Lesson
8th Grade Math – Coordinate Geometry, Logical Reasoning, Justification and Proof
Clip 6/11: Coordinate Geometry Lesson Part 6
Overview
Continuing the whole-group sharing of strategies, Antoinette Villarin asks her eighth-grade geometry students, “Did anybody solve it a different way?”
In sharing out, one student talks about and demonstrates her work on the document camera, describing how she found the difference in height in units, then in length. Then the student divided by two to find the midpoint, using two different slope triangles. Antoinette repeats what the student shared to confirm understanding. Then Antoinette asks the whole group to discuss the strategy the student used. “How does this help you find the midpoint?”
In pairs, students discuss how slope triangles help them find the midpoint. Antoinette follows up by asking if any students found it a third way. Another student shares her strategy of using a ruler and measurement to calculate the midpoint. Antoinette connects this student’s approach to one that she had anticipated but not shared thus far: folding the graph paper in half.
Teacher Commentary
Teacher Commentary
In having students develop the ability to critique each other’s strategies, I use sentence frames like, “I agree” or “I disagree,” or “How did you get that problem? Where did this number come from?” Sentence frames encourage them to have a constructive dialogue versus, like, “Okay, I get your answer,” while asking questions for going deeper into it.
When this student shared, I saw her hand hesitate, and I said, “Well, why don't you come up here and share it?” And I think she called it stupid. I said, “No.” I wish I had homed in on that a little bit more, like, in hindsight when you think about the lesson. But I told her “No strategy is stupid. I'd like you to share.”
I feel like it was a perfect segue, because as I was walking around and seeing students solve it, I thought one of the strategies would be that students would, like, fold their paper in half, because we had started with some constructions at the beginning of the year, looking at how shapes, like, dilate and form; so, we had folded isosceles triangles in half and seen what properties they had. ... So, I was thinking that would be a strategy they would use, and nobody did it.
So, when she did it, I mean, I feel like it was a perfect transition into showing her that there's even simple ways of folding a paper. I mean, she got the correct answer when I looked at where her midpoint was. So it worked. I loved when I said, “Is that any less than anybody's strategy?” And Logan's like, “Of course not.” So it was perfect.
Just creating that space where there's different ways to solve it, because I do have lots of different abilities, also, within this kind of advanced group.