Summary
In this lesson, students will explore the culture of the Seminole tribe and their patchwork. They will then use these patterns to explore transformations, specifically translations represented graphically, algebraically, verbally, and with vectors. Students will apply what they have learned to create their own patchwork design and demonstrate their understanding of translations. This is the first 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 Seminole patchwork.
Explore
Students make observations and discover patterns through an I Notice, I Wonder activity.
Explain
Students complete guided notes with the class and formalize their understanding of translations, focusing on different representations: algebraic notation, vectors, graphical, and verbal.
Extend
Students apply what they have learned to graph translations, then write procedural rules and create generalizations to apply to other problems.
Evaluate
Students create their own personally meaningful patchwork pattern with two examples of translations; they then swap designs and find and record the mathematical translation of their peer’s design.
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)
Detailed Designs 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)
Trying Translations handout (attached; one per student; printed front only)
Translating Me handout (attached; one per student; printed front only)
Pencils
Paper
Compass (one per student)
Straightedge (one per student)
Patty Paper (optional; 1-2 per student)
Individual grid dry erase boards (optional; one per student)
Dry erase markers (optional; one per student)
Engage
15 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 the class to the extent you feel necessary.
Show slide 5 and introduce the “Seminole Patchwork and Translations” video on the slide, which is of Jaylee Lowe, a Seminole patchwork maker, sharing her knowledge of her tribe and how she uses translations in her Seminole patchwork creations.
After the video, transition to slide 6 and introduce the class to the Caption This instructional strategy. Direct students to get a piece of paper and write a caption for the photograph on the slide using the information they learned from the video. If time allows, ask for a few volunteers to share with the whole class.
Explore
10 Minute(s)
Show slide 7 and pass out a copy of the attached Detailed Designs handout to each student. Have students find partners or assign partners. Then introduce students to the I Notice, I Wonder instructional strategy. Explain that they will focus on what they notice for this activity and will later be asked about what they wonder.
Share with students that during this activity, they will be working with a specific Seminole patchwork pattern known as Man on Horse. Direct students to identify the corresponding points from the initial unshaded image to the final shaded image and complete the table for each graph. Tell students to pause at the end of each question, look for patterns in the table, and write what they notice.
As students complete question 1, transition to slide 8. Give students a moment to check their work with what is on the slide and make corrections as needed. Then bring the class together for a discussion and ask for volunteers to share what they noticed.
Repeat this procedure with the next two questions using slides 9-10.
Move to slide 11 and ask the class to share anything else they noticed and whether there is now anything they wonder.
Facilitate a discussion about what they wonder and push the conversation toward wondering if there is an easier way to describe corresponding points or an easy way to write the pattern of what changed between corresponding points. Use this idea of efficiency in notation to transition to the Explain portion of the lesson where proper vocabulary is introduced.
Explain
20 Minute(s)
Display slide 12 and provide the attached Guided Notes handout to each student.
Introduce the following vocabulary to the class: transformation, translation, preimage, image, and rigid motion. Guide students to write the vocabulary words on their handout. Then talk through the table on the handout, explaining the different ways to represent a transformation: graphically, verbally, and algebraically. Remind students that mapping notation here is just like mapping domain and range values from Algebra 1.
Then introduce the concept of a vector to students as well as its notation.
Direct students’ attention to the back of their handout and complete the examples together as a class. After example 1, consider asking the students to try example 2 on their own before bringing the class back together to ensure everyone is understanding.
Give each student a compass and straightedge, then guide the class through how to complete a translation not on the coordinate plane with example 3.
Have students add their completed Guided Notes to their math notebooks if that is a classroom norm.
Extend
25 Minute(s)
Now it is time for students to apply what they have learned; display slide 13. Give each student a copy of the Trying Translations handout. Here students are given a preimage and either a verbal description, algebraic rule, or vector to apply and sketch the image.
Have students work with their partner from before or direct them to find a new partner to complete questions 1-2. As pairs work, remind them to pick and label 6 points on the preimage and the 6 corresponding points on the image.
Challenge students to work independently on question 3.
Once students complete their handout, display slide 17. Divide the class into 4 groups. This can be done by numbering students 1-4 or by grouping students based on where they are seated. The groups should be approximately equal in size. At this point, students just need an assigned group number and do not need to physically get into a group.
A modified Inverted Pyramid strategy is used for this activity. Have students write their work for this activity on the back of their Trying Translations handout.
Explain that each group will be given a different translation process to describe. Based on their assigned group number, direct students to independently write the steps for their groups’ procedure.
Group 1: Students in Group 1 should each write the steps needed to take a graphical representation of a translation and represent it as an algebraic rule.
Group 2: Students in Group 2 should each write the steps needed to take a graphical representation of a translation and represent it as a vector.
Group 3: Students in Group 3 should each write the steps needed to take an algebraic rule and apply it graphically (draw the translation).
Group 4: Students in Group 4 should each write the steps needed to take a vector and apply it graphically (draw the translation).
Encourage students to use their own words and apply what they have learned today to write their steps. At this time, they should not be working with a partner. Give students a few minutes to complete this step.
Display slide 18 and direct students to find one (1) partner that has their same group number. Instruct pairs to compare their steps and work together to write a new set of steps that is more efficient and still general. Ask if there are places where steps could be combined or are not actually needed to reach the goal. Encourage students to use variables instead of specific numerical values to help generalize their steps (allowing their steps to apply to more than just one problem). Give students a few minutes to complete this step.
Show slide 19 and have everyone with the same group number come together. In other words, your classroom will have a total of 4 large groups. Instruct students to compare their steps again and create one set of steps for the whole group that everyone agrees upon. Give students several minutes to complete this step, depending on your class size.
Transition to slide 20 and ask the groups to each select a spokesperson. Have each spokesperson share out with the class. Consider having a recorder from each group write the steps on the board or on a piece of chart paper. Allow students time to ask questions and provide feedback. Encourage students to take notes on the agreed upon steps.
Evaluate
15 Minute(s)
Show slide 21 and give each student a copy of the attached Translating Me handout. Remind students that the Seminole patchwork patterns often represent the creator. Have students think about how to symbolize something important to them: something important from their school or home life or something from their personal interests. Tell students that once they think of a (school appropriate) design, they need to add this preimage to the jacket and to be sure to leave enough room to translate the image twice.
Remind students that their image will likely need to be a little abstract to create a polygon. Also let them know that later they will be asked to share the meaning of their design with a partner. Tell students your preference regarding whether or not it is okay for their preimages and images to overlap. There is not a right answer here; just be sure to clearly communicate expectations.
Instruct students to draw their preimage and two translations on the jacket; then label each preimage, image 1, and image 2. The two translations are each independent translations from the same preimage. In other words, students translate the preimage to create image 1, then apply a different translation to the preimage to create image 2.
Display slide 22 and instruct students to find a partner and trade papers. Instruct students to complete questions 1-2 at the bottom portion of the handout and represent image 1 with an algebraic rule and image 2 with a vector.
Remind the class of the Caption This instructional strategy. Show slide 23 and direct students to talk with their partner and check their translations. Is what Person B described algebraically what Person A planned/graphed?
After a couple of minutes, instruct students to now share about the meaning of their preimage design with their partner. After a few minutes, direct students to question 3 and have them write a 1-3 sentence caption about the meaning of the design and the math involved for their partner’s jacket based on their conversation.
Use the activities from Extend and Evaluate to determine whether students are ready for the next lesson or whether students need additional practice. Consider having students practice with more basic shapes, like translating triangles or even just individual points. Extra practice can be done quick and easily on individual grid dry erase boards.
The “Traditional Transformations, Part 2” lesson is about reflections, reflective symmetry, and Osage ribbonwork.
Resources
K20 Center. (n.d.). Caption this. Strategies. https://learn.k20center.ou.edu/strategy/82
K20 Center. (n.d.). Desmos classroom. Tech Tools. https://learn.k20center.ou.edu/tech-tool/1081
K20 Center. (n.d.). I notice, I wonder. Strategies. https://learn.k20center.ou.edu/strategy/180
K20 Center. (n.d.). Inverted pyramid. Strategies. https://learn.k20center.ou.edu/strategy/173
K20 Center. (2023, July 5). Seminole Patchwork and Translations [Video]. YouTube. https://www.youtube.com/watch?v=As9ckub13eM
