Lesson
8th Grade Math – Coordinate Geometry, Logical Reasoning, Justification and Proof
Clip 4/11: Coordinate Geometry Lesson Part 4
Overview
As Antoinette Villarin’s eighth-grade geometry students dig deeper into their problem, she pauses their work, noting, “I want to make sure that everyone understands what the question is asking us to do.” Various students respond. Antoinette reminds the students that when they are defining terms (e.g., midpoint) they might encounter new vocabulary. She challenges the students to find the midpoint using a strategy that is unique to them and one they would be willing to share with the group: “Be ready to share how you’re finding the midpoint, how do you know, and can you find it another way.”
Antoinette restates the lesson goal: to start to use coordinate geometry to justify their thinking. She checks in with mathematics coach and colleague Cecilio Dimas from the Silicon Valley Mathematics Initiative (with whom she debriefs the lesson, and whose teaching is also documented on Inside Mathematics). That includes sharing an aside with Cecilio that she was “hoping someone would try folding [the paper], but nobody’s done that yet.”
Teacher Commentary
Teacher Commentary
As I was walking around while the students worked, I said, “You need to put your pencil down and make sure that you share with each other what the question is asking you, and how you’re starting it.”
I did hear a student or two say, “It's asking for midpoint. What is midpoint?” and I love that. That was my favorite thing, because I felt it gave them a reason to start to learn what midpoint was, very informally.