### Summary

In this lesson, students will explore the culture of the Plains tribes and their Star Quilts. They will then use patterns to explore rotations and discover algebraic rules for common rotations. Students will apply what they learn to create their own quilt block and demonstrate their understanding of rotations and rotational symmetry. Prerequisite vocabulary knowledge for this lesson includes transformation, preimage, image, and rigid motion, which are all included in the Traditional Transformations, Part 1 lesson. This is the third 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 the tradition of Plains Star Quilts.

**Explore**

Students make observations and discover patterns for rotations about the origin.

**Explain**

Students complete guided notes with the class and formalize their understanding of common and uncommon rotations.

**Extend**

Students apply what they have learned to identify different types of transformations and create their own quilt blocks using rotations.

**Evaluate**

Students demonstrate their understanding by rotating a point 180° about another point.

### Instructional Formats

The term "Multimodality" refers to the ability of a lesson to be offered in more than one modality (i.e. face-to-face, online, blended). This lesson has been designed to be offered in multiple formats, while still meeting the same standards and learning objectives. Though fundamentally the same lesson, you will notice that the different modalities may require the lesson to be approached differently. Select the modality that you are interested in to be taken to the section of the course designed for that form of instruction.

### Materials

Lesson Slides (attached)

Tribal Transformations handout (attached; one per student; printed front/back)

Guided Notes handout (attached; one per student; printed front/back)

Guided Notes (Teacher Guide and Model Notes) document (attached; for teacher use)

Star Quilt Transformations handout (attached; one per student; printed front only)

Rotation Exit Ticket handout (attached; one quarter per student; printed front only)

Pencils

Paper

Graph paper

Creating Quilt Blocks handout (optional; attached; one per student; printed front only)

Compass (one per student)

Protractor (one per student)

Patty Paper (optional; 1–2 per student)

### Engage

15 Minute(s)

Introduce the lesson using the attached **Lesson Slides**. Review the lesson series’ essential question on **slide 3** and the lesson’s learning objectives on **slide 4** to the extent you feel necessary.

Display **slide 5** and introduce the GramIt instructional strategy. Let students know that they are about to watch a video of Crystal Pewo Lightfoot, a member of the Apache Tribe of Oklahoma and a descendant of the Kiowa Tribe, sharing her knowledge of her tribal culture and how she uses rotations in her Star Quilt creations. Explain that, after watching the video, they will be asked to create two hashtags: one representing an aspect of the culture they learned about, and another representing a mathematical concept they learned.

Show **slide 6** and play the “Plains Star Quilts and Rotations” embedded video on the slide.

Move to **slide 7** and have students take out a piece of paper. Then, ask them to write two hashtags, each representing a cultural and mathematical aspect they learned from the video.

If time allows, ask for volunteers to share their answers with the class.

### Explore

15 Minute(s)

Show **slide 8** and pass out a copy of the attached **Tribal Transformations** handout to each student. Share with students that, for this activity, they will work with an arrow symbol from a Plains-style quilt design.

Ask students to partner up or assign them their partners to complete the Tribal Transformations handout. For question 1, direct them to complete the table next to the coordinate plane. Then, ask students to use that table to try to figure out an algebraic rule for that transformation and to then describe the transformation.

Have students repeat this procedure for questions 2–3.

### Explain

20 Minute(s)

Display **slide 9** and provide the attached **Guided Notes** handout to each student.

Introduce the vocabulary of *rotation* and *angle of rotation *to the class and guide them to write those vocabulary words on their handout. Remind students of the difference between *clockwise* and *counterclockwise* and let them know that all rotations are assumed to be counterclockwise unless otherwise stated. Then ask for a volunteer to answer, “Is a rotation an example of rigid motion?” Make sure to ask the student to provide their reasoning. Have students record the answer (“yes”) with justification on their handout.

Now, go through the special rotation algebraic rules for rotations of 90°, 180°, and 270° about the origin. Have students use the illustration on their Guided Notes and their work from the Explore part to develop the rules.

Ask the class to finish the following prompts at the bottom of their handout:

Rotating a figure 90° CCW is the same as rotating the figure …°.

Rotating a figure 180° CCW is the same as rotating the figure …°.

Rotating a figure 90° CW is the same as rotating the figure …°.

Help students see that their algebraic rules work when they rotate a figure about the origin. Moreover, they can still apply the same rules to other figures about any point.

Give each student a compass and protractor. Then, with example 3, guide the class through rotating a figure that is not on a coordinate plane.

Have students add their completed Guided Notes to their math notebooks if it is a classroom norm.

### Extend

35 Minute(s)

Display **slide 10** and remind students what *rotational symmetry* and the *center of symmetry* mean.

Transition to **slide 11** and facilitate a whole-class discussion regarding the question, “Where else do you see rotational symmetry?”

Show **slide 12** and give each student a copy of the attached **Star Quilt Transformations** handout and four coloring utensils that students can share. Have students work individually to color code their Star Quilt pattern: one color should be the preimage, and the other three colors should each indicate either a translation, reflection, or rotation. Let students know that not every rhombus needs to be fully colored by the end of this activity.

Encourage students to collaborate with a partner to help each other see the different transformations.

Once students complete the activity, get them into groups of four and compare their results. As time allows, ask for volunteers to share any observations with the whole class.

Transition to **slide 14** and give each student a piece of graph paper or the attached **Creating Quilt Blocks** handout. If students are using graph paper, ask them to draw the *x*- and *y*-axes in the center of the page.

Share the Pass the Problem strategy with the class. Explain that each group will work together to create four unique quilt blocks. Explain that each person will create their own preimage in Quadrant III, then pass the problem around to complete the quilt block design collaboratively. Tell students that their preimage creation can be a tessellation—like the Plains Star Quilt pattern—but is not required to be. Take a moment to introduce or remind students of the vocabulary *tessellations*, which is the repetition of one or more shapes such that the shapes cover a surface with no gaps or overlap.

Show **slide 15** and direct each student to create their own preimage in Quadrant III. Then instruct them to label at least four vertices.

After a few minutes, transition to **slide 16** and have everyone pass their paper to their right. On the paper they received, have them draw the image by rotating the preimage 270° about the origin, then have them label the corresponding vertices.

After a few minutes, show **slide 17** and have everyone pass their paper to their right. Ask them to check the work of the previous student, draw another image by rotating the preimage 180° about the origin, and label the corresponding vertices.

After a few minutes, display **slide 18** and have everyone pass their paper to their right, check the previous student’s work, draw the image by rotating the preimage 90° about the origin, and label the corresponding vertices. Encourage students to work together to adjust any points that need to be corrected.

After a few minutes, transition to **slide 19** and have everyone pass their paper to their right. The paper should now return to the student who drew the preimage. Have them check the previous work and for rotational symmetry.

Consider having students display their quilt blocks on the wall to make a class quilt.

### Evaluate

5 Minute(s)

Display **slide 20** and use the Exit Ticket strategy to individually assess what students have learned from the lesson. Give each student a quarter sheet of the attached **Rotation Exit Ticket** handout. Alternatively, give students a sticky note or an index card to write their responses. Use the hidden **slide 21** for a sample response.

Collect student responses and use them to determine if your students need additional practice or if they are ready for the next lesson. If students need additional practice, consider having students practice with more basic shapes, like rotating triangles or even just individual points about the origin 90°, 180°, or 270°.

The “Traditional Transformations, Part 4” lesson will discuss dilations and beadwork.

### Resources

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

K20 Center. (n.d.). Desmos classroom. Tech Tools. https://learn.k20center.ou.edu/tech-tool/1081

K20 Center. (n.d.). Gramit. Strategies. https://learn.k20center.ou.edu/strategy/2554

K20 Center. (n.d.). Pass the Problem. Strategies. https://learn.k20center.ou.edu/strategy/2554

K20 Center (2023, July 5).

*Plains star quilts and rotations*[Video]. YouTube. https://youtu.be/YJxmt0dt3mw