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.

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.

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.

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.

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.

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:

 

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).

 

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:

1. 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.

2. 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.

3. 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.

4. 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.

5. 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.

6. 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