# Hands-on Exploring Translations in the Plane Continued

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## Objective

Students will be able to connect a horizontal + a vertical translation as equivalent to a diagonal translation for application in a later lesson.

#### Big Idea

Students are preparing to understand angle relationships along parallel lines cut by a transversal in future lesson.

## Warm-up: Review of Previous Material

15 minutes

I began the second day of this lesson by again reviewing the properties of translations.  I specifically asked students in which direction do we slide figures with a translations (I want to be explicit that I do not allow students to call translations a slide, we use proper vocabulary.  We use the work slide to describe the motion of a translation).  When students begin to list directions for movement I script them and all other review notes on the board for reference during the lesson.  Both of my classes did something really unexpected during this section of the review.  Students called out up, down, left, right and then diagonal.  I asked students to look back at the second translation from the previous day.  I sketched the pentagon and asked about the movement.   I labeled with a diagram the left 1.5 inches and up 2 inches.  This sparked a student in both classes to say, you moved it along the hypotenuse.  I called those students up to show the class what they meant.  Here is a picture of the work one student presented to the class.  This student input was the perfect segue into the lesson today and both of my classes had students who made this connection.

Extensions and Scaffolds:

The lesson today really sets students up for the wonderful connection to angle relationships along parallel lines cut by a transversal latter in this unit.  We study angle relationships along transversals through the use of movement to translate, reflect, and rotate angles to map on top of each other or next to each other along a line.  Exploring translations along a line instead of just through horizontal and vertical movement gets students prepared for transversal applications.  My students created the most exciting diagram during the introduction of this lesson and I will share the image of student work from my board when a student connected a diagonal translation to the Pythagorean Theorem and distance formula.

This lesson is a visual hands-ons experience for students as they begin to experiment with the movement of a translation and experiment with the tracing paper.  I use the document camera and overhead projector regularly throughout the lesson to show students how to use the tracing paper or better yet, allow other students to come to the board and show the class how to apply the tracing paper. I have never taught translations along a line before, but my students really connected to this and we discussed which is faster and easier, to translate horizontally and then vertically or to just translate diagonally.  I was very hands-on with my students checking their progress over and over throughout the class period to ensure no one was working incorrectly.

## Continuing the Activity

30 minutes

Today students will begin to translate along a diagonal line today.  I help students through the first translation by asking them, "How do you think we should translate this square along the line?"  I encourage them to explore and make suggestions for the group to try because it is easy to experiment with tracing paper and then just throw it away if we make a mistake.  As a class, I take suggestions from any student as long as he/she can explain why the suggestions might be a good idea.  Below is a short tutorial video for how to translate along a line.

After everyone has successfully translated question three then I allow time to complete questions four to the end of the handout within their partnerships as I move about the room assessing and answering questions.  Before students begin to work with the translations on the last page using graph paper I have a group discussion about taking translations onto the coordinate plane.  We discuss standardized tests such as the ACT and SAT which do not allow students to use tracing paper.  Therefore, there must be another way to translate without needing extra materials which is why I am introducing the graph paper and coordinates.  Then allow students to work with the graph paper and their partners to translate without tracing paper.

## Wrapping up the Lesson

10 minutes

I pull a student up to the document camera to present his/her translation for question 4 along the line.  We then discuss the translations on the back, translations in the coordinate plane.  I again allow students to show work under the document camera so everyone can consolidate their thinking about translations in the coordinate plane.  I ask who prefers the coordinate plan and why do you prefer the coordinate plane?  If time allows, I ask students to write the translations from the coordinate plane as function rules, example:  a translation left of five units could be written as x - 5 for each vertex.  A translation up of 2 units could be written as y + 2.  I give students the practice sheet from Kuta Software for homework practice.