# Traditional Transformations, Part 5

## Composition of Transformation: Fashion Design

Michell Eike, Laura Halstied, Teresa Lansford, Patricia McDaniels-Gomez | Published: December 18th, 2023 by K20 Center

• Grade Level 9th, 10th
• Subject Mathematics
• Course Geometry
• Time Frame 100-120 minutes
• Duration 2-3 class periods
• ICAP Resource Individual Career Academic Plan (ICAP)

### Summary

In this lesson, students will explore the mathematics behind fashion design and summarize their knowledge of transformations. They will then apply what they have learned to solve a puzzle and demonstrate their understanding of composition of transformations. Prerequisite knowledge for this lesson includes the following vocabulary: transformation, preimage, image, translations, reflections, rotations, and dilations. This is the fifth lesson of five in the "Traditional Transformations" lesson series.

### Essential Question(s)

How are transformations and symbolism used through indigenous cultures?

### Snapshot

Engage

Students watch a video about a fashion designer and how she integrates her culture into her creations.

Explore

Students sort photographs by type of transformation and then reflect on their learning of transformations and indigenous culture.

Explain

Students complete a foldable with the class and formalize their understanding of compositions of transformations.

Extend

Students apply what they have learned about composition of transformations to solve a puzzle.

Evaluate

Students demonstrate their understanding by finding the unknown transformation given the preimage and image.

### Materials

• Lesson Slides (attached)

• Identity Chart handout (attached; one per pair; printed front only)

• Foldable handout (attached; one per student; printed front/back)

• Multiple Transformations (attached; one per student; printed front only)

• Transformation Puzzle handout (attached; one per pair; printed front/back)

• Transformation Puzzle (Key) document (attached; for teacher use)

• Composition Exit Ticket handout (attached; one half per student; printed front only)

• Pencils

• Paper

• Scissors (one per student)

• Coloring utensils (optional)

### Engage

10 Minute(s)

Introduce the lesson using the attached Lesson Slides. Slide 3 displays the lesson series’ essential question. Slide 4 identifies the lesson’s learning objectives. Review each of these with your class to the extent you feel necessary.

Show slide 5 and introduce the “Apparel Designing and Culture” video on the slide, which is of Leslie Deer sharing her knowledge of her tribe and how her culture influences her work in her career as a fashion designer.

### Explore

15 Minute(s)

Display slide 6 and provide students with your session code. Then, have students go to student.desmos.com and enter the session code.

Introduce students to the Card Sort instructional strategy and have students work independently to sort cards into the following categories.

• Translations

• Reflections

• Rotations

• Dilations

Challenge students to put at least two cards in each category.

Use the Dashboard to observe students’ progress. Once students finish sorting their cards, have them find a partner or assign partners. Have pairs spend a few minutes discussing their cards and how they chose to sort them. As time allows, consider showing a volunteer’s set of cards and having the volunteer share his/her reasoning.

Now, display slide 8 and introduce the Identity Chart strategy. Give each pair of students a copy of the attached Identity Chart handout and direct them to write words or phrases at the end of each arrow describing what they have learned during this lesson series on transformations.

If you have the space, consider having students hang their Identity Charts on the wall for everyone to see. This can give students a sense of pride in their learning—they know so much more now than they did before!

### Explain

10 Minute(s)

Display slide 9 and give each student a copy of the attached Foldable handout and a pair of scissors. Instruct students to fold along the solid lines and cut along the dashed lines. The only dashed lines that should not be cut are the ones adjacent to the words “Reflections” and “Dilations.” Use the slide to help point to students where they should and should not cut. Let students know that the goal is to have four flaps, one for each type of transformation.

Transition to slide 10 and direct students to create their own preimage on the center graph. Let them know that they need to label at least 3 vertices.

Show slide 11 and instruct students to open one flap of the Foldable and apply a transformation of their choice that represents that transformation and to write the rules for that transformation inside the flap. For example, if students unfold the “Reflections” flap, they can choose the line they want to reflect their preimage over. If they choose to reflect their preimage over the x-axis, then they should write, “Reflection over the x-axis” and draw the resulting image on the provided graph. Then in the empty space, have students use prior resources or recall the algebraic rules for reflections and record those in that space. Have students repeat these steps for the remaining corners. Let students know that they are bringing all of their knowledge about transformations together into one place for easy reference.

As students complete writing in the four corners, direct their attention to the center. Have students write the definition of “Transformation” in their own words or have a class discussion and have them write the agreed upon definition in their foldable: “Transformations are …”

Transition to slide 12 and explain that a composition of transformations is when more than one transformation is applied to a figure.

### Extend

40 Minute(s)

Display slide 13 and introduce the vocabulary of glide reflection. Then, give each student a copy of the attached Multiple Transformations handout.

Move to slide 14 and let the class know that some compositions of transformations can be represented in more than one way, sometimes even as a single transformation. Direct their attention to Example 1 and have students write two different ways to transform the preimage to the image.

As students finish Example 1, show slide 15 and ask for volunteers to share. Students will see the most common transformations on the screen: two reflections or one translation.

Use slides 16-17 to repeat these steps for Example 2.

Show slide 18 and give each pair a copy of the attached Transformation Puzzle handouts. These handouts include one page (front/back) for Student A, one page (front/back) for Student B, and the graph (front only) for both students to share. Have students decide among themselves who is Student A and who is Student B – it does not matter. Let them know that they are each responsible for completing half of the puzzle. For example, Student A is given one preimage to use for questions 1-3. Questions 1-3 are 3 separate compositions of transformations that Student A needs to complete, then draw each image on the graph paper. Student B has the same procedure, but a different preimage or a different composition of transformations to complete. Each student has 12 tasks to complete. When both students are done, their transformations will create a tribal pattern: a thunderbird. Use the attached Transformation Puzzle (Key) document to see the expected results.

### Evaluate

5 Minute(s)

Display slide 19 and use the Exit Ticket strategy to individually assess what students have learned from the lesson. Give each student a half-sheet of the attached Composition Exit Ticket handout. Use the hidden slides 20-25 for a sample response.

Collect student responses and check for understanding.