### 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.

### Resources

K20 Center. (n.d.). Bell Ringers and Exit Tickets. Strategies. https://learn.k20center.ou.edu/strategy/125

K20 Center. (n.d.). Card Sort. Strategies. https://learn.k20center.ou.edu/strategy/147

K20 Center. (n.d.). Identity Chart. Strategies. https://learn.k20center.ou.edu/strategy/2729

K20 Center. (2023, July 5).

*K20 ICAP - Apparel designing and culture*[Video]. YouTube. https://youtu.be/nKjKx2iDJnM