While this learning module was made with 8th grade students and standards in mind, it can also be used in high school geometry, advanced 7th grade, or a general STEAM course. This module combines geometry, art, and advertising to encourage students to start seeing math in the world around them. 

Before starting this learning module, students should be able to:

• Name basic shapes and figures
• Graph points (x, y) on a coordinate plane
• Identify points (x, y) on a coordinate plane

Supports for gaps in this prior knowledge has been linked in the student side of this section. A pre-assessment in section 1 may also be used to identify students who are struggling with this prior knowledge.

This learning module is designed for a remote or hybrid setting. Options to modify the lessons depending on the setting will be given. If teaching this module in a hybrid setting, I would recommend that Lessons 4, 5, and 6 be taught in-person, as fewer programs exist for accurately graphing rotations. Manipulatives may also be used in an in-person environment, such as reflectors, patty paper, and protractors. This learning module should take about 7 instructional days to complete; however, more time may be given for project completion and peer review at the teacher's discretion. 

Students will need access to the following materials:

• Pencil
• Graph paper
• Ruler or straightedge
• Chromebook or tablet
• Colored pencils, markers, or crayons

This learning module aligns with the Common Core standards for 8th grade Geometry, as listed on the student side.

Learning Target: Students will be able to identify common logos and explain why logos are an important part of company advertising.

The first lesson of the learning module has two purposes: to assess what students already know about rigid transformations and to get them thinking about logos and advertising.

I used Jamboard during remote learning as a way to collaborate as a group. If doing this lesson in-person, students could either use the Jamboard or Post-it sheet paper for that activity. on Jamboard, students can insert text boxes, sticky notes, images, and drawings to create a multimodal presentation. Here is an example of a Jamboard activity we did last year:

Example of Multimodal Jamboard

The pre-assessment covers the following Common Core standards (2012):

• CCSS.MATH.CONTENT.5.G.A.1: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
• CCSS.MATH.CONTENT.8.G.A.1: Verify experimentally the properties of rotations, reflections, and translations

The pre-assessment can be given remotely as a Google Form or in-person as a printed quiz. Emphasize that it is not graded on correctness; it should only be used to determine what students already know. Based on the results from the pre-assessment, you may need to spend an extra day on graphing in the coordinate plane. Depending on how your course is graded, you could grade the pre-assessment for completion, but that is optional. 

Learning Target: Students will be able to describe translations using either written descriptions or (x + a, y + b) notation. Students will be able to perform translations on a coordinate plane.

This lesson works best when taught wither in-person or over a synchronous remote class so that discussion can be encouraged. The warm up of this lesson connects back to the logo focus of this learning module by asking students to analyze a group of logos and determine which one is different. Any of these logos could be the different one, depending on the argument being made, which allows students to see different perspectives and critically think about possible solutions.

The note-taking portion gives students a brief overview of translations, as in previous years, they may have only been named as slides. Students may take notes on their own or guided notes could be provided for struggling students. 

Desmos is a fantastic tool that we used a lot in remote learning. During the activity, teachers can monitor student work, take screenshots of exemplars, and limit which slides students can work on. This allows both for discussion and formative assessment as the activity progresses while still allowing students to work at their own pace. A more guided tutorial on the Desmos teacher platform is included below. 

Video 3: Desmos Teacher Dashboard Running an Activity (Best, 2018)

For students who would benefit for more procedural practice, I included an IXL link to a self-paced digital activity. The program adjusts to student progress, and includes hints and mini lessons for struggling students. 

The update post encourages students to think more deeply about translations, as they not only have to find the correct answer, but catch and discuss common errors. These errors are ones that I have seen in my own classroom, and by seeing and analyzing them in this update, students will show deeper conceptual understanding than just solving a problem.

Learning Target: Students will be able to describe and draw reflections of a given figure over the x-axis or y-axis on a coordinate plane.

This lesson is best done in-person due to the manipulatives that can be used. In the warm up, print the image if possible and give students access to patty/ tracing paper and/ or reflectors. This will help to broaden their thinking and expand the number of strategies used. If you teach this lesson remotely, encourage students to use programs like Paint to draw their figures. 

Geogebra is a geometry tool similar to Desmos. Applets like the one used in today's lesson can be used to explore geometric concepts either remotely or in person. If possible, allow students to pair up for the exploration to further mathematical discourse. If teaching this lesson in-person, you may print each part of the exploration and allow students to use manipulatives like tracing paper, or they may use the applet in pairs. 

The activity with Geogebra builds conceptual understanding, while the IXL activity builds procedural fluency. IXL does require a school account; if your school does not have one, you can use a regular worksheet as well. Once rostered, you can see students' progress and missed questions on each problem set. More information about using the teacher dashboard is included in the video below.

Video 5: IXL *is* personalized learning- Overview for Teachers and Administrators (IXL, 2020)

Learning Target: I will be able to perform a rotation of a given figure 90, 180, 270, or 360 degrees around the origin (0, 0).

Rotations are the hardest transformation to do remotely, so if possible, teach this lesson in-person. For the warm up, students are doing an activity that they may have done in elementary school: making a paper snowflake. This allows students to experience transformations in a tactile way. Depending on the snowflakes that students make, there is the opportunity to discuss minimally translations and reflections. 

Like the translations lesson, students will use Desmos to explore rotations about the rotation and about a point. This Desmos activity has built-in discussion points, so it is best if this lesson is done synchronously so that students can discuss their findings in real time. If done in-person, the different animations can be supplemented with physical graphs, protractors, and tracing paper. Whether done in-person or remotely, the Desmos lesson allows students to gain conceptual knowledge through exploration, rather than through rote memorization.

Since this is the last rigid transformation before the project, the update has students describe a transformation in their own words and explain a real-life application of their chosen transformation. This will create a reference library that students can look back on for extra help during the project. 

Learning Target: Students will be able to identify translations, reflections, and rotations in different logos. Students will be able to describe why transformations are important in advertising and apply it to their own logo.

Today, students will work on identifying rigid transformations in real-world logos. This project is structured as one lesson, but depending on class length and student progress it may take up to three days. 

The project will be assigned through CG Scholar. Students will be able to upload images of their logos and write out explanations. They should have five sections to their work: one for each transformation, an explanation of logos in adversiting, and a references list. To edit images, they may use the Paint application (on Windows) or a similar application on Chromebooks or tablets. 

As students submit their work, you can manually assign two peer reviewers. Each student should peer review two other students' works. You can either provide class time for this process or assign it as homework. If assigned as homework, I would recommend giving students 2-3 days to complete their reviews. A rubric is provided for them rate their peers' work, and they should leave at least 5 annotations. You can see the rubric posted on CG Scholar below:

Logo Project Rubric: Identifying Transformations

Learning Target: Students will be able to use rigid transformations to design their own logo.

This is the final learning module of the Logo Transformations Module. It can be done either in-person or in a synchrnous online class. If the online class must be asynchronous, you can use Google Forms or a similar survey tool to collet data.

In this final module, students are first asked to reflect on the peer review process. Since this is likely the first time students have gone through the full peer review process, students should think about what worked, what did not, and how they can use and give feedback more effectively.

Students will then create their own logo using at least two rigid transformations. Geogebra can be used to create the logo remotely or in-person, or students can use regualr graph paper and upload a picture. On the Geogebra calculator suite, there are tools to automatically perform transformations. Depending on the time frame for this lesson, you can either allow use of these tools or have students do the transformations manually. More on how to use these tools here:

Video 10: Geogebra Rigid Transformation Tools (Merkin, 2020)

Students will then present their work using an update. This will create a collection of student work that other students can then react and comment on, thereby creating a virtual gallery walk. You could either take an extra day for this part of the project, or assign it as homework. 

Finally, there is a post-assessment that is directly related to the original pre-assessment. The post and pre-assessments are both given in Google Forms, which should allow you to easily compare student data from before and after the learning module in Google Sheets.