After studying the basics of geometry and its basic relationships among lines and angles, we move on to our transformations unit. Specifically, congruence transformations. We will not learn about dilations until we reach our similarity unit. This unit has one big advantage: Much of what we learn here is actually repeated from 8th grade. Keep reading to see how I teach my high school geometry transformations unit.

## Introduction to Transformations Unit

To kick off our transformations unit, we start with basic vocabulary related to transformations. Some of the vocabulary, such as pre-image, image, and rigid motion, is new for students. We also talk about the notation of transformations and how a prime will appear after a letter for each transformation. 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 use the dilation as a counterexample for the rigid motions. Then, students practice identifying translations, reflections, and rotations with a card sort. (Paper Card Sort, Digital Card Sort)

## Translations

After the introduction to transformations, we learn about the 3 rigid motions one day at a time, starting with translations. To begin the lesson, we define translations and look at the different notations for them. We practice determining rules of translations using graphs, graphing translations, and determining the preimage given the vertices of the image and rule.’

## Transformations Unit: Reflections

For reflections, we start with not just vocabulary and notation, but also the properties of a line of reflection. To practice, we determine the line of reflection given a graph of reflections, and then we graph a few reflections. We also practice applying the rules for the special reflections (x-axis, y-axis, y = x, y = -x). I always enjoyed teaching the special reflections, but they are no longer used as frequently in our state assessments

## Rotations

For the sake of consistency, we follow the same format as we did for translations and reflections when we learn rotations. In addition to the vocabulary and notation, we spend time discussing clockwise and counterclockwise rotations, and how to determine the angle of rotation. (We only use 90, 180, and 270 degree angles of rotation.) For practice, we identify the angles of rotation given graphs. Next, we talk about the rules for special rotations (90, 180, and 270) before practicing applying and graphing them. But again, special rotations are barely referenced on the state exam. I only teach these because I enjoy teaching them.

## Transformations Unit: Line & Rotational Symmetry

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. For this lesson, students complete a table as they complete a hands-on discovery activity. Students use patty paper to trace shapes and determine how many lines of symmetry they have. 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.

Prior to beginning the activity, I demonstrate what to do using a rectangle. I show how I fold the patty paper that I traced a rectangle onto to test its line symmetry. And, I show how I spin a rectangle around the 360 degree protractor to test its rotational symmetry. After this activity, students understand line and rotational symmetry very well, and are able to determine the symmetry without using any tools.

## Sequence of Transformations

In the past, this lesson was all about performing sequences of transformations, especially using the rules for special reflections and rotations. Since we started using common core standards, however, the emphasis is on analyzing sequences. Students are asked to determine which two transformations were used given a graph of two figures. Also, they are often given a graph depicting 3 figures, and asked what one transformation would map the preimage onto the final image.

In this lesson, we focus on the aforementioned concepts, but still practice graphing sequences of transformations.

## Congruence

Our final lesson of the transformations unit focuses on congruence. These are all congruence transformations after all. We define congruent and correspondence before analyzing two examples. In those examples, we are looking for which angles and which line segments are corresponding and congruent. After that, we practice using transformations to justify the congruence of two figures. This lesson directly sets us up for our next unit on triangles.

Are you preparing to teach your transformations unit? Whether you are teaching in person or online, you can use interactive notebooks to teach transformations. What I love about interactive notebooks is that students are able to refer to their notes anytime they need – which is very helpful with all of those rules for special reflections and rotations. You can get everything I use to teach the transformations in one convenient bundle. A digital interactive notebook of this unit is also available.