Lesson
8th Grade Math – Coordinate Geometry, Logical Reasoning, Justification and Proof
Clip 1/11: Coordinate Geometry Lesson Part 1
Overview
Antoinette Villarin opens her lesson on coordinate geometry with her students by having them read and reread the problem scenario (which is provided below). In the first read, she asks students to attend to the general idea of the problem. In the second read, she asks students to share the numbers or quantities that they heard in a turn-and-talk with a partner.
“Whitebeard, the notorious pirate of the West Bay, buried treasure on Tiki Island over 200 years ago. Archeologists recently discovered a map showing the location of the treasure. The location has generated quite a bit of media attention, much to the dismay of the archeologists. In order to allow both the media and archaeologists to work together, officials have decided to erect two fences around the location, allowing the media access to the site, yet allowing the archeologists room to work. One fence encloses the actual area where the archeologists will work. Another fence surrounds the enclosed dig area. Descriptions of the fencing locations have been provided to the media so that they may indicate accessible areas for their employees. Use the given information to draw and label a quadrilateral on graph paper indicating the location of the two fences.”
Teacher Commentary
Teacher Commentary
Antoinette Villarin
This is my first year here, and currently we're working on triangles and special right triangles in geometry and trigonometry. And, since I've started, I've noticed that this group, though they would be considered what they say are advanced learners, they need more practice with justification and proving their work. They're very eager to solve a problem and move on to the next task without really sharing what they're doing.
It’s something I've been working on since, I feel like, the first week when I noticed it. We've talked constantly about what it means to be a mathematician: getting the correct answer, but also being able to communicate your thinking, being able to justify how you got your work and share [your thinking] with somebody who's not a math student. Because oftentimes when they would show work, it would be all over the place, and I would tell them, “I understood it, but somebody else didn't.” Justification has been something that I've been really working on to make sure that they understand that getting the right answer is one part of math, but also, explaining it and making sure that they communicate it.
I felt like this task introduced coordinate geometry, which they've had some exposure with since they're taking algebra currently. But they also don't know what midpoint is. I'd never told them what midpoint is, so, I felt like it is a fun problem to actually see how they would approach it, not really knowing even the vocabulary of what it meant.