Hands-on Exploring Translations in the Plane

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SWBAT use tracing paper to translate figures in the plane.

Big Idea

With appropriate tools, such as tracing paper, learners can perform translations in the plane while constructing understanding of the mathematics of rigid motions.

Opening the Lesson - Warm up

15 minutes

I like to begin the lesson by brainstorming everything the students already know about translations.  We put a description of the movement of a translation on their organizer yesterday - sliding.  I tell the students that today, we are exploring how to translate figures in the plane, and then we discuss the definition of a plane.  When I pass out the activity Exploring Translations in the Plane  I allow students to work with their partners to translate the first triangle.  I provide rulers but that is all.  I tell students that while they work, I will play motivational music and they have until  the end of the song to translate question 1.  Here is the link to a good four minute version of The Electric Slide if your school allows access to youtube. 


While students are working, I am moving about the room assessing and assisting students with questions.  After about five minutes, I ask a group to put their paper under the document camera and explain their work to the rest of us (I always select the group as I am moving about the room and I only select correct answers.  If two groups finished the correct translations differently, then I ask both groups to present.  This first translation has notes about correct labeling at the bottom of the page an I really emphasize the labeling using prime notation.  I have even had students ask about Transformers the movie and if Optimus Prime the leader got his name from prime notation.  It is a great connection most students understand. 

Continuing The Activity

35 minutes

Ask students to flip the activity over to the second translation, a pentagon.  During the triangle translation, I always have student presenters discuss what exactly they translated - all three vertices and then reconnected the points.  Then, we discuss how many parts need to be translated in question 2 - all five vertices.  Here is where I introduce the tracing paper.  I ask students would they be interested in only translating one point and using tracing paper to move the other four?  They usually agree and I then explain how to use the patty paper, always asking questions and moving about the room between each step to ensure each student is understanding.  I did not make it past this example on day one because students needed time learn how to use the tracing paper.  Use only pencil on tracing paper, not ink pen.


Below is a video tutorial on how to use the tracing paper to correctly translate the pentagon in question 2. 

Wrapping up the Lesson

5 minutes

If you have time, then it would be great to ask the group questions about what was learned today in order to consolidate their learning.  I ran out of time to formally close the lesson because students spent a good deal of time learning to use the tracing paper for the first time and then you need to have a plan for keeping and reusing tracing paper.  I have a community bucket for gently used patty paper or students may keep their own paper until the following day.