Geometry : Unit #3 - Transformers and Transformations : Lesson #2

Rocking Rotations

Objective: SWBAT identify and draw rotations of polygons on the coordinate plane.
Standards: HSG-CO.A HSG-CO.A.3 HSG-CO.A.4
Subject(s): Math
90 minutes
1 Lesson Beginning - 15 minutes

Do Now:  In this Do Now, students will ask students to first try and identify a rotation using a Yankee symbol.  Teachers who do not live in New York may want to change this to another sports symbol.  The second question will also ask students to review reflecting about the x and y-axis.  This is a great time for teachers to review key vocabulary from previous lesson like pre-image, image and transformation.

Teachers can also review the agenda and objective for this lesson.

Introduction to New Vocabulary:

Before starting the middle of the lesson, teachers can review key vocabulary for this lesson, counterclockwise and clockwise as well as a movement (or rotation) of 90 degrees.  The graphics of the cats will help to review this topic with students.  

Making Math Hands-On
Connection to Prior Knowledge

To begin the activity for this first part of class notes (on page 1), I asked students to use graph paper, pencil and scissors to create a triangle that is congruent to the given triangle, YUM.  Instead of providing more directions on how students could complete this, I found that most of my class traced their triangle and then cut out a congruent new triangle, which we named Y'U'M'.  This act of tracing and then cutting out two triangles that were congruent really cemented for my students that the pre-image and image were congruent shapes (see this Beginning Student Example)

Then, as students rotated the image (triangle Y'U'M') it was easy for them to see that the new shape would be an isometry.  Furthermore, I found that while working together, my students were able to discover a rule for how to rotate 90 CCW. It was exciting to see my students drawing from prior knowledge and applying this to generalize a rule for this type of transformation (see this second, Beginning Student Example)


2 Lesson Middle - 40 minutes
Rocking Rotation_Middle_Video
Incorporating Math Language
ELL Students

Throughout my years of teaching, particularly ELL students, I have found that all students really benefit when I am more explicit about how and when to use specific math terms.  In today's class on rotations, I specifically practiced with the class how to state the image of a shape.  For example, in classnotes, we discussed that B' is said "B prime." This is new vocabularly, and also can be confusing, especially when we add on multiple transformations to a shape and hence, multiple primes.

This example shows that I asked students to write in quotations, how to say B'.  Furthermore, I find that actually practicing this out loud - asking students to pronounce challenging words or repeat these helps to build student knowledge and confidence of the subject matter.  By taking 1 minute to review this in today's lesson, I hopefully will avoid confusion for my students in the future!

3 Lesson End + Homework - 25 minutes


After completing in class examples, students should be encouraged to work in pairs or small groups on practice questions and a worksheet with examples, which can be found in student notes.   Teachers can circulate and answer student questions.  After giving students 15-20 minutes to work on this assignment, teachers can ask students to put their work on the board and then review these questions with the entire class.  This is a great opportunity for teachers to reinforce vocabulary and also ask students some important summary questions like,

  • How are rotations different from reflections?
  • How do rotations change a pre-image? 
  • What transformations have we covered so far?  Which have been the most challenging for you?  Why?
  • What is the definition of transformation?


Exit Ticket:

The Exit Ticket for this lesson reviews how to complete a rotation for CCW 90 and CCW 180.  Please find the enclosed resources. 

Checking Student Work

In order to check the activity for today's class, I like to go around the room and check one to two problems for every student.  I don't necessarily check for right and wrong answers but more for completion.  This (along with the exit ticket) helps me to see what we still need to review and cover for the next day's class.  In this particularly activity, I saw that many of my students were not labeling their image points correctly which we then reviewed in the next day. 

Also, in this example, you can see that I stamped the student's work with a flower.  In order to receive credit for starting the activity, as I check work, I stamp each student's paper.  This allows me to hold them accountable and if a student hasn't started work they will not receive a stamp (and thus, not credit!)