Taking Apart Translations

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Objective

SWBAT accurately describe or draw the result of translating a figure. Students will understand a precise definition of translation in the context of segments and parallel lines.

Big Idea

Using geometric constructions and measurement to learn the properties of rigid motion via translation.

Lesson Open

8 minutes

The warm-up prompt for this lesson asks students to review the properties of reflections, which we studied in the last lesson.  The warm-up follows our Team Warm-up routine.  I choose students at random to write the team's answer on the board.  

Following the warm-up, I display the agenda and learning targets for the lesson.  To activate prior knowledge, I ask the class to help me name three different ways to move an object without changing its size and shape.  I tell class that today we will focus on the properties of translations.

 

Constructing a Translation

25 minutes

During this part of the lesson, students use construction tools to create the image of a triangle under translation.  The goal of this hands-on activity is to help students to focus on the properties of translations. 

I often let students choose their partners within their cooperative learning teams for paired activities, but for this activity I direct them to work with their shoulder partners.  I want a more-capable student in each pair, because they will need to follow directions carefully. Then, I distribute the handout for the activity, 2 copies for every team of 3-4 students.

I give instructions with the help of the slide for the activity.  Students will need a straight-edge, compass, and protractor.  I ask students to get out their notes on constructing parallels from the previous lessons.  I ask them to place their desks in pinwheels.  They will be working in pairs, so that they can help each other with the constructions.  I ask students to use the Rally Coach routine.  

As students get started on the activity, I circulate around the classroom offering help where needed. I am on the lookout for:

  • Are students constructing parallel lines, or are they simply drawing parallel lines 'by eyeball'? This is a difficult construction.  I acknowledge students' clever strategies, but remind them that they will learn more by constructing the parallel lines correctly.
  • Are students locating the image of each vertex on the parallel correctly?  Instead of measuring the length of the given vector with a compass and copying this distance to find the location of the image of the vertex, students will often use construction marks left over from constructing the perpendicular bisector as the location of the image of the vertex.  
  • Do students see that the image of each point is the same distance and direction from the pre-image?  Do they see that this applies to all the points in the figure, not just the vertices (MP7)?  In later lessons, they will use the fact that each point is translated by the same vector in a translation.
  • Do students see that the image of each line segment is parallel to the pre-image (MP7)?  In the next lesson, we will prove the Line Translation Theorem.  For now, I point out to students that they can use this fact to help them sketch the image of a figure under translation.

If many students are struggling to understand the directions, I call the class's attention to the front board, where I can demonstrate the first steps of the construction using the document camera.

Once students have completed the construction, I ask them how they expect the sides and angles of the reflected image to compare to the sides and angles of the original.  I ask them to use their compass and a protractor to verify that corresponding sides and angles of the image and pre-image are have equal measures.

Summarizing Translations

15 minutes

In this section, we use Guided Notes to summarize the properties of translations.  

I begin by displaying a model sample of student work from the Constructing a Translation activity on the front board using a document camera and asking the class to help me summarize its properties. 

 

 

Lesson Close and Homework

5 minutes

Individual Size-Up

 

The lesson close follows our Individual Size-Up Routine.  The Lesson Close prompt asks students to describe the properties of a translation.

Homework

For homework, I assign problems #32-34 of Homework Set 2.  Problem #32 gives students an opportunity to review the properties of translations.  I encourage them to look for the answers in their notes.  Problem #33 asks students to visualize and draw the image of a polygon under translation along a vector.  Problem #34 gives students the opportunity to apply the properties of rigid motions to solve a real world problem.