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• ### Kyle Ferreira van Leer

Member
June 26, 2020 at 12:05 pm

Given that we are in break, I’m thinking towards the start of the year when I reflect on a lesson. I’m considering how I want to start building conceptual understanding of isometries in the plane (reflections, rotations, and reflections) and how congruency is related to them.

Attention: I plan on getting students attention by having them look at various visualizations of these isometries in the real world. I will have them notice and wonder about the things happening. I also plan on having them follow some “dance” moves with me to experience the various isometries, without naming any of them.

Generalization: I want to provide students with two images that seem to be congruent, by looking at them, and notice and wonder about them. Then they will have to prove, using the various methods we have begun to experience and name (probably at this point with more student generated language — like turn, flip, and move) how to get from one to the other. This will require students to think about the ways that things move to get from one place to another, to prove congruency. There will be multiple ways of doing it as well, but they have to figure that out. Students will be working in groups to determine the series of steps it takes to get from one spot to the other, using a set of rigid transformations.

Emotion: By having students work with an open ended problem, they are given choice in the way that they solve. Activation through the use of visuals and dancing is also a way to build emotions in the math space — I don’t like them having to stay in their seats for long periods of time. I will provide feedback as I walk around to groups at their vertical white boards who are trying to prove the two shapes are the same, as they figure out a “dance” that gets them from one to the other. And this builds fairness in that they are constructing their own conceptual knowledge of transformational geometry without me having front-loaded any information.

Spacing: This work will be just the beginning of the transformational geometry concept. We will return to this concept later in the year when we look at slope and slope triangles, and when we examine angles from transversals. I want to try and connect it to as many different topics as possible. When we talk about the y-intercept, we will explore how that is a manifestation of a translation in the plane.