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# Reviewing Rigid Motions

Lesson 15 of 17

## Objective: SWBAT describe a transformation that carries one figure onto another so that specific points, rays, or segments coincide. Students will understand why a transformation may not make all parts of two figures coincide.

#### Lesson Open

*8 min*

The warm-up prompt for this lesson asks students to describe the rotations that carry a regular pentagon to itself. The warm-up follows our Team Warm-up routine. I choose students at random to write the team's answer on the board.

I ask the class to look at the drawings each team has made on the board. This is an opportunity to check for understanding and help students who need it.

I display the Agenda and Learning Targets for the lesson. Today we are reviewing for the unit quiz, which students will take tomorrow. We will take notes to summarize what we learned about transformations in the last lesson, then review the homework set. I challenge students to ask any questions they still have about the unit before tomorrow's quiz.

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The class completes the Precise Transformations notes to summarize the properties of transformations which students investigated during the last lesson.

These notes provide students with a handy reference on the properties of transformations which can be used to prove congruence. Students must understand that these transformations can be shown to carry figures together so that specific points, segments, or rays coincide--as contrasted with transformations that merely "look like" they will work. Students must understand and be convinced of this distinction to appreciate the conditions required to show triangle congruence (SAS, ASA, SSS) which will be developed in the next unit.

For this reason, the properties are represented in the form of theorems. I do not spend time proving the theorems formally in class, because the practice activities of the last few lessons provide ample opportunity to examine their validity in the context of solving problems. In general, the arguments appeal to the definitions of reflections, rotations, and translations, segments and angles, and linear and angular measure.(**MP3)**

The notes also introduce notation for representing transformations. Students will need to become familiar with that notation to understand transformation proofs. I have also included a general description of how I use guided notes in my classroom.

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#### Homework Review

*25 min*

We use the Team Homework Review variation of our homework review procedure to review Rigid Homework Set 2.

As students are checking their homework for accuracy, I circulate to see what questions students still have. If a student needs additional practice on a skill, I can work with them using one of the practice problems left over an earlier lesson. I also check in with students to see how they have done on their portfolio problems and to see if they need any help correcting their pre-tests.

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The lesson close follows our Individual Size-Up Routine. The prompt gives students a chance to see why "looks like" is not good enough to support a claim that a transformation brings two points together--and allows me to check for student understanding.

**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 team points scores I assign to each team next to them.

**Homework**

For homework, I tell students to put together their unit learning portfolio checklist, which they will turn in after the unit quiz. For more on how I use learning portfolios in teaching and assessment, see my Learning Portfolios write up.

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- UNIT 1: Models and Constructions
- UNIT 2: Dimension and Structure
- UNIT 3: Congruence and Rigid Motions
- UNIT 4: Triangles and Congruence
- UNIT 5: Area Relationships
- UNIT 6: Scaling Up- Dilations, Similarity and Proportional Relationships
- UNIT 7: Introduction to Trigonometry
- UNIT 8: Volume of Cones, Pyramids, and Spheres

- LESSON 1: Previewing Congruence and Rigid Motions
- LESSON 2: Congruence and Coincidence
- LESSON 3: Re-Discovering Symmetry
- LESSON 4: Perfect Polygons
- LESSON 5: Bisector Bonanza
- LESSON 6: The Shortest Segment
- LESSON 7: From Perpendiculars to Parallels
- LESSON 8: Reviewing Congruence
- LESSON 9: Re-Examining Reflections
- LESSON 10: Reconsidering Rotations
- LESSON 11: Taking Apart Translations
- LESSON 12: Visualizing Transformations
- LESSON 13: Reasoning About Rigid Motions
- LESSON 14: Analyzing the Symmetry of a Polygon
- LESSON 15: Reviewing Rigid Motions
- LESSON 16: Rigid Motion and Congruence Unit Quiz
- LESSON 17: Describing Precise Transformations