We define congruent and correspondence before analyzing two examples. These are all congruence transformations after all. Our final lesson of the transformations unit focuses on congruence. In this lesson, we focus on the aforementioned concepts, but still practice graphing sequences of transformations. Also, they are often given a graph depicting 3 figures, and asked what one transformation would map the preimage onto the final image. Students are asked to determine which two transformations were used given a graph of two figures. Since we started using common core standards, however, the emphasis is on analyzing sequences.
In the past, this lesson was all about performing sequences of transformations, especially using the rules for special reflections and rotations. After this activity, students understand line and rotational symmetry very well, and are able to determine the symmetry without using any tools. And, I show how I spin a rectangle around the 360 degree protractor to test its rotational symmetry. I show how I fold the patty paper that I traced a rectangle onto to test its line symmetry. Prior to beginning the activity, I demonstrate what to do using a rectangle. They also use folders that I attach shapes and a 360 degree protractor to so they can actually rotate the shapes to determine their rotational symmetry. Students use patty paper to trace shapes and determine how many lines of symmetry they have. For this lesson, students complete a table as they complete a hands-on discovery activity.
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.
After studying the basics of geometry and its basic relationships among lines and angles, we move on to our transformations unit.