Transformational Geometry Performance Task Day 1

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SWBAT apply transformations to a real world setting.

Big Idea

This is the first day for the Transformational Geometry Performance Task. Students create a tessellating design using transformations in the context of solving a problem for the Red Queen from Lewis Carroll's book, Through the Looking Glass.

Do Now

7 minutes

As students walk in the room, I give them the Transformational Geometry Performance Task Explanation. Students are instructed to read the explanation, look at the rubric and write a description of the expectations for the task in their notebook.  After about 4 minutes, we go over the task.  I ask a student to explain the task and then ask a second student to reiterate the task. 

We look at the pictures on the bottom of the page and discuss how the picture depicts a tessellation. The chessboard is a tessellation of square tiles transformed about the garden. I ask the students which type of transformation can be used to tessellate the square. Because the tiles are equilateral and equiangular, they can be translated, rotated or reflected.

We then review the rubric and discuss the criteria for attaining a 4 in each row.


13 minutes

After the Do Now, I hand out a Tessellation Template to each student. In the previous lesson, students created a tile by translation. If students had difficulty translating their templates in the previous lesson, they can try to create a new template with a simpler design. Some students use their previous design, but create the template using rotations, instead of translations. Students who would like more of a challenge, can create a template using reflections. In order to create a tessellation template by reflection, students reflect their figures and rotate the piece to the side or the bottom. 


20 minutes

When the students finish their design, I hand out the Transformational Geometry Performance Task Day 1 papers. Students answer questions 1 and 2 based on the tiles shown in the question.  They then write an explanation of how to replicate their tiles using precise mathematical vocabulary. I usually have the students write the explanation in their notebooks before writing on the task sheet.


As students are working, I circulate around the room and read over their answers and explanations. I help them articulate their thoughts and remind them to include the correct mathematical vocabulary.


If students finish parts 1, 2 and 3 of the task, they can begin their floor plan.  Most of the students, however, will not be ready to begin their floor plan until the next lesson. 


5 minutes

At the end of the lesson, we review the task rubric again. I have the students look at their work and think about where they fall in the rubric. We discuss the task and I answer any further questions students have. Students will complete their task during the next lesson.