opportunity to feel that they are mathematical authorities in the classroom while gaining confidence in their ideas. 

I will make sure we spend time discussing at least two ways of solving Problem #12 because it gives students the chance to make connections between different approaches and to critique each other’s reasoning (MP3).

Think-Group-Share: Three Polygons Meet at Point B

25 minutes

I use a Think-Group-Share activity structure for this problem:

Three Regular Hexagons Meet at Point B  

My goals in structuring the activity are:

  • For all students to have an opportunity to access the problem
  • For as many students as possible to share their ideas
  • For students to respond to each other with high-quality feedback
  • For all students to be ready for a robust whole-class discussion

Through the Think-Group-Share approach I expect that most of my students will find more than one opportunity to participate actively. My role will be to monitor participation, to help students articulate their perspectives, and to enable students to make connections between different perspectives on the problem (MP1MP3).

Patience and organization are really important for the above goals to be met. 

  1. Think: Students need individual think time (3-4 minutes) so no one person in the group will take over the problem, dominate the group discussion, and essentially stop the thinking of others.  
  2. Group: The small group discussion is essential for students to safely share out initial ideas, making sure everyone has had the chance to speak once before others can add onto the ideas or raise questions about the ideas (3-4 minutes).  
  3. Share: Ideally, before any one group has completely finished solving the problem, I call the class’ attention for a whole-class discussion.  I display sentence stems I want students to use when sharing out their thinking or commenting on the thinking of others (“I agree…”, “I disagree…”, “I also saw…”, “What I am stuck on is…”, “I don’t know what to do now that I’ve gotten to this part…”). It is important to start the whole-class discussion before any one student has finished solving so that we can have multiple voices in the conversation and greater participation from the class as a whole. I find it easier to attain a group dynamic organically when the problem is still a problem. 

After the whole-class discussion, I hold students accountable to the learning by having each student individually write up their work. I request that they pay particular attention to writing an explanation that justifies the answer to the problem in their own words.