![]() ![]() Line and rotational symmetry is my favorite lesson of the unit! Most students have a knowledge of symmetry before geometry from art classes, and possibly elementary school. Transformations Unit: Line & Rotational Symmetry I only teach these because I enjoy teaching them. But again, special rotations are barely referenced on the state exam. Next, we talk about the rules for special rotations (90, 180, and 270) before practicing applying and graphing them. (We only use 90, 180, and 270 degree angles of rotation.) For practice, we identify the angles of rotation given graphs. In addition to the vocabulary and notation, we spend time discussing clockwise and counterclockwise rotations, and how to determine the angle of rotation. I always enjoyed teaching the special reflections, but they are no longer used as frequently in our state assessments Rotationsįor the sake of consistency, we follow the same format as we did for translations and reflections when we learn rotations. We also practice applying the rules for the special reflections (x-axis, y-axis, y = x, y = -x). To practice, we determine the line of reflection given a graph of reflections, and then we graph a few reflections. We practice determining rules of translations using graphs, graphing translations, and determining the preimage given the vertices of the image and rule.’ Transformations Unit: Reflectionsįor reflections, we start with not just vocabulary and notation, but also the properties of a line of reflection. To begin the lesson, we define translations and look at the different notations for them. ( Paper Card Sort, Digital Card Sort) TranslationsĪfter the introduction to transformations, we learn about the 3 rigid motions one day at a time, starting with translations. Then, students practice identifying translations, reflections, and rotations with a card sort. We use the dilation as a counterexample for the rigid motions. After vocabulary, we look at four transformations and students identify them as a translation, reflection, rotation, and dilation using their prior knowledge from 8th grade. We also talk about the notation of transformations and how a prime will appear after a letter for each transformation. Some of the vocabulary, such as pre-image, image, and rigid motion, is new for students. To kick off our transformations unit, we start with basic vocabulary related to transformations. Keep reading to see how I teach my high school geometry transformations unit. This unit has one big advantage: Much of what we learn here is actually repeated from 8th grade. We will not learn about dilations until we reach our similarity unit. Specifically, congruence transformations. So from 0 degrees you take (x, y) and make them negative (-x, -y) and then you've made a 180 degree rotation.After studying the basics of geometry and its basic relationships among lines and angles, we move on to our transformations unit. When you rotate by 180 degrees, you take your original x and y, and make them negative. If you have a point on (2, 1) and rotate it by 180 degrees, it will end up at (-2, -1) We do the same thing, except X becomes a negative instead of Y. If you understand everything so far, then rotating by -90 degrees should be no issue for you. ![]() Our point is as (-2, -1) so when we rotate it 90 degrees, it will be at (1, -2)Īnother 90 degrees will bring us back where we started. What about 90 degrees again? Same thing! But remember that a negative and a negative gives a positive so when we swap X and Y, and make Y negative, Y actually becomes positive. ![]() Our point is at (-1, 2) so when we rotate it 90 degrees, it will be at (-2, -1) What if we rotate another 90 degrees? Same thing. So from 0 degrees you take (x, y), swap them, and make y negative (-y, x) and then you have made a 90 degree rotation. When you rotate by 90 degrees, you take your original X and Y, swap them, and make Y negative. If you have a point on (2, 1) and rotate it by 90 degrees, it will end up at (-1, 2) In case the algebraic method can help you: ![]()
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