Angle Chase Justification

I give this Angle Chase Warm-Up (which comes from the Discovering Geometry textbook) to students because it allows them to apply their understanding of angle relationships on parallel lines. When debriefing the Warm-Up, I make sure to ask students how they came up with the measure of angle q. This is important to surface this in the class discussion since finding the measure for this angle often is the most challenging (MP1) since students must use the transitive property to draw the correct conclusions.

I like to have students work in pairs on the Angle Chase Justification because it creates a safe environment for them to not only apply their understanding of angle relationships on parallel lines, but to write a convincing argument by giving a reason for every statement they make (MP3).  I like to have pairs of students working on it together, each writing in a different color, taking turns to find a new angle's measure and giving a reason for how they know.      

To accommodate different learning styles in the classroom, I like to have students work at stations, where each station features a different problem to solve (MP1).  When doing station work, students can choose whether they would like to work individually, with a partner who will go from station to station with him/her, or with the people who are currently at the station.  Stations give students the chance to collaborate with different people, as well as get the moving around the room, which is important on a long, block schedule.

I write up my expectations for students' process on the whiteboard:

1. Draw the diagram
2. Solve the problem and show enough work so anyone can reproduce your results
3. Justify your work by writing the angle relationships you used alongside your work

I tell students that their primary goals are:

• To understand the types of angle relationships posed in a problem and to be able to justify their work using angle relationships correctly
• To increase students' accountability for communicating clearly in their work and in their explanations

I tell them one of their peers will evaluate their work and provide them with feedback--I have found that explicitly telling students how they will be held accountable helps keep them focused and on task.

For this homework assignment, I want students to practice applying their understanding of angle relationships and to justify reasoning by writing two proofs.  I scaffolded the homework by incorporating a "tool box" of reasons students can pair with their statements when writing their proofs.