Describing Precise Transformations

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Objective

SWBAT describe a transformation that carries one figure onto another so that specific points or lines coincide. Students will understand what it means to be precise when describing a transformation.

Big Idea

Using dynamic geometry software, students learn to determine the precise vector, line of reflection, or center and angle of rotation that will bring parts of a triangle together.

Lesson Open

8 minutes

The warm-up prompt for this lesson asks students to describe a transformation that brings two vertices of a triangle together.  The warm-up follows our Team Warm-up routine.  I choose students at random to write the team's answer on the board.  

We review the team answers as a class.  Are the descriptions specific enough?  What properties would a line of reflection need, for example, to make the two vertices coincide, based on the properties of rigid motions (MP6)?  Are there other transformations that would work? 

I display the agenda and learning targets for the lesson.   Precision in describing transformations has been emphasized in previous lessons.  Up to now, we have used the properties of rigid motions to reason about the properties required in points of rotation, angles of rotation, and lines of reflection (MP7).  In this lesson, students will have the opportunity to experiment and see for themselves (MP5).

Investigating Precise Transformations

40 minutes

In this activity, students use WinGeom, a dynamic geometry program, to experiment with transformations.  The goal is for students to learn to specify a precise vector of translation, line of reflection, or center and angle of rotation that can be relied upon to bring a given pair of points or lines together (MP6).  This level of rigor is required if students are to appreciate conditions for triangle congruence (SSS, ASA, SAS) later.

This activity requires one computer per pair of students.  Ideally, each student will have their own computer.

I distribute the handout for the investigation, and students bring up WinGeom on their computers.  I also distribute the guided notes we will use to summarize our findings in the next lesson so that students may begin to complete them if they wish. 

A sample file from this WinGeom activity can be downloaded from my class website.

 

Lesson Close and Homework

5 minutes

The lesson close follows our individual size-up routine.  The prompt re-visits the warm-up problem. This time, students are asked to describe two different transformations that will bring the points together.

Recognizing Good Work

While the class is completing the lesson close activity, I invite a student from each team to assign his or her team a score for the lesson.  Student scorekeepers write the score in a spot on the front board, and I write the scores I assign to each team next to them. 

You can read more about how I assign Team Points for cooperative learning activities in my Strategies folder.  

Homework

For  homework, I assign problems #13-14 of Homework Set 2 for this unit.  Problem #13 gives students additional practice in describing the transformations that carry a polygon onto itself. Problem #14 introduces a sequence of transformations and highlights three kinds of transformations that students will use to show that polygons are congruent in the next unit.  In addition, students should revise their unit pre-test as part of the learning portfolio that they will turn in at the end of the unit.