As we near the end of this unit on triangle congruence and proof, students must be able to:
In my experience, checking one’s own reasoning is a difficult thing for students to do. So, to begin today's lesson I ask students to analyze a sample proof (Warm-Up: Critique Someone Else's Reasoning), checking for the following features of high-quality proofs:
After students check for those features, I ask them to identify changes that can be made to improve the proof, explaining why/how those changes improved the quality of the proof.
Since today’s warm-up is an individual endeavor, I want students to share their work in a structured way because I want to develop students’ habits of mind when they write proofs. I follow up the individual work with one or more of these interventions.
During this group assessment students work on two types of problems.
The first type of problem requires students to analyze given diagrams of pairs of triangles to decide whether there the triangles are congruent. This kind of problem is great for student discussion because students must use the given information to draw other conclusions before using one of the triangle congruence shortcuts to draw a conclusion about the triangles.
The second type of problem is the writing of a proof. Students will have three proofs to write together, which will give them the opportunity to share ideas about possible proof paths to take. Working together on these proofs will also give them the opportunity to check for the features of high-quality proof, which we discussed in the warm-up.
When students complete the Group Assessment I distribute the Proof Challenge 1, a set of proof writing challenges that I will ask all of my students to work on for homework this evening. I find that this type of assignment works well after a Group Assessment, because students have the opportunity to extend themselves individually.