Introduction to Transformations

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Objective

SWBAT perform the various transformations upon points, segments, and polygons.

Big Idea

Students are introduced to the notion of rigid and non-rigid motion, including translations, rotations, reflections, and dilations.

A Introduction to Transformations

15 minutes

My students have been exposed to transformations in previous grades.  Therefore I begin this unit with the assumption that they have a basic understanding of translations, rotations, reflections, and dilations. I list these terms on the board and we discuss the meaning of each. As our discussion progresses, I continue to add vocabulary terms to our list. (These terms will go on our word wall.)

Next I display a GeoGebra* applet on my SMART Board. This applet contains two tigers' heads (a pre-image and its image); every time you hit the "update" button, the image changes.  I ask the students to describe the transformation that created the image. In this discussion I introduce the word symmetry.

We then briefly discuss the term "rigid" motion.  I contrast this with "non-rigid" motion, in which the shape of the object changes.  I use a solid sphere (a marble, for example) and a squishy ball to demonstrate this idea, and introduce and add the word isometry to our vocabulary list.  I also show and discuss a very brief video on YouTube that demonstrates the motion of water - a very non-rigid transformation:

          

and then another video, featuring a marching band, that demonstrates a variety of rigid transformations:

          

I stop this video at various points to discuss the examples of transformations and symmetry that are demonstrated by it.

 

Teacher's Note: GeoGebra is a dynamic geometry software that can be found here. Some introductory materials for using it are available in this lesson

Notes on Transformations

20 minutes

I hand out the Notes on Transformations, as well as graph paper, and ask the students to work on completing the assignment in their groups.  They need to read the handout and figure out what goes in the blanks.  I anticipate that the students will need a good deal of prompting as I circulate around the room.  I am ready with suggestions and leading questions:

  • what happens to the coordinates of a point when you reflect it across the x-axis? 
  • the y-axis? 
  • what do you think it means to reflect something across the origin? 
  • what does it mean to dilate a figure? 

In this way, the students develop general rules through repeated reasoning (MP 8).

When it appears that all of the groups have finished, we go over the answers as a class, to ensure that everyone has the correct information on their sheets and that everyone understands the material.  I call the students' attention to the different notations for the transformations.

Fluency in Transformations

15 minutes

I realize that some people may not agree with me, but I think that fluency in the rules for transformations is important, and I discuss this briefly in this video. I give my students time to practice on the handout entitled Work on Fluency, and then we go over the answers.  I explain that we will have a number of quizzes throughout the unit just like this exercise, and that they need to make sure they are ready for them.

 

Teacher's Note: The Work on Fluency handout is designed to be cut in half.

Group Work

35 minutes

Next I pass out the Worksheet on Transformations on which the students can work in their groups.  This creates opportunities for MP 3. Again I circulate around the room, answering questions from groups when an entire group appears stumped or confused.

Through this group work, I believe my students begin to use and become familiar with the vocabulary, as they ask each other questions and debate answers.  I also believe this is an opportunity for the students to use each other as a resource for clearing up confusion - sometimes an explanation given by a peer makes more sense to a student than mine! 

Ticket Out the Door

5 minutes

I announce that the students' homework is to finish the Worksheet on Transformations, and distribute the Ticket Out the Door. This Ticket Out the Door is intended to give me feedback about the day's lesson. By reading the students' responses, I will have an idea of where they stand with respect to the "big ideas" delivered in this lesson, and this will help to inform my planning for the upcoming days' lessons.