Angle Relationships Review and Focus on Justification
Lesson 5 of 6
Objective: Students will be able to justify their reasoning about angle relationships.
In this Warm-Up, students solve two problems that ask them to find the indicated angle measure and to justify their reasoning. As I circulate the room, I encourage students to justify their reasoning by using precise mathematical vocabulary. The ultimate goal of the warm-up is to give students an opportunity to practice using the correct words to support their ideas, which they need to do on the Collective Proof, a task they will work on later in the lesson.
I have students work in pairs in this Reciprocal Teaching activity. Each person has silent time to solve his/her own problem. Then, when both partners are done, they take turns teaching each other about their problem and justifying their work by using correct angle vocabulary.
While pairs work, I circulate the room looking for exemplary student work--that is, work shown clearly and correctly, correct use of angle vocabulary, given information marked clearly in the diagram. I select students to project their work on the document camera so other students in the class have a clear picture of what they should strive for. Because the diagrams for the Reciprocal Teaching activity are largely blank, I look out for students who have introduced their own variables into the diagram to help make their reasoning clearer and easier to follow.
In the Collective Proof, students each tackle one part of a larger proof. The practice writing a small justification, exchange papers to get feedback from another member of their group, and then then bring together their best proof writing to try to write a full, coherent, clear proof (MP3).
On the whiteboard, I make my expectations clear to students by writing out "High Quality Justifications Include..." and showing them specific ways they should attend to precision (MP6):
- State the given information you need to draw logical conclusions
- Re-state what you need to show (the goal of the proof)
- Put a "because" on it (or a "therefore," or a "thus") or use "If...then..." language throughout the proof
- Check that there is always be a "why" for every "what" you state
- Check that your proof reads well (clear, concise, not gaps in logic)
Resource Citation: I want to acknowledge Shira Helft, math teacher at Gateway High School in San Francisco, who shared this "collective proof" task with me.