Reflections

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Objective

SWBAT describe and perform reflections on objects in the coordinate plane.

Big Idea

Students explore mathematical reflections in the coordinate plane and make connections between reflections and the book, Through the Looking Glass, by Lewis Carroll.

Do Now

7 minutes

As students walk in the room, I hand them a grid with triangles plotted on it. Students are instructed to describe the reflections that map triangles onto other triangles. This activity is designed to identify students’ prior knowledge about reflecting objects on the coordinate plane. It leads into the lesson where students will use functions to describe reflections (G.CO.2).

An additional question asks students to explain how a quote relates to transformations. The quote, from Through the Looking Glass by Lewis Carroll, said by Alice, is about mirror images and reflections. I like to use this quote to add some literacy and real-world connections to the lesson. We usually have a brief discussion about the term “drawing room” for context and “looking-glass” for content.

As an alternative, I have included a Reflections Refresher for students who need a bit more scaffolding before they start the lesson. 

 

Mini-Lesson

10 minutes

In the Mini Lesson, students are guided through the steps for writing a rule to reflect an object across the y-axis. They apply the same steps to different reflections during the practice section. 

In a previous lesson, students learned how to describe components of transformations, i.e. pre-image, image, and the general notation, i.e. P, P’. For this activity, students are given a rectangle and its image and are asked to identify the coordinates of points and their images and describe the transformation that maps the rectangle to its image.

Since the rectangle looks the same when reflected over the y-axis, I put writing inside the rectangle. The writing I used is the first verse in the poem, “The Jabberwocky” from Through the Looking Glass by Lewis Carroll.  In the actual text of the book, this verse is reflected and unreadable without using a mirror.  Interestingly without prompting I often see students pull out mirrors to look at the words.

I guide students through questions 3 through 5 on the worksheet. I call on a student to read the question out loud and ask another student to answer the question. We work together to come up with complete, mathematically coherent answers. Students often have difficulty putting their thoughts into words and may be unsure how to write the rule in mathematical notation.  

 

Activity

22 minutes

To practice, I have the students work in pairs to complete the sheet Students can use their sheets from the Mini-Lesson to help them, if needed. When completed, this sheet can be used as a reference in later lessons.  I have students glue their sheets into their notebooks.

Because students have difficulty with reflections in the origin, I have written the rule in mathematical notation as an example.

As the students work, I circulate around the room to ensure students are on the right path. I usually have to remind them to graph the line y = x  for that reflection. After about 15 minutes, we go over the rules and then the students continue working on the last two reflections on the sheet. 

Summary

5 minutes

Students are given the following writing prompt as an exit ticket

Sam says, “There is no general rule for reflecting any point over the line y =3.” Do you agree or disagree with Sam?   Support your answer. The use of the graph is optional.

This is where students are able to engage in math practice #3 as they critique Sam's statement and think more deeply about how the rules of reflection are written and applied.