This Learning Module is based upon the Common Core State Standards Initiative for 8th Grade Mathematics, Geometry. Upon completing this learning module, students will be able to: -Identify properties of transformations including orientation, similarity, and congruency. -Perform translations, reflections, rotations, and dilations on the coordinate plane and give the coordinates of the new image. -Determine the sequence of transformations that occurred given the pre-image and image on a coordinate plane. -Write an algebraic rule given a verbal description, pre-image and image on the coordinate plane, or a set of coordinate points of pre-image and image. The Common Core State Standards that align with this modeule (Common Core State Standards Initiative, 2018: CCSS.MATH.CONTENT.8.G.A.1 Verify experimentally the properties of rotations, reflections, and translations. CCSS.MATH.CONTENT.8.G.A.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. CCSS.MATH.CONTENT.8.G.A.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. CCSS.MATH.CONTENT.8.G.A.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

Transformation, Translation, Reflection, Rotation, Dilation, Orientation, Congruence, Similarity

This Learning Module is based upon the Common Core State Standards Initiative for 8th Grade Mathematics, Geometry. Upon completing this learning module, students will be able to:

- Identify properties of transformations including orientation, similarity, and congruency.
- Perform translations, reflections, rotations, and dilations on the coordinate plane and give the coordinates of the new image.
- Determine the sequence of transformations that occurred given the pre-image and image on a coordinate plane.
- Write an algebraic rule given a verbal description, pre-image and image on the coordinate plane, or a set of coordinate points of pre-image and image.

The Common Core State Standards that align with this modeule (Common Core State Standards Initiative, 2018):

- CCSS.MATH.CONTENT.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. - CCSS.MATH.CONTENT.8.G.A.2

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. - CCSS.MATH.CONTENT.8.G.A.3

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. - CCSS.MATH.CONTENT.8.G.A.4

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

We will be using this platform, CG Scholar, to participate in this learning module. If you are having trouble, please view these tutorials for CG Scholar. Inform your instructor if you are still having difficulty after looking over the tutorials.

**Learning Objective:** To understand my background knowledge on transformations, including translations, reflections, rotations, and dilations.

**Learning Standards:** 8G1, 8G2, 8G3, & 8G4

In this learning module, we will explore how to perform transformations, how to describe sequences of transformations, and properties of transformation. In order to have a basic understanding of the unit, let's see what you already know.

*Activity 1:* Take the attached SURVEY to see a preview of these topics. This will not count for a grade -- it is just giving your mind some ideas to brainstorm the upcoming unit.

*Activity 2*: Please take out a sheet of lined paper and label it "8G1-8G4 Vocabulary Investigation." Using a math dictionary (or online math dictionary), search for the best mathematical definition to the following words. Copy down the definitions you find onto your sheet of lined paper:

- Transformation
- Translation
- Reflection
- Rotation
- Dilation

*Comment*: Based upon the survey questions, do you have any predictions about what we will be learning? What skills (that you already know) do you think will help you succeed in this learning module?

**Lesson Objective:** To understand students' background knowledge on geometric transformations.

**Student Materials:** Computer, lined paper, pencil

**Teacher Materials:** Computer

**Academic Standards**

CCSS.MATH.CONTENT.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations:

- CCSS.MATH.CONTENT.8.G.A.1.A: Lines are taken to lines, and line segments to line segments of the same length.
- CCSS.MATH.CONTENT.8.G.A.1.B: Angles are taken to angles of the same measure.
- CCSS.MATH.CONTENT.8.G.A.1.C: Parallel lines are taken to parallel lines.

CCSS.MATH.CONTENT.8.G.A.2

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

CCSS.MATH.CONTENT.8.G.A.3

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

CCSS.MATH.CONTENT.8.G.A.4

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

**Lesson Structure**

*Activity 1: Survey*

Making connections to previous knowledge is extremely important in the math classroom. This short information survey allows the instructor to learn what prior knowledge students have about geometric transformations. The teacher can use the results of the survey to help inform instruction. For example, if there is a particular topic in which many students are familiar, then the instructor can spend less time reviewing that concept and more time on the concepts unfamiliar to the class. The survey covers the four Common Core State Standards addressed in the learning module, as noted above.

*Activity 2: 8G1-8G4 Vocabulary Investigation*

Now that students have had a little exposure to some of the concepts related to the learning module, they have the opportunity to use a tool, the dictionary, to discover more information about key vocabulary words and concepts they will learn. Since there are many definitions of these words, there are no correct or incorrect answers -- this is just to get students thinking about the unit. This would be a great place to hold a class discussion, whiparound, or Socratic Seminar.

**Learning Objective:** To identify properties of translations and perform them on a coordinate plane.

**Mini Lesson:** Watch the video below while filling out this notes sheet.

You will now complete various activities to practice your skills in applying properties of translations. Show work for your activities on the Task Card below:

*Activity 1 (Technology):* Khan Academy assignment called "Translate Shapes." There is no work to show on the task card for this assignment. Your task is to manipulate the green points to form the image based on the pre-image's translations. If you do not earn 100%, you must press "practice again" and repeat until achieving 100%. Take a screenshot of your 100% completion. There are four questions.

*Activity 2 (Teacher Demo):* Check for understanding problem. Your task is to draw the pre-image of the triangle and perform two different transformations on it. Please use a different color for each triangle.

*Activity 3 (Individual Task):* Emoji Translation. Your task is to translate the 16 objects to their new locations on the bottom graph. When you are finished, you will see a common emoji.

Please turn in the completed task card to your teacher. They will then give you this homework assignment to complete. It is due the day after you receive it.

*Comment:* Two words mentioned in the homework assignment that may be unfamiliar are **orientation** and **congruent**. What do you think these words mean? How do you think these words affect a shape before or after the translation?

*Create an Update:* Find a real-world application of translation. How does it work? How does the movement relate to translations on the coordinate plane? Comment on 3 updates once you have created your own.

**Lesson Objective:** To identify properties of translations and perform them on a coordinate plane.

**Student Materials:** Computer, headphones, pencil, ruler, colored pens or pencils

**Teacher Materials:** Computer, notes sheet (1 per student), task card (1 per student), homework (1 per student)

**Academic Standards**

CCSS.MATH.CONTENT.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations:

CCSS.MATH.CONTENT.8.G.A.1.A

Lines are taken to lines, and line segments to line segments of the same length.

CCSS.MATH.CONTENT.8.G.A.1.B

Angles are taken to angles of the same measure.

CCSS.MATH.CONTENT.8.G.A.1.C

Parallel lines are taken to parallel lines.

CCSS.MATH.CONTENT.8.G.A.3

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

**Lesson Structure**

This lesson gives students a basic overview of translations. Student will begin by learning our mathematical definition of transformation and translation. This will allow students a point of comparison from the activity completed in the pre-assessment section.

The video goes through how to perform translations on the graph, how to describe them verbally, and how to write an algebraic rule for translations. Example 2 is purposely left blank so students can complete it at a later time. This is a great way for students to self-assess, since the instructor will not check this particular example.

The task card provides students with the opportunity to practice what they have learned about translations through various activities. The Khan Academy is a manipulative for students to use to perform the transformations. The Check for Understanding allows students to practice translations by hand and to demonstrate student knowledge of the algebraic rules. It is really a formative assessment to help the teacher inform instruction. The emoji translation is a fun way for students to apply their understanding of translations. The final product is the house emoji. The answers to the task card are listed below:

The homework assignment allows students to continue to practice with translations. The answer key is below:

Monitor the student discussion in the comments section. Students are challenged to think about the meaning of **orientation** and **congruence**. Students may have some background knowledge, while others may have no idea or may try to look it up. This gives students a preview of the fifth lesson of this learning module. The update allows students to think to make real-world connections with mathematics.

**Learning Objective:** To identify properties of reflections and perform them on a coordinate plane.

**Mini Lesson:** Watch the video below while filling out this notes sheet.

You will now complete various activities to practice your skills in applying properties of translations. Show work for your activities on the Task Card below:

*Activity 1 (Technology):* Khan Academy assignment called "Reflect Shapes." There is no work to show on the task card for this assignment. Your task is to manipulate the green points to form the image based on the pre-image's translations. If you do not earn 100%, you must press "practice again" and repeat until achieving 100%. Take a screenshot of your 100% completion. There are four questions.

*Activity 2 (Teacher Demo):* Check for understanding problem. Your task is to draw the pre-image of the triangle and perform two different reflections on it. Please use a different color for each triangle.

*Activity 3 (Individual Task):* Emoji Reflection. Your task is to reflect the 8 objects to their new locations on the bottom graph. When you are finished, you will see a common emoji.

Please turn in the completed task card to your teacher. They will then give you this homework assignment to complete. It is due the day after you receive it.

*Comment:* The two challenge problems do not reflect over the x-axis or y-axis. Where do you think these lines are? What do you think the images look like for the two pre-images? How do you think you would reflect something over the line y = x? y = -x?

*Create an Update:* Find a real-world application of reflection (needs to be more specific than a mirror). How does it work? How does the movement relate to reflection on the coordinate plane? Comment on 3 updates once you have created your own.

**Lesson Objective:** To identify properties of reflections and perform them on a coordinate plane.

**Student Materials:** Computer, headphones, pencil, ruler, colored pens or pencils

**Teacher Materials:** Computer, notes sheet (1 per student), task card (1 per student), homework (1 per student)

**Academic Standards**

CCSS.MATH.CONTENT.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations:

CCSS.MATH.CONTENT.8.G.A.1.A

Lines are taken to lines, and line segments to line segments of the same length.

CCSS.MATH.CONTENT.8.G.A.1.B

Angles are taken to angles of the same measure.

CCSS.MATH.CONTENT.8.G.A.1.C

Parallel lines are taken to parallel lines.

CCSS.MATH.CONTENT.8.G.A.3

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

**Lesson Structure**

This lesson gives students a basic overview of reflections. Student will begin by learning our mathematical definition of reflection. This will allow students a point of comparison from the activity completed in the pre-assessment section.

The video goes through how to do reflections on the graph, how to describe them verbally, and how to write an algebraic rule for reflections. Example 3 is purposely left blank so students can complete it at a later time. This is a great way for students to self-assess, since the instructor will not be checking this particular example.

The task card provides students with the opportunity to practice what they have learned about reflections through various activities. The Khan Academy is a manipulative for students to use to perform the reflections. The Check for Understanding allows students to practice reflections by hand and to demonstrate student knowledge of how to write the algebraic rules. It is really a formative assessment to help the teacher inform instruction. The emoji reflection is a fun way for students to apply their understanding of reflections. The final product is the pencil emoji. The answers to the task card can be found below:

The homework assignment allows students to continue to practice with reflections. The answer key is below:

Monitor the student discussion in the comments section. The prompt challenges students to think about how reflections would change if they are not over the x-axis or y-axis. This is a section for students to make predictions, as this content will not be assessed on the summative assessment. The update allows students to think to make real-world connections with mathematics.

**Learning Objective:** To identify properties of rotations and perform them on a coordinate plane.

**Mini Lesson:** Watch the video below while filling out this notes sheet.

You will now complete various activities to practice your skills in applying properties of rotations. Show work for your activities on the Task Card below:

*Activity 1 (Technology):* Khan Academy assignment called "Determine Rotations." There is no work to show on the task card for this assignment. Your task is to manipulate the green points to form the image based on the pre-image's translations. If you do not earn 100%, you must press "practice again" and repeat until achieving 100%. Take a screenshot of your 100% completion. There are four questions.

*Activity 2 (Teacher Demo):* Check for understanding problem. Your task is to draw the pre-image of the rectangle and perform a rotation on it. Please use a different color for each rectangle.

*Activity 3 (Individual Task):* Emoji Rotation. Your task is to rotate the 6 objects to their new locations on the bottom graph. When you are finished, you will see a common emoji.

Please turn in the completed task card to your teacher. They will then give you this homework assignment to complete. It is due the day after you receive it.

*Comment:* How do you feel about your understanding of the three types of transformations we have discussed? Which is the most difficult for you and why? Would you be ready to take a short quiz on translations, reflections, and rotations? Explain why or why not. If you are ready, see your instructor to take it. If you are not ready, see your instructor to come up with a plan to prepare for it. You cannot move on to the next lesson until you take it.

*Create an Update:* Find a real-world application of rotation. How does it work? How does the movement relate to on the coordinate plane? Comment on 3 updates once you have created your own.

**Lesson Objective:** To identify properties of rotations and perform them on a coordinate plane.

**Student Materials:** Computer, headphones, pencil, ruler, colored pens or pencils

**Teacher Materials:** Computer, notes sheet (1 per student), task card (1 per student), homework (1 per student)

**Academic Standards**

CCSS.MATH.CONTENT.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations:

CCSS.MATH.CONTENT.8.G.A.1.A

Lines are taken to lines, and line segments to line segments of the same length.

CCSS.MATH.CONTENT.8.G.A.1.B

Angles are taken to angles of the same measure.

CCSS.MATH.CONTENT.8.G.A.1.C

Parallel lines are taken to parallel lines.

CCSS.MATH.CONTENT.8.G.A.3

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

**Lesson Structure**

This lesson gives students a basic overview of rotations. Student will begin by learning our mathematical definition of rortation. This will allow students a point of comparison from the activity completed in the pre-assessment section.

The video goes through how to perform rotations on the graph, how to describe them verbally, and how to write an algebraic rule for rotations. This lesson is a bit longer because there are three different rotations that can occur.

Note that our center of rotation is the origin for these problems. This allows us to perform the rotation without using tracing paper. Some students may find this to be difficult. If so, you may want to provide them with tracing paper and have them use it to perform rotations. If this applies to any of your students, please send them the following video to help increase their understanding.

The task card provides students with the opportunity to practice what they have learned about rotations through various activities. The Khan Academy is a manipulative for students to use to perform the rotations. The Check for Understanding allows students to practice a rotation by hand. It is really a formative assessment to help the teacher inform instruction. The emoji rotation is a fun way for students to apply their understanding of rotations. The final product is the lightning bolt emoji. The answers to the task card are listed below:

The homework assignment allows students to continue to practice with rotations. The answer key is below:

Monitor the student discussion in the comments section. This question serves as a form of self-reflection for the students. The students will approach you either asking for the quiz or asking for ways to help prepare for the quiz. The quiz can be found below:

Students cannot move on to the next lesson (Dilations) until they take the quiz. They must be approaching standards, at a minimum, to move on to the lesson. Otherwise, they will need to review and retake the quiz.

The update allows students to think to make real-world connections with mathematics.

Learning Objective: To identify properties of dilations and perform them on a coordinate plane.

Mini Lesson: Watch the video below while filling out this notes sheet.

You will now complete various activities to practice your skills in applying properties of dilations. Show work for your activities on the Task Card below:

*Activity 1 (Technology):* Khan Academy assignment called "Dilations: Scale Factor." There is no work to show on the task card for this assignment. Your task is answer the questions to determine the scale factor or side lengths of the pre-image (blue) or image (pink). If you do not earn 100%, you must press "practice again" and repeat until achieving 100%. Take a screenshot of your 100% completion.There are four questions.

*Activity 2 (Teacher Demo):* Check for understanding problem. Your task is to draw the pre-image of the triangle and dilate it. Then, you need to perform a rotation with your newly dilated shape. Please use a different color for each step.

*Activity 3 (Individual Task):* Emoji Dilation. Your task is to dilate the 10 points of the start emoji to their new locations on the bottom graph. Make sure you fill out the table, draw all new points, and connect all the new points..

*Comment:* Now that you have learned about all four types of transformations, how are they similar? How are they different? Explain your answer thoroughly.

*Create an Update:* Find a real-world application of dilation. How does it work? How does the movement relate to dilation on the coordinate plane? Comment on 3 updates once you have created your own.

**Lesson Objective:** To identify properties of dilations and perform them on a coordinate plane.

**Student Materials:** Computer, headphones, pencil, ruler, colored pens or pencils

**Teacher Materials:** Computer, notes sheet (1 per student), task card (1 per student), homework (1 per student)

**Academic Standards**

CCSS.MATH.CONTENT.8.G.A.3

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

CCSS.MATH.CONTENT.8.G.A.4

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

**Lesson Structure**

This lesson gives students a basic overview of dilations. Student will begin by learning our mathematical definition of dilations. This will allow students a point of comparison from the activity completed in the pre-assessment section.

The video goes through how to perform dilations on the graph, how to describe them verbally, and how to write an algebraic rule for dilations. We go through the notes section here since there is not too much information about dilations -- they are fairly straightforward.

The task card provides students with the opportunity to practice what they have learned about dilations through various activities. The Khan Academy allows students to use critical thinking to compare the pre-image with the image for dilated images. The Check for Understanding allows students to practice dilations by hand. It is really a formative assessment to help the teacher inform instruction. The emoji dilation is a fun way for students to apply their understanding of dilations. This time, students already know that we are dilating the star emoji. The answers to the task card are listed below:

The homework assignment allows students to continue to practice with dilations. The answer key is below:

Monitor the student discussion in the comments section. The prompt challenges students to think about similarities and differences between the four types of transformations. The update allows students to think to make real-world connections with mathematics.

**Learning Objective:** To determine the changes in congruence and orientation of transformations.

**Mini Lesson #1:** Watch the video below and take your own notes.

*Activity #1 (Technology):* Khan Academy assignment called "Congruence & Transformations." Your task is to determine whether the pre-image and image given are congruent. If you do not earn 100%, you must press "practice again" and repeat until achieving 100%. Take a screenshot of your 100% completion. There are four questions.

**Mini Lesson #2:** Watch the video below and take your own notes.

Activity #2 (Technology): Khan Academy assignment called "Similarity & Transformations." Your task is to determine whether the pre-image and image given are similar. If you do not earn 100%, you must press "practice again" and repeat until achieving 100%. Take a screenshot of your 100% completion. There are four questions.

Please show your teacher both screenshots from the Khan Academy assignments. They will then give you this practice test to complete. It is due the day after you receive it.

*Comment:* After taking the practice test, which questions were relatively easy? Which questions were difficult? Based on your confidence of completing the practice test, what do you think you need to study more and why?

**Lesson Objective:** To determine the changes in congruence, similarity, and orientation of transformations

**Student Materials:** Computer, headphones, pencil

**Teacher Materials:** Computer, practice test (1 per student)

**Academic Standards**

CCSS.MATH.CONTENT.8.G.A.2

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

CCSS.MATH.CONTENT.8.G.A.4

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

**Lesson Structure**

This lesson structure is a bit differently from the other lessons. Instead of discussing a type of transformations, we are discussing properties that may or may not apply to the four types of transformations.

The first video takes students through orientation and congruence. It mainly focuses on translations, reflections, and rotations. Students learn definitions for orientation and congruence and how it affects these specific transformations. They then complete a Khan Academy assignment to solidify their understanding.

The second video takes students through similarity and mainly focuses on dilations. Students learn its definition and how it affects transformations. They then complete a Khan Academy assignment to solidify their understanding.

Issue students the practice test when they have shown you both screenshots of 100% on the Khan Academy assignments. Monitor the comments section to see which questions cause students the most difficulty. The answer key to the practice test can be found below:

**Learning Objective**: To review and demonstrate understanding of geometric transformations.

**Learning Standards: **8G1, 8G2, 8G3, and 8G4

To review, we have learned many essential skills within the realm of 8th Grade Geometry.

**Pre-Assessment:**We investigated the topics that we would learn about throughout the learning module.**Translations:**Our first lesson focused on recognizing transformations and performing them on the coordinate plane.**Reflections:**Our second lesson focused on recognizing reflections and performing them on the coordinate plane.**Rotations:**Our third lesson focused on recognizing rotations and performing them on the coordinate plane.**Dilations:**Our fourth lesson focused on recognizing dilations and performing them on the coordinate plane.**Properties of Transformations:**Our fifth lesson focused on determining orientation, congruence, and similarity of transformations.

*Comment:* What is your favorite transformation and why? What do you wish we learned about in this module that we did not cover? Explain your reasoning completely.

*Activity #1:* Review over material as you feel necessary. There are three activities for you provided below:

**Review Packet:**This review packet covers all the lessons of this module and serves as great preparation for the assessment.**Scavenger Hunt:**This scavenger hunt is a great practice for graphing the transformations in a fun way. You may start at any lettered problem. When you find your answer, look for that coordinate point in the top left corner of a different page. That letter will be the next problem you complete. If you cannot find your answer OR if you reach a problem you have already completed before finishing every problem, then you did something incorrectly. Use this recording sheet to display your answers.**Math Lib*:**This math lib is a fun way to perform transformations. When you graph the problem and find your answer, it will correspond with a word or phrase. Then, transfer the word or phrase to the short paragraph on the backside. You will repeat this process for the remaining nine problems. When you finish, you will be able to read a silly sentence. Like the scavenger hunt, if you find an answer that is not one of your options, you did something incorrectly. Use this recording sheet for your Math Lib.

*Activity #2:* When you feel ready to take the post-assessment, bring your materials to your teacher to get checked, including those completed in Activity #1 above. When your teacher approves of them, you will take the post-assessment. You will have 60 minutes to complete the assessment. You may NOT use a calculator.

***The Math Lib is very similar to Mad Libs. There is a "story" that is completed by filling in the blanks. To fill in the blanks, instead of asking someone for a random part of speech, you complete a math problem whose answer corresponds with the word or phrase that fills in the blank.**

**Lesson Objective:** To understand students' background knowledge on geometric transformations.

**Student Materials:** Computer, pencil, ruler

**Teacher Materials:** Computer, review packet (1 per student), scavenger hunt recording sheet (1 per student), math lib recording sheet (1 per student), post-assessment (1 per student)

**Academic Standards**

CCSS.MATH.CONTENT.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations:

CCSS.MATH.CONTENT.8.G.A.1.A: Lines are taken to lines, and line segments to line segments of the same length.

CCSS.MATH.CONTENT.8.G.A.1.B: Angles are taken to angles of the same measure.

CCSS.MATH.CONTENT.8.G.A.1.C: Parallel lines are taken to parallel lines.

CCSS.MATH.CONTENT.8.G.A.2

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

CCSS.MATH.CONTENT.8.G.A.3

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

CCSS.MATH.CONTENT.8.G.A.4

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

**Lesson Structure**

The first section of this lesson outlines what students have learned throughout this learning module. This serves as a quick refresher for students on the basic content that will appear on their summative assessment.

The second section provides students with materials to use to prepare for that assessment. It is up to the student how much or how little they would like to study. I have listed the answer keys to each review activity below:

When students feel that have adequately prepared for the post-assessment, they will bring you all materials from the unit. Check over them to make sure they are completely correctly. If not, instruct students to revisit their answers and resubmit the materials once they correct their errors. If the student is prepared, give them the summative assessment included below. The student will have 60 minutes to complete it and they cannot use anything besides pencils, rulers, colored pens, and tracing paper (optional).

**Learning Objective:** To apply my understanding of properties of geometric transformations.

**Learning Standards:** 8G1, 8G2, 8G3, and 8G4

You will now apply everything you have learned into a virtual poster project. You have spent this unit discovering properties of transformations and completing transformations to form emojis. On your poster project, you will create your own emoji or photograph transformation. To create your virtual poster project, you will need to go to the "Creator" tab here on CG Scholar's top menu and start a new work. Here are the requirements for choosing your emoji transformation:

- You MUST select an actual emoji OR a photograph that you or someone you know has taken. You can find a list of emojis (with pictures) at this website. The website separates them by category. If you choose to use a photograph, you must credit the photographer.
- You CANNOT select one of the four emojis used in the learning module.
- You must include AT LEAST two steps for each transformation, meaning, you must have a minimum of two translations, two reflections, two rotations, and two dilations. This means your shape must have at least 8 parts.

Once you have selected the emoji you would like to use, you are ready to begin your work. You must include the following prompts. Separate each by creating new headings in the "Structure" setting of CG Scholar:

- The emoji or photograph transformation you have created. This includes picture of a coordinate plane with the pre-image of your emoji or photo. Each part of the emoji/photo must have a numerical label. You must also include each step to transform each pre-image into the proper image. If an outsider is looking at this section, they should be able to complete all steps to discover your emoji/photo.
- The answer key to your emoji/photo transformation. This section should contain a picture of the coordinate plane with your selected emoji colored in lightly. This is the end product that should result from correctly following the steps in the first section.
- Algebraic rules for each step from Section One. You must write an algebraic rule for each part of the emoji to describe the transformation that occurred.
- A description in words for each step from Section One. This includes being specific, with respect to direction, distance, degree measures, scale factors, etc.
- A congruency or similarity statement for each step from Section One and whether the orientation has changed or remains preserved.
- A short paragraph explaining why you chose this particular emoji.

Upon completing your virtual poster project, the system will assign you two other virtual posters to peer review. You and your peers will be using the rubric below for evaluation:

Once you have reviewed your peers' projects and they have reviewed yours, you will receive their feedback. Make any changes you feel necessary before submitting your final project to your teacher. Your teacher will grade it using the same rubric used for peer evaluation, and you will receive your final grades for the project at the end of the unit.

*Comment:* Explain how the peer review process worked for you. Were you able to follow the steps and discover your peer's emoji? Why or why not? Did you like the Virtual Poster Project? Why or why not?

*Create an Update:* You have just created your own emoji or photo transformation, congratulations! By creating a step-by-step process to create something, you have completed a scaled-down version of computer programming. Conduct your own research on computer programming. How does it work? Choose a mobile gaming app or a computer game. How does is the process of your game relate to this emoji/photo project? How is it different? Comment on 3 updates once you have created your own.

**Lesson Objective:** To apply my understanding of properties of geometric transformations.

**Student Materials:** Computer, coordinate grids, pencils, colored pens, tracing paper (optional)

**Teacher Materials:** Computer

**Academic Standards**

CCSS.MATH.CONTENT.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations:

CCSS.MATH.CONTENT.8.G.A.1.A: Lines are taken to lines, and line segments to line segments of the same length.

CCSS.MATH.CONTENT.8.G.A.1.B: Angles are taken to angles of the same measure.

CCSS.MATH.CONTENT.8.G.A.1.C: Parallel lines are taken to parallel lines.

CCSS.MATH.CONTENT.8.G.A.2

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

CCSS.MATH.CONTENT.8.G.A.3

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

CCSS.MATH.CONTENT.8.G.A.4

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

**Lesson Structure**

This project gives students the opportunity to apply everything they have learned about geometric transformations to showcase their full understanding. Students will be creating their OWN emoji transformation virtual poster project. It is very detailed and requires students to combine their knowledge and understanding into a work on CG Scholar. Here are their rules for choosing their emoji:

- Students MUST select an actual emoji OR a photograph that you or someone they know has taken. They can find a list of emojis (with pictures) at this website. The website separates them by category. If they choose to use a photograph, they must credit the photographer.
- Students CANNOT select one of the four emojis used in the learning module. This means that the house, pencil, lightning bolt, and star emojis are off-limits.
- Students must include AT LEAST two steps for each transformation, meaning, they must have a minimum of two translations, two reflections, two rotations, and two dilations. This means their shape must have at least 8 parts.

The Student Virtual Poster Project is divided into 6 portions/prompts:

**Translations:**Students must fully apply their understanding of translations by including at least two translation steps. They will graph the translations, write their algebraic rules, and verbally describe the translations. They must include both distance and direction.-
**Reflections:**Students must fully apply their understanding of reflections by including at least two reflection steps. They will graph the reflection, write their algebraic rules, and verbally describe the reflections. They must include the line of reflection. -
**Rotations:**Students must fully apply their understanding of rotations by including at least two rotation steps. They will graph the rotations, write their algebraic rules, and verbally describe the rotations. They must include both direction and degree of rotation. -
**Dilations:**Students must fully apply their understanding of dilations by including at least two dilation steps. They will graph the dilations, write their algebraic rules, and verbally describe the dilations. They must include both scale factor and whether the dilation is an enlargement or reduction. -
**Properties of Transformations:**Students must fully apply their understanding of properties of transformations by including congruency statements, similarity statements, and status of orientations. They must include either a congruency statement or similarity statement for each step, and they must include whether the orientation has changed or remains preserved. -
**Organization and Communication:**Students must convey their information in a way that is easy to understand. They should organize each section by using the Structure tool on CG Scholar. It should be clear that the author proofread their project and put much time and effort into it.

The rubric for each component for this project are included below. Students are given this rubric to help guide their project and for them to use when peer reviewing their classmates' projects.

After submitting their project for review, students will be assigned two other projects to review. This allows students to assess their peers while also assessing themselves. When students see other projects, they compare those projects with their own. This allows them the opportunity to see how they feel about their project and to help guide revisions. When students submit the final project, assign them grades based on the rubric above.

The comment for this module allows students to reflect on their experience with the virtual poster project. Use the comments to revise the project as you feel necessary for the following year. The update gives students exposure to the field of computer programming. Students just created a set of steps for a person to follow to create their desired image. That is exactly how computer programs work. This field is often overlooked in mathematics classrooms, but it is extremely important in our world today as we become more dependent on technology. Students will choose a computer-programmed game and compare it to the virtual poster project. This gives students a direct application to math's use in the real world and may inspire them to continue to pursue computer programming through high school, college, and even their career.

**Translations**

**Reflections**

**Rotations**

Rotation Mini Lesson

**Dilations**

**Review Activities**

**Translations**

**Reflections**

**Rotations**

Rotation Mini Lesson

**Dilations**

**Review Activities**

Bulbapedia. (n.d.). Ditto Transform Gen III[PNG].

Common Core State Standards Initiative. (2019). Grade 8 » Geometry. Retrieved from http://www.corestandards.org/Math/Content/8/G/

Math, R. (2016, April 25). Retrieved April 28, 2019, from https://www.youtube.com/watch?v=-FTsjYg3sNw

Mrs. Minor. (2015, February 04). Orientation and Congruence. Retrieved from https://youtu.be/Bm3AcjDq_GU

Tandle, N. (2019, April 27). 8G1 Rotations. Retrieved from https://youtu.be/wk2TisSbknE

Teacher Kasmir Loves Maths. (2017, September 29). Rotation Using Tracing Papers. Retrieved April 27, 2019, from https://youtu.be/CrVRETO0Y3s